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<!DOCTYPE html> <html lang="en"> <head> <meta content="text/html; charset=utf-8" http-equiv="content-type"/> <title>Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection</title>  <meta content="width=device-width, initial-scale=1, shrink-to-fit=no" name="viewport"/> <link href="https://cdn.jsdelivr.net/npm/bootstrap@5.3.0/dist/css/bootstrap.min.css" rel="stylesheet" type="text/css"/> <link href="/static/browse/0.3.4/css/ar5iv.0.7.9.min.css" rel="stylesheet" type="text/css"/> <link href="/static/browse/0.3.4/css/ar5iv-fonts.0.7.9.min.css" rel="stylesheet" type="text/css"/> <link href="/static/browse/0.3.4/css/latexml_styles.css" rel="stylesheet" type="text/css"/> <script src="https://cdn.jsdelivr.net/npm/bootstrap@5.3.0/dist/js/bootstrap.bundle.min.js"></script> <script src="https://cdnjs.cloudflare.com/ajax/libs/html2canvas/1.3.3/html2canvas.min.js"></script> <script src="/static/browse/0.3.4/js/addons_new.js"></script> <script src="/static/browse/0.3.4/js/feedbackOverlay.js"></script> <meta content=" Semantic communication, 3D object detection, stereo vision, deep learning. " lang="en" name="keywords"/> <base href="/html/2502.12735v1/"/></head> <body> <nav class="ltx_page_navbar"> <nav class="ltx_TOC"> <ol class="ltx_toclist"> <li class="ltx_tocentry ltx_tocentry_section"><a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S1" title="In Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">I </span><span class="ltx_text ltx_font_smallcaps">Introduction</span></span></a></li> <li class="ltx_tocentry ltx_tocentry_section"> <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S2" title="In Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">II </span><span class="ltx_text ltx_font_smallcaps">System Model</span></span></a> <ol class="ltx_toclist ltx_toclist_section"> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S2.SS1" title="In II System Model ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref"><span class="ltx_text">II-A</span> </span><span class="ltx_text ltx_font_italic">The Semantic Encoder Network</span></span></a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S2.SS2" title="In II System Model ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref"><span class="ltx_text">II-B</span> </span><span class="ltx_text ltx_font_italic">The Channel Encoder and Decoder Networks </span></span></a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S2.SS3" title="In II System Model ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref"><span class="ltx_text">II-C</span> </span><span class="ltx_text ltx_font_italic">The Semantic Decoder Network</span></span></a></li> </ol> </li> <li class="ltx_tocentry ltx_tocentry_section"> <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S3" title="In Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">III </span><span class="ltx_text ltx_font_smallcaps">Transceiver Design for Proposed Semantic Communication System</span></span></a> <ol class="ltx_toclist ltx_toclist_section"> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S3.SS1" title="In III Transceiver Design for Proposed Semantic Communication System ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref"><span class="ltx_text">III-A</span> </span><span class="ltx_text ltx_font_italic">Structure of The Key Area Information Network</span></span></a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S3.SS2" title="In III Transceiver Design for Proposed Semantic Communication System ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref"><span class="ltx_text">III-B</span> </span><span class="ltx_text ltx_font_italic">Structure of The Global Information Network</span></span></a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S3.SS3" title="In III Transceiver Design for Proposed Semantic Communication System ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref"><span class="ltx_text">III-C</span> </span><span class="ltx_text ltx_font_italic">Structure of The Fusion Network</span></span></a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S3.SS4" title="In III Transceiver Design for Proposed Semantic Communication System ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref"><span class="ltx_text">III-D</span> </span><span class="ltx_text ltx_font_italic">Structure of The Channel Codec Network</span></span></a></li> </ol> </li> <li class="ltx_tocentry ltx_tocentry_section"><a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S4" title="In Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">IV </span><span class="ltx_text ltx_font_smallcaps">Training Strategy</span></span></a></li> <li class="ltx_tocentry ltx_tocentry_section"> <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5" title="In Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">V </span><span class="ltx_text ltx_font_smallcaps">Simulation Results and Discussions</span></span></a> <ol class="ltx_toclist ltx_toclist_section"> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.SS1" title="In V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref"><span class="ltx_text">V-A</span> </span><span class="ltx_text ltx_font_italic">Performance Metrics</span></span></a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.SS2" title="In V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref"><span class="ltx_text">V-B</span> </span><span class="ltx_text ltx_font_italic">Simulation Results</span></span></a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.SS3" title="In V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref"><span class="ltx_text">V-C</span> </span><span class="ltx_text ltx_font_italic">Ablation Study</span></span></a></li> <li class="ltx_tocentry ltx_tocentry_subsection"><a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.SS4" title="In V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref"><span class="ltx_text">V-D</span> </span><span class="ltx_text ltx_font_italic">Complexity Analysis</span></span></a></li> </ol> </li> <li class="ltx_tocentry ltx_tocentry_section"><a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S6" title="In Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">VI </span><span class="ltx_text ltx_font_smallcaps">Conclusion</span></span></a></li> <li class="ltx_tocentry ltx_tocentry_appendix"><a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#A1" title="In Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">A </span>The Parameters of The Proposed Network</span></a></li> <li class="ltx_tocentry ltx_tocentry_appendix"><a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#A2" title="In Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_title"><span class="ltx_tag ltx_tag_ref">B </span>The Settings of The Proposed Training Strategy</span></a></li> </ol></nav> </nav> <div class="ltx_page_main"> <div class="ltx_page_content"> <article class="ltx_document ltx_authors_1line"> <h1 class="ltx_title ltx_title_document">Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection</h1> <div class="ltx_authors"> <span class="ltx_creator ltx_role_author"> <span class="ltx_personname"> Zijian Cao, Hua Zhang, Le Liang, Haotian Wang, Shi Jin, and Geoffrey Ye Li </span><span class="ltx_author_notes"> Zijian Cao, Hua Zhang, Haotian Wang and Shi Jin are with the National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China (e-mail: caozijian@seu.edu.cn; huazhang@seu.edu.cn; haotian_wang@seu.edu.cn; jinshi@seu.edu.cn). Zijian Cao is also with the Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, UK. Le Liang is with the National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China, and also with Purple Mountain Laboratories, Nanjing 211111, China (e-mail: lliang@seu.edu.cn). G. Y. Li is with the Department of Electrical and Electronic Engineering, Imperial College London, London SW7 2AZ, UK (e-mail: geoffrey.li@imperial.ac.uk). </span></span> </div> <div class="ltx_abstract"> <h6 class="ltx_title ltx_title_abstract">Abstract</h6> <p class="ltx_p" id="id1.id1">With the development of computer vision, 3D object detection has become increasingly important in many real-world applications. Limited by the computing power of sensor-side hardware, the detection task is sometimes deployed on remote computing devices or the cloud to execute complex algorithms, which brings massive data transmission overhead. In response, this paper proposes an optical flow-driven semantic communication framework for the stereo-vision 3D object detection task. The proposed framework fully exploits the dependence of stereo-vision 3D detection on semantic information in images and prioritizes the transmission of this semantic information to reduce total transmission data sizes while ensuring the detection accuracy. Specifically, we develop an optical flow-driven module to jointly extract and recover semantics from the left and right images to reduce the loss of the left-right photometric alignment semantic information and improve the accuracy of depth inference. Then, we design a 2D semantic extraction module to identify and extract semantic meaning around the objects to enhance the transmission of semantic information in the key areas. Finally, a fusion network is used to fuse the recovered semantics, and reconstruct the stereo-vision images for 3D detection. Simulation results show that the proposed method improves the detection accuracy by nearly 70% and outperforms the traditional method, especially for the low signal-to-noise ratio regime.</p> </div> <div class="ltx_keywords"> <h6 class="ltx_title ltx_title_keywords">Index Terms: </h6> Semantic communication, 3D object detection, stereo vision, deep learning. </div> <section class="ltx_section" id="S1"> <h2 class="ltx_title ltx_title_section"> <span class="ltx_tag ltx_tag_section">I </span><span class="ltx_text ltx_font_smallcaps" id="S1.1.1">Introduction</span> </h2> <div class="ltx_para" id="S1.p1"> <p class="ltx_p" id="S1.p1.1">As a promising research direction of computer vision, 3D object detection has played an important role in intelligent video surveillance, robot navigation, autonomous driving <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib1" title="">1</a>, <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib2" title="">2</a>]</cite>, etc. Based on the cameras or the laser radars (LiDARs), it can identify and locate objects in a 3D environment and provide the detection results for subsequent decision-making by intelligent agents. However, limited by the computing power on the sensor side, complex 3D detection algorithms are sometimes deployed on remote computing devices or clouds, which brings challenges in data exchange between sensors and remote devices <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib3" title="">3</a>, <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib4" title="">4</a>, <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib5" title="">5</a>]</cite>. Whether it is the point cloud data required for LiDAR detection methods <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib6" title="">6</a>]</cite> or the RGB images needed for monocular <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib7" title="">7</a>]</cite> or stereo-vision detection methods <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib8" title="">8</a>]</cite>, transmitting massive sensor data under limited communication bandwidth has always been a challenge and thus has become an important area of communication research. Meanwhile, the distortion of these sensor data will directly affect the 3D detection accuracy.</p> </div> <div class="ltx_para" id="S1.p2"> <p class="ltx_p" id="S1.p2.1">To solve this problem, several research focuses on optimizing communication resource allocation between sensors and remote computing devices <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib5" title="">5</a>, <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib9" title="">9</a>, <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib10" title="">10</a>]</cite>. By optimizing transmission power, bandwidth allocation, beamforming vectors, etc., these studies can improve the transmission efficiency of the entire system. Meanwhile, another line of research focuses on compressing the transmission data, hence reducing the communication payload sizes. For example, the variational image compression algorithm in <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib11" title="">11</a>]</cite> compresses the extracted features from the LiDAR point cloud. Then, the 1D convolutional autoencoder in <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib12" title="">12</a>, <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib13" title="">13</a>, <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib14" title="">14</a>]</cite> is trained to improve the detection performance under limited bandwidth. <span class="ltx_text" id="S1.p2.1.1">However, these methods treat all parts of the transmitted data equally during compression, overlooking that different parts contribute differently to detection performance. Given this disparity in contribution, segments with a more significant impact on detection performance should be subjected to less compression to preserve critical information. In contrast, segments with less impact can be compressed at a higher ratio for more significant data reduction.<span class="ltx_text" id="S1.p2.1.1.1"> Besides, various works, e.g., teacher-student distillation method <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib12" title="">12</a>]</cite>, handshake communication mechanism <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib15" title="">15</a>]</cite>, ego evaluation cropping method <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib16" title="">16</a>]</cite>, etc., are proposed from difference perspectives for performance-bandwidth trade-off. These works are mainly oriented to collaborative perception tasks. The methods in <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib12" title="">12</a>]</cite> and <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib15" title="">15</a>]</cite> reduce the overall data transmission by judiciously deciding on which agent to communicate at each transmission opportunity. However, they are unable to cope with the challenge in each scheduled communication link that is tasked with delivering a large payload. The work in <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib16" title="">16</a>]</cite> reduces the transmitted data by cropping the transmitted sensor data based on the evaluation range of the receiver, i.e., the ego agent. However, this method requires both agents to have detection capabilities and overlapping detection areas, which is unsuitable for single sensor systems since the remote computing device usually lacks detection capabilities.</span></span></p> </div> <div class="ltx_para" id="S1.p3"> <p class="ltx_p" id="S1.p3.1">To address the above challenges, semantic communication is introduced to improve the downstream task performance under limited communication bandwidth. Unlike traditional methods, semantic communication considers the meaning or semantics contained in the transmitted data, i.e., semantic information, during the transmission process. It attempts to deliver task-related semantic information over noisy channels rather than achieving bit- or symbol-level error-free transmission <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib17" title="">17</a>]</cite>. By designing specialized semantic and channel codecs, semantic communication systems can selectively extract and compress task-related semantic information and effectively overcome channel impairments to improve communication efficiency under limited bandwidth. Currently, semantic communication has achieved outstanding performance in single modal transmission tasks including, e.g., text <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib18" title="">18</a>, <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib19" title="">19</a>]</cite>, images <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib20" title="">20</a>, <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib21" title="">21</a>]</cite>, and speech <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib22" title="">22</a>, <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib23" title="">23</a>]</cite>, and multimodal transmission tasks <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib24" title="">24</a>, <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib25" title="">25</a>]</cite>. For the 3D object detection task, the spatial confidence-aware communication strategy in <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib26" title="">26</a>]</cite> compresses and transmits task-related semantic information in LiDAR point clouds or monocular images, reducing the requirement for communication bandwidth. The novel semantic communication architecture in <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib27" title="">27</a>]</cite> is designed for LiDAR-based 3D object detection tasks in autonomous driving. It can only extract and compress semantic information related to 3D detection from the LiDAR point cloud based on a specialized channel codec network.</p> </div> <div class="ltx_para" id="S1.p4"> <p class="ltx_p" id="S1.p4.1">However, the above works mainly focus on transmitting LiDAR point cloud data and are not readily applicable to stereo vision 3D detection tasks. Unlike LiDAR-based methods that rely on point cloud data, stereo-vision methods perform 3D position estimation based on left and right RGB images <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib8" title="">8</a>, <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib28" title="">28</a>]</cite>. Compared to the LiDAR-based methods, the stereo-vision methods offer a wider detection range, richer semantic information, and lower cost <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib28" title="">28</a>]</cite>. In contrast to monocular-based methods, stereo cameras provide more precise depth information through left-right photometric alignment. Therefore, stereo vision-based detection has a desirable trade-off in costs and performance and holds significant potential in addressing 3D detection tasks <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib28" title="">28</a>]</cite>. Motivated by this, we study the transmission of stereo-vision images for 3D object detection tasks and propose a semantic communication framework based on deep neural networks (DNNs) to improve the detection accuracy under limited communication bandwidth.</p> </div> <div class="ltx_para" id="S1.p5"> <p class="ltx_p" id="S1.p5.1">The proposed semantic communication architecture attempts to address two essential requirements of data transmission in stereo-vision 3D object detection. First, the design of the transmitter needs to be lightweight enough to be deployed on the sensor-side equipment. Second, the transceiver needs to reduce the transmitted data while retaining the image semantic information to improve 3D detection under limited communication bandwidth. <span class="ltx_text" id="S1.p5.1.1">Specifically, to meet the first requirement, we only perform semantic information extraction and compression at the transmitter to alleviate the computing pressure on the sensor side. Afterwards, complex feature extraction, optical flow-based image reconstruction, and 3D detection are performed later on the receiver side, which has sufficient computing resources.<span class="ltx_text" id="S1.p5.1.1.1"> For the second requirement, we study the operations of stereo-vision 3D detection and split it into two sub-processes. Resembling human eyes, the detection scheme first performs 2D object detection on a single image and then uses the photometric alignment <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib28" title="">28</a>]</cite> between images to infer depth information. Thus, in the first sub-process, a 2D detection network is introduced to extract the semantic information related to detected targets on a single image. In the second sub-process, a convolutional neural network (CNN)-based extraction network is proposed to jointly extract global information from the stereo images, which contains photometric alignment information and is used for depth inference. The extracted semantics are then compressed by CNNs to reduce the transmitted data. Correspondingly, two sets of recovery networks are deployed at the receiver to recover the semantic information. <span class="ltx_text" id="S1.p5.1.1.1.1">The first recovery network consists of residual networks, which recover the target-related semantics. The second network is driven by an optical flow module, where optical flow <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib29" title="">29</a>]</cite> refers to the apparent motion of objects or features between consecutive frames or views. This module calculates the optical flow between the stereo images and further estimates the feature motion caused by the relative perspective of the binocular camera, enabling the second network to restore photometric alignment semantic information based on the estimated motion information.<span class="ltx_text" id="S1.p5.1.1.1.1.1"> Then, a CNN-based fusion network is proposed to fuse the recovered semantics and obtain the restored stereo-images. Moreover, CNN-based channel codecs are deployed at the transmitter and receiver to overcome the channel impairments on the semantic transmission. Our main contributions are as follows,</span></span></span></span></p> <ul class="ltx_itemize" id="S1.I1"> <li class="ltx_item" id="S1.I1.ix1" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item"><math alttext="\bullet" class="ltx_Math" display="inline" id="S1.I1.ix1.1.1.m1.1"><semantics id="S1.I1.ix1.1.1.m1.1b"><mo id="S1.I1.ix1.1.1.m1.1.1" xref="S1.I1.ix1.1.1.m1.1.1.cmml">∙</mo><annotation-xml encoding="MathML-Content" id="S1.I1.ix1.1.1.m1.1c"><ci id="S1.I1.ix1.1.1.m1.1.1.cmml" xref="S1.I1.ix1.1.1.m1.1.1">∙</ci></annotation-xml><annotation encoding="application/x-tex" id="S1.I1.ix1.1.1.m1.1d">\bullet</annotation><annotation encoding="application/x-llamapun" id="S1.I1.ix1.1.1.m1.1e">∙</annotation></semantics></math></span> <div class="ltx_para" id="S1.I1.ix1.p1"> <p class="ltx_p" id="S1.I1.ix1.p1.1">We propose a DNN-based semantic communication framework for stereo vision-based 3D object detection tasks, in which two sets of semantic codecs are used to extract and process two types of semantic information, and a set of CNN-based channel codecs are used to overcome channel impairments. The proposed framework can improve the accuracy of 3D detection tasks under limited communication bandwidth.</p> </div> </li> <li class="ltx_item" id="S1.I1.ix2" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item"><math alttext="\bullet" class="ltx_Math" display="inline" id="S1.I1.ix2.1.1.m1.1"><semantics id="S1.I1.ix2.1.1.m1.1b"><mo id="S1.I1.ix2.1.1.m1.1.1" xref="S1.I1.ix2.1.1.m1.1.1.cmml">∙</mo><annotation-xml encoding="MathML-Content" id="S1.I1.ix2.1.1.m1.1c"><ci id="S1.I1.ix2.1.1.m1.1.1.cmml" xref="S1.I1.ix2.1.1.m1.1.1">∙</ci></annotation-xml><annotation encoding="application/x-tex" id="S1.I1.ix2.1.1.m1.1d">\bullet</annotation><annotation encoding="application/x-llamapun" id="S1.I1.ix2.1.1.m1.1e">∙</annotation></semantics></math></span> <div class="ltx_para" id="S1.I1.ix2.p1"> <p class="ltx_p" id="S1.I1.ix2.p1.1">We introduce a 2D detection network to identify the objects and propose a set of CNN-based networks, collectively referred to as the key area information network, to extract, compress, and recover the object-related semantic information, providing accurate 2D information for the subsequent 3D object detection task.</p> </div> </li> <li class="ltx_item" id="S1.I1.ix3" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item"><math alttext="\bullet" class="ltx_Math" display="inline" id="S1.I1.ix3.1.1.m1.1"><semantics id="S1.I1.ix3.1.1.m1.1b"><mo id="S1.I1.ix3.1.1.m1.1.1" xref="S1.I1.ix3.1.1.m1.1.1.cmml">∙</mo><annotation-xml encoding="MathML-Content" id="S1.I1.ix3.1.1.m1.1c"><ci id="S1.I1.ix3.1.1.m1.1.1.cmml" xref="S1.I1.ix3.1.1.m1.1.1">∙</ci></annotation-xml><annotation encoding="application/x-tex" id="S1.I1.ix3.1.1.m1.1d">\bullet</annotation><annotation encoding="application/x-llamapun" id="S1.I1.ix3.1.1.m1.1e">∙</annotation></semantics></math></span> <div class="ltx_para" id="S1.I1.ix3.p1"> <p class="ltx_p" id="S1.I1.ix3.p1.1">We design a CNN-based network, termed global information network, to extract semantic information related to photometic alignment from the stereo images. An optical flow-driven recovery network is correspondingly proposed at the receiver to recover the semantic information. The proposed scheme can reduce the loss of the left-right photometric alignment information and improve the accuracy of depth inference.</p> </div> </li> <li class="ltx_item" id="S1.I1.ix4" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item"><math alttext="\bullet" class="ltx_Math" display="inline" id="S1.I1.ix4.1.1.m1.1"><semantics id="S1.I1.ix4.1.1.m1.1b"><mo id="S1.I1.ix4.1.1.m1.1.1" xref="S1.I1.ix4.1.1.m1.1.1.cmml">∙</mo><annotation-xml encoding="MathML-Content" id="S1.I1.ix4.1.1.m1.1c"><ci id="S1.I1.ix4.1.1.m1.1.1.cmml" xref="S1.I1.ix4.1.1.m1.1.1">∙</ci></annotation-xml><annotation encoding="application/x-tex" id="S1.I1.ix4.1.1.m1.1d">\bullet</annotation><annotation encoding="application/x-llamapun" id="S1.I1.ix4.1.1.m1.1e">∙</annotation></semantics></math></span> <div class="ltx_para" id="S1.I1.ix4.p1"> <p class="ltx_p" id="S1.I1.ix4.p1.1">We develop a five-step strategy to train the network with different loss functions for each step. The proposed five-step training method can effectively improve training speed and network performance.</p> </div> </li> </ul> </div> <div class="ltx_para" id="S1.p6"> <p class="ltx_p" id="S1.p6.1">The rest of this paper is organized as follows. Section II describes the system model and framework of our semantic communication system. Section III presents the details of the proposed semantic network. The training strategy is introduced in Section IV. Later, simulation results are discussed in Section V. Section VI concludes this paper.</p> </div> </section> <section class="ltx_section" id="S2"> <h2 class="ltx_title ltx_title_section"> <span class="ltx_tag ltx_tag_section">II </span><span class="ltx_text ltx_font_smallcaps" id="S2.1.1">System Model</span> </h2> <div class="ltx_para" id="S2.p1"> <p class="ltx_p" id="S2.p1.1"><span class="ltx_text" id="S2.p1.1.1">As shown in Fig. <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S2.F1" title="Figure 1 ‣ II System Model ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">1</span></a>, the proposed semantic system for stereo-vision 3D object detection tasks adopts the classical architecture similar to <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib18" title="">18</a>]</cite>, where the semantic encoder and decoder are responsible for extracting and recovering semantic information, and the channel encoder and decoder are used to mitigate the impacts of wireless channels. The recovered stereo-vision images will be input to another well-trained network for 3D object detection<span class="ltx_note ltx_role_footnote" id="footnote1"><sup class="ltx_note_mark">1</sup><span class="ltx_note_outer"><span class="ltx_note_content"><sup class="ltx_note_mark">1</sup><span class="ltx_tag ltx_tag_note">1</span><span class="ltx_text" id="footnote1.1">In this paper, we restore the original image rather than jointly train the semantic communication network with a specific 3D detection network, aiming to enhance the compatibility of the semantic system with various 3D detection networks.</span></span></span></span>. <span class="ltx_text" id="S2.p1.1.1.1"></span></span></p> </div> <figure class="ltx_figure" id="S2.F1"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="165" id="S2.F1.g1" src="x1.png" width="477"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 1: </span>Model of the proposed semantic communication system.</figcaption> </figure> <figure class="ltx_figure" id="S2.F2"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="428" id="S2.F2.g1" src="x2.png" width="941"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 2: </span>Illustration of (a) the proposed semantic encoder and (b) the proposed semantic decoder.</figcaption> </figure> <div class="ltx_para" id="S2.p2"> <p class="ltx_p" id="S2.p2.1"><span class="ltx_text" id="S2.p2.1.1">The structure of the semantic codec is shown in Fig. <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S2.F2" title="Figure 2 ‣ II System Model ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">2</span></a>. Specifically, the proposed semantic codec includes two sets of DNNs to extract, compress, and recover two types of semantic information, i.e., the object-related semantic information for 2D detection and the global semantics containing photometric alignment information for depth inference. Considering the object-related semantic information is exclusively linked to the key area to which objects belong while the second type of semantic information is associated with the images’ global information, these two groups of DNNs are referred to as the key area information network and the global information network, respectively. Besides, two fusion networks are used to fuse the recovered semantic information. In the following, we briefly discuss the functions of the networks in both semantic and channel encoders/decoders. The structure of these networks will be presented in detail in Section III.<span class="ltx_text" id="S2.p2.1.1.1"></span></span></p> </div> <section class="ltx_subsection" id="S2.SS1"> <h3 class="ltx_title ltx_title_subsection"> <span class="ltx_tag ltx_tag_subsection"><span class="ltx_text" id="S2.SS1.5.1.1">II-A</span> </span><span class="ltx_text ltx_font_italic" id="S2.SS1.6.2">The Semantic Encoder Network</span> </h3> <div class="ltx_para" id="S2.SS1.p1"> <p class="ltx_p" id="S2.SS1.p1.1"><span class="ltx_text" id="S2.SS1.p1.1.1">As shown in Fig. <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S2.F2" title="Figure 2 ‣ II System Model ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">2</span></a>, the semantic encoder network consists of two groups of semantic extraction and compression networks, which correspond to the key area and the global information networks, respectively.<span class="ltx_text" id="S2.SS1.p1.1.1.1"></span></span></p> </div> <div class="ltx_para" id="S2.SS1.p2"> <p class="ltx_p" id="S2.SS1.p2.4"><span class="ltx_text" id="S2.SS1.p2.4.4">Specifically, for the key area information network, the semantic extraction networks first use a 2D detection module to estimate the 2D position of vehicles on the left and right images, denoted by <math alttext="I_{l}" class="ltx_Math" display="inline" id="S2.SS1.p2.1.1.m1.1"><semantics id="S2.SS1.p2.1.1.m1.1a"><msub id="S2.SS1.p2.1.1.m1.1.1" xref="S2.SS1.p2.1.1.m1.1.1.cmml"><mi id="S2.SS1.p2.1.1.m1.1.1.2" xref="S2.SS1.p2.1.1.m1.1.1.2.cmml">I</mi><mi id="S2.SS1.p2.1.1.m1.1.1.3" xref="S2.SS1.p2.1.1.m1.1.1.3.cmml">l</mi></msub><annotation-xml encoding="MathML-Content" id="S2.SS1.p2.1.1.m1.1b"><apply id="S2.SS1.p2.1.1.m1.1.1.cmml" xref="S2.SS1.p2.1.1.m1.1.1"><csymbol cd="ambiguous" id="S2.SS1.p2.1.1.m1.1.1.1.cmml" xref="S2.SS1.p2.1.1.m1.1.1">subscript</csymbol><ci id="S2.SS1.p2.1.1.m1.1.1.2.cmml" xref="S2.SS1.p2.1.1.m1.1.1.2">𝐼</ci><ci id="S2.SS1.p2.1.1.m1.1.1.3.cmml" xref="S2.SS1.p2.1.1.m1.1.1.3">𝑙</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p2.1.1.m1.1c">I_{l}</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p2.1.1.m1.1d">italic_I start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT</annotation></semantics></math> and <math alttext="I_{r}" class="ltx_Math" display="inline" id="S2.SS1.p2.2.2.m2.1"><semantics id="S2.SS1.p2.2.2.m2.1a"><msub id="S2.SS1.p2.2.2.m2.1.1" xref="S2.SS1.p2.2.2.m2.1.1.cmml"><mi id="S2.SS1.p2.2.2.m2.1.1.2" xref="S2.SS1.p2.2.2.m2.1.1.2.cmml">I</mi><mi id="S2.SS1.p2.2.2.m2.1.1.3" xref="S2.SS1.p2.2.2.m2.1.1.3.cmml">r</mi></msub><annotation-xml encoding="MathML-Content" id="S2.SS1.p2.2.2.m2.1b"><apply id="S2.SS1.p2.2.2.m2.1.1.cmml" xref="S2.SS1.p2.2.2.m2.1.1"><csymbol cd="ambiguous" id="S2.SS1.p2.2.2.m2.1.1.1.cmml" xref="S2.SS1.p2.2.2.m2.1.1">subscript</csymbol><ci id="S2.SS1.p2.2.2.m2.1.1.2.cmml" xref="S2.SS1.p2.2.2.m2.1.1.2">𝐼</ci><ci id="S2.SS1.p2.2.2.m2.1.1.3.cmml" xref="S2.SS1.p2.2.2.m2.1.1.3">𝑟</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p2.2.2.m2.1c">I_{r}</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p2.2.2.m2.1d">italic_I start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT</annotation></semantics></math>, respectively. 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xref="S2.SS1.p2.4.4.m4.2.2.2.2.2">𝐾</ci><ci id="S2.SS1.p2.4.4.m4.2.2.2.2.3.cmml" xref="S2.SS1.p2.4.4.m4.2.2.2.2.3">𝑟</ci></apply></set></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p2.4.4.m4.2c">\left\{{{K_{l}},{K_{r}}}\right\}</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p2.4.4.m4.2d">{ italic_K start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , italic_K start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT }</annotation></semantics></math>, given by</span></p> <table class="ltx_equation ltx_eqn_table" id="S2.E1"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="\left\{{\begin{array}[]{*{20}{c}}{{S_{l}}=T^{l}_{\alpha}\left({{I_{l}}}\right)% }\text{,}\\ {{S_{r}}=T^{r}_{\alpha}\left({{I_{r}}}\right)}\text{,}\end{array}}\right." class="ltx_Math" display="block" id="S2.E1.m1.2"><semantics id="S2.E1.m1.2a"><mrow 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id="S2.E1.m1.2c">\left\{{\begin{array}[]{*{20}{c}}{{S_{l}}=T^{l}_{\alpha}\left({{I_{l}}}\right)% }\text{,}\\ {{S_{r}}=T^{r}_{\alpha}\left({{I_{r}}}\right)}\text{,}\end{array}}\right.</annotation><annotation encoding="application/x-llamapun" id="S2.E1.m1.2d">{ start_ARRAY start_ROW start_CELL italic_S start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_α end_POSTSUBSCRIPT ( italic_I start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT ) , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW start_ROW start_CELL italic_S start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_α end_POSTSUBSCRIPT ( italic_I start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ) , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW end_ARRAY</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(1)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S2.SS1.p2.11">and</p> <table class="ltx_equation ltx_eqn_table" id="S2.E2"> <tbody><tr class="ltx_equation ltx_eqn_row 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xref="S2.E2.m1.2.2">missing-subexpression</csymbol></cerror><cerror id="S2.E2.m1.2.2bm.cmml" xref="S2.E2.m1.2.2"><csymbol cd="ambiguous" id="S2.E2.m1.2.2bn.cmml" xref="S2.E2.m1.2.2">missing-subexpression</csymbol></cerror><cerror id="S2.E2.m1.2.2bo.cmml" xref="S2.E2.m1.2.2"><csymbol cd="ambiguous" id="S2.E2.m1.2.2bp.cmml" xref="S2.E2.m1.2.2">missing-subexpression</csymbol></cerror><cerror id="S2.E2.m1.2.2bq.cmml" xref="S2.E2.m1.2.2"><csymbol cd="ambiguous" id="S2.E2.m1.2.2br.cmml" xref="S2.E2.m1.2.2">missing-subexpression</csymbol></cerror><cerror id="S2.E2.m1.2.2bs.cmml" xref="S2.E2.m1.2.2"><csymbol cd="ambiguous" id="S2.E2.m1.2.2bt.cmml" xref="S2.E2.m1.2.2">missing-subexpression</csymbol></cerror><cerror id="S2.E2.m1.2.2bu.cmml" xref="S2.E2.m1.2.2"><csymbol cd="ambiguous" id="S2.E2.m1.2.2bv.cmml" xref="S2.E2.m1.2.2">missing-subexpression</csymbol></cerror><cerror id="S2.E2.m1.2.2bw.cmml" xref="S2.E2.m1.2.2"><csymbol cd="ambiguous" id="S2.E2.m1.2.2bx.cmml" xref="S2.E2.m1.2.2">missing-subexpression</csymbol></cerror><cerror id="S2.E2.m1.2.2by.cmml" xref="S2.E2.m1.2.2"><csymbol cd="ambiguous" id="S2.E2.m1.2.2bz.cmml" xref="S2.E2.m1.2.2">missing-subexpression</csymbol></cerror></matrixrow></matrix></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.E2.m1.2c">\left\{{\begin{array}[]{*{20}{c}}{{K_{l}}=T^{l}_{\beta}\left({{S_{l}}}\right)}% \text{,}\\ {{K_{r}}=T^{r}_{\beta}\left({{S_{r}}}\right)}\text{,}\end{array}}\right.</annotation><annotation encoding="application/x-llamapun" id="S2.E2.m1.2d">{ start_ARRAY start_ROW start_CELL italic_K start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_β end_POSTSUBSCRIPT ( italic_S start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT ) , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW start_ROW start_CELL italic_K start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_β end_POSTSUBSCRIPT ( italic_S start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ) , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW end_ARRAY</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(2)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S2.SS1.p2.10">where <math alttext="T^{l}_{\alpha}" class="ltx_Math" display="inline" id="S2.SS1.p2.5.m1.1"><semantics id="S2.SS1.p2.5.m1.1a"><msubsup id="S2.SS1.p2.5.m1.1.1" xref="S2.SS1.p2.5.m1.1.1.cmml"><mi id="S2.SS1.p2.5.m1.1.1.2.2" xref="S2.SS1.p2.5.m1.1.1.2.2.cmml">T</mi><mi id="S2.SS1.p2.5.m1.1.1.3" xref="S2.SS1.p2.5.m1.1.1.3.cmml">α</mi><mi id="S2.SS1.p2.5.m1.1.1.2.3" xref="S2.SS1.p2.5.m1.1.1.2.3.cmml">l</mi></msubsup><annotation-xml encoding="MathML-Content" id="S2.SS1.p2.5.m1.1b"><apply id="S2.SS1.p2.5.m1.1.1.cmml" xref="S2.SS1.p2.5.m1.1.1"><csymbol cd="ambiguous" id="S2.SS1.p2.5.m1.1.1.1.cmml" xref="S2.SS1.p2.5.m1.1.1">subscript</csymbol><apply id="S2.SS1.p2.5.m1.1.1.2.cmml" xref="S2.SS1.p2.5.m1.1.1"><csymbol cd="ambiguous" id="S2.SS1.p2.5.m1.1.1.2.1.cmml" xref="S2.SS1.p2.5.m1.1.1">superscript</csymbol><ci id="S2.SS1.p2.5.m1.1.1.2.2.cmml" xref="S2.SS1.p2.5.m1.1.1.2.2">𝑇</ci><ci id="S2.SS1.p2.5.m1.1.1.2.3.cmml" xref="S2.SS1.p2.5.m1.1.1.2.3">𝑙</ci></apply><ci id="S2.SS1.p2.5.m1.1.1.3.cmml" xref="S2.SS1.p2.5.m1.1.1.3">𝛼</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p2.5.m1.1c">T^{l}_{\alpha}</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p2.5.m1.1d">italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_α end_POSTSUBSCRIPT</annotation></semantics></math> and <math alttext="T^{r}_{\alpha}" class="ltx_Math" display="inline" id="S2.SS1.p2.6.m2.1"><semantics id="S2.SS1.p2.6.m2.1a"><msubsup id="S2.SS1.p2.6.m2.1.1" xref="S2.SS1.p2.6.m2.1.1.cmml"><mi id="S2.SS1.p2.6.m2.1.1.2.2" xref="S2.SS1.p2.6.m2.1.1.2.2.cmml">T</mi><mi id="S2.SS1.p2.6.m2.1.1.3" xref="S2.SS1.p2.6.m2.1.1.3.cmml">α</mi><mi id="S2.SS1.p2.6.m2.1.1.2.3" xref="S2.SS1.p2.6.m2.1.1.2.3.cmml">r</mi></msubsup><annotation-xml encoding="MathML-Content" id="S2.SS1.p2.6.m2.1b"><apply id="S2.SS1.p2.6.m2.1.1.cmml" xref="S2.SS1.p2.6.m2.1.1"><csymbol cd="ambiguous" id="S2.SS1.p2.6.m2.1.1.1.cmml" xref="S2.SS1.p2.6.m2.1.1">subscript</csymbol><apply id="S2.SS1.p2.6.m2.1.1.2.cmml" xref="S2.SS1.p2.6.m2.1.1"><csymbol cd="ambiguous" id="S2.SS1.p2.6.m2.1.1.2.1.cmml" xref="S2.SS1.p2.6.m2.1.1">superscript</csymbol><ci id="S2.SS1.p2.6.m2.1.1.2.2.cmml" xref="S2.SS1.p2.6.m2.1.1.2.2">𝑇</ci><ci id="S2.SS1.p2.6.m2.1.1.2.3.cmml" xref="S2.SS1.p2.6.m2.1.1.2.3">𝑟</ci></apply><ci id="S2.SS1.p2.6.m2.1.1.3.cmml" xref="S2.SS1.p2.6.m2.1.1.3">𝛼</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p2.6.m2.1c">T^{r}_{\alpha}</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p2.6.m2.1d">italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_α end_POSTSUBSCRIPT</annotation></semantics></math> denote the semantic extraction networks of the key area information network parameterized by <math alttext="\alpha" class="ltx_Math" display="inline" id="S2.SS1.p2.7.m3.1"><semantics id="S2.SS1.p2.7.m3.1a"><mi id="S2.SS1.p2.7.m3.1.1" xref="S2.SS1.p2.7.m3.1.1.cmml">α</mi><annotation-xml encoding="MathML-Content" id="S2.SS1.p2.7.m3.1b"><ci id="S2.SS1.p2.7.m3.1.1.cmml" xref="S2.SS1.p2.7.m3.1.1">𝛼</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p2.7.m3.1c">\alpha</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p2.7.m3.1d">italic_α</annotation></semantics></math> while <math alttext="T^{l}_{\beta}" class="ltx_Math" display="inline" id="S2.SS1.p2.8.m4.1"><semantics id="S2.SS1.p2.8.m4.1a"><msubsup id="S2.SS1.p2.8.m4.1.1" xref="S2.SS1.p2.8.m4.1.1.cmml"><mi id="S2.SS1.p2.8.m4.1.1.2.2" xref="S2.SS1.p2.8.m4.1.1.2.2.cmml">T</mi><mi id="S2.SS1.p2.8.m4.1.1.3" xref="S2.SS1.p2.8.m4.1.1.3.cmml">β</mi><mi id="S2.SS1.p2.8.m4.1.1.2.3" xref="S2.SS1.p2.8.m4.1.1.2.3.cmml">l</mi></msubsup><annotation-xml encoding="MathML-Content" id="S2.SS1.p2.8.m4.1b"><apply id="S2.SS1.p2.8.m4.1.1.cmml" xref="S2.SS1.p2.8.m4.1.1"><csymbol cd="ambiguous" id="S2.SS1.p2.8.m4.1.1.1.cmml" xref="S2.SS1.p2.8.m4.1.1">subscript</csymbol><apply id="S2.SS1.p2.8.m4.1.1.2.cmml" xref="S2.SS1.p2.8.m4.1.1"><csymbol cd="ambiguous" id="S2.SS1.p2.8.m4.1.1.2.1.cmml" xref="S2.SS1.p2.8.m4.1.1">superscript</csymbol><ci id="S2.SS1.p2.8.m4.1.1.2.2.cmml" xref="S2.SS1.p2.8.m4.1.1.2.2">𝑇</ci><ci id="S2.SS1.p2.8.m4.1.1.2.3.cmml" xref="S2.SS1.p2.8.m4.1.1.2.3">𝑙</ci></apply><ci id="S2.SS1.p2.8.m4.1.1.3.cmml" xref="S2.SS1.p2.8.m4.1.1.3">𝛽</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p2.8.m4.1c">T^{l}_{\beta}</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p2.8.m4.1d">italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_β end_POSTSUBSCRIPT</annotation></semantics></math> and <math alttext="T^{r}_{\beta}" class="ltx_Math" display="inline" id="S2.SS1.p2.9.m5.1"><semantics id="S2.SS1.p2.9.m5.1a"><msubsup id="S2.SS1.p2.9.m5.1.1" xref="S2.SS1.p2.9.m5.1.1.cmml"><mi id="S2.SS1.p2.9.m5.1.1.2.2" xref="S2.SS1.p2.9.m5.1.1.2.2.cmml">T</mi><mi id="S2.SS1.p2.9.m5.1.1.3" xref="S2.SS1.p2.9.m5.1.1.3.cmml">β</mi><mi id="S2.SS1.p2.9.m5.1.1.2.3" xref="S2.SS1.p2.9.m5.1.1.2.3.cmml">r</mi></msubsup><annotation-xml encoding="MathML-Content" id="S2.SS1.p2.9.m5.1b"><apply id="S2.SS1.p2.9.m5.1.1.cmml" xref="S2.SS1.p2.9.m5.1.1"><csymbol cd="ambiguous" id="S2.SS1.p2.9.m5.1.1.1.cmml" xref="S2.SS1.p2.9.m5.1.1">subscript</csymbol><apply id="S2.SS1.p2.9.m5.1.1.2.cmml" xref="S2.SS1.p2.9.m5.1.1"><csymbol cd="ambiguous" id="S2.SS1.p2.9.m5.1.1.2.1.cmml" xref="S2.SS1.p2.9.m5.1.1">superscript</csymbol><ci id="S2.SS1.p2.9.m5.1.1.2.2.cmml" xref="S2.SS1.p2.9.m5.1.1.2.2">𝑇</ci><ci id="S2.SS1.p2.9.m5.1.1.2.3.cmml" xref="S2.SS1.p2.9.m5.1.1.2.3">𝑟</ci></apply><ci id="S2.SS1.p2.9.m5.1.1.3.cmml" xref="S2.SS1.p2.9.m5.1.1.3">𝛽</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p2.9.m5.1c">T^{r}_{\beta}</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p2.9.m5.1d">italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_β end_POSTSUBSCRIPT</annotation></semantics></math> are the compression networks in the key area information network, parameterized by <math alttext="{\beta}" class="ltx_Math" display="inline" id="S2.SS1.p2.10.m6.1"><semantics id="S2.SS1.p2.10.m6.1a"><mi id="S2.SS1.p2.10.m6.1.1" xref="S2.SS1.p2.10.m6.1.1.cmml">β</mi><annotation-xml encoding="MathML-Content" id="S2.SS1.p2.10.m6.1b"><ci id="S2.SS1.p2.10.m6.1.1.cmml" xref="S2.SS1.p2.10.m6.1.1">𝛽</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p2.10.m6.1c">{\beta}</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p2.10.m6.1d">italic_β</annotation></semantics></math>, to process the semantic features extracted from left and right images, respectively.<span class="ltx_text" id="S2.SS1.p2.10.1"></span></p> </div> <div class="ltx_para" id="S2.SS1.p3"> <p class="ltx_p" id="S2.SS1.p3.3"><span class="ltx_text" id="S2.SS1.p3.3.3">Meanwhile, since the key area information only includes features about the detected objects in a single left or right image, the global information, including photometric alignment information, must also be transmitted to ensure the accuracy of depth inference critical for subsequent 3D detection. Therefore, a joint semantic extraction network is used to jointly extract global semantic features <math alttext="\left\{{{F_{l}},{F_{r}}}\right\}" class="ltx_Math" display="inline" id="S2.SS1.p3.1.1.m1.2"><semantics id="S2.SS1.p3.1.1.m1.2a"><mrow id="S2.SS1.p3.1.1.m1.2.2.2" xref="S2.SS1.p3.1.1.m1.2.2.3.cmml"><mo id="S2.SS1.p3.1.1.m1.2.2.2.3" xref="S2.SS1.p3.1.1.m1.2.2.3.cmml">{</mo><msub id="S2.SS1.p3.1.1.m1.1.1.1.1" xref="S2.SS1.p3.1.1.m1.1.1.1.1.cmml"><mi id="S2.SS1.p3.1.1.m1.1.1.1.1.2" xref="S2.SS1.p3.1.1.m1.1.1.1.1.2.cmml">F</mi><mi id="S2.SS1.p3.1.1.m1.1.1.1.1.3" xref="S2.SS1.p3.1.1.m1.1.1.1.1.3.cmml">l</mi></msub><mo id="S2.SS1.p3.1.1.m1.2.2.2.4" xref="S2.SS1.p3.1.1.m1.2.2.3.cmml">,</mo><msub id="S2.SS1.p3.1.1.m1.2.2.2.2" xref="S2.SS1.p3.1.1.m1.2.2.2.2.cmml"><mi id="S2.SS1.p3.1.1.m1.2.2.2.2.2" xref="S2.SS1.p3.1.1.m1.2.2.2.2.2.cmml">F</mi><mi id="S2.SS1.p3.1.1.m1.2.2.2.2.3" xref="S2.SS1.p3.1.1.m1.2.2.2.2.3.cmml">r</mi></msub><mo id="S2.SS1.p3.1.1.m1.2.2.2.5" xref="S2.SS1.p3.1.1.m1.2.2.3.cmml">}</mo></mrow><annotation-xml encoding="MathML-Content" id="S2.SS1.p3.1.1.m1.2b"><set id="S2.SS1.p3.1.1.m1.2.2.3.cmml" xref="S2.SS1.p3.1.1.m1.2.2.2"><apply id="S2.SS1.p3.1.1.m1.1.1.1.1.cmml" xref="S2.SS1.p3.1.1.m1.1.1.1.1"><csymbol cd="ambiguous" id="S2.SS1.p3.1.1.m1.1.1.1.1.1.cmml" xref="S2.SS1.p3.1.1.m1.1.1.1.1">subscript</csymbol><ci id="S2.SS1.p3.1.1.m1.1.1.1.1.2.cmml" xref="S2.SS1.p3.1.1.m1.1.1.1.1.2">𝐹</ci><ci id="S2.SS1.p3.1.1.m1.1.1.1.1.3.cmml" xref="S2.SS1.p3.1.1.m1.1.1.1.1.3">𝑙</ci></apply><apply id="S2.SS1.p3.1.1.m1.2.2.2.2.cmml" xref="S2.SS1.p3.1.1.m1.2.2.2.2"><csymbol cd="ambiguous" id="S2.SS1.p3.1.1.m1.2.2.2.2.1.cmml" xref="S2.SS1.p3.1.1.m1.2.2.2.2">subscript</csymbol><ci id="S2.SS1.p3.1.1.m1.2.2.2.2.2.cmml" xref="S2.SS1.p3.1.1.m1.2.2.2.2.2">𝐹</ci><ci id="S2.SS1.p3.1.1.m1.2.2.2.2.3.cmml" xref="S2.SS1.p3.1.1.m1.2.2.2.2.3">𝑟</ci></apply></set></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p3.1.1.m1.2c">\left\{{{F_{l}},{F_{r}}}\right\}</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p3.1.1.m1.2d">{ italic_F start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , italic_F start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT }</annotation></semantics></math> from the stereo-images, where the left and right features are merged to exploit the photometric alignment information between the left and right images. Then, <math alttext="\left\{{{F_{l}},{F_{r}}}\right\}" class="ltx_Math" display="inline" id="S2.SS1.p3.2.2.m2.2"><semantics id="S2.SS1.p3.2.2.m2.2a"><mrow id="S2.SS1.p3.2.2.m2.2.2.2" xref="S2.SS1.p3.2.2.m2.2.2.3.cmml"><mo id="S2.SS1.p3.2.2.m2.2.2.2.3" xref="S2.SS1.p3.2.2.m2.2.2.3.cmml">{</mo><msub id="S2.SS1.p3.2.2.m2.1.1.1.1" xref="S2.SS1.p3.2.2.m2.1.1.1.1.cmml"><mi id="S2.SS1.p3.2.2.m2.1.1.1.1.2" xref="S2.SS1.p3.2.2.m2.1.1.1.1.2.cmml">F</mi><mi id="S2.SS1.p3.2.2.m2.1.1.1.1.3" xref="S2.SS1.p3.2.2.m2.1.1.1.1.3.cmml">l</mi></msub><mo id="S2.SS1.p3.2.2.m2.2.2.2.4" xref="S2.SS1.p3.2.2.m2.2.2.3.cmml">,</mo><msub id="S2.SS1.p3.2.2.m2.2.2.2.2" xref="S2.SS1.p3.2.2.m2.2.2.2.2.cmml"><mi id="S2.SS1.p3.2.2.m2.2.2.2.2.2" xref="S2.SS1.p3.2.2.m2.2.2.2.2.2.cmml">F</mi><mi id="S2.SS1.p3.2.2.m2.2.2.2.2.3" xref="S2.SS1.p3.2.2.m2.2.2.2.2.3.cmml">r</mi></msub><mo id="S2.SS1.p3.2.2.m2.2.2.2.5" xref="S2.SS1.p3.2.2.m2.2.2.3.cmml">}</mo></mrow><annotation-xml encoding="MathML-Content" id="S2.SS1.p3.2.2.m2.2b"><set id="S2.SS1.p3.2.2.m2.2.2.3.cmml" xref="S2.SS1.p3.2.2.m2.2.2.2"><apply id="S2.SS1.p3.2.2.m2.1.1.1.1.cmml" xref="S2.SS1.p3.2.2.m2.1.1.1.1"><csymbol cd="ambiguous" id="S2.SS1.p3.2.2.m2.1.1.1.1.1.cmml" xref="S2.SS1.p3.2.2.m2.1.1.1.1">subscript</csymbol><ci id="S2.SS1.p3.2.2.m2.1.1.1.1.2.cmml" xref="S2.SS1.p3.2.2.m2.1.1.1.1.2">𝐹</ci><ci id="S2.SS1.p3.2.2.m2.1.1.1.1.3.cmml" xref="S2.SS1.p3.2.2.m2.1.1.1.1.3">𝑙</ci></apply><apply id="S2.SS1.p3.2.2.m2.2.2.2.2.cmml" xref="S2.SS1.p3.2.2.m2.2.2.2.2"><csymbol cd="ambiguous" id="S2.SS1.p3.2.2.m2.2.2.2.2.1.cmml" xref="S2.SS1.p3.2.2.m2.2.2.2.2">subscript</csymbol><ci id="S2.SS1.p3.2.2.m2.2.2.2.2.2.cmml" xref="S2.SS1.p3.2.2.m2.2.2.2.2.2">𝐹</ci><ci id="S2.SS1.p3.2.2.m2.2.2.2.2.3.cmml" xref="S2.SS1.p3.2.2.m2.2.2.2.2.3">𝑟</ci></apply></set></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p3.2.2.m2.2c">\left\{{{F_{l}},{F_{r}}}\right\}</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p3.2.2.m2.2d">{ italic_F start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , italic_F start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT }</annotation></semantics></math> are compressed by the compression networks of the global information network as global information <math alttext="\left\{{{G_{l}},{G_{r}}}\right\}" class="ltx_Math" display="inline" id="S2.SS1.p3.3.3.m3.2"><semantics id="S2.SS1.p3.3.3.m3.2a"><mrow id="S2.SS1.p3.3.3.m3.2.2.2" xref="S2.SS1.p3.3.3.m3.2.2.3.cmml"><mo id="S2.SS1.p3.3.3.m3.2.2.2.3" xref="S2.SS1.p3.3.3.m3.2.2.3.cmml">{</mo><msub id="S2.SS1.p3.3.3.m3.1.1.1.1" xref="S2.SS1.p3.3.3.m3.1.1.1.1.cmml"><mi id="S2.SS1.p3.3.3.m3.1.1.1.1.2" xref="S2.SS1.p3.3.3.m3.1.1.1.1.2.cmml">G</mi><mi id="S2.SS1.p3.3.3.m3.1.1.1.1.3" xref="S2.SS1.p3.3.3.m3.1.1.1.1.3.cmml">l</mi></msub><mo id="S2.SS1.p3.3.3.m3.2.2.2.4" xref="S2.SS1.p3.3.3.m3.2.2.3.cmml">,</mo><msub id="S2.SS1.p3.3.3.m3.2.2.2.2" xref="S2.SS1.p3.3.3.m3.2.2.2.2.cmml"><mi id="S2.SS1.p3.3.3.m3.2.2.2.2.2" xref="S2.SS1.p3.3.3.m3.2.2.2.2.2.cmml">G</mi><mi id="S2.SS1.p3.3.3.m3.2.2.2.2.3" xref="S2.SS1.p3.3.3.m3.2.2.2.2.3.cmml">r</mi></msub><mo id="S2.SS1.p3.3.3.m3.2.2.2.5" xref="S2.SS1.p3.3.3.m3.2.2.3.cmml">}</mo></mrow><annotation-xml encoding="MathML-Content" id="S2.SS1.p3.3.3.m3.2b"><set id="S2.SS1.p3.3.3.m3.2.2.3.cmml" xref="S2.SS1.p3.3.3.m3.2.2.2"><apply id="S2.SS1.p3.3.3.m3.1.1.1.1.cmml" xref="S2.SS1.p3.3.3.m3.1.1.1.1"><csymbol cd="ambiguous" id="S2.SS1.p3.3.3.m3.1.1.1.1.1.cmml" xref="S2.SS1.p3.3.3.m3.1.1.1.1">subscript</csymbol><ci id="S2.SS1.p3.3.3.m3.1.1.1.1.2.cmml" xref="S2.SS1.p3.3.3.m3.1.1.1.1.2">𝐺</ci><ci id="S2.SS1.p3.3.3.m3.1.1.1.1.3.cmml" xref="S2.SS1.p3.3.3.m3.1.1.1.1.3">𝑙</ci></apply><apply id="S2.SS1.p3.3.3.m3.2.2.2.2.cmml" xref="S2.SS1.p3.3.3.m3.2.2.2.2"><csymbol cd="ambiguous" id="S2.SS1.p3.3.3.m3.2.2.2.2.1.cmml" xref="S2.SS1.p3.3.3.m3.2.2.2.2">subscript</csymbol><ci id="S2.SS1.p3.3.3.m3.2.2.2.2.2.cmml" xref="S2.SS1.p3.3.3.m3.2.2.2.2.2">𝐺</ci><ci id="S2.SS1.p3.3.3.m3.2.2.2.2.3.cmml" xref="S2.SS1.p3.3.3.m3.2.2.2.2.3">𝑟</ci></apply></set></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p3.3.3.m3.2c">\left\{{{G_{l}},{G_{r}}}\right\}</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p3.3.3.m3.2d">{ italic_G start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , italic_G start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT }</annotation></semantics></math>, given by</span></p> <table class="ltx_equation ltx_eqn_table" id="S2.E3"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="\left[F_{l},F_{r}\right]=T_{\gamma}\left(I_{l},I_{r}\right)\text{,}" class="ltx_Math" display="block" id="S2.E3.m1.4"><semantics id="S2.E3.m1.4a"><mrow id="S2.E3.m1.4.4" xref="S2.E3.m1.4.4.cmml"><mrow id="S2.E3.m1.2.2.2.2" xref="S2.E3.m1.2.2.2.3.cmml"><mo id="S2.E3.m1.2.2.2.2.3" xref="S2.E3.m1.2.2.2.3.cmml">[</mo><msub id="S2.E3.m1.1.1.1.1.1" xref="S2.E3.m1.1.1.1.1.1.cmml"><mi id="S2.E3.m1.1.1.1.1.1.2" xref="S2.E3.m1.1.1.1.1.1.2.cmml">F</mi><mi id="S2.E3.m1.1.1.1.1.1.3" xref="S2.E3.m1.1.1.1.1.1.3.cmml">l</mi></msub><mo id="S2.E3.m1.2.2.2.2.4" xref="S2.E3.m1.2.2.2.3.cmml">,</mo><msub id="S2.E3.m1.2.2.2.2.2" xref="S2.E3.m1.2.2.2.2.2.cmml"><mi id="S2.E3.m1.2.2.2.2.2.2" xref="S2.E3.m1.2.2.2.2.2.2.cmml">F</mi><mi id="S2.E3.m1.2.2.2.2.2.3" xref="S2.E3.m1.2.2.2.2.2.3.cmml">r</mi></msub><mo id="S2.E3.m1.2.2.2.2.5" xref="S2.E3.m1.2.2.2.3.cmml">]</mo></mrow><mo id="S2.E3.m1.4.4.5" xref="S2.E3.m1.4.4.5.cmml">=</mo><mrow id="S2.E3.m1.4.4.4" xref="S2.E3.m1.4.4.4.cmml"><msub id="S2.E3.m1.4.4.4.4" xref="S2.E3.m1.4.4.4.4.cmml"><mi id="S2.E3.m1.4.4.4.4.2" xref="S2.E3.m1.4.4.4.4.2.cmml">T</mi><mi id="S2.E3.m1.4.4.4.4.3" xref="S2.E3.m1.4.4.4.4.3.cmml">γ</mi></msub><mo id="S2.E3.m1.4.4.4.3" xref="S2.E3.m1.4.4.4.3.cmml">⁢</mo><mrow id="S2.E3.m1.4.4.4.2.2" xref="S2.E3.m1.4.4.4.2.3.cmml"><mo id="S2.E3.m1.4.4.4.2.2.3" xref="S2.E3.m1.4.4.4.2.3.cmml">(</mo><msub id="S2.E3.m1.3.3.3.1.1.1" xref="S2.E3.m1.3.3.3.1.1.1.cmml"><mi id="S2.E3.m1.3.3.3.1.1.1.2" xref="S2.E3.m1.3.3.3.1.1.1.2.cmml">I</mi><mi id="S2.E3.m1.3.3.3.1.1.1.3" xref="S2.E3.m1.3.3.3.1.1.1.3.cmml">l</mi></msub><mo id="S2.E3.m1.4.4.4.2.2.4" xref="S2.E3.m1.4.4.4.2.3.cmml">,</mo><msub id="S2.E3.m1.4.4.4.2.2.2" xref="S2.E3.m1.4.4.4.2.2.2.cmml"><mi id="S2.E3.m1.4.4.4.2.2.2.2" xref="S2.E3.m1.4.4.4.2.2.2.2.cmml">I</mi><mi id="S2.E3.m1.4.4.4.2.2.2.3" xref="S2.E3.m1.4.4.4.2.2.2.3.cmml">r</mi></msub><mo id="S2.E3.m1.4.4.4.2.2.5" xref="S2.E3.m1.4.4.4.2.3.cmml">)</mo></mrow><mo id="S2.E3.m1.4.4.4.3a" xref="S2.E3.m1.4.4.4.3.cmml">⁢</mo><mtext id="S2.E3.m1.4.4.4.5" xref="S2.E3.m1.4.4.4.5a.cmml">,</mtext></mrow></mrow><annotation-xml encoding="MathML-Content" id="S2.E3.m1.4b"><apply id="S2.E3.m1.4.4.cmml" xref="S2.E3.m1.4.4"><eq id="S2.E3.m1.4.4.5.cmml" xref="S2.E3.m1.4.4.5"></eq><interval closure="closed" id="S2.E3.m1.2.2.2.3.cmml" xref="S2.E3.m1.2.2.2.2"><apply id="S2.E3.m1.1.1.1.1.1.cmml" xref="S2.E3.m1.1.1.1.1.1"><csymbol cd="ambiguous" id="S2.E3.m1.1.1.1.1.1.1.cmml" xref="S2.E3.m1.1.1.1.1.1">subscript</csymbol><ci id="S2.E3.m1.1.1.1.1.1.2.cmml" xref="S2.E3.m1.1.1.1.1.1.2">𝐹</ci><ci id="S2.E3.m1.1.1.1.1.1.3.cmml" xref="S2.E3.m1.1.1.1.1.1.3">𝑙</ci></apply><apply id="S2.E3.m1.2.2.2.2.2.cmml" xref="S2.E3.m1.2.2.2.2.2"><csymbol cd="ambiguous" id="S2.E3.m1.2.2.2.2.2.1.cmml" xref="S2.E3.m1.2.2.2.2.2">subscript</csymbol><ci id="S2.E3.m1.2.2.2.2.2.2.cmml" xref="S2.E3.m1.2.2.2.2.2.2">𝐹</ci><ci id="S2.E3.m1.2.2.2.2.2.3.cmml" xref="S2.E3.m1.2.2.2.2.2.3">𝑟</ci></apply></interval><apply id="S2.E3.m1.4.4.4.cmml" xref="S2.E3.m1.4.4.4"><times id="S2.E3.m1.4.4.4.3.cmml" xref="S2.E3.m1.4.4.4.3"></times><apply id="S2.E3.m1.4.4.4.4.cmml" xref="S2.E3.m1.4.4.4.4"><csymbol cd="ambiguous" id="S2.E3.m1.4.4.4.4.1.cmml" xref="S2.E3.m1.4.4.4.4">subscript</csymbol><ci id="S2.E3.m1.4.4.4.4.2.cmml" xref="S2.E3.m1.4.4.4.4.2">𝑇</ci><ci id="S2.E3.m1.4.4.4.4.3.cmml" xref="S2.E3.m1.4.4.4.4.3">𝛾</ci></apply><interval closure="open" id="S2.E3.m1.4.4.4.2.3.cmml" xref="S2.E3.m1.4.4.4.2.2"><apply id="S2.E3.m1.3.3.3.1.1.1.cmml" xref="S2.E3.m1.3.3.3.1.1.1"><csymbol cd="ambiguous" id="S2.E3.m1.3.3.3.1.1.1.1.cmml" xref="S2.E3.m1.3.3.3.1.1.1">subscript</csymbol><ci id="S2.E3.m1.3.3.3.1.1.1.2.cmml" xref="S2.E3.m1.3.3.3.1.1.1.2">𝐼</ci><ci id="S2.E3.m1.3.3.3.1.1.1.3.cmml" xref="S2.E3.m1.3.3.3.1.1.1.3">𝑙</ci></apply><apply id="S2.E3.m1.4.4.4.2.2.2.cmml" xref="S2.E3.m1.4.4.4.2.2.2"><csymbol cd="ambiguous" id="S2.E3.m1.4.4.4.2.2.2.1.cmml" xref="S2.E3.m1.4.4.4.2.2.2">subscript</csymbol><ci id="S2.E3.m1.4.4.4.2.2.2.2.cmml" xref="S2.E3.m1.4.4.4.2.2.2.2">𝐼</ci><ci id="S2.E3.m1.4.4.4.2.2.2.3.cmml" xref="S2.E3.m1.4.4.4.2.2.2.3">𝑟</ci></apply></interval><ci id="S2.E3.m1.4.4.4.5a.cmml" xref="S2.E3.m1.4.4.4.5"><mtext id="S2.E3.m1.4.4.4.5.cmml" xref="S2.E3.m1.4.4.4.5">,</mtext></ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.E3.m1.4c">\left[F_{l},F_{r}\right]=T_{\gamma}\left(I_{l},I_{r}\right)\text{,}</annotation><annotation encoding="application/x-llamapun" id="S2.E3.m1.4d">[ italic_F start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , italic_F start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ] = italic_T start_POSTSUBSCRIPT italic_γ end_POSTSUBSCRIPT ( italic_I start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , italic_I start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ) ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(3)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S2.SS1.p3.9">and</p> <table class="ltx_equation ltx_eqn_table" id="S2.E4"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="\left\{{\begin{array}[]{*{20}{c}}G_{l}=T^{l}_{\varphi}\left(F_{l}\right)\text{% ,}\\ G_{r}=T^{r}_{\varphi}\left(F_{r}\right)\text{,}\end{array}}\right." class="ltx_Math" display="block" id="S2.E4.m1.2"><semantics id="S2.E4.m1.2a"><mrow id="S2.E4.m1.2.3.2" xref="S2.E4.m1.2.3.1.cmml"><mo id="S2.E4.m1.2.3.2.1" xref="S2.E4.m1.2.3.1.1.cmml">{</mo><mtable columnspacing="5pt" displaystyle="true" id="S2.E4.m1.2.2" rowspacing="0pt" xref="S2.E4.m1.2.2.cmml"><mtr id="S2.E4.m1.2.2a" xref="S2.E4.m1.2.2.cmml"><mtd id="S2.E4.m1.2.2b" xref="S2.E4.m1.2.2.cmml"><mrow id="S2.E4.m1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.cmml"><msub id="S2.E4.m1.1.1.1.1.1.3" xref="S2.E4.m1.1.1.1.1.1.3.cmml"><mi id="S2.E4.m1.1.1.1.1.1.3.2" xref="S2.E4.m1.1.1.1.1.1.3.2.cmml">G</mi><mi id="S2.E4.m1.1.1.1.1.1.3.3" xref="S2.E4.m1.1.1.1.1.1.3.3.cmml">l</mi></msub><mo id="S2.E4.m1.1.1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.1.2.cmml">=</mo><mrow id="S2.E4.m1.1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.1.cmml"><msubsup id="S2.E4.m1.1.1.1.1.1.1.3" xref="S2.E4.m1.1.1.1.1.1.1.3.cmml"><mi id="S2.E4.m1.1.1.1.1.1.1.3.2.2" xref="S2.E4.m1.1.1.1.1.1.1.3.2.2.cmml">T</mi><mi id="S2.E4.m1.1.1.1.1.1.1.3.3" xref="S2.E4.m1.1.1.1.1.1.1.3.3.cmml">φ</mi><mi id="S2.E4.m1.1.1.1.1.1.1.3.2.3" xref="S2.E4.m1.1.1.1.1.1.1.3.2.3.cmml">l</mi></msubsup><mo id="S2.E4.m1.1.1.1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.1.1.2.cmml">⁢</mo><mrow id="S2.E4.m1.1.1.1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.cmml"><mo id="S2.E4.m1.1.1.1.1.1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.cmml">(</mo><msub id="S2.E4.m1.1.1.1.1.1.1.1.1.1" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.cmml"><mi id="S2.E4.m1.1.1.1.1.1.1.1.1.1.2" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.2.cmml">F</mi><mi id="S2.E4.m1.1.1.1.1.1.1.1.1.1.3" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.3.cmml">l</mi></msub><mo id="S2.E4.m1.1.1.1.1.1.1.1.1.3" xref="S2.E4.m1.1.1.1.1.1.1.1.1.1.cmml">)</mo></mrow><mo id="S2.E4.m1.1.1.1.1.1.1.2a" xref="S2.E4.m1.1.1.1.1.1.1.2.cmml">⁢</mo><mtext id="S2.E4.m1.1.1.1.1.1.1.4" xref="S2.E4.m1.1.1.1.1.1.1.4a.cmml">,</mtext></mrow></mrow></mtd><mtd id="S2.E4.m1.2.2c" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2d" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2e" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2f" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2g" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2h" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2i" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2j" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2k" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2l" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2m" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2n" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2o" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2p" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2q" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2r" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2s" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2t" xref="S2.E4.m1.2.2.cmml"></mtd><mtd id="S2.E4.m1.2.2u" xref="S2.E4.m1.2.2.cmml"></mtd></mtr><mtr id="S2.E4.m1.2.2v" xref="S2.E4.m1.2.2.cmml"><mtd id="S2.E4.m1.2.2w" xref="S2.E4.m1.2.2.cmml"><mrow id="S2.E4.m1.2.2.2.1.1" xref="S2.E4.m1.2.2.2.1.1.cmml"><msub id="S2.E4.m1.2.2.2.1.1.3" xref="S2.E4.m1.2.2.2.1.1.3.cmml"><mi id="S2.E4.m1.2.2.2.1.1.3.2" xref="S2.E4.m1.2.2.2.1.1.3.2.cmml">G</mi><mi id="S2.E4.m1.2.2.2.1.1.3.3" xref="S2.E4.m1.2.2.2.1.1.3.3.cmml">r</mi></msub><mo id="S2.E4.m1.2.2.2.1.1.2" xref="S2.E4.m1.2.2.2.1.1.2.cmml">=</mo><mrow id="S2.E4.m1.2.2.2.1.1.1" xref="S2.E4.m1.2.2.2.1.1.1.cmml"><msubsup id="S2.E4.m1.2.2.2.1.1.1.3" xref="S2.E4.m1.2.2.2.1.1.1.3.cmml"><mi id="S2.E4.m1.2.2.2.1.1.1.3.2.2" xref="S2.E4.m1.2.2.2.1.1.1.3.2.2.cmml">T</mi><mi id="S2.E4.m1.2.2.2.1.1.1.3.3" xref="S2.E4.m1.2.2.2.1.1.1.3.3.cmml">φ</mi><mi id="S2.E4.m1.2.2.2.1.1.1.3.2.3" 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end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW start_ROW start_CELL italic_G start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_φ end_POSTSUBSCRIPT ( italic_F start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ) , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW end_ARRAY</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(4)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S2.SS1.p3.8">where <math alttext="T_{\gamma}" class="ltx_Math" display="inline" id="S2.SS1.p3.4.m1.1"><semantics id="S2.SS1.p3.4.m1.1a"><msub id="S2.SS1.p3.4.m1.1.1" xref="S2.SS1.p3.4.m1.1.1.cmml"><mi id="S2.SS1.p3.4.m1.1.1.2" xref="S2.SS1.p3.4.m1.1.1.2.cmml">T</mi><mi id="S2.SS1.p3.4.m1.1.1.3" xref="S2.SS1.p3.4.m1.1.1.3.cmml">γ</mi></msub><annotation-xml encoding="MathML-Content" id="S2.SS1.p3.4.m1.1b"><apply id="S2.SS1.p3.4.m1.1.1.cmml" xref="S2.SS1.p3.4.m1.1.1"><csymbol cd="ambiguous" id="S2.SS1.p3.4.m1.1.1.1.cmml" xref="S2.SS1.p3.4.m1.1.1">subscript</csymbol><ci id="S2.SS1.p3.4.m1.1.1.2.cmml" xref="S2.SS1.p3.4.m1.1.1.2">𝑇</ci><ci id="S2.SS1.p3.4.m1.1.1.3.cmml" xref="S2.SS1.p3.4.m1.1.1.3">𝛾</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p3.4.m1.1c">T_{\gamma}</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p3.4.m1.1d">italic_T start_POSTSUBSCRIPT italic_γ end_POSTSUBSCRIPT</annotation></semantics></math> denotes the joint semantic extraction network parameterized by <math alttext="\gamma" class="ltx_Math" display="inline" id="S2.SS1.p3.5.m2.1"><semantics id="S2.SS1.p3.5.m2.1a"><mi id="S2.SS1.p3.5.m2.1.1" xref="S2.SS1.p3.5.m2.1.1.cmml">γ</mi><annotation-xml encoding="MathML-Content" id="S2.SS1.p3.5.m2.1b"><ci id="S2.SS1.p3.5.m2.1.1.cmml" xref="S2.SS1.p3.5.m2.1.1">𝛾</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p3.5.m2.1c">\gamma</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p3.5.m2.1d">italic_γ</annotation></semantics></math> while <math alttext="T^{l}_{\varphi}" class="ltx_Math" display="inline" id="S2.SS1.p3.6.m3.1"><semantics id="S2.SS1.p3.6.m3.1a"><msubsup id="S2.SS1.p3.6.m3.1.1" xref="S2.SS1.p3.6.m3.1.1.cmml"><mi id="S2.SS1.p3.6.m3.1.1.2.2" xref="S2.SS1.p3.6.m3.1.1.2.2.cmml">T</mi><mi id="S2.SS1.p3.6.m3.1.1.3" xref="S2.SS1.p3.6.m3.1.1.3.cmml">φ</mi><mi id="S2.SS1.p3.6.m3.1.1.2.3" xref="S2.SS1.p3.6.m3.1.1.2.3.cmml">l</mi></msubsup><annotation-xml encoding="MathML-Content" id="S2.SS1.p3.6.m3.1b"><apply id="S2.SS1.p3.6.m3.1.1.cmml" xref="S2.SS1.p3.6.m3.1.1"><csymbol cd="ambiguous" id="S2.SS1.p3.6.m3.1.1.1.cmml" xref="S2.SS1.p3.6.m3.1.1">subscript</csymbol><apply id="S2.SS1.p3.6.m3.1.1.2.cmml" xref="S2.SS1.p3.6.m3.1.1"><csymbol cd="ambiguous" id="S2.SS1.p3.6.m3.1.1.2.1.cmml" xref="S2.SS1.p3.6.m3.1.1">superscript</csymbol><ci id="S2.SS1.p3.6.m3.1.1.2.2.cmml" xref="S2.SS1.p3.6.m3.1.1.2.2">𝑇</ci><ci id="S2.SS1.p3.6.m3.1.1.2.3.cmml" xref="S2.SS1.p3.6.m3.1.1.2.3">𝑙</ci></apply><ci id="S2.SS1.p3.6.m3.1.1.3.cmml" xref="S2.SS1.p3.6.m3.1.1.3">𝜑</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p3.6.m3.1c">T^{l}_{\varphi}</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p3.6.m3.1d">italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_φ end_POSTSUBSCRIPT</annotation></semantics></math> and <math alttext="T^{r}_{\varphi}" class="ltx_Math" display="inline" id="S2.SS1.p3.7.m4.1"><semantics id="S2.SS1.p3.7.m4.1a"><msubsup id="S2.SS1.p3.7.m4.1.1" xref="S2.SS1.p3.7.m4.1.1.cmml"><mi id="S2.SS1.p3.7.m4.1.1.2.2" xref="S2.SS1.p3.7.m4.1.1.2.2.cmml">T</mi><mi id="S2.SS1.p3.7.m4.1.1.3" xref="S2.SS1.p3.7.m4.1.1.3.cmml">φ</mi><mi id="S2.SS1.p3.7.m4.1.1.2.3" xref="S2.SS1.p3.7.m4.1.1.2.3.cmml">r</mi></msubsup><annotation-xml encoding="MathML-Content" id="S2.SS1.p3.7.m4.1b"><apply id="S2.SS1.p3.7.m4.1.1.cmml" xref="S2.SS1.p3.7.m4.1.1"><csymbol cd="ambiguous" id="S2.SS1.p3.7.m4.1.1.1.cmml" xref="S2.SS1.p3.7.m4.1.1">subscript</csymbol><apply id="S2.SS1.p3.7.m4.1.1.2.cmml" xref="S2.SS1.p3.7.m4.1.1"><csymbol cd="ambiguous" id="S2.SS1.p3.7.m4.1.1.2.1.cmml" xref="S2.SS1.p3.7.m4.1.1">superscript</csymbol><ci id="S2.SS1.p3.7.m4.1.1.2.2.cmml" xref="S2.SS1.p3.7.m4.1.1.2.2">𝑇</ci><ci id="S2.SS1.p3.7.m4.1.1.2.3.cmml" xref="S2.SS1.p3.7.m4.1.1.2.3">𝑟</ci></apply><ci id="S2.SS1.p3.7.m4.1.1.3.cmml" xref="S2.SS1.p3.7.m4.1.1.3">𝜑</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p3.7.m4.1c">T^{r}_{\varphi}</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p3.7.m4.1d">italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_φ end_POSTSUBSCRIPT</annotation></semantics></math> are the compression networks of the global information network, parameterized by <math alttext="{\varphi}" class="ltx_Math" display="inline" id="S2.SS1.p3.8.m5.1"><semantics id="S2.SS1.p3.8.m5.1a"><mi id="S2.SS1.p3.8.m5.1.1" xref="S2.SS1.p3.8.m5.1.1.cmml">φ</mi><annotation-xml encoding="MathML-Content" id="S2.SS1.p3.8.m5.1b"><ci id="S2.SS1.p3.8.m5.1.1.cmml" xref="S2.SS1.p3.8.m5.1.1">𝜑</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.SS1.p3.8.m5.1c">{\varphi}</annotation><annotation encoding="application/x-llamapun" id="S2.SS1.p3.8.m5.1d">italic_φ</annotation></semantics></math>.<span class="ltx_text" id="S2.SS1.p3.8.1"></span></p> </div> </section> <section class="ltx_subsection" id="S2.SS2"> <h3 class="ltx_title ltx_title_subsection"> <span class="ltx_tag ltx_tag_subsection"><span class="ltx_text" id="S2.SS2.5.1.1">II-B</span> </span><span class="ltx_text ltx_font_italic" id="S2.SS2.6.2">The Channel Encoder and Decoder Networks </span> </h3> <div class="ltx_para" id="S2.SS2.p1"> <p class="ltx_p" id="S2.SS2.p1.1"><span class="ltx_text" id="S2.SS2.p1.1.1">After the semantic encoder, the channel codec is used to overcome the channel noise. At the transmitter, the channel encoder first encodes the key area and the global information and transmits the encoded information <math alttext="\left\{{{X}_{K},{X}_{G}}\right\}" class="ltx_Math" display="inline" id="S2.SS2.p1.1.1.m1.2"><semantics id="S2.SS2.p1.1.1.m1.2a"><mrow id="S2.SS2.p1.1.1.m1.2.2.2" xref="S2.SS2.p1.1.1.m1.2.2.3.cmml"><mo id="S2.SS2.p1.1.1.m1.2.2.2.3" xref="S2.SS2.p1.1.1.m1.2.2.3.cmml">{</mo><msub id="S2.SS2.p1.1.1.m1.1.1.1.1" xref="S2.SS2.p1.1.1.m1.1.1.1.1.cmml"><mi id="S2.SS2.p1.1.1.m1.1.1.1.1.2" xref="S2.SS2.p1.1.1.m1.1.1.1.1.2.cmml">X</mi><mi id="S2.SS2.p1.1.1.m1.1.1.1.1.3" xref="S2.SS2.p1.1.1.m1.1.1.1.1.3.cmml">K</mi></msub><mo id="S2.SS2.p1.1.1.m1.2.2.2.4" xref="S2.SS2.p1.1.1.m1.2.2.3.cmml">,</mo><msub id="S2.SS2.p1.1.1.m1.2.2.2.2" xref="S2.SS2.p1.1.1.m1.2.2.2.2.cmml"><mi id="S2.SS2.p1.1.1.m1.2.2.2.2.2" xref="S2.SS2.p1.1.1.m1.2.2.2.2.2.cmml">X</mi><mi id="S2.SS2.p1.1.1.m1.2.2.2.2.3" xref="S2.SS2.p1.1.1.m1.2.2.2.2.3.cmml">G</mi></msub><mo id="S2.SS2.p1.1.1.m1.2.2.2.5" xref="S2.SS2.p1.1.1.m1.2.2.3.cmml">}</mo></mrow><annotation-xml encoding="MathML-Content" id="S2.SS2.p1.1.1.m1.2b"><set id="S2.SS2.p1.1.1.m1.2.2.3.cmml" xref="S2.SS2.p1.1.1.m1.2.2.2"><apply id="S2.SS2.p1.1.1.m1.1.1.1.1.cmml" xref="S2.SS2.p1.1.1.m1.1.1.1.1"><csymbol cd="ambiguous" id="S2.SS2.p1.1.1.m1.1.1.1.1.1.cmml" xref="S2.SS2.p1.1.1.m1.1.1.1.1">subscript</csymbol><ci id="S2.SS2.p1.1.1.m1.1.1.1.1.2.cmml" xref="S2.SS2.p1.1.1.m1.1.1.1.1.2">𝑋</ci><ci id="S2.SS2.p1.1.1.m1.1.1.1.1.3.cmml" xref="S2.SS2.p1.1.1.m1.1.1.1.1.3">𝐾</ci></apply><apply id="S2.SS2.p1.1.1.m1.2.2.2.2.cmml" xref="S2.SS2.p1.1.1.m1.2.2.2.2"><csymbol cd="ambiguous" id="S2.SS2.p1.1.1.m1.2.2.2.2.1.cmml" xref="S2.SS2.p1.1.1.m1.2.2.2.2">subscript</csymbol><ci id="S2.SS2.p1.1.1.m1.2.2.2.2.2.cmml" xref="S2.SS2.p1.1.1.m1.2.2.2.2.2">𝑋</ci><ci id="S2.SS2.p1.1.1.m1.2.2.2.2.3.cmml" xref="S2.SS2.p1.1.1.m1.2.2.2.2.3">𝐺</ci></apply></set></annotation-xml><annotation encoding="application/x-tex" id="S2.SS2.p1.1.1.m1.2c">\left\{{{X}_{K},{X}_{G}}\right\}</annotation><annotation encoding="application/x-llamapun" id="S2.SS2.p1.1.1.m1.2d">{ italic_X start_POSTSUBSCRIPT italic_K end_POSTSUBSCRIPT , italic_X start_POSTSUBSCRIPT italic_G end_POSTSUBSCRIPT }</annotation></semantics></math> over the wireless channel, which can be expressed as</span></p> <table class="ltx_equation ltx_eqn_table" id="S2.E5"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="\left\{{\begin{array}[]{*{20}{c}}{X}_{K}=T_{c_{e}}\left(K_{l},K_{r}\right)% \text{,}\\ {X}_{G}=T_{c_{e}}\left(G_{l},G_{r}\right)\text{,}\end{array}}\right." class="ltx_Math" display="block" id="S2.E5.m1.4"><semantics id="S2.E5.m1.4a"><mrow id="S2.E5.m1.4.5.2" xref="S2.E5.m1.4.5.1.cmml"><mo id="S2.E5.m1.4.5.2.1" xref="S2.E5.m1.4.5.1.1.cmml">{</mo><mtable columnspacing="5pt" displaystyle="true" id="S2.E5.m1.4.4" 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start_POSTSUBSCRIPT italic_c start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT end_POSTSUBSCRIPT ( italic_K start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , italic_K start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ) , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW start_ROW start_CELL italic_X start_POSTSUBSCRIPT italic_G end_POSTSUBSCRIPT = italic_T start_POSTSUBSCRIPT italic_c start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT end_POSTSUBSCRIPT ( italic_G start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , italic_G start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ) , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW end_ARRAY</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(5)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S2.SS2.p1.3">where <math alttext="T_{c_{e}}" class="ltx_Math" display="inline" id="S2.SS2.p1.2.m1.1"><semantics id="S2.SS2.p1.2.m1.1a"><msub id="S2.SS2.p1.2.m1.1.1" xref="S2.SS2.p1.2.m1.1.1.cmml"><mi id="S2.SS2.p1.2.m1.1.1.2" xref="S2.SS2.p1.2.m1.1.1.2.cmml">T</mi><msub id="S2.SS2.p1.2.m1.1.1.3" xref="S2.SS2.p1.2.m1.1.1.3.cmml"><mi id="S2.SS2.p1.2.m1.1.1.3.2" xref="S2.SS2.p1.2.m1.1.1.3.2.cmml">c</mi><mi id="S2.SS2.p1.2.m1.1.1.3.3" xref="S2.SS2.p1.2.m1.1.1.3.3.cmml">e</mi></msub></msub><annotation-xml encoding="MathML-Content" id="S2.SS2.p1.2.m1.1b"><apply id="S2.SS2.p1.2.m1.1.1.cmml" xref="S2.SS2.p1.2.m1.1.1"><csymbol cd="ambiguous" id="S2.SS2.p1.2.m1.1.1.1.cmml" xref="S2.SS2.p1.2.m1.1.1">subscript</csymbol><ci id="S2.SS2.p1.2.m1.1.1.2.cmml" xref="S2.SS2.p1.2.m1.1.1.2">𝑇</ci><apply id="S2.SS2.p1.2.m1.1.1.3.cmml" xref="S2.SS2.p1.2.m1.1.1.3"><csymbol cd="ambiguous" id="S2.SS2.p1.2.m1.1.1.3.1.cmml" xref="S2.SS2.p1.2.m1.1.1.3">subscript</csymbol><ci id="S2.SS2.p1.2.m1.1.1.3.2.cmml" xref="S2.SS2.p1.2.m1.1.1.3.2">𝑐</ci><ci id="S2.SS2.p1.2.m1.1.1.3.3.cmml" xref="S2.SS2.p1.2.m1.1.1.3.3">𝑒</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS2.p1.2.m1.1c">T_{c_{e}}</annotation><annotation encoding="application/x-llamapun" id="S2.SS2.p1.2.m1.1d">italic_T start_POSTSUBSCRIPT italic_c start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT end_POSTSUBSCRIPT</annotation></semantics></math> denotes the channel encoder network parameterized by <math alttext="c_{e}" class="ltx_Math" display="inline" id="S2.SS2.p1.3.m2.1"><semantics id="S2.SS2.p1.3.m2.1a"><msub id="S2.SS2.p1.3.m2.1.1" xref="S2.SS2.p1.3.m2.1.1.cmml"><mi id="S2.SS2.p1.3.m2.1.1.2" xref="S2.SS2.p1.3.m2.1.1.2.cmml">c</mi><mi id="S2.SS2.p1.3.m2.1.1.3" xref="S2.SS2.p1.3.m2.1.1.3.cmml">e</mi></msub><annotation-xml encoding="MathML-Content" id="S2.SS2.p1.3.m2.1b"><apply id="S2.SS2.p1.3.m2.1.1.cmml" xref="S2.SS2.p1.3.m2.1.1"><csymbol cd="ambiguous" id="S2.SS2.p1.3.m2.1.1.1.cmml" xref="S2.SS2.p1.3.m2.1.1">subscript</csymbol><ci id="S2.SS2.p1.3.m2.1.1.2.cmml" xref="S2.SS2.p1.3.m2.1.1.2">𝑐</ci><ci id="S2.SS2.p1.3.m2.1.1.3.cmml" xref="S2.SS2.p1.3.m2.1.1.3">𝑒</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS2.p1.3.m2.1c">c_{e}</annotation><annotation encoding="application/x-llamapun" id="S2.SS2.p1.3.m2.1d">italic_c start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT</annotation></semantics></math>. Assuming the transmitted signal undergoes the additive white Gaussian noise (AWGN) channel, the received signal is given by</p> <table class="ltx_equation ltx_eqn_table" id="S2.E6"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="\left\{{\begin{array}[]{*{20}{c}}{Y}_{K}={X}_{K}+{W}_{K}\text{,}\\ {Y}_{G}={X}_{G}+{W}_{G}\text{,}\end{array}}\right." class="ltx_Math" display="block" id="S2.E6.m1.1"><semantics id="S2.E6.m1.1a"><mrow id="S2.E6.m1.1.2.2" xref="S2.E6.m1.1.2.1.cmml"><mo id="S2.E6.m1.1.2.2.1" xref="S2.E6.m1.1.2.1.1.cmml">{</mo><mtable columnspacing="5pt" displaystyle="true" id="S2.E6.m1.1.1" rowspacing="0pt" xref="S2.E6.m1.1.1.cmml"><mtr id="S2.E6.m1.1.1a" xref="S2.E6.m1.1.1.cmml"><mtd id="S2.E6.m1.1.1b" xref="S2.E6.m1.1.1.cmml"><mrow id="S2.E6.m1.1.1.1.1.1" xref="S2.E6.m1.1.1.1.1.1.cmml"><msub id="S2.E6.m1.1.1.1.1.1.2" 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start_POSTSUBSCRIPT italic_K end_POSTSUBSCRIPT + italic_W start_POSTSUBSCRIPT italic_K end_POSTSUBSCRIPT , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW start_ROW start_CELL italic_Y start_POSTSUBSCRIPT italic_G end_POSTSUBSCRIPT = italic_X start_POSTSUBSCRIPT italic_G end_POSTSUBSCRIPT + italic_W start_POSTSUBSCRIPT italic_G end_POSTSUBSCRIPT , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW end_ARRAY</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(6)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S2.SS2.p1.5">where <math alttext="W_{K}" class="ltx_Math" display="inline" id="S2.SS2.p1.4.m1.1"><semantics id="S2.SS2.p1.4.m1.1a"><msub id="S2.SS2.p1.4.m1.1.1" xref="S2.SS2.p1.4.m1.1.1.cmml"><mi id="S2.SS2.p1.4.m1.1.1.2" xref="S2.SS2.p1.4.m1.1.1.2.cmml">W</mi><mi id="S2.SS2.p1.4.m1.1.1.3" xref="S2.SS2.p1.4.m1.1.1.3.cmml">K</mi></msub><annotation-xml encoding="MathML-Content" id="S2.SS2.p1.4.m1.1b"><apply id="S2.SS2.p1.4.m1.1.1.cmml" xref="S2.SS2.p1.4.m1.1.1"><csymbol cd="ambiguous" id="S2.SS2.p1.4.m1.1.1.1.cmml" xref="S2.SS2.p1.4.m1.1.1">subscript</csymbol><ci id="S2.SS2.p1.4.m1.1.1.2.cmml" xref="S2.SS2.p1.4.m1.1.1.2">𝑊</ci><ci id="S2.SS2.p1.4.m1.1.1.3.cmml" xref="S2.SS2.p1.4.m1.1.1.3">𝐾</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS2.p1.4.m1.1c">W_{K}</annotation><annotation encoding="application/x-llamapun" id="S2.SS2.p1.4.m1.1d">italic_W start_POSTSUBSCRIPT italic_K end_POSTSUBSCRIPT</annotation></semantics></math> and <math alttext="W_{G}" class="ltx_Math" display="inline" id="S2.SS2.p1.5.m2.1"><semantics id="S2.SS2.p1.5.m2.1a"><msub id="S2.SS2.p1.5.m2.1.1" xref="S2.SS2.p1.5.m2.1.1.cmml"><mi id="S2.SS2.p1.5.m2.1.1.2" xref="S2.SS2.p1.5.m2.1.1.2.cmml">W</mi><mi id="S2.SS2.p1.5.m2.1.1.3" xref="S2.SS2.p1.5.m2.1.1.3.cmml">G</mi></msub><annotation-xml encoding="MathML-Content" id="S2.SS2.p1.5.m2.1b"><apply id="S2.SS2.p1.5.m2.1.1.cmml" xref="S2.SS2.p1.5.m2.1.1"><csymbol cd="ambiguous" id="S2.SS2.p1.5.m2.1.1.1.cmml" xref="S2.SS2.p1.5.m2.1.1">subscript</csymbol><ci id="S2.SS2.p1.5.m2.1.1.2.cmml" xref="S2.SS2.p1.5.m2.1.1.2">𝑊</ci><ci id="S2.SS2.p1.5.m2.1.1.3.cmml" xref="S2.SS2.p1.5.m2.1.1.3">𝐺</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS2.p1.5.m2.1c">W_{G}</annotation><annotation encoding="application/x-llamapun" id="S2.SS2.p1.5.m2.1d">italic_W start_POSTSUBSCRIPT italic_G end_POSTSUBSCRIPT</annotation></semantics></math> are the AWGN of the channel. More complicated channel models can be considered as in <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib27" title="">27</a>]</cite>.<span class="ltx_text" id="S2.SS2.p1.5.1"></span></p> </div> <div class="ltx_para" id="S2.SS2.p2"> <p class="ltx_p" id="S2.SS2.p2.3"><span class="ltx_text" id="S2.SS2.p2.3.3">Correspondingly, at the receiver, the channel decoder recovers information <math alttext="\left\{{{\hat{K}_{r}},{\hat{K}_{l}}}\right\}" class="ltx_Math" display="inline" id="S2.SS2.p2.1.1.m1.2"><semantics id="S2.SS2.p2.1.1.m1.2a"><mrow id="S2.SS2.p2.1.1.m1.2.2.2" xref="S2.SS2.p2.1.1.m1.2.2.3.cmml"><mo id="S2.SS2.p2.1.1.m1.2.2.2.3" xref="S2.SS2.p2.1.1.m1.2.2.3.cmml">{</mo><msub id="S2.SS2.p2.1.1.m1.1.1.1.1" xref="S2.SS2.p2.1.1.m1.1.1.1.1.cmml"><mover accent="true" id="S2.SS2.p2.1.1.m1.1.1.1.1.2" xref="S2.SS2.p2.1.1.m1.1.1.1.1.2.cmml"><mi id="S2.SS2.p2.1.1.m1.1.1.1.1.2.2" xref="S2.SS2.p2.1.1.m1.1.1.1.1.2.2.cmml">K</mi><mo 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id="S2.SS2.p2.1.1.m1.1.1.1.1.1.cmml" xref="S2.SS2.p2.1.1.m1.1.1.1.1">subscript</csymbol><apply id="S2.SS2.p2.1.1.m1.1.1.1.1.2.cmml" xref="S2.SS2.p2.1.1.m1.1.1.1.1.2"><ci id="S2.SS2.p2.1.1.m1.1.1.1.1.2.1.cmml" xref="S2.SS2.p2.1.1.m1.1.1.1.1.2.1">^</ci><ci id="S2.SS2.p2.1.1.m1.1.1.1.1.2.2.cmml" xref="S2.SS2.p2.1.1.m1.1.1.1.1.2.2">𝐾</ci></apply><ci id="S2.SS2.p2.1.1.m1.1.1.1.1.3.cmml" xref="S2.SS2.p2.1.1.m1.1.1.1.1.3">𝑟</ci></apply><apply id="S2.SS2.p2.1.1.m1.2.2.2.2.cmml" xref="S2.SS2.p2.1.1.m1.2.2.2.2"><csymbol cd="ambiguous" id="S2.SS2.p2.1.1.m1.2.2.2.2.1.cmml" xref="S2.SS2.p2.1.1.m1.2.2.2.2">subscript</csymbol><apply id="S2.SS2.p2.1.1.m1.2.2.2.2.2.cmml" xref="S2.SS2.p2.1.1.m1.2.2.2.2.2"><ci id="S2.SS2.p2.1.1.m1.2.2.2.2.2.1.cmml" xref="S2.SS2.p2.1.1.m1.2.2.2.2.2.1">^</ci><ci id="S2.SS2.p2.1.1.m1.2.2.2.2.2.2.cmml" xref="S2.SS2.p2.1.1.m1.2.2.2.2.2.2">𝐾</ci></apply><ci id="S2.SS2.p2.1.1.m1.2.2.2.2.3.cmml" xref="S2.SS2.p2.1.1.m1.2.2.2.2.3">𝑙</ci></apply></set></annotation-xml><annotation encoding="application/x-tex" id="S2.SS2.p2.1.1.m1.2c">\left\{{{\hat{K}_{r}},{\hat{K}_{l}}}\right\}</annotation><annotation encoding="application/x-llamapun" id="S2.SS2.p2.1.1.m1.2d">{ over^ start_ARG italic_K end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT , over^ start_ARG italic_K end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT }</annotation></semantics></math> and <math alttext="\left\{{{\hat{G}_{r}},{\hat{G}_{l}}}\right\}" class="ltx_Math" display="inline" id="S2.SS2.p2.2.2.m2.2"><semantics id="S2.SS2.p2.2.2.m2.2a"><mrow id="S2.SS2.p2.2.2.m2.2.2.2" xref="S2.SS2.p2.2.2.m2.2.2.3.cmml"><mo id="S2.SS2.p2.2.2.m2.2.2.2.3" xref="S2.SS2.p2.2.2.m2.2.2.3.cmml">{</mo><msub id="S2.SS2.p2.2.2.m2.1.1.1.1" xref="S2.SS2.p2.2.2.m2.1.1.1.1.cmml"><mover accent="true" id="S2.SS2.p2.2.2.m2.1.1.1.1.2" xref="S2.SS2.p2.2.2.m2.1.1.1.1.2.cmml"><mi id="S2.SS2.p2.2.2.m2.1.1.1.1.2.2" xref="S2.SS2.p2.2.2.m2.1.1.1.1.2.2.cmml">G</mi><mo id="S2.SS2.p2.2.2.m2.1.1.1.1.2.1" xref="S2.SS2.p2.2.2.m2.1.1.1.1.2.1.cmml">^</mo></mover><mi id="S2.SS2.p2.2.2.m2.1.1.1.1.3" xref="S2.SS2.p2.2.2.m2.1.1.1.1.3.cmml">r</mi></msub><mo id="S2.SS2.p2.2.2.m2.2.2.2.4" xref="S2.SS2.p2.2.2.m2.2.2.3.cmml">,</mo><msub id="S2.SS2.p2.2.2.m2.2.2.2.2" xref="S2.SS2.p2.2.2.m2.2.2.2.2.cmml"><mover accent="true" id="S2.SS2.p2.2.2.m2.2.2.2.2.2" xref="S2.SS2.p2.2.2.m2.2.2.2.2.2.cmml"><mi id="S2.SS2.p2.2.2.m2.2.2.2.2.2.2" xref="S2.SS2.p2.2.2.m2.2.2.2.2.2.2.cmml">G</mi><mo id="S2.SS2.p2.2.2.m2.2.2.2.2.2.1" xref="S2.SS2.p2.2.2.m2.2.2.2.2.2.1.cmml">^</mo></mover><mi id="S2.SS2.p2.2.2.m2.2.2.2.2.3" xref="S2.SS2.p2.2.2.m2.2.2.2.2.3.cmml">l</mi></msub><mo id="S2.SS2.p2.2.2.m2.2.2.2.5" xref="S2.SS2.p2.2.2.m2.2.2.3.cmml">}</mo></mrow><annotation-xml encoding="MathML-Content" id="S2.SS2.p2.2.2.m2.2b"><set id="S2.SS2.p2.2.2.m2.2.2.3.cmml" xref="S2.SS2.p2.2.2.m2.2.2.2"><apply id="S2.SS2.p2.2.2.m2.1.1.1.1.cmml" xref="S2.SS2.p2.2.2.m2.1.1.1.1"><csymbol cd="ambiguous" id="S2.SS2.p2.2.2.m2.1.1.1.1.1.cmml" xref="S2.SS2.p2.2.2.m2.1.1.1.1">subscript</csymbol><apply id="S2.SS2.p2.2.2.m2.1.1.1.1.2.cmml" xref="S2.SS2.p2.2.2.m2.1.1.1.1.2"><ci id="S2.SS2.p2.2.2.m2.1.1.1.1.2.1.cmml" xref="S2.SS2.p2.2.2.m2.1.1.1.1.2.1">^</ci><ci id="S2.SS2.p2.2.2.m2.1.1.1.1.2.2.cmml" xref="S2.SS2.p2.2.2.m2.1.1.1.1.2.2">𝐺</ci></apply><ci id="S2.SS2.p2.2.2.m2.1.1.1.1.3.cmml" xref="S2.SS2.p2.2.2.m2.1.1.1.1.3">𝑟</ci></apply><apply id="S2.SS2.p2.2.2.m2.2.2.2.2.cmml" xref="S2.SS2.p2.2.2.m2.2.2.2.2"><csymbol cd="ambiguous" id="S2.SS2.p2.2.2.m2.2.2.2.2.1.cmml" xref="S2.SS2.p2.2.2.m2.2.2.2.2">subscript</csymbol><apply id="S2.SS2.p2.2.2.m2.2.2.2.2.2.cmml" xref="S2.SS2.p2.2.2.m2.2.2.2.2.2"><ci id="S2.SS2.p2.2.2.m2.2.2.2.2.2.1.cmml" xref="S2.SS2.p2.2.2.m2.2.2.2.2.2.1">^</ci><ci id="S2.SS2.p2.2.2.m2.2.2.2.2.2.2.cmml" xref="S2.SS2.p2.2.2.m2.2.2.2.2.2.2">𝐺</ci></apply><ci id="S2.SS2.p2.2.2.m2.2.2.2.2.3.cmml" xref="S2.SS2.p2.2.2.m2.2.2.2.2.3">𝑙</ci></apply></set></annotation-xml><annotation encoding="application/x-tex" id="S2.SS2.p2.2.2.m2.2c">\left\{{{\hat{G}_{r}},{\hat{G}_{l}}}\right\}</annotation><annotation encoding="application/x-llamapun" id="S2.SS2.p2.2.2.m2.2d">{ over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT }</annotation></semantics></math> from received signals <math alttext="\left\{{{Y}_{K},{Y}_{G}}\right\}" class="ltx_Math" display="inline" id="S2.SS2.p2.3.3.m3.2"><semantics id="S2.SS2.p2.3.3.m3.2a"><mrow id="S2.SS2.p2.3.3.m3.2.2.2" xref="S2.SS2.p2.3.3.m3.2.2.3.cmml"><mo id="S2.SS2.p2.3.3.m3.2.2.2.3" xref="S2.SS2.p2.3.3.m3.2.2.3.cmml">{</mo><msub id="S2.SS2.p2.3.3.m3.1.1.1.1" xref="S2.SS2.p2.3.3.m3.1.1.1.1.cmml"><mi id="S2.SS2.p2.3.3.m3.1.1.1.1.2" xref="S2.SS2.p2.3.3.m3.1.1.1.1.2.cmml">Y</mi><mi id="S2.SS2.p2.3.3.m3.1.1.1.1.3" xref="S2.SS2.p2.3.3.m3.1.1.1.1.3.cmml">K</mi></msub><mo id="S2.SS2.p2.3.3.m3.2.2.2.4" xref="S2.SS2.p2.3.3.m3.2.2.3.cmml">,</mo><msub id="S2.SS2.p2.3.3.m3.2.2.2.2" xref="S2.SS2.p2.3.3.m3.2.2.2.2.cmml"><mi id="S2.SS2.p2.3.3.m3.2.2.2.2.2" xref="S2.SS2.p2.3.3.m3.2.2.2.2.2.cmml">Y</mi><mi id="S2.SS2.p2.3.3.m3.2.2.2.2.3" xref="S2.SS2.p2.3.3.m3.2.2.2.2.3.cmml">G</mi></msub><mo id="S2.SS2.p2.3.3.m3.2.2.2.5" xref="S2.SS2.p2.3.3.m3.2.2.3.cmml">}</mo></mrow><annotation-xml encoding="MathML-Content" id="S2.SS2.p2.3.3.m3.2b"><set id="S2.SS2.p2.3.3.m3.2.2.3.cmml" xref="S2.SS2.p2.3.3.m3.2.2.2"><apply id="S2.SS2.p2.3.3.m3.1.1.1.1.cmml" xref="S2.SS2.p2.3.3.m3.1.1.1.1"><csymbol cd="ambiguous" id="S2.SS2.p2.3.3.m3.1.1.1.1.1.cmml" xref="S2.SS2.p2.3.3.m3.1.1.1.1">subscript</csymbol><ci id="S2.SS2.p2.3.3.m3.1.1.1.1.2.cmml" xref="S2.SS2.p2.3.3.m3.1.1.1.1.2">𝑌</ci><ci id="S2.SS2.p2.3.3.m3.1.1.1.1.3.cmml" xref="S2.SS2.p2.3.3.m3.1.1.1.1.3">𝐾</ci></apply><apply id="S2.SS2.p2.3.3.m3.2.2.2.2.cmml" xref="S2.SS2.p2.3.3.m3.2.2.2.2"><csymbol cd="ambiguous" id="S2.SS2.p2.3.3.m3.2.2.2.2.1.cmml" xref="S2.SS2.p2.3.3.m3.2.2.2.2">subscript</csymbol><ci id="S2.SS2.p2.3.3.m3.2.2.2.2.2.cmml" xref="S2.SS2.p2.3.3.m3.2.2.2.2.2">𝑌</ci><ci id="S2.SS2.p2.3.3.m3.2.2.2.2.3.cmml" xref="S2.SS2.p2.3.3.m3.2.2.2.2.3">𝐺</ci></apply></set></annotation-xml><annotation encoding="application/x-tex" id="S2.SS2.p2.3.3.m3.2c">\left\{{{Y}_{K},{Y}_{G}}\right\}</annotation><annotation encoding="application/x-llamapun" id="S2.SS2.p2.3.3.m3.2d">{ italic_Y start_POSTSUBSCRIPT italic_K end_POSTSUBSCRIPT , italic_Y start_POSTSUBSCRIPT italic_G end_POSTSUBSCRIPT }</annotation></semantics></math>, expressed as</span></p> <table class="ltx_equation ltx_eqn_table" id="S2.E7"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="\left\{{\begin{array}[]{*{20}{c}}\left\{{{\hat{K}_{l}},{\hat{K}_{r}}}\right\}=% T_{c_{d}}\left(Y_{K}\right)\text{,}\\ \left\{{{\hat{G}_{l}},{\hat{G}_{r}}}\right\}=T_{c_{d}}\left(Y_{G}\right)\text{% ,}\end{array}}\right." class="ltx_Math" display="block" id="S2.E7.m1.6"><semantics id="S2.E7.m1.6a"><mrow id="S2.E7.m1.6.7.2" xref="S2.E7.m1.6.7.1.cmml"><mo id="S2.E7.m1.6.7.2.1" xref="S2.E7.m1.6.7.1.1.cmml">{</mo><mtable columnspacing="5pt" displaystyle="true" id="S2.E7.m1.6.6" rowspacing="0pt" xref="S2.E7.m1.6.6.cmml"><mtr id="S2.E7.m1.6.6a" xref="S2.E7.m1.6.6.cmml"><mtd id="S2.E7.m1.6.6b" xref="S2.E7.m1.6.6.cmml"><mrow id="S2.E7.m1.3.3.3.3.3" xref="S2.E7.m1.3.3.3.3.3.cmml"><mrow id="S2.E7.m1.2.2.2.2.2.2.2" xref="S2.E7.m1.2.2.2.2.2.2.3.cmml"><mo id="S2.E7.m1.2.2.2.2.2.2.2.3" xref="S2.E7.m1.2.2.2.2.2.2.3.cmml">{</mo><msub id="S2.E7.m1.1.1.1.1.1.1.1.1" xref="S2.E7.m1.1.1.1.1.1.1.1.1.cmml"><mover accent="true" id="S2.E7.m1.1.1.1.1.1.1.1.1.2" xref="S2.E7.m1.1.1.1.1.1.1.1.1.2.cmml"><mi id="S2.E7.m1.1.1.1.1.1.1.1.1.2.2" xref="S2.E7.m1.1.1.1.1.1.1.1.1.2.2.cmml">K</mi><mo id="S2.E7.m1.1.1.1.1.1.1.1.1.2.1" xref="S2.E7.m1.1.1.1.1.1.1.1.1.2.1.cmml">^</mo></mover><mi id="S2.E7.m1.1.1.1.1.1.1.1.1.3" xref="S2.E7.m1.1.1.1.1.1.1.1.1.3.cmml">l</mi></msub><mo id="S2.E7.m1.2.2.2.2.2.2.2.4" xref="S2.E7.m1.2.2.2.2.2.2.3.cmml">,</mo><msub id="S2.E7.m1.2.2.2.2.2.2.2.2" xref="S2.E7.m1.2.2.2.2.2.2.2.2.cmml"><mover accent="true" id="S2.E7.m1.2.2.2.2.2.2.2.2.2" xref="S2.E7.m1.2.2.2.2.2.2.2.2.2.cmml"><mi id="S2.E7.m1.2.2.2.2.2.2.2.2.2.2" xref="S2.E7.m1.2.2.2.2.2.2.2.2.2.2.cmml">K</mi><mo id="S2.E7.m1.2.2.2.2.2.2.2.2.2.1" xref="S2.E7.m1.2.2.2.2.2.2.2.2.2.1.cmml">^</mo></mover><mi id="S2.E7.m1.2.2.2.2.2.2.2.2.3" xref="S2.E7.m1.2.2.2.2.2.2.2.2.3.cmml">r</mi></msub><mo id="S2.E7.m1.2.2.2.2.2.2.2.5" xref="S2.E7.m1.2.2.2.2.2.2.3.cmml">}</mo></mrow><mo id="S2.E7.m1.3.3.3.3.3.4" xref="S2.E7.m1.3.3.3.3.3.4.cmml">=</mo><mrow id="S2.E7.m1.3.3.3.3.3.3" xref="S2.E7.m1.3.3.3.3.3.3.cmml"><msub id="S2.E7.m1.3.3.3.3.3.3.3" xref="S2.E7.m1.3.3.3.3.3.3.3.cmml"><mi id="S2.E7.m1.3.3.3.3.3.3.3.2" xref="S2.E7.m1.3.3.3.3.3.3.3.2.cmml">T</mi><msub id="S2.E7.m1.3.3.3.3.3.3.3.3" xref="S2.E7.m1.3.3.3.3.3.3.3.3.cmml"><mi 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italic_K end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , over^ start_ARG italic_K end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT } = italic_T start_POSTSUBSCRIPT italic_c start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT end_POSTSUBSCRIPT ( italic_Y start_POSTSUBSCRIPT italic_K end_POSTSUBSCRIPT ) , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW start_ROW start_CELL { over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT } = italic_T start_POSTSUBSCRIPT italic_c start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT end_POSTSUBSCRIPT ( italic_Y start_POSTSUBSCRIPT italic_G end_POSTSUBSCRIPT ) , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW end_ARRAY</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(7)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S2.SS2.p2.5">where <math alttext="T_{c_{d}}" class="ltx_Math" display="inline" id="S2.SS2.p2.4.m1.1"><semantics id="S2.SS2.p2.4.m1.1a"><msub id="S2.SS2.p2.4.m1.1.1" xref="S2.SS2.p2.4.m1.1.1.cmml"><mi id="S2.SS2.p2.4.m1.1.1.2" xref="S2.SS2.p2.4.m1.1.1.2.cmml">T</mi><msub id="S2.SS2.p2.4.m1.1.1.3" xref="S2.SS2.p2.4.m1.1.1.3.cmml"><mi id="S2.SS2.p2.4.m1.1.1.3.2" xref="S2.SS2.p2.4.m1.1.1.3.2.cmml">c</mi><mi id="S2.SS2.p2.4.m1.1.1.3.3" xref="S2.SS2.p2.4.m1.1.1.3.3.cmml">d</mi></msub></msub><annotation-xml encoding="MathML-Content" id="S2.SS2.p2.4.m1.1b"><apply id="S2.SS2.p2.4.m1.1.1.cmml" xref="S2.SS2.p2.4.m1.1.1"><csymbol cd="ambiguous" id="S2.SS2.p2.4.m1.1.1.1.cmml" xref="S2.SS2.p2.4.m1.1.1">subscript</csymbol><ci id="S2.SS2.p2.4.m1.1.1.2.cmml" xref="S2.SS2.p2.4.m1.1.1.2">𝑇</ci><apply id="S2.SS2.p2.4.m1.1.1.3.cmml" xref="S2.SS2.p2.4.m1.1.1.3"><csymbol cd="ambiguous" id="S2.SS2.p2.4.m1.1.1.3.1.cmml" xref="S2.SS2.p2.4.m1.1.1.3">subscript</csymbol><ci id="S2.SS2.p2.4.m1.1.1.3.2.cmml" xref="S2.SS2.p2.4.m1.1.1.3.2">𝑐</ci><ci id="S2.SS2.p2.4.m1.1.1.3.3.cmml" xref="S2.SS2.p2.4.m1.1.1.3.3">𝑑</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS2.p2.4.m1.1c">T_{c_{d}}</annotation><annotation encoding="application/x-llamapun" id="S2.SS2.p2.4.m1.1d">italic_T start_POSTSUBSCRIPT italic_c start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT end_POSTSUBSCRIPT</annotation></semantics></math> denotes the channel decoder network parameterized by <math alttext="c_{d}" class="ltx_Math" display="inline" id="S2.SS2.p2.5.m2.1"><semantics id="S2.SS2.p2.5.m2.1a"><msub id="S2.SS2.p2.5.m2.1.1" xref="S2.SS2.p2.5.m2.1.1.cmml"><mi id="S2.SS2.p2.5.m2.1.1.2" xref="S2.SS2.p2.5.m2.1.1.2.cmml">c</mi><mi id="S2.SS2.p2.5.m2.1.1.3" xref="S2.SS2.p2.5.m2.1.1.3.cmml">d</mi></msub><annotation-xml encoding="MathML-Content" id="S2.SS2.p2.5.m2.1b"><apply id="S2.SS2.p2.5.m2.1.1.cmml" xref="S2.SS2.p2.5.m2.1.1"><csymbol cd="ambiguous" id="S2.SS2.p2.5.m2.1.1.1.cmml" xref="S2.SS2.p2.5.m2.1.1">subscript</csymbol><ci id="S2.SS2.p2.5.m2.1.1.2.cmml" xref="S2.SS2.p2.5.m2.1.1.2">𝑐</ci><ci id="S2.SS2.p2.5.m2.1.1.3.cmml" xref="S2.SS2.p2.5.m2.1.1.3">𝑑</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS2.p2.5.m2.1c">c_{d}</annotation><annotation encoding="application/x-llamapun" id="S2.SS2.p2.5.m2.1d">italic_c start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT</annotation></semantics></math>.<span class="ltx_text" id="S2.SS2.p2.5.1"></span></p> </div> </section> <section class="ltx_subsection" id="S2.SS3"> <h3 class="ltx_title ltx_title_subsection"> <span class="ltx_tag ltx_tag_subsection"><span class="ltx_text" id="S2.SS3.5.1.1">II-C</span> </span><span class="ltx_text ltx_font_italic" id="S2.SS3.6.2">The Semantic Decoder Network</span> </h3> <div class="ltx_para" id="S2.SS3.p1"> <p class="ltx_p" id="S2.SS3.p1.1"><span class="ltx_text" id="S2.SS3.p1.1.1">Corresponding to the semantic encoder network, the semantic decoder network consists of two sets of semantic recovery networks: the key area information network and the global information network, which are responsible for recovering the key area and global semantic features, respectively. The semantic decoder network also includes two fusion networks to combine these two types of semantic features and obtain the recovered stereo images.<span class="ltx_text" id="S2.SS3.p1.1.1.1"></span></span></p> </div> <div class="ltx_para" id="S2.SS3.p2"> <p class="ltx_p" id="S2.SS3.p2.5"><span class="ltx_text" id="S2.SS3.p2.5.5">Specifically, for the key area information network, two recovery networks <math alttext="T^{l}_{\theta}(\cdot)" class="ltx_Math" display="inline" id="S2.SS3.p2.1.1.m1.1"><semantics id="S2.SS3.p2.1.1.m1.1a"><mrow id="S2.SS3.p2.1.1.m1.1.2" xref="S2.SS3.p2.1.1.m1.1.2.cmml"><msubsup id="S2.SS3.p2.1.1.m1.1.2.2" xref="S2.SS3.p2.1.1.m1.1.2.2.cmml"><mi id="S2.SS3.p2.1.1.m1.1.2.2.2.2" xref="S2.SS3.p2.1.1.m1.1.2.2.2.2.cmml">T</mi><mi id="S2.SS3.p2.1.1.m1.1.2.2.3" xref="S2.SS3.p2.1.1.m1.1.2.2.3.cmml">θ</mi><mi id="S2.SS3.p2.1.1.m1.1.2.2.2.3" xref="S2.SS3.p2.1.1.m1.1.2.2.2.3.cmml">l</mi></msubsup><mo id="S2.SS3.p2.1.1.m1.1.2.1" xref="S2.SS3.p2.1.1.m1.1.2.1.cmml">⁢</mo><mrow id="S2.SS3.p2.1.1.m1.1.2.3.2" xref="S2.SS3.p2.1.1.m1.1.2.cmml"><mo id="S2.SS3.p2.1.1.m1.1.2.3.2.1" stretchy="false" xref="S2.SS3.p2.1.1.m1.1.2.cmml">(</mo><mo id="S2.SS3.p2.1.1.m1.1.1" lspace="0em" rspace="0em" xref="S2.SS3.p2.1.1.m1.1.1.cmml">⋅</mo><mo id="S2.SS3.p2.1.1.m1.1.2.3.2.2" stretchy="false" xref="S2.SS3.p2.1.1.m1.1.2.cmml">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="S2.SS3.p2.1.1.m1.1b"><apply id="S2.SS3.p2.1.1.m1.1.2.cmml" xref="S2.SS3.p2.1.1.m1.1.2"><times id="S2.SS3.p2.1.1.m1.1.2.1.cmml" xref="S2.SS3.p2.1.1.m1.1.2.1"></times><apply id="S2.SS3.p2.1.1.m1.1.2.2.cmml" xref="S2.SS3.p2.1.1.m1.1.2.2"><csymbol cd="ambiguous" id="S2.SS3.p2.1.1.m1.1.2.2.1.cmml" xref="S2.SS3.p2.1.1.m1.1.2.2">subscript</csymbol><apply id="S2.SS3.p2.1.1.m1.1.2.2.2.cmml" xref="S2.SS3.p2.1.1.m1.1.2.2"><csymbol cd="ambiguous" id="S2.SS3.p2.1.1.m1.1.2.2.2.1.cmml" xref="S2.SS3.p2.1.1.m1.1.2.2">superscript</csymbol><ci id="S2.SS3.p2.1.1.m1.1.2.2.2.2.cmml" xref="S2.SS3.p2.1.1.m1.1.2.2.2.2">𝑇</ci><ci id="S2.SS3.p2.1.1.m1.1.2.2.2.3.cmml" xref="S2.SS3.p2.1.1.m1.1.2.2.2.3">𝑙</ci></apply><ci id="S2.SS3.p2.1.1.m1.1.2.2.3.cmml" xref="S2.SS3.p2.1.1.m1.1.2.2.3">𝜃</ci></apply><ci id="S2.SS3.p2.1.1.m1.1.1.cmml" xref="S2.SS3.p2.1.1.m1.1.1">⋅</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p2.1.1.m1.1c">T^{l}_{\theta}(\cdot)</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p2.1.1.m1.1d">italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_θ end_POSTSUBSCRIPT ( ⋅ )</annotation></semantics></math> and <math alttext="T^{r}_{\theta}(\cdot)" class="ltx_Math" display="inline" id="S2.SS3.p2.2.2.m2.1"><semantics id="S2.SS3.p2.2.2.m2.1a"><mrow id="S2.SS3.p2.2.2.m2.1.2" xref="S2.SS3.p2.2.2.m2.1.2.cmml"><msubsup id="S2.SS3.p2.2.2.m2.1.2.2" xref="S2.SS3.p2.2.2.m2.1.2.2.cmml"><mi id="S2.SS3.p2.2.2.m2.1.2.2.2.2" xref="S2.SS3.p2.2.2.m2.1.2.2.2.2.cmml">T</mi><mi id="S2.SS3.p2.2.2.m2.1.2.2.3" xref="S2.SS3.p2.2.2.m2.1.2.2.3.cmml">θ</mi><mi id="S2.SS3.p2.2.2.m2.1.2.2.2.3" xref="S2.SS3.p2.2.2.m2.1.2.2.2.3.cmml">r</mi></msubsup><mo id="S2.SS3.p2.2.2.m2.1.2.1" xref="S2.SS3.p2.2.2.m2.1.2.1.cmml">⁢</mo><mrow id="S2.SS3.p2.2.2.m2.1.2.3.2" xref="S2.SS3.p2.2.2.m2.1.2.cmml"><mo id="S2.SS3.p2.2.2.m2.1.2.3.2.1" stretchy="false" xref="S2.SS3.p2.2.2.m2.1.2.cmml">(</mo><mo id="S2.SS3.p2.2.2.m2.1.1" lspace="0em" rspace="0em" xref="S2.SS3.p2.2.2.m2.1.1.cmml">⋅</mo><mo id="S2.SS3.p2.2.2.m2.1.2.3.2.2" stretchy="false" xref="S2.SS3.p2.2.2.m2.1.2.cmml">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="S2.SS3.p2.2.2.m2.1b"><apply id="S2.SS3.p2.2.2.m2.1.2.cmml" xref="S2.SS3.p2.2.2.m2.1.2"><times id="S2.SS3.p2.2.2.m2.1.2.1.cmml" xref="S2.SS3.p2.2.2.m2.1.2.1"></times><apply id="S2.SS3.p2.2.2.m2.1.2.2.cmml" xref="S2.SS3.p2.2.2.m2.1.2.2"><csymbol cd="ambiguous" id="S2.SS3.p2.2.2.m2.1.2.2.1.cmml" xref="S2.SS3.p2.2.2.m2.1.2.2">subscript</csymbol><apply id="S2.SS3.p2.2.2.m2.1.2.2.2.cmml" xref="S2.SS3.p2.2.2.m2.1.2.2"><csymbol cd="ambiguous" id="S2.SS3.p2.2.2.m2.1.2.2.2.1.cmml" xref="S2.SS3.p2.2.2.m2.1.2.2">superscript</csymbol><ci id="S2.SS3.p2.2.2.m2.1.2.2.2.2.cmml" xref="S2.SS3.p2.2.2.m2.1.2.2.2.2">𝑇</ci><ci id="S2.SS3.p2.2.2.m2.1.2.2.2.3.cmml" xref="S2.SS3.p2.2.2.m2.1.2.2.2.3">𝑟</ci></apply><ci id="S2.SS3.p2.2.2.m2.1.2.2.3.cmml" xref="S2.SS3.p2.2.2.m2.1.2.2.3">𝜃</ci></apply><ci id="S2.SS3.p2.2.2.m2.1.1.cmml" xref="S2.SS3.p2.2.2.m2.1.1">⋅</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p2.2.2.m2.1c">T^{r}_{\theta}(\cdot)</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p2.2.2.m2.1d">italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_θ end_POSTSUBSCRIPT ( ⋅ )</annotation></semantics></math>, parameterized by <math alttext="{\theta}" class="ltx_Math" display="inline" id="S2.SS3.p2.3.3.m3.1"><semantics id="S2.SS3.p2.3.3.m3.1a"><mi id="S2.SS3.p2.3.3.m3.1.1" xref="S2.SS3.p2.3.3.m3.1.1.cmml">θ</mi><annotation-xml encoding="MathML-Content" id="S2.SS3.p2.3.3.m3.1b"><ci id="S2.SS3.p2.3.3.m3.1.1.cmml" xref="S2.SS3.p2.3.3.m3.1.1">𝜃</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p2.3.3.m3.1c">{\theta}</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p2.3.3.m3.1d">italic_θ</annotation></semantics></math>, are used to recover key area semantic features <math alttext="\left\{{{\hat{S}_{l}},{\hat{S}_{r}}}\right\}" class="ltx_Math" display="inline" id="S2.SS3.p2.4.4.m4.2"><semantics id="S2.SS3.p2.4.4.m4.2a"><mrow id="S2.SS3.p2.4.4.m4.2.2.2" xref="S2.SS3.p2.4.4.m4.2.2.3.cmml"><mo id="S2.SS3.p2.4.4.m4.2.2.2.3" xref="S2.SS3.p2.4.4.m4.2.2.3.cmml">{</mo><msub id="S2.SS3.p2.4.4.m4.1.1.1.1" xref="S2.SS3.p2.4.4.m4.1.1.1.1.cmml"><mover accent="true" id="S2.SS3.p2.4.4.m4.1.1.1.1.2" xref="S2.SS3.p2.4.4.m4.1.1.1.1.2.cmml"><mi id="S2.SS3.p2.4.4.m4.1.1.1.1.2.2" xref="S2.SS3.p2.4.4.m4.1.1.1.1.2.2.cmml">S</mi><mo id="S2.SS3.p2.4.4.m4.1.1.1.1.2.1" xref="S2.SS3.p2.4.4.m4.1.1.1.1.2.1.cmml">^</mo></mover><mi id="S2.SS3.p2.4.4.m4.1.1.1.1.3" xref="S2.SS3.p2.4.4.m4.1.1.1.1.3.cmml">l</mi></msub><mo id="S2.SS3.p2.4.4.m4.2.2.2.4" xref="S2.SS3.p2.4.4.m4.2.2.3.cmml">,</mo><msub id="S2.SS3.p2.4.4.m4.2.2.2.2" xref="S2.SS3.p2.4.4.m4.2.2.2.2.cmml"><mover accent="true" id="S2.SS3.p2.4.4.m4.2.2.2.2.2" xref="S2.SS3.p2.4.4.m4.2.2.2.2.2.cmml"><mi id="S2.SS3.p2.4.4.m4.2.2.2.2.2.2" xref="S2.SS3.p2.4.4.m4.2.2.2.2.2.2.cmml">S</mi><mo id="S2.SS3.p2.4.4.m4.2.2.2.2.2.1" xref="S2.SS3.p2.4.4.m4.2.2.2.2.2.1.cmml">^</mo></mover><mi id="S2.SS3.p2.4.4.m4.2.2.2.2.3" xref="S2.SS3.p2.4.4.m4.2.2.2.2.3.cmml">r</mi></msub><mo id="S2.SS3.p2.4.4.m4.2.2.2.5" xref="S2.SS3.p2.4.4.m4.2.2.3.cmml">}</mo></mrow><annotation-xml encoding="MathML-Content" id="S2.SS3.p2.4.4.m4.2b"><set id="S2.SS3.p2.4.4.m4.2.2.3.cmml" xref="S2.SS3.p2.4.4.m4.2.2.2"><apply id="S2.SS3.p2.4.4.m4.1.1.1.1.cmml" xref="S2.SS3.p2.4.4.m4.1.1.1.1"><csymbol cd="ambiguous" id="S2.SS3.p2.4.4.m4.1.1.1.1.1.cmml" xref="S2.SS3.p2.4.4.m4.1.1.1.1">subscript</csymbol><apply id="S2.SS3.p2.4.4.m4.1.1.1.1.2.cmml" xref="S2.SS3.p2.4.4.m4.1.1.1.1.2"><ci id="S2.SS3.p2.4.4.m4.1.1.1.1.2.1.cmml" xref="S2.SS3.p2.4.4.m4.1.1.1.1.2.1">^</ci><ci id="S2.SS3.p2.4.4.m4.1.1.1.1.2.2.cmml" xref="S2.SS3.p2.4.4.m4.1.1.1.1.2.2">𝑆</ci></apply><ci id="S2.SS3.p2.4.4.m4.1.1.1.1.3.cmml" xref="S2.SS3.p2.4.4.m4.1.1.1.1.3">𝑙</ci></apply><apply id="S2.SS3.p2.4.4.m4.2.2.2.2.cmml" xref="S2.SS3.p2.4.4.m4.2.2.2.2"><csymbol cd="ambiguous" id="S2.SS3.p2.4.4.m4.2.2.2.2.1.cmml" xref="S2.SS3.p2.4.4.m4.2.2.2.2">subscript</csymbol><apply id="S2.SS3.p2.4.4.m4.2.2.2.2.2.cmml" xref="S2.SS3.p2.4.4.m4.2.2.2.2.2"><ci id="S2.SS3.p2.4.4.m4.2.2.2.2.2.1.cmml" xref="S2.SS3.p2.4.4.m4.2.2.2.2.2.1">^</ci><ci id="S2.SS3.p2.4.4.m4.2.2.2.2.2.2.cmml" xref="S2.SS3.p2.4.4.m4.2.2.2.2.2.2">𝑆</ci></apply><ci id="S2.SS3.p2.4.4.m4.2.2.2.2.3.cmml" xref="S2.SS3.p2.4.4.m4.2.2.2.2.3">𝑟</ci></apply></set></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p2.4.4.m4.2c">\left\{{{\hat{S}_{l}},{\hat{S}_{r}}}\right\}</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p2.4.4.m4.2d">{ over^ start_ARG italic_S end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , over^ start_ARG italic_S end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT }</annotation></semantics></math> from the received key area information <math alttext="\left\{{\hat{K}_{l},\hat{K}_{r}}\right\}" class="ltx_Math" display="inline" id="S2.SS3.p2.5.5.m5.2"><semantics id="S2.SS3.p2.5.5.m5.2a"><mrow id="S2.SS3.p2.5.5.m5.2.2.2" xref="S2.SS3.p2.5.5.m5.2.2.3.cmml"><mo id="S2.SS3.p2.5.5.m5.2.2.2.3" xref="S2.SS3.p2.5.5.m5.2.2.3.cmml">{</mo><msub id="S2.SS3.p2.5.5.m5.1.1.1.1" xref="S2.SS3.p2.5.5.m5.1.1.1.1.cmml"><mover accent="true" id="S2.SS3.p2.5.5.m5.1.1.1.1.2" xref="S2.SS3.p2.5.5.m5.1.1.1.1.2.cmml"><mi id="S2.SS3.p2.5.5.m5.1.1.1.1.2.2" xref="S2.SS3.p2.5.5.m5.1.1.1.1.2.2.cmml">K</mi><mo id="S2.SS3.p2.5.5.m5.1.1.1.1.2.1" xref="S2.SS3.p2.5.5.m5.1.1.1.1.2.1.cmml">^</mo></mover><mi id="S2.SS3.p2.5.5.m5.1.1.1.1.3" xref="S2.SS3.p2.5.5.m5.1.1.1.1.3.cmml">l</mi></msub><mo id="S2.SS3.p2.5.5.m5.2.2.2.4" xref="S2.SS3.p2.5.5.m5.2.2.3.cmml">,</mo><msub id="S2.SS3.p2.5.5.m5.2.2.2.2" xref="S2.SS3.p2.5.5.m5.2.2.2.2.cmml"><mover accent="true" id="S2.SS3.p2.5.5.m5.2.2.2.2.2" xref="S2.SS3.p2.5.5.m5.2.2.2.2.2.cmml"><mi id="S2.SS3.p2.5.5.m5.2.2.2.2.2.2" xref="S2.SS3.p2.5.5.m5.2.2.2.2.2.2.cmml">K</mi><mo id="S2.SS3.p2.5.5.m5.2.2.2.2.2.1" xref="S2.SS3.p2.5.5.m5.2.2.2.2.2.1.cmml">^</mo></mover><mi id="S2.SS3.p2.5.5.m5.2.2.2.2.3" xref="S2.SS3.p2.5.5.m5.2.2.2.2.3.cmml">r</mi></msub><mo id="S2.SS3.p2.5.5.m5.2.2.2.5" xref="S2.SS3.p2.5.5.m5.2.2.3.cmml">}</mo></mrow><annotation-xml encoding="MathML-Content" id="S2.SS3.p2.5.5.m5.2b"><set id="S2.SS3.p2.5.5.m5.2.2.3.cmml" xref="S2.SS3.p2.5.5.m5.2.2.2"><apply id="S2.SS3.p2.5.5.m5.1.1.1.1.cmml" xref="S2.SS3.p2.5.5.m5.1.1.1.1"><csymbol cd="ambiguous" id="S2.SS3.p2.5.5.m5.1.1.1.1.1.cmml" xref="S2.SS3.p2.5.5.m5.1.1.1.1">subscript</csymbol><apply id="S2.SS3.p2.5.5.m5.1.1.1.1.2.cmml" xref="S2.SS3.p2.5.5.m5.1.1.1.1.2"><ci id="S2.SS3.p2.5.5.m5.1.1.1.1.2.1.cmml" xref="S2.SS3.p2.5.5.m5.1.1.1.1.2.1">^</ci><ci id="S2.SS3.p2.5.5.m5.1.1.1.1.2.2.cmml" xref="S2.SS3.p2.5.5.m5.1.1.1.1.2.2">𝐾</ci></apply><ci id="S2.SS3.p2.5.5.m5.1.1.1.1.3.cmml" xref="S2.SS3.p2.5.5.m5.1.1.1.1.3">𝑙</ci></apply><apply id="S2.SS3.p2.5.5.m5.2.2.2.2.cmml" xref="S2.SS3.p2.5.5.m5.2.2.2.2"><csymbol cd="ambiguous" id="S2.SS3.p2.5.5.m5.2.2.2.2.1.cmml" xref="S2.SS3.p2.5.5.m5.2.2.2.2">subscript</csymbol><apply id="S2.SS3.p2.5.5.m5.2.2.2.2.2.cmml" xref="S2.SS3.p2.5.5.m5.2.2.2.2.2"><ci id="S2.SS3.p2.5.5.m5.2.2.2.2.2.1.cmml" xref="S2.SS3.p2.5.5.m5.2.2.2.2.2.1">^</ci><ci id="S2.SS3.p2.5.5.m5.2.2.2.2.2.2.cmml" xref="S2.SS3.p2.5.5.m5.2.2.2.2.2.2">𝐾</ci></apply><ci id="S2.SS3.p2.5.5.m5.2.2.2.2.3.cmml" xref="S2.SS3.p2.5.5.m5.2.2.2.2.3">𝑟</ci></apply></set></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p2.5.5.m5.2c">\left\{{\hat{K}_{l},\hat{K}_{r}}\right\}</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p2.5.5.m5.2d">{ over^ start_ARG italic_K end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , over^ start_ARG italic_K end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT }</annotation></semantics></math>, which can be expressed as</span></p> <table class="ltx_equation ltx_eqn_table" id="S2.E8"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="\left\{{\begin{array}[]{*{20}{c}}\hat{S}_{l}=T^{l}_{\theta}\left(\hat{K}_{l}% \right)\text{,}\\ \hat{S}_{r}=T^{r}_{\theta}\left(\hat{K}_{r}\right)\text{,}\end{array}}\right." 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xref="S2.E8.m1.2.2">missing-subexpression</csymbol></cerror><cerror id="S2.E8.m1.2.2bw.cmml" xref="S2.E8.m1.2.2"><csymbol cd="ambiguous" id="S2.E8.m1.2.2bx.cmml" xref="S2.E8.m1.2.2">missing-subexpression</csymbol></cerror><cerror id="S2.E8.m1.2.2by.cmml" xref="S2.E8.m1.2.2"><csymbol cd="ambiguous" id="S2.E8.m1.2.2bz.cmml" xref="S2.E8.m1.2.2">missing-subexpression</csymbol></cerror></matrixrow></matrix></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.E8.m1.2c">\left\{{\begin{array}[]{*{20}{c}}\hat{S}_{l}=T^{l}_{\theta}\left(\hat{K}_{l}% \right)\text{,}\\ \hat{S}_{r}=T^{r}_{\theta}\left(\hat{K}_{r}\right)\text{,}\end{array}}\right.</annotation><annotation encoding="application/x-llamapun" id="S2.E8.m1.2d">{ start_ARRAY start_ROW start_CELL over^ start_ARG italic_S end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_θ end_POSTSUBSCRIPT ( over^ start_ARG italic_K end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT ) , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW start_ROW start_CELL over^ start_ARG italic_S end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_θ end_POSTSUBSCRIPT ( over^ start_ARG italic_K end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ) , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW end_ARRAY</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(8)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S2.SS3.p2.6">where <math alttext="\left\{{\hat{K}_{l},\hat{K}_{r}}\right\}" class="ltx_Math" display="inline" id="S2.SS3.p2.6.m1.2"><semantics id="S2.SS3.p2.6.m1.2a"><mrow id="S2.SS3.p2.6.m1.2.2.2" xref="S2.SS3.p2.6.m1.2.2.3.cmml"><mo id="S2.SS3.p2.6.m1.2.2.2.3" xref="S2.SS3.p2.6.m1.2.2.3.cmml">{</mo><msub id="S2.SS3.p2.6.m1.1.1.1.1" xref="S2.SS3.p2.6.m1.1.1.1.1.cmml"><mover accent="true" id="S2.SS3.p2.6.m1.1.1.1.1.2" xref="S2.SS3.p2.6.m1.1.1.1.1.2.cmml"><mi id="S2.SS3.p2.6.m1.1.1.1.1.2.2" xref="S2.SS3.p2.6.m1.1.1.1.1.2.2.cmml">K</mi><mo id="S2.SS3.p2.6.m1.1.1.1.1.2.1" xref="S2.SS3.p2.6.m1.1.1.1.1.2.1.cmml">^</mo></mover><mi id="S2.SS3.p2.6.m1.1.1.1.1.3" xref="S2.SS3.p2.6.m1.1.1.1.1.3.cmml">l</mi></msub><mo id="S2.SS3.p2.6.m1.2.2.2.4" xref="S2.SS3.p2.6.m1.2.2.3.cmml">,</mo><msub id="S2.SS3.p2.6.m1.2.2.2.2" xref="S2.SS3.p2.6.m1.2.2.2.2.cmml"><mover accent="true" id="S2.SS3.p2.6.m1.2.2.2.2.2" xref="S2.SS3.p2.6.m1.2.2.2.2.2.cmml"><mi id="S2.SS3.p2.6.m1.2.2.2.2.2.2" xref="S2.SS3.p2.6.m1.2.2.2.2.2.2.cmml">K</mi><mo id="S2.SS3.p2.6.m1.2.2.2.2.2.1" xref="S2.SS3.p2.6.m1.2.2.2.2.2.1.cmml">^</mo></mover><mi id="S2.SS3.p2.6.m1.2.2.2.2.3" xref="S2.SS3.p2.6.m1.2.2.2.2.3.cmml">r</mi></msub><mo id="S2.SS3.p2.6.m1.2.2.2.5" xref="S2.SS3.p2.6.m1.2.2.3.cmml">}</mo></mrow><annotation-xml encoding="MathML-Content" id="S2.SS3.p2.6.m1.2b"><set id="S2.SS3.p2.6.m1.2.2.3.cmml" xref="S2.SS3.p2.6.m1.2.2.2"><apply id="S2.SS3.p2.6.m1.1.1.1.1.cmml" xref="S2.SS3.p2.6.m1.1.1.1.1"><csymbol cd="ambiguous" id="S2.SS3.p2.6.m1.1.1.1.1.1.cmml" xref="S2.SS3.p2.6.m1.1.1.1.1">subscript</csymbol><apply id="S2.SS3.p2.6.m1.1.1.1.1.2.cmml" xref="S2.SS3.p2.6.m1.1.1.1.1.2"><ci id="S2.SS3.p2.6.m1.1.1.1.1.2.1.cmml" xref="S2.SS3.p2.6.m1.1.1.1.1.2.1">^</ci><ci id="S2.SS3.p2.6.m1.1.1.1.1.2.2.cmml" xref="S2.SS3.p2.6.m1.1.1.1.1.2.2">𝐾</ci></apply><ci id="S2.SS3.p2.6.m1.1.1.1.1.3.cmml" xref="S2.SS3.p2.6.m1.1.1.1.1.3">𝑙</ci></apply><apply id="S2.SS3.p2.6.m1.2.2.2.2.cmml" xref="S2.SS3.p2.6.m1.2.2.2.2"><csymbol cd="ambiguous" id="S2.SS3.p2.6.m1.2.2.2.2.1.cmml" xref="S2.SS3.p2.6.m1.2.2.2.2">subscript</csymbol><apply id="S2.SS3.p2.6.m1.2.2.2.2.2.cmml" xref="S2.SS3.p2.6.m1.2.2.2.2.2"><ci id="S2.SS3.p2.6.m1.2.2.2.2.2.1.cmml" xref="S2.SS3.p2.6.m1.2.2.2.2.2.1">^</ci><ci id="S2.SS3.p2.6.m1.2.2.2.2.2.2.cmml" xref="S2.SS3.p2.6.m1.2.2.2.2.2.2">𝐾</ci></apply><ci id="S2.SS3.p2.6.m1.2.2.2.2.3.cmml" xref="S2.SS3.p2.6.m1.2.2.2.2.3">𝑟</ci></apply></set></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p2.6.m1.2c">\left\{{\hat{K}_{l},\hat{K}_{r}}\right\}</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p2.6.m1.2d">{ over^ start_ARG italic_K end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , over^ start_ARG italic_K end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT }</annotation></semantics></math> represent the received key area information that is subject to distortion caused by wireless transmission.<span class="ltx_text" id="S2.SS3.p2.6.1"></span></p> </div> <div class="ltx_para" id="S2.SS3.p3"> <p class="ltx_p" id="S2.SS3.p3.4"><span class="ltx_text" id="S2.SS3.p3.4.4">For the global information network, a joint semantic recovery network first uses an optical-flow module to calculate the optical flows <math alttext="\left\{{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle\rightarrow$}}% \over{\mathcal{O}}}},{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle% \leftarrow$}}\over{\mathcal{O}}}}\right\}" class="ltx_Math" display="inline" id="S2.SS3.p3.1.1.m1.2"><semantics id="S2.SS3.p3.1.1.m1.2a"><mrow id="S2.SS3.p3.1.1.m1.2.3.2" xref="S2.SS3.p3.1.1.m1.2.3.1.cmml"><mo id="S2.SS3.p3.1.1.m1.2.3.2.1" xref="S2.SS3.p3.1.1.m1.2.3.1.cmml">{</mo><mover id="S2.SS3.p3.1.1.m1.1.1.1" xref="S2.SS3.p3.1.1.m1.1.1.1a.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.SS3.p3.1.1.m1.1.1.1.3" xref="S2.SS3.p3.1.1.m1.1.1.1.3.cmml">𝒪</mi><mpadded id="S2.SS3.p3.1.1.m1.1.1.1.1" voffset="-3.0pt" xref="S2.SS3.p3.1.1.m1.1.1.1.1.cmml"><mo id="S2.SS3.p3.1.1.m1.1.1.1.1a" mathsize="71%" stretchy="false" xref="S2.SS3.p3.1.1.m1.1.1.1.1.cmml">→</mo></mpadded></mover><mo id="S2.SS3.p3.1.1.m1.2.3.2.2" xref="S2.SS3.p3.1.1.m1.2.3.1.cmml">,</mo><mover id="S2.SS3.p3.1.1.m1.2.2.1" xref="S2.SS3.p3.1.1.m1.2.2.1a.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.SS3.p3.1.1.m1.2.2.1.3" xref="S2.SS3.p3.1.1.m1.2.2.1.3.cmml">𝒪</mi><mpadded id="S2.SS3.p3.1.1.m1.2.2.1.1" voffset="-3.0pt" xref="S2.SS3.p3.1.1.m1.2.2.1.1.cmml"><mo id="S2.SS3.p3.1.1.m1.2.2.1.1a" mathsize="71%" stretchy="false" xref="S2.SS3.p3.1.1.m1.2.2.1.1.cmml">←</mo></mpadded></mover><mo id="S2.SS3.p3.1.1.m1.2.3.2.3" xref="S2.SS3.p3.1.1.m1.2.3.1.cmml">}</mo></mrow><annotation-xml encoding="MathML-Content" id="S2.SS3.p3.1.1.m1.2b"><set id="S2.SS3.p3.1.1.m1.2.3.1.cmml" xref="S2.SS3.p3.1.1.m1.2.3.2"><ci id="S2.SS3.p3.1.1.m1.1.1.1a.cmml" xref="S2.SS3.p3.1.1.m1.1.1.1"><mover id="S2.SS3.p3.1.1.m1.1.1.1.cmml" xref="S2.SS3.p3.1.1.m1.1.1.1"><mi class="ltx_font_mathcaligraphic" id="S2.SS3.p3.1.1.m1.1.1.1.3.cmml" xref="S2.SS3.p3.1.1.m1.1.1.1.3">𝒪</mi><mpadded id="S2.SS3.p3.1.1.m1.1.1.1.1.cmml" voffset="-3.0pt" xref="S2.SS3.p3.1.1.m1.1.1.1.1"><mo id="S2.SS3.p3.1.1.m1.1.1.1.1a.cmml" mathsize="71%" stretchy="false" xref="S2.SS3.p3.1.1.m1.1.1.1.1">→</mo></mpadded></mover></ci><ci id="S2.SS3.p3.1.1.m1.2.2.1a.cmml" xref="S2.SS3.p3.1.1.m1.2.2.1"><mover id="S2.SS3.p3.1.1.m1.2.2.1.cmml" xref="S2.SS3.p3.1.1.m1.2.2.1"><mi class="ltx_font_mathcaligraphic" id="S2.SS3.p3.1.1.m1.2.2.1.3.cmml" xref="S2.SS3.p3.1.1.m1.2.2.1.3">𝒪</mi><mpadded id="S2.SS3.p3.1.1.m1.2.2.1.1.cmml" voffset="-3.0pt" xref="S2.SS3.p3.1.1.m1.2.2.1.1"><mo id="S2.SS3.p3.1.1.m1.2.2.1.1a.cmml" mathsize="71%" stretchy="false" xref="S2.SS3.p3.1.1.m1.2.2.1.1">←</mo></mpadded></mover></ci></set></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p3.1.1.m1.2c">\left\{{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle\rightarrow$}}% \over{\mathcal{O}}}},{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle% \leftarrow$}}\over{\mathcal{O}}}}\right\}</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p3.1.1.m1.2d">{ start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG → end_ARG end_ID , start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG ← end_ARG end_ID }</annotation></semantics></math> based on the received global information, where <math alttext="\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle\rightarrow$}}\over{% \mathcal{O}}}" class="ltx_Math" display="inline" id="S2.SS3.p3.2.2.m2.1"><semantics id="S2.SS3.p3.2.2.m2.1a"><mover id="S2.SS3.p3.2.2.m2.1.1.1" xref="S2.SS3.p3.2.2.m2.1.1.1a.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.SS3.p3.2.2.m2.1.1.1.3" xref="S2.SS3.p3.2.2.m2.1.1.1.3.cmml">𝒪</mi><mpadded id="S2.SS3.p3.2.2.m2.1.1.1.1" voffset="-3.0pt" xref="S2.SS3.p3.2.2.m2.1.1.1.1.cmml"><mo id="S2.SS3.p3.2.2.m2.1.1.1.1a" mathsize="71%" stretchy="false" xref="S2.SS3.p3.2.2.m2.1.1.1.1.cmml">→</mo></mpadded></mover><annotation-xml encoding="MathML-Content" id="S2.SS3.p3.2.2.m2.1b"><ci id="S2.SS3.p3.2.2.m2.1.1.1a.cmml" xref="S2.SS3.p3.2.2.m2.1.1.1"><mover id="S2.SS3.p3.2.2.m2.1.1.1.cmml" xref="S2.SS3.p3.2.2.m2.1.1.1"><mi class="ltx_font_mathcaligraphic" id="S2.SS3.p3.2.2.m2.1.1.1.3.cmml" xref="S2.SS3.p3.2.2.m2.1.1.1.3">𝒪</mi><mpadded id="S2.SS3.p3.2.2.m2.1.1.1.1.cmml" voffset="-3.0pt" xref="S2.SS3.p3.2.2.m2.1.1.1.1"><mo id="S2.SS3.p3.2.2.m2.1.1.1.1a.cmml" mathsize="71%" stretchy="false" xref="S2.SS3.p3.2.2.m2.1.1.1.1">→</mo></mpadded></mover></ci></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p3.2.2.m2.1c">\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle\rightarrow$}}\over{% \mathcal{O}}}</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p3.2.2.m2.1d">start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG → end_ARG end_ID</annotation></semantics></math> and <math alttext="\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle\leftarrow$}}\over{% \mathcal{O}}}" class="ltx_Math" display="inline" id="S2.SS3.p3.3.3.m3.1"><semantics id="S2.SS3.p3.3.3.m3.1a"><mover id="S2.SS3.p3.3.3.m3.1.1.1" xref="S2.SS3.p3.3.3.m3.1.1.1a.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.SS3.p3.3.3.m3.1.1.1.3" xref="S2.SS3.p3.3.3.m3.1.1.1.3.cmml">𝒪</mi><mpadded id="S2.SS3.p3.3.3.m3.1.1.1.1" voffset="-3.0pt" xref="S2.SS3.p3.3.3.m3.1.1.1.1.cmml"><mo id="S2.SS3.p3.3.3.m3.1.1.1.1a" mathsize="71%" stretchy="false" xref="S2.SS3.p3.3.3.m3.1.1.1.1.cmml">←</mo></mpadded></mover><annotation-xml encoding="MathML-Content" id="S2.SS3.p3.3.3.m3.1b"><ci id="S2.SS3.p3.3.3.m3.1.1.1a.cmml" xref="S2.SS3.p3.3.3.m3.1.1.1"><mover id="S2.SS3.p3.3.3.m3.1.1.1.cmml" xref="S2.SS3.p3.3.3.m3.1.1.1"><mi class="ltx_font_mathcaligraphic" id="S2.SS3.p3.3.3.m3.1.1.1.3.cmml" xref="S2.SS3.p3.3.3.m3.1.1.1.3">𝒪</mi><mpadded id="S2.SS3.p3.3.3.m3.1.1.1.1.cmml" voffset="-3.0pt" xref="S2.SS3.p3.3.3.m3.1.1.1.1"><mo id="S2.SS3.p3.3.3.m3.1.1.1.1a.cmml" mathsize="71%" stretchy="false" xref="S2.SS3.p3.3.3.m3.1.1.1.1">←</mo></mpadded></mover></ci></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p3.3.3.m3.1c">\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle\leftarrow$}}\over{% \mathcal{O}}}</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p3.3.3.m3.1d">start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG ← end_ARG end_ID</annotation></semantics></math> represent the optical flows from left-to-right and right-to-left features. Optical flows can effectively describe pixel motions between images or feature maps, assisting in recovering photometric alignment in stereo-vision images. Thus, guided by the optical flows, two CNN modules are then used to recover the global semantic features <math alttext="\left\{{{\hat{F}_{l}},{\hat{F}_{r}}}\right\}" class="ltx_Math" display="inline" id="S2.SS3.p3.4.4.m4.2"><semantics id="S2.SS3.p3.4.4.m4.2a"><mrow id="S2.SS3.p3.4.4.m4.2.2.2" xref="S2.SS3.p3.4.4.m4.2.2.3.cmml"><mo id="S2.SS3.p3.4.4.m4.2.2.2.3" xref="S2.SS3.p3.4.4.m4.2.2.3.cmml">{</mo><msub id="S2.SS3.p3.4.4.m4.1.1.1.1" xref="S2.SS3.p3.4.4.m4.1.1.1.1.cmml"><mover accent="true" id="S2.SS3.p3.4.4.m4.1.1.1.1.2" xref="S2.SS3.p3.4.4.m4.1.1.1.1.2.cmml"><mi id="S2.SS3.p3.4.4.m4.1.1.1.1.2.2" xref="S2.SS3.p3.4.4.m4.1.1.1.1.2.2.cmml">F</mi><mo id="S2.SS3.p3.4.4.m4.1.1.1.1.2.1" xref="S2.SS3.p3.4.4.m4.1.1.1.1.2.1.cmml">^</mo></mover><mi id="S2.SS3.p3.4.4.m4.1.1.1.1.3" xref="S2.SS3.p3.4.4.m4.1.1.1.1.3.cmml">l</mi></msub><mo id="S2.SS3.p3.4.4.m4.2.2.2.4" xref="S2.SS3.p3.4.4.m4.2.2.3.cmml">,</mo><msub id="S2.SS3.p3.4.4.m4.2.2.2.2" xref="S2.SS3.p3.4.4.m4.2.2.2.2.cmml"><mover 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end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT }</annotation></semantics></math>, given by</span></p> <table class="ltx_equation ltx_eqn_table" id="S2.E9"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="\left[{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle\rightarrow$}}% \over{\mathcal{O}}}},{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle% \leftarrow$}}\over{\mathcal{O}}}}\right]=T_{\phi}\left(\hat{G}_{l},\hat{G}_{r}% \right)\text{,}" class="ltx_Math" display="block" id="S2.E9.m1.4"><semantics id="S2.E9.m1.4a"><mrow id="S2.E9.m1.4.4" xref="S2.E9.m1.4.4.cmml"><mrow id="S2.E9.m1.4.4.4.2" xref="S2.E9.m1.4.4.4.1.cmml"><mo id="S2.E9.m1.4.4.4.2.1" xref="S2.E9.m1.4.4.4.1.cmml">[</mo><mover id="S2.E9.m1.1.1.1" xref="S2.E9.m1.1.1.1a.cmml"><mi class="ltx_font_mathcaligraphic" id="S2.E9.m1.1.1.1.3" xref="S2.E9.m1.1.1.1.3.cmml">𝒪</mi><mpadded 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encoding="application/x-tex" id="S2.E9.m1.4c">\left[{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle\rightarrow$}}% \over{\mathcal{O}}}},{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle% \leftarrow$}}\over{\mathcal{O}}}}\right]=T_{\phi}\left(\hat{G}_{l},\hat{G}_{r}% \right)\text{,}</annotation><annotation encoding="application/x-llamapun" id="S2.E9.m1.4d">[ start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG → end_ARG end_ID , start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG ← end_ARG end_ID ] = italic_T start_POSTSUBSCRIPT italic_ϕ end_POSTSUBSCRIPT ( over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ) ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(9)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S2.SS3.p3.11">and</p> <table class="ltx_equation ltx_eqn_table" id="S2.E10"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="\left\{{\begin{array}[]{*{20}{c}}\hat{F}_{l}=T^{l}_{\chi}\left({\mathord{% \buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle\leftarrow$}}\over{\mathcal{O}}% }},\hat{G}_{l},\hat{G}_{r}\right)\text{,}\\ \hat{F}_{r}=T^{r}_{\chi}\left({\mathord{\buildrel{\lower 3.0pt\hbox{$% \scriptscriptstyle\rightarrow$}}\over{\mathcal{O}}}},\hat{G}_{r},\hat{G}_{l}% \right)\text{,}\end{array}}\right." class="ltx_Math" display="block" id="S2.E10.m1.6"><semantics id="S2.E10.m1.6a"><mrow id="S2.E10.m1.6.7.2" xref="S2.E10.m1.6.7.1.cmml"><mo id="S2.E10.m1.6.7.2.1" xref="S2.E10.m1.6.7.1.1.cmml">{</mo><mtable columnspacing="5pt" displaystyle="true" id="S2.E10.m1.6.6" rowspacing="0pt" 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encoding="application/x-tex" id="S2.E10.m1.6c">\left\{{\begin{array}[]{*{20}{c}}\hat{F}_{l}=T^{l}_{\chi}\left({\mathord{% \buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle\leftarrow$}}\over{\mathcal{O}}% }},\hat{G}_{l},\hat{G}_{r}\right)\text{,}\\ \hat{F}_{r}=T^{r}_{\chi}\left({\mathord{\buildrel{\lower 3.0pt\hbox{$% \scriptscriptstyle\rightarrow$}}\over{\mathcal{O}}}},\hat{G}_{r},\hat{G}_{l}% \right)\text{,}\end{array}}\right.</annotation><annotation encoding="application/x-llamapun" id="S2.E10.m1.6d">{ start_ARRAY start_ROW start_CELL over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_χ end_POSTSUBSCRIPT ( start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG ← end_ARG end_ID , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ) , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW start_ROW start_CELL over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_χ end_POSTSUBSCRIPT ( start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG → end_ARG end_ID , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT ) , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW end_ARRAY</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(10)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S2.SS3.p3.10">where <math alttext="\left\{{\hat{G}_{l},\hat{G}_{r}}\right\}" class="ltx_Math" display="inline" id="S2.SS3.p3.5.m1.2"><semantics id="S2.SS3.p3.5.m1.2a"><mrow id="S2.SS3.p3.5.m1.2.2.2" xref="S2.SS3.p3.5.m1.2.2.3.cmml"><mo id="S2.SS3.p3.5.m1.2.2.2.3" xref="S2.SS3.p3.5.m1.2.2.3.cmml">{</mo><msub id="S2.SS3.p3.5.m1.1.1.1.1" xref="S2.SS3.p3.5.m1.1.1.1.1.cmml"><mover accent="true" id="S2.SS3.p3.5.m1.1.1.1.1.2" xref="S2.SS3.p3.5.m1.1.1.1.1.2.cmml"><mi id="S2.SS3.p3.5.m1.1.1.1.1.2.2" xref="S2.SS3.p3.5.m1.1.1.1.1.2.2.cmml">G</mi><mo id="S2.SS3.p3.5.m1.1.1.1.1.2.1" xref="S2.SS3.p3.5.m1.1.1.1.1.2.1.cmml">^</mo></mover><mi id="S2.SS3.p3.5.m1.1.1.1.1.3" xref="S2.SS3.p3.5.m1.1.1.1.1.3.cmml">l</mi></msub><mo id="S2.SS3.p3.5.m1.2.2.2.4" xref="S2.SS3.p3.5.m1.2.2.3.cmml">,</mo><msub id="S2.SS3.p3.5.m1.2.2.2.2" xref="S2.SS3.p3.5.m1.2.2.2.2.cmml"><mover accent="true" id="S2.SS3.p3.5.m1.2.2.2.2.2" xref="S2.SS3.p3.5.m1.2.2.2.2.2.cmml"><mi id="S2.SS3.p3.5.m1.2.2.2.2.2.2" xref="S2.SS3.p3.5.m1.2.2.2.2.2.2.cmml">G</mi><mo id="S2.SS3.p3.5.m1.2.2.2.2.2.1" xref="S2.SS3.p3.5.m1.2.2.2.2.2.1.cmml">^</mo></mover><mi id="S2.SS3.p3.5.m1.2.2.2.2.3" xref="S2.SS3.p3.5.m1.2.2.2.2.3.cmml">r</mi></msub><mo id="S2.SS3.p3.5.m1.2.2.2.5" xref="S2.SS3.p3.5.m1.2.2.3.cmml">}</mo></mrow><annotation-xml encoding="MathML-Content" id="S2.SS3.p3.5.m1.2b"><set id="S2.SS3.p3.5.m1.2.2.3.cmml" xref="S2.SS3.p3.5.m1.2.2.2"><apply 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xref="S2.SS3.p3.5.m1.2.2.2.2.3">𝑟</ci></apply></set></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p3.5.m1.2c">\left\{{\hat{G}_{l},\hat{G}_{r}}\right\}</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p3.5.m1.2d">{ over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT }</annotation></semantics></math> represents the received global information, <math alttext="T_{\phi}" class="ltx_Math" display="inline" id="S2.SS3.p3.6.m2.1"><semantics id="S2.SS3.p3.6.m2.1a"><msub id="S2.SS3.p3.6.m2.1.1" xref="S2.SS3.p3.6.m2.1.1.cmml"><mi id="S2.SS3.p3.6.m2.1.1.2" xref="S2.SS3.p3.6.m2.1.1.2.cmml">T</mi><mi id="S2.SS3.p3.6.m2.1.1.3" xref="S2.SS3.p3.6.m2.1.1.3.cmml">ϕ</mi></msub><annotation-xml encoding="MathML-Content" id="S2.SS3.p3.6.m2.1b"><apply id="S2.SS3.p3.6.m2.1.1.cmml" xref="S2.SS3.p3.6.m2.1.1"><csymbol cd="ambiguous" id="S2.SS3.p3.6.m2.1.1.1.cmml" xref="S2.SS3.p3.6.m2.1.1">subscript</csymbol><ci id="S2.SS3.p3.6.m2.1.1.2.cmml" xref="S2.SS3.p3.6.m2.1.1.2">𝑇</ci><ci id="S2.SS3.p3.6.m2.1.1.3.cmml" xref="S2.SS3.p3.6.m2.1.1.3">italic-ϕ</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p3.6.m2.1c">T_{\phi}</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p3.6.m2.1d">italic_T start_POSTSUBSCRIPT italic_ϕ end_POSTSUBSCRIPT</annotation></semantics></math> denotes the optical-flow module parameterized by <math alttext="\phi" class="ltx_Math" display="inline" id="S2.SS3.p3.7.m3.1"><semantics id="S2.SS3.p3.7.m3.1a"><mi id="S2.SS3.p3.7.m3.1.1" xref="S2.SS3.p3.7.m3.1.1.cmml">ϕ</mi><annotation-xml encoding="MathML-Content" id="S2.SS3.p3.7.m3.1b"><ci id="S2.SS3.p3.7.m3.1.1.cmml" xref="S2.SS3.p3.7.m3.1.1">italic-ϕ</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p3.7.m3.1c">\phi</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p3.7.m3.1d">italic_ϕ</annotation></semantics></math>, <math alttext="T^{l}_{\chi}" class="ltx_Math" display="inline" id="S2.SS3.p3.8.m4.1"><semantics id="S2.SS3.p3.8.m4.1a"><msubsup id="S2.SS3.p3.8.m4.1.1" xref="S2.SS3.p3.8.m4.1.1.cmml"><mi id="S2.SS3.p3.8.m4.1.1.2.2" xref="S2.SS3.p3.8.m4.1.1.2.2.cmml">T</mi><mi id="S2.SS3.p3.8.m4.1.1.3" xref="S2.SS3.p3.8.m4.1.1.3.cmml">χ</mi><mi id="S2.SS3.p3.8.m4.1.1.2.3" xref="S2.SS3.p3.8.m4.1.1.2.3.cmml">l</mi></msubsup><annotation-xml encoding="MathML-Content" id="S2.SS3.p3.8.m4.1b"><apply id="S2.SS3.p3.8.m4.1.1.cmml" xref="S2.SS3.p3.8.m4.1.1"><csymbol cd="ambiguous" id="S2.SS3.p3.8.m4.1.1.1.cmml" xref="S2.SS3.p3.8.m4.1.1">subscript</csymbol><apply id="S2.SS3.p3.8.m4.1.1.2.cmml" xref="S2.SS3.p3.8.m4.1.1"><csymbol cd="ambiguous" id="S2.SS3.p3.8.m4.1.1.2.1.cmml" xref="S2.SS3.p3.8.m4.1.1">superscript</csymbol><ci id="S2.SS3.p3.8.m4.1.1.2.2.cmml" xref="S2.SS3.p3.8.m4.1.1.2.2">𝑇</ci><ci id="S2.SS3.p3.8.m4.1.1.2.3.cmml" xref="S2.SS3.p3.8.m4.1.1.2.3">𝑙</ci></apply><ci id="S2.SS3.p3.8.m4.1.1.3.cmml" xref="S2.SS3.p3.8.m4.1.1.3">𝜒</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p3.8.m4.1c">T^{l}_{\chi}</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p3.8.m4.1d">italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_χ end_POSTSUBSCRIPT</annotation></semantics></math> and <math alttext="T^{r}_{\chi}" class="ltx_Math" display="inline" id="S2.SS3.p3.9.m5.1"><semantics id="S2.SS3.p3.9.m5.1a"><msubsup id="S2.SS3.p3.9.m5.1.1" xref="S2.SS3.p3.9.m5.1.1.cmml"><mi id="S2.SS3.p3.9.m5.1.1.2.2" xref="S2.SS3.p3.9.m5.1.1.2.2.cmml">T</mi><mi id="S2.SS3.p3.9.m5.1.1.3" xref="S2.SS3.p3.9.m5.1.1.3.cmml">χ</mi><mi id="S2.SS3.p3.9.m5.1.1.2.3" xref="S2.SS3.p3.9.m5.1.1.2.3.cmml">r</mi></msubsup><annotation-xml encoding="MathML-Content" id="S2.SS3.p3.9.m5.1b"><apply id="S2.SS3.p3.9.m5.1.1.cmml" xref="S2.SS3.p3.9.m5.1.1"><csymbol cd="ambiguous" id="S2.SS3.p3.9.m5.1.1.1.cmml" xref="S2.SS3.p3.9.m5.1.1">subscript</csymbol><apply id="S2.SS3.p3.9.m5.1.1.2.cmml" xref="S2.SS3.p3.9.m5.1.1"><csymbol cd="ambiguous" id="S2.SS3.p3.9.m5.1.1.2.1.cmml" xref="S2.SS3.p3.9.m5.1.1">superscript</csymbol><ci id="S2.SS3.p3.9.m5.1.1.2.2.cmml" xref="S2.SS3.p3.9.m5.1.1.2.2">𝑇</ci><ci id="S2.SS3.p3.9.m5.1.1.2.3.cmml" xref="S2.SS3.p3.9.m5.1.1.2.3">𝑟</ci></apply><ci id="S2.SS3.p3.9.m5.1.1.3.cmml" xref="S2.SS3.p3.9.m5.1.1.3">𝜒</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p3.9.m5.1c">T^{r}_{\chi}</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p3.9.m5.1d">italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_χ end_POSTSUBSCRIPT</annotation></semantics></math> are the remaining modules of the recovery networks in the global information network, parameterized by <math alttext="{\chi}" class="ltx_Math" display="inline" id="S2.SS3.p3.10.m6.1"><semantics id="S2.SS3.p3.10.m6.1a"><mi id="S2.SS3.p3.10.m6.1.1" xref="S2.SS3.p3.10.m6.1.1.cmml">χ</mi><annotation-xml encoding="MathML-Content" id="S2.SS3.p3.10.m6.1b"><ci id="S2.SS3.p3.10.m6.1.1.cmml" xref="S2.SS3.p3.10.m6.1.1">𝜒</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p3.10.m6.1c">{\chi}</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p3.10.m6.1d">italic_χ</annotation></semantics></math>.<span class="ltx_text" id="S2.SS3.p3.10.1"></span></p> </div> <div class="ltx_para" id="S2.SS3.p4"> <p class="ltx_p" id="S2.SS3.p4.1"><span class="ltx_text" id="S2.SS3.p4.1.1">After recovering the semantic features, two fusion networks in the semantic codec are used to fuse the semantic features and obtain the recovered stereo images <math alttext="\left\{{{\hat{I}_{l}},{\hat{I}_{r}}}\right\}" class="ltx_Math" display="inline" id="S2.SS3.p4.1.1.m1.2"><semantics id="S2.SS3.p4.1.1.m1.2a"><mrow id="S2.SS3.p4.1.1.m1.2.2.2" xref="S2.SS3.p4.1.1.m1.2.2.3.cmml"><mo id="S2.SS3.p4.1.1.m1.2.2.2.3" xref="S2.SS3.p4.1.1.m1.2.2.3.cmml">{</mo><msub id="S2.SS3.p4.1.1.m1.1.1.1.1" xref="S2.SS3.p4.1.1.m1.1.1.1.1.cmml"><mover accent="true" id="S2.SS3.p4.1.1.m1.1.1.1.1.2" xref="S2.SS3.p4.1.1.m1.1.1.1.1.2.cmml"><mi id="S2.SS3.p4.1.1.m1.1.1.1.1.2.2" xref="S2.SS3.p4.1.1.m1.1.1.1.1.2.2.cmml">I</mi><mo id="S2.SS3.p4.1.1.m1.1.1.1.1.2.1" xref="S2.SS3.p4.1.1.m1.1.1.1.1.2.1.cmml">^</mo></mover><mi id="S2.SS3.p4.1.1.m1.1.1.1.1.3" xref="S2.SS3.p4.1.1.m1.1.1.1.1.3.cmml">l</mi></msub><mo id="S2.SS3.p4.1.1.m1.2.2.2.4" xref="S2.SS3.p4.1.1.m1.2.2.3.cmml">,</mo><msub id="S2.SS3.p4.1.1.m1.2.2.2.2" xref="S2.SS3.p4.1.1.m1.2.2.2.2.cmml"><mover accent="true" id="S2.SS3.p4.1.1.m1.2.2.2.2.2" xref="S2.SS3.p4.1.1.m1.2.2.2.2.2.cmml"><mi id="S2.SS3.p4.1.1.m1.2.2.2.2.2.2" xref="S2.SS3.p4.1.1.m1.2.2.2.2.2.2.cmml">I</mi><mo id="S2.SS3.p4.1.1.m1.2.2.2.2.2.1" xref="S2.SS3.p4.1.1.m1.2.2.2.2.2.1.cmml">^</mo></mover><mi id="S2.SS3.p4.1.1.m1.2.2.2.2.3" 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id="S2.SS3.p4.1.1.m1.2.2.2.2.2.cmml" xref="S2.SS3.p4.1.1.m1.2.2.2.2.2"><ci id="S2.SS3.p4.1.1.m1.2.2.2.2.2.1.cmml" xref="S2.SS3.p4.1.1.m1.2.2.2.2.2.1">^</ci><ci id="S2.SS3.p4.1.1.m1.2.2.2.2.2.2.cmml" xref="S2.SS3.p4.1.1.m1.2.2.2.2.2.2">𝐼</ci></apply><ci id="S2.SS3.p4.1.1.m1.2.2.2.2.3.cmml" xref="S2.SS3.p4.1.1.m1.2.2.2.2.3">𝑟</ci></apply></set></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p4.1.1.m1.2c">\left\{{{\hat{I}_{l}},{\hat{I}_{r}}}\right\}</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p4.1.1.m1.2d">{ over^ start_ARG italic_I end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , over^ start_ARG italic_I end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT }</annotation></semantics></math>, given by</span></p> <table class="ltx_equation ltx_eqn_table" id="S2.E11"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math 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end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_ν end_POSTSUBSCRIPT ( over^ start_ARG italic_S end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT ) , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW start_ROW start_CELL over^ start_ARG italic_I end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_ν end_POSTSUBSCRIPT ( over^ start_ARG italic_S end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT , over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ) , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW end_ARRAY</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(11)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S2.SS3.p4.4">where <math alttext="T^{l}_{\nu}" class="ltx_Math" display="inline" id="S2.SS3.p4.2.m1.1"><semantics id="S2.SS3.p4.2.m1.1a"><msubsup id="S2.SS3.p4.2.m1.1.1" xref="S2.SS3.p4.2.m1.1.1.cmml"><mi id="S2.SS3.p4.2.m1.1.1.2.2" xref="S2.SS3.p4.2.m1.1.1.2.2.cmml">T</mi><mi id="S2.SS3.p4.2.m1.1.1.3" xref="S2.SS3.p4.2.m1.1.1.3.cmml">ν</mi><mi id="S2.SS3.p4.2.m1.1.1.2.3" xref="S2.SS3.p4.2.m1.1.1.2.3.cmml">l</mi></msubsup><annotation-xml encoding="MathML-Content" id="S2.SS3.p4.2.m1.1b"><apply id="S2.SS3.p4.2.m1.1.1.cmml" xref="S2.SS3.p4.2.m1.1.1"><csymbol cd="ambiguous" id="S2.SS3.p4.2.m1.1.1.1.cmml" xref="S2.SS3.p4.2.m1.1.1">subscript</csymbol><apply id="S2.SS3.p4.2.m1.1.1.2.cmml" xref="S2.SS3.p4.2.m1.1.1"><csymbol cd="ambiguous" id="S2.SS3.p4.2.m1.1.1.2.1.cmml" xref="S2.SS3.p4.2.m1.1.1">superscript</csymbol><ci id="S2.SS3.p4.2.m1.1.1.2.2.cmml" xref="S2.SS3.p4.2.m1.1.1.2.2">𝑇</ci><ci id="S2.SS3.p4.2.m1.1.1.2.3.cmml" xref="S2.SS3.p4.2.m1.1.1.2.3">𝑙</ci></apply><ci id="S2.SS3.p4.2.m1.1.1.3.cmml" xref="S2.SS3.p4.2.m1.1.1.3">𝜈</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p4.2.m1.1c">T^{l}_{\nu}</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p4.2.m1.1d">italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_ν end_POSTSUBSCRIPT</annotation></semantics></math> and <math alttext="T^{r}_{\nu}" class="ltx_Math" display="inline" id="S2.SS3.p4.3.m2.1"><semantics id="S2.SS3.p4.3.m2.1a"><msubsup id="S2.SS3.p4.3.m2.1.1" xref="S2.SS3.p4.3.m2.1.1.cmml"><mi id="S2.SS3.p4.3.m2.1.1.2.2" xref="S2.SS3.p4.3.m2.1.1.2.2.cmml">T</mi><mi id="S2.SS3.p4.3.m2.1.1.3" xref="S2.SS3.p4.3.m2.1.1.3.cmml">ν</mi><mi id="S2.SS3.p4.3.m2.1.1.2.3" xref="S2.SS3.p4.3.m2.1.1.2.3.cmml">r</mi></msubsup><annotation-xml encoding="MathML-Content" id="S2.SS3.p4.3.m2.1b"><apply id="S2.SS3.p4.3.m2.1.1.cmml" xref="S2.SS3.p4.3.m2.1.1"><csymbol cd="ambiguous" id="S2.SS3.p4.3.m2.1.1.1.cmml" xref="S2.SS3.p4.3.m2.1.1">subscript</csymbol><apply id="S2.SS3.p4.3.m2.1.1.2.cmml" xref="S2.SS3.p4.3.m2.1.1"><csymbol cd="ambiguous" id="S2.SS3.p4.3.m2.1.1.2.1.cmml" xref="S2.SS3.p4.3.m2.1.1">superscript</csymbol><ci id="S2.SS3.p4.3.m2.1.1.2.2.cmml" xref="S2.SS3.p4.3.m2.1.1.2.2">𝑇</ci><ci id="S2.SS3.p4.3.m2.1.1.2.3.cmml" xref="S2.SS3.p4.3.m2.1.1.2.3">𝑟</ci></apply><ci id="S2.SS3.p4.3.m2.1.1.3.cmml" xref="S2.SS3.p4.3.m2.1.1.3">𝜈</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p4.3.m2.1c">T^{r}_{\nu}</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p4.3.m2.1d">italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_ν end_POSTSUBSCRIPT</annotation></semantics></math> denote the fusion networks, parameterized by <math alttext="{\nu}" class="ltx_Math" display="inline" id="S2.SS3.p4.4.m3.1"><semantics id="S2.SS3.p4.4.m3.1a"><mi id="S2.SS3.p4.4.m3.1.1" xref="S2.SS3.p4.4.m3.1.1.cmml">ν</mi><annotation-xml encoding="MathML-Content" id="S2.SS3.p4.4.m3.1b"><ci id="S2.SS3.p4.4.m3.1.1.cmml" xref="S2.SS3.p4.4.m3.1.1">𝜈</ci></annotation-xml><annotation encoding="application/x-tex" id="S2.SS3.p4.4.m3.1c">{\nu}</annotation><annotation encoding="application/x-llamapun" id="S2.SS3.p4.4.m3.1d">italic_ν</annotation></semantics></math>, to recover left and right images, respectively.<span class="ltx_text" id="S2.SS3.p4.4.1"></span></p> </div> <div class="ltx_para" id="S2.SS3.p5"> <p class="ltx_p" id="S2.SS3.p5.1"><span class="ltx_text" id="S2.SS3.p5.1.1">The final recovered images are fed into a well-trained 3D detection network to estimate the 3D position of the objects. In this paper, the Stereo-RCNN <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib28" title="">28</a>]</cite> is used to verify the transmission performance of the proposed communication system, which can also be replaced by other stereo-vision detection networks, e.g., <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib8" title="">8</a>]</cite>, <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib30" title="">30</a>]</cite>, and <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib31" title="">31</a>]</cite>, if needed.<span class="ltx_text" id="S2.SS3.p5.1.1.1"></span></span></p> </div> </section> </section> <section class="ltx_section" id="S3"> <h2 class="ltx_title ltx_title_section"> <span class="ltx_tag ltx_tag_section">III </span><span class="ltx_text ltx_font_smallcaps" id="S3.1.1">Transceiver Design for Proposed Semantic Communication System</span> </h2> <div class="ltx_para" id="S3.p1"> <p class="ltx_p" id="S3.p1.1">This section describes the detailed structure of the proposed 3D object detection semantic communication system. Based on the system model in section II, the structure is comprised of four parts, the key area information network, the global information network, the fusion network, and the channel codec network.</p> </div> <section class="ltx_subsection" id="S3.SS1"> <h3 class="ltx_title ltx_title_subsection"> <span class="ltx_tag ltx_tag_subsection"><span class="ltx_text" id="S3.SS1.5.1.1">III-A</span> </span><span class="ltx_text ltx_font_italic" id="S3.SS1.6.2">Structure of The Key Area Information Network</span> </h3> <figure class="ltx_figure" id="S3.F3"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="222" id="S3.F3.g1" src="x3.png" width="478"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 3: </span>Structure of the semantic extraction network.</figcaption> </figure> <div class="ltx_para" id="S3.SS1.p1"> <p class="ltx_p" id="S3.SS1.p1.11">As shown in Fig. <a class="ltx_ref" 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)</annotation></semantics></math> are the coordinates of the upper left and lower right corners of the bounding box, and <math alttext="c" class="ltx_Math" display="inline" id="S3.SS1.p1.8.m8.1"><semantics id="S3.SS1.p1.8.m8.1a"><mi id="S3.SS1.p1.8.m8.1.1" xref="S3.SS1.p1.8.m8.1.1.cmml">c</mi><annotation-xml encoding="MathML-Content" id="S3.SS1.p1.8.m8.1b"><ci id="S3.SS1.p1.8.m8.1.1.cmml" xref="S3.SS1.p1.8.m8.1.1">𝑐</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p1.8.m8.1c">c</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p1.8.m8.1d">italic_c</annotation></semantics></math> is the confidence value, <span class="ltx_text" id="S3.SS1.p1.11.3">quantifying the predicted probability that the detected region contains an object.<span class="ltx_text" id="S3.SS1.p1.11.3.3"> Due to the lightweight requirements of the transmitter, this paper uses a low-complexity network, Yolov5n, as the 2D detection network. 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id="S3.SS1.p1.11.3.3.3.3.3.2"> <span class="ltx_text" id="S3.SS1.p1.11.3.3.3.3.3.2.2">Assuming that the bounding box parameters are transmitted along with the semantic data, the receiver can use these parameters to determine the same mask as the transmitter. Given that the bounding box data is small in amount yet crucial for semantic information reconstruction, similar to control signaling in traditional communication protocols, we assume using a highly reliable transmission scheme to ensure error-free transmission of this data.<span class="ltx_text" id="S3.SS1.p1.11.3.3.3.3.3.2.2.2"> By transmitting only the area inside the bounding box along with the very few bounding box parameters, the communication overhead is substantially reduced. 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href="https://arxiv.org/html/2502.12735v1#S2.E1" title="In II-A The Semantic Encoder Network ‣ II System Model ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">1</span></a>).</span></span></span></span></span></span></span></span></p> </div> <figure class="ltx_figure" id="S3.F4"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="280" id="S3.F4.g1" src="x4.png" width="477"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 4: </span>Structure of the semantic compression and recovery module.</figcaption> </figure> <div class="ltx_para" id="S3.SS1.p2"> <p class="ltx_p" id="S3.SS1.p2.14">After semantic extraction, two CNN-based networks are used for semantic compression and recovery at the transmitter and receiver, respectively. <span class="ltx_text" id="S3.SS1.p2.14.14">As shown in Fig. <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S3.F4" title="Figure 4 ‣ III-A Structure of The Key Area Information Network ‣ III Transceiver Design for Proposed Semantic Communication System ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">4</span></a>, the extracted semantic features, <math alttext="S_{l}" class="ltx_Math" display="inline" id="S3.SS1.p2.1.1.m1.1"><semantics id="S3.SS1.p2.1.1.m1.1a"><msub id="S3.SS1.p2.1.1.m1.1.1" xref="S3.SS1.p2.1.1.m1.1.1.cmml"><mi id="S3.SS1.p2.1.1.m1.1.1.2" xref="S3.SS1.p2.1.1.m1.1.1.2.cmml">S</mi><mi id="S3.SS1.p2.1.1.m1.1.1.3" xref="S3.SS1.p2.1.1.m1.1.1.3.cmml">l</mi></msub><annotation-xml encoding="MathML-Content" id="S3.SS1.p2.1.1.m1.1b"><apply id="S3.SS1.p2.1.1.m1.1.1.cmml" xref="S3.SS1.p2.1.1.m1.1.1"><csymbol cd="ambiguous" id="S3.SS1.p2.1.1.m1.1.1.1.cmml" xref="S3.SS1.p2.1.1.m1.1.1">subscript</csymbol><ci id="S3.SS1.p2.1.1.m1.1.1.2.cmml" xref="S3.SS1.p2.1.1.m1.1.1.2">𝑆</ci><ci 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The output from the sub-pixel CNN is then combined with the results of <math alttext="n\times" class="ltx_math_unparsed" display="inline" id="S3.SS1.p2.5.5.m5.1"><semantics id="S3.SS1.p2.5.5.m5.1a"><mrow id="S3.SS1.p2.5.5.m5.1b"><mi id="S3.SS1.p2.5.5.m5.1.1">n</mi><mo id="S3.SS1.p2.5.5.m5.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S3.SS1.p2.5.5.m5.1c">n\times</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p2.5.5.m5.1d">italic_n ×</annotation></semantics></math> bilinear downsampling, which acts as the branch of the residual network, obtaining key area information <math alttext="{{K_{l}},{K_{r}}}\in{\mathbb{R}^{{w/n}\times{h/n}\times 3}}" class="ltx_Math" display="inline" id="S3.SS1.p2.6.6.m6.2"><semantics id="S3.SS1.p2.6.6.m6.2a"><mrow id="S3.SS1.p2.6.6.m6.2.2" xref="S3.SS1.p2.6.6.m6.2.2.cmml"><mrow id="S3.SS1.p2.6.6.m6.2.2.2.2" xref="S3.SS1.p2.6.6.m6.2.2.2.3.cmml"><msub id="S3.SS1.p2.6.6.m6.1.1.1.1.1" 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xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.cmml"><mrow id="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.2" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.2.cmml"><mi id="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.2.2" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.2.2.cmml">w</mi><mo id="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.2.1" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.2.1.cmml">/</mo><mi id="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.2.3" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.2.3.cmml">n</mi></mrow><mo id="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.1" lspace="0.222em" rspace="0.222em" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.1.cmml">×</mo><mi id="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.3" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.3.cmml">h</mi></mrow><mo id="S3.SS1.p2.6.6.m6.2.2.4.3.2.1" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.1.cmml">/</mo><mi id="S3.SS1.p2.6.6.m6.2.2.4.3.2.3" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.3.cmml">n</mi></mrow><mo id="S3.SS1.p2.6.6.m6.2.2.4.3.1" lspace="0.222em" rspace="0.222em" xref="S3.SS1.p2.6.6.m6.2.2.4.3.1.cmml">×</mo><mn id="S3.SS1.p2.6.6.m6.2.2.4.3.3" xref="S3.SS1.p2.6.6.m6.2.2.4.3.3.cmml">3</mn></mrow></msup></mrow><annotation-xml encoding="MathML-Content" id="S3.SS1.p2.6.6.m6.2b"><apply id="S3.SS1.p2.6.6.m6.2.2.cmml" xref="S3.SS1.p2.6.6.m6.2.2"><in id="S3.SS1.p2.6.6.m6.2.2.3.cmml" xref="S3.SS1.p2.6.6.m6.2.2.3"></in><list id="S3.SS1.p2.6.6.m6.2.2.2.3.cmml" xref="S3.SS1.p2.6.6.m6.2.2.2.2"><apply id="S3.SS1.p2.6.6.m6.1.1.1.1.1.cmml" xref="S3.SS1.p2.6.6.m6.1.1.1.1.1"><csymbol cd="ambiguous" id="S3.SS1.p2.6.6.m6.1.1.1.1.1.1.cmml" xref="S3.SS1.p2.6.6.m6.1.1.1.1.1">subscript</csymbol><ci id="S3.SS1.p2.6.6.m6.1.1.1.1.1.2.cmml" xref="S3.SS1.p2.6.6.m6.1.1.1.1.1.2">𝐾</ci><ci id="S3.SS1.p2.6.6.m6.1.1.1.1.1.3.cmml" xref="S3.SS1.p2.6.6.m6.1.1.1.1.1.3">𝑙</ci></apply><apply id="S3.SS1.p2.6.6.m6.2.2.2.2.2.cmml" xref="S3.SS1.p2.6.6.m6.2.2.2.2.2"><csymbol cd="ambiguous" id="S3.SS1.p2.6.6.m6.2.2.2.2.2.1.cmml" xref="S3.SS1.p2.6.6.m6.2.2.2.2.2">subscript</csymbol><ci id="S3.SS1.p2.6.6.m6.2.2.2.2.2.2.cmml" xref="S3.SS1.p2.6.6.m6.2.2.2.2.2.2">𝐾</ci><ci id="S3.SS1.p2.6.6.m6.2.2.2.2.2.3.cmml" xref="S3.SS1.p2.6.6.m6.2.2.2.2.2.3">𝑟</ci></apply></list><apply id="S3.SS1.p2.6.6.m6.2.2.4.cmml" xref="S3.SS1.p2.6.6.m6.2.2.4"><csymbol cd="ambiguous" id="S3.SS1.p2.6.6.m6.2.2.4.1.cmml" xref="S3.SS1.p2.6.6.m6.2.2.4">superscript</csymbol><ci id="S3.SS1.p2.6.6.m6.2.2.4.2.cmml" xref="S3.SS1.p2.6.6.m6.2.2.4.2">ℝ</ci><apply id="S3.SS1.p2.6.6.m6.2.2.4.3.cmml" xref="S3.SS1.p2.6.6.m6.2.2.4.3"><times id="S3.SS1.p2.6.6.m6.2.2.4.3.1.cmml" xref="S3.SS1.p2.6.6.m6.2.2.4.3.1"></times><apply id="S3.SS1.p2.6.6.m6.2.2.4.3.2.cmml" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2"><divide id="S3.SS1.p2.6.6.m6.2.2.4.3.2.1.cmml" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.1"></divide><apply id="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.cmml" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.2"><times id="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.1.cmml" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.1"></times><apply id="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.2.cmml" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.2"><divide id="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.2.1.cmml" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.2.1"></divide><ci id="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.2.2.cmml" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.2.2">𝑤</ci><ci id="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.2.3.cmml" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.2.3">𝑛</ci></apply><ci id="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.3.cmml" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.2.3">ℎ</ci></apply><ci id="S3.SS1.p2.6.6.m6.2.2.4.3.2.3.cmml" xref="S3.SS1.p2.6.6.m6.2.2.4.3.2.3">𝑛</ci></apply><cn id="S3.SS1.p2.6.6.m6.2.2.4.3.3.cmml" type="integer" xref="S3.SS1.p2.6.6.m6.2.2.4.3.3">3</cn></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p2.6.6.m6.2c">{{K_{l}},{K_{r}}}\in{\mathbb{R}^{{w/n}\times{h/n}\times 3}}</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p2.6.6.m6.2d">italic_K start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , italic_K start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT italic_w / italic_n × italic_h / italic_n × 3 end_POSTSUPERSCRIPT</annotation></semantics></math>.<span class="ltx_text" id="S3.SS1.p2.14.14.8"> Correspondingly, the recovery network utilizes two sets of sub-pixel CNNs to upsample images progressively. The two sets of upsampling have magnifications of <math alttext="n_{1}" class="ltx_Math" display="inline" id="S3.SS1.p2.7.7.1.m1.1"><semantics id="S3.SS1.p2.7.7.1.m1.1a"><msub id="S3.SS1.p2.7.7.1.m1.1.1" xref="S3.SS1.p2.7.7.1.m1.1.1.cmml"><mi id="S3.SS1.p2.7.7.1.m1.1.1.2" xref="S3.SS1.p2.7.7.1.m1.1.1.2.cmml">n</mi><mn id="S3.SS1.p2.7.7.1.m1.1.1.3" xref="S3.SS1.p2.7.7.1.m1.1.1.3.cmml">1</mn></msub><annotation-xml encoding="MathML-Content" id="S3.SS1.p2.7.7.1.m1.1b"><apply id="S3.SS1.p2.7.7.1.m1.1.1.cmml" xref="S3.SS1.p2.7.7.1.m1.1.1"><csymbol cd="ambiguous" id="S3.SS1.p2.7.7.1.m1.1.1.1.cmml" xref="S3.SS1.p2.7.7.1.m1.1.1">subscript</csymbol><ci id="S3.SS1.p2.7.7.1.m1.1.1.2.cmml" xref="S3.SS1.p2.7.7.1.m1.1.1.2">𝑛</ci><cn id="S3.SS1.p2.7.7.1.m1.1.1.3.cmml" type="integer" xref="S3.SS1.p2.7.7.1.m1.1.1.3">1</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p2.7.7.1.m1.1c">n_{1}</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p2.7.7.1.m1.1d">italic_n start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT</annotation></semantics></math> and <math alttext="n_{2}" class="ltx_Math" display="inline" id="S3.SS1.p2.8.8.2.m2.1"><semantics id="S3.SS1.p2.8.8.2.m2.1a"><msub id="S3.SS1.p2.8.8.2.m2.1.1" xref="S3.SS1.p2.8.8.2.m2.1.1.cmml"><mi id="S3.SS1.p2.8.8.2.m2.1.1.2" xref="S3.SS1.p2.8.8.2.m2.1.1.2.cmml">n</mi><mn id="S3.SS1.p2.8.8.2.m2.1.1.3" xref="S3.SS1.p2.8.8.2.m2.1.1.3.cmml">2</mn></msub><annotation-xml encoding="MathML-Content" id="S3.SS1.p2.8.8.2.m2.1b"><apply id="S3.SS1.p2.8.8.2.m2.1.1.cmml" xref="S3.SS1.p2.8.8.2.m2.1.1"><csymbol cd="ambiguous" id="S3.SS1.p2.8.8.2.m2.1.1.1.cmml" xref="S3.SS1.p2.8.8.2.m2.1.1">subscript</csymbol><ci id="S3.SS1.p2.8.8.2.m2.1.1.2.cmml" xref="S3.SS1.p2.8.8.2.m2.1.1.2">𝑛</ci><cn id="S3.SS1.p2.8.8.2.m2.1.1.3.cmml" type="integer" xref="S3.SS1.p2.8.8.2.m2.1.1.3">2</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p2.8.8.2.m2.1c">n_{2}</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p2.8.8.2.m2.1d">italic_n start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT</annotation></semantics></math>, respectively, where <math alttext="n_{1}\times n_{2}=n" class="ltx_Math" display="inline" id="S3.SS1.p2.9.9.3.m3.1"><semantics id="S3.SS1.p2.9.9.3.m3.1a"><mrow id="S3.SS1.p2.9.9.3.m3.1.1" xref="S3.SS1.p2.9.9.3.m3.1.1.cmml"><mrow id="S3.SS1.p2.9.9.3.m3.1.1.2" xref="S3.SS1.p2.9.9.3.m3.1.1.2.cmml"><msub id="S3.SS1.p2.9.9.3.m3.1.1.2.2" xref="S3.SS1.p2.9.9.3.m3.1.1.2.2.cmml"><mi id="S3.SS1.p2.9.9.3.m3.1.1.2.2.2" xref="S3.SS1.p2.9.9.3.m3.1.1.2.2.2.cmml">n</mi><mn id="S3.SS1.p2.9.9.3.m3.1.1.2.2.3" xref="S3.SS1.p2.9.9.3.m3.1.1.2.2.3.cmml">1</mn></msub><mo id="S3.SS1.p2.9.9.3.m3.1.1.2.1" lspace="0.222em" rspace="0.222em" xref="S3.SS1.p2.9.9.3.m3.1.1.2.1.cmml">×</mo><msub id="S3.SS1.p2.9.9.3.m3.1.1.2.3" xref="S3.SS1.p2.9.9.3.m3.1.1.2.3.cmml"><mi id="S3.SS1.p2.9.9.3.m3.1.1.2.3.2" xref="S3.SS1.p2.9.9.3.m3.1.1.2.3.2.cmml">n</mi><mn id="S3.SS1.p2.9.9.3.m3.1.1.2.3.3" xref="S3.SS1.p2.9.9.3.m3.1.1.2.3.3.cmml">2</mn></msub></mrow><mo id="S3.SS1.p2.9.9.3.m3.1.1.1" xref="S3.SS1.p2.9.9.3.m3.1.1.1.cmml">=</mo><mi id="S3.SS1.p2.9.9.3.m3.1.1.3" xref="S3.SS1.p2.9.9.3.m3.1.1.3.cmml">n</mi></mrow><annotation-xml encoding="MathML-Content" id="S3.SS1.p2.9.9.3.m3.1b"><apply id="S3.SS1.p2.9.9.3.m3.1.1.cmml" xref="S3.SS1.p2.9.9.3.m3.1.1"><eq id="S3.SS1.p2.9.9.3.m3.1.1.1.cmml" xref="S3.SS1.p2.9.9.3.m3.1.1.1"></eq><apply id="S3.SS1.p2.9.9.3.m3.1.1.2.cmml" xref="S3.SS1.p2.9.9.3.m3.1.1.2"><times id="S3.SS1.p2.9.9.3.m3.1.1.2.1.cmml" xref="S3.SS1.p2.9.9.3.m3.1.1.2.1"></times><apply id="S3.SS1.p2.9.9.3.m3.1.1.2.2.cmml" xref="S3.SS1.p2.9.9.3.m3.1.1.2.2"><csymbol cd="ambiguous" id="S3.SS1.p2.9.9.3.m3.1.1.2.2.1.cmml" xref="S3.SS1.p2.9.9.3.m3.1.1.2.2">subscript</csymbol><ci id="S3.SS1.p2.9.9.3.m3.1.1.2.2.2.cmml" xref="S3.SS1.p2.9.9.3.m3.1.1.2.2.2">𝑛</ci><cn id="S3.SS1.p2.9.9.3.m3.1.1.2.2.3.cmml" type="integer" xref="S3.SS1.p2.9.9.3.m3.1.1.2.2.3">1</cn></apply><apply id="S3.SS1.p2.9.9.3.m3.1.1.2.3.cmml" xref="S3.SS1.p2.9.9.3.m3.1.1.2.3"><csymbol cd="ambiguous" id="S3.SS1.p2.9.9.3.m3.1.1.2.3.1.cmml" xref="S3.SS1.p2.9.9.3.m3.1.1.2.3">subscript</csymbol><ci id="S3.SS1.p2.9.9.3.m3.1.1.2.3.2.cmml" xref="S3.SS1.p2.9.9.3.m3.1.1.2.3.2">𝑛</ci><cn id="S3.SS1.p2.9.9.3.m3.1.1.2.3.3.cmml" type="integer" xref="S3.SS1.p2.9.9.3.m3.1.1.2.3.3">2</cn></apply></apply><ci id="S3.SS1.p2.9.9.3.m3.1.1.3.cmml" xref="S3.SS1.p2.9.9.3.m3.1.1.3">𝑛</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p2.9.9.3.m3.1c">n_{1}\times n_{2}=n</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p2.9.9.3.m3.1d">italic_n start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT × italic_n start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT = italic_n</annotation></semantics></math>. <span class="ltx_text" id="S3.SS1.p2.14.14.8.5">The recovered semantic features<span class="ltx_text" id="S3.SS1.p2.14.14.8.5.5"> can be expressed as <math alttext="{{\hat{S}_{l}},{\hat{S}_{r}}}\in{\mathbb{R}^{w\times h\times 3}}" class="ltx_Math" display="inline" id="S3.SS1.p2.10.10.4.1.1.m1.2"><semantics id="S3.SS1.p2.10.10.4.1.1.m1.2a"><mrow id="S3.SS1.p2.10.10.4.1.1.m1.2.2" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.cmml"><mrow id="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.3.cmml"><msub id="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1" xref="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.cmml"><mover accent="true" id="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.2" xref="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.2.cmml"><mi id="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.2.2" xref="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.2.2.cmml">S</mi><mo id="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.2.1" xref="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.2.1.cmml">^</mo></mover><mi id="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.3" xref="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.3.cmml">l</mi></msub><mo id="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.3" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.3.cmml">,</mo><msub id="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.cmml"><mover accent="true" id="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.2" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.2.cmml"><mi id="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.2.2" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.2.2.cmml">S</mi><mo id="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.2.1" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.2.1.cmml">^</mo></mover><mi id="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.3" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.3.cmml">r</mi></msub></mrow><mo id="S3.SS1.p2.10.10.4.1.1.m1.2.2.3" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.3.cmml">∈</mo><msup id="S3.SS1.p2.10.10.4.1.1.m1.2.2.4" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.cmml"><mi id="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.2" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.2.cmml">ℝ</mi><mrow id="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.cmml"><mi id="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.2" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.2.cmml">w</mi><mo id="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.1" lspace="0.222em" rspace="0.222em" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.1.cmml">×</mo><mi id="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.3" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.3.cmml">h</mi><mo id="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.1a" lspace="0.222em" rspace="0.222em" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.1.cmml">×</mo><mn id="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.4" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.4.cmml">3</mn></mrow></msup></mrow><annotation-xml encoding="MathML-Content" id="S3.SS1.p2.10.10.4.1.1.m1.2b"><apply id="S3.SS1.p2.10.10.4.1.1.m1.2.2.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2"><in id="S3.SS1.p2.10.10.4.1.1.m1.2.2.3.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.3"></in><list id="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.3.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2"><apply id="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1"><csymbol cd="ambiguous" id="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.1.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1">subscript</csymbol><apply id="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.2.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.2"><ci id="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.2.1.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.2.1">^</ci><ci id="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.2.2.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.2.2">𝑆</ci></apply><ci id="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.3.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.1.1.1.1.1.3">𝑙</ci></apply><apply id="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2"><csymbol cd="ambiguous" id="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.1.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2">subscript</csymbol><apply id="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.2.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.2"><ci id="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.2.1.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.2.1">^</ci><ci id="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.2.2.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.2.2">𝑆</ci></apply><ci id="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.3.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.2.2.2.3">𝑟</ci></apply></list><apply id="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.4"><csymbol cd="ambiguous" id="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.1.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.4">superscript</csymbol><ci id="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.2.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.2">ℝ</ci><apply id="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3"><times id="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.1.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.1"></times><ci id="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.2.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.2">𝑤</ci><ci id="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.3.cmml" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.3">ℎ</ci><cn id="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.4.cmml" type="integer" xref="S3.SS1.p2.10.10.4.1.1.m1.2.2.4.3.4">3</cn></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p2.10.10.4.1.1.m1.2c">{{\hat{S}_{l}},{\hat{S}_{r}}}\in{\mathbb{R}^{w\times h\times 3}}</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p2.10.10.4.1.1.m1.2d">over^ start_ARG italic_S end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , over^ start_ARG italic_S end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT italic_w × italic_h × 3 end_POSTSUPERSCRIPT</annotation></semantics></math>. The compression processes correspond to <math alttext="T^{l}_{\beta}(\cdot)" class="ltx_Math" display="inline" id="S3.SS1.p2.11.11.5.2.2.m2.1"><semantics id="S3.SS1.p2.11.11.5.2.2.m2.1a"><mrow id="S3.SS1.p2.11.11.5.2.2.m2.1.2" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.cmml"><msubsup id="S3.SS1.p2.11.11.5.2.2.m2.1.2.2" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.cmml"><mi id="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.2.2" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.2.2.cmml">T</mi><mi id="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.3" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.3.cmml">β</mi><mi id="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.2.3" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.2.3.cmml">l</mi></msubsup><mo id="S3.SS1.p2.11.11.5.2.2.m2.1.2.1" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.1.cmml">⁢</mo><mrow id="S3.SS1.p2.11.11.5.2.2.m2.1.2.3.2" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.cmml"><mo id="S3.SS1.p2.11.11.5.2.2.m2.1.2.3.2.1" stretchy="false" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.cmml">(</mo><mo id="S3.SS1.p2.11.11.5.2.2.m2.1.1" lspace="0em" rspace="0em" xref="S3.SS1.p2.11.11.5.2.2.m2.1.1.cmml">⋅</mo><mo id="S3.SS1.p2.11.11.5.2.2.m2.1.2.3.2.2" stretchy="false" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.cmml">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="S3.SS1.p2.11.11.5.2.2.m2.1b"><apply id="S3.SS1.p2.11.11.5.2.2.m2.1.2.cmml" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2"><times id="S3.SS1.p2.11.11.5.2.2.m2.1.2.1.cmml" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.1"></times><apply id="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.cmml" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.2"><csymbol cd="ambiguous" id="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.1.cmml" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.2">subscript</csymbol><apply id="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.2.cmml" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.2"><csymbol cd="ambiguous" id="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.2.1.cmml" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.2">superscript</csymbol><ci id="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.2.2.cmml" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.2.2">𝑇</ci><ci id="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.2.3.cmml" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.2.3">𝑙</ci></apply><ci id="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.3.cmml" xref="S3.SS1.p2.11.11.5.2.2.m2.1.2.2.3">𝛽</ci></apply><ci id="S3.SS1.p2.11.11.5.2.2.m2.1.1.cmml" xref="S3.SS1.p2.11.11.5.2.2.m2.1.1">⋅</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p2.11.11.5.2.2.m2.1c">T^{l}_{\beta}(\cdot)</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p2.11.11.5.2.2.m2.1d">italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_β end_POSTSUBSCRIPT ( ⋅ )</annotation></semantics></math> and <math alttext="T^{r}_{\beta}(\cdot)" class="ltx_Math" display="inline" id="S3.SS1.p2.12.12.6.3.3.m3.1"><semantics id="S3.SS1.p2.12.12.6.3.3.m3.1a"><mrow id="S3.SS1.p2.12.12.6.3.3.m3.1.2" xref="S3.SS1.p2.12.12.6.3.3.m3.1.2.cmml"><msubsup id="S3.SS1.p2.12.12.6.3.3.m3.1.2.2" xref="S3.SS1.p2.12.12.6.3.3.m3.1.2.2.cmml"><mi id="S3.SS1.p2.12.12.6.3.3.m3.1.2.2.2.2" 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xref="S3.SS1.p2.12.12.6.3.3.m3.1.2.1"></times><apply id="S3.SS1.p2.12.12.6.3.3.m3.1.2.2.cmml" xref="S3.SS1.p2.12.12.6.3.3.m3.1.2.2"><csymbol cd="ambiguous" id="S3.SS1.p2.12.12.6.3.3.m3.1.2.2.1.cmml" xref="S3.SS1.p2.12.12.6.3.3.m3.1.2.2">subscript</csymbol><apply id="S3.SS1.p2.12.12.6.3.3.m3.1.2.2.2.cmml" xref="S3.SS1.p2.12.12.6.3.3.m3.1.2.2"><csymbol cd="ambiguous" id="S3.SS1.p2.12.12.6.3.3.m3.1.2.2.2.1.cmml" xref="S3.SS1.p2.12.12.6.3.3.m3.1.2.2">superscript</csymbol><ci id="S3.SS1.p2.12.12.6.3.3.m3.1.2.2.2.2.cmml" xref="S3.SS1.p2.12.12.6.3.3.m3.1.2.2.2.2">𝑇</ci><ci id="S3.SS1.p2.12.12.6.3.3.m3.1.2.2.2.3.cmml" xref="S3.SS1.p2.12.12.6.3.3.m3.1.2.2.2.3">𝑟</ci></apply><ci id="S3.SS1.p2.12.12.6.3.3.m3.1.2.2.3.cmml" xref="S3.SS1.p2.12.12.6.3.3.m3.1.2.2.3">𝛽</ci></apply><ci id="S3.SS1.p2.12.12.6.3.3.m3.1.1.cmml" xref="S3.SS1.p2.12.12.6.3.3.m3.1.1">⋅</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p2.12.12.6.3.3.m3.1c">T^{r}_{\beta}(\cdot)</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p2.12.12.6.3.3.m3.1d">italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_β end_POSTSUBSCRIPT ( ⋅ )</annotation></semantics></math> in (<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S2.E2" title="In II-A The Semantic Encoder Network ‣ II System Model ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">2</span></a>), and the recovery processes are represented by the operation <math alttext="T^{l}_{\theta}(\cdot)" class="ltx_Math" display="inline" id="S3.SS1.p2.13.13.7.4.4.m4.1"><semantics id="S3.SS1.p2.13.13.7.4.4.m4.1a"><mrow id="S3.SS1.p2.13.13.7.4.4.m4.1.2" xref="S3.SS1.p2.13.13.7.4.4.m4.1.2.cmml"><msubsup id="S3.SS1.p2.13.13.7.4.4.m4.1.2.2" xref="S3.SS1.p2.13.13.7.4.4.m4.1.2.2.cmml"><mi id="S3.SS1.p2.13.13.7.4.4.m4.1.2.2.2.2" 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The Semantic Decoder Network ‣ II System Model ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">8</span></a>).</span></span></span></span></p> </div> <figure class="ltx_figure" id="S3.F5"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="346" id="S3.F5.g1" src="x5.png" width="477"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 5: </span>Structure of the sub-pixel CNN.</figcaption> </figure> <div class="ltx_para" id="S3.SS1.p3"> <p class="ltx_p" id="S3.SS1.p3.4">As shown in Fig. <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S3.F5" title="Figure 5 ‣ III-A Structure of The Key Area Information Network ‣ III Transceiver Design for Proposed Semantic Communication System ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">5</span></a>, the structure of sub-pixel CNNs contains two parts, a CNN module for increasing or reducing the feature channels and a pixel-shuffle module to rearrange the pixels of different channels. <span class="ltx_text" id="S3.SS1.p3.4.4">Taking <math alttext="n" class="ltx_Math" display="inline" id="S3.SS1.p3.1.1.m1.1"><semantics id="S3.SS1.p3.1.1.m1.1a"><mi id="S3.SS1.p3.1.1.m1.1.1" xref="S3.SS1.p3.1.1.m1.1.1.cmml">n</mi><annotation-xml encoding="MathML-Content" id="S3.SS1.p3.1.1.m1.1b"><ci id="S3.SS1.p3.1.1.m1.1.1.cmml" xref="S3.SS1.p3.1.1.m1.1.1">𝑛</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p3.1.1.m1.1c">n</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p3.1.1.m1.1d">italic_n</annotation></semantics></math> times upsampling as an example (the downsampling can be regarded as the inverse operation of upsampling), for an input of size <math alttext="w\times h\times c" class="ltx_Math" display="inline" id="S3.SS1.p3.2.2.m2.1"><semantics id="S3.SS1.p3.2.2.m2.1a"><mrow 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id="S3.SS1.p3.2.2.m2.1c">w\times h\times c</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p3.2.2.m2.1d">italic_w × italic_h × italic_c</annotation></semantics></math>, the sub-pixel CNN first uses multiple convolutional layers to increase its feature channels to <math alttext="n^{2}c" class="ltx_Math" display="inline" id="S3.SS1.p3.3.3.m3.1"><semantics id="S3.SS1.p3.3.3.m3.1a"><mrow id="S3.SS1.p3.3.3.m3.1.1" xref="S3.SS1.p3.3.3.m3.1.1.cmml"><msup id="S3.SS1.p3.3.3.m3.1.1.2" xref="S3.SS1.p3.3.3.m3.1.1.2.cmml"><mi id="S3.SS1.p3.3.3.m3.1.1.2.2" xref="S3.SS1.p3.3.3.m3.1.1.2.2.cmml">n</mi><mn id="S3.SS1.p3.3.3.m3.1.1.2.3" xref="S3.SS1.p3.3.3.m3.1.1.2.3.cmml">2</mn></msup><mo id="S3.SS1.p3.3.3.m3.1.1.1" xref="S3.SS1.p3.3.3.m3.1.1.1.cmml">⁢</mo><mi id="S3.SS1.p3.3.3.m3.1.1.3" xref="S3.SS1.p3.3.3.m3.1.1.3.cmml">c</mi></mrow><annotation-xml encoding="MathML-Content" id="S3.SS1.p3.3.3.m3.1b"><apply id="S3.SS1.p3.3.3.m3.1.1.cmml" xref="S3.SS1.p3.3.3.m3.1.1"><times id="S3.SS1.p3.3.3.m3.1.1.1.cmml" xref="S3.SS1.p3.3.3.m3.1.1.1"></times><apply id="S3.SS1.p3.3.3.m3.1.1.2.cmml" xref="S3.SS1.p3.3.3.m3.1.1.2"><csymbol cd="ambiguous" id="S3.SS1.p3.3.3.m3.1.1.2.1.cmml" xref="S3.SS1.p3.3.3.m3.1.1.2">superscript</csymbol><ci id="S3.SS1.p3.3.3.m3.1.1.2.2.cmml" xref="S3.SS1.p3.3.3.m3.1.1.2.2">𝑛</ci><cn id="S3.SS1.p3.3.3.m3.1.1.2.3.cmml" type="integer" xref="S3.SS1.p3.3.3.m3.1.1.2.3">2</cn></apply><ci id="S3.SS1.p3.3.3.m3.1.1.3.cmml" xref="S3.SS1.p3.3.3.m3.1.1.3">𝑐</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p3.3.3.m3.1c">n^{2}c</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p3.3.3.m3.1d">italic_n start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_c</annotation></semantics></math> and then rearrange the elements in different feature channels to form a new tensor of size <math alttext="nw\times nh\times c" class="ltx_Math" display="inline" id="S3.SS1.p3.4.4.m4.1"><semantics id="S3.SS1.p3.4.4.m4.1a"><mrow id="S3.SS1.p3.4.4.m4.1.1" xref="S3.SS1.p3.4.4.m4.1.1.cmml"><mrow id="S3.SS1.p3.4.4.m4.1.1.2" xref="S3.SS1.p3.4.4.m4.1.1.2.cmml"><mrow id="S3.SS1.p3.4.4.m4.1.1.2.2" xref="S3.SS1.p3.4.4.m4.1.1.2.2.cmml"><mrow id="S3.SS1.p3.4.4.m4.1.1.2.2.2" xref="S3.SS1.p3.4.4.m4.1.1.2.2.2.cmml"><mi id="S3.SS1.p3.4.4.m4.1.1.2.2.2.2" xref="S3.SS1.p3.4.4.m4.1.1.2.2.2.2.cmml">n</mi><mo id="S3.SS1.p3.4.4.m4.1.1.2.2.2.1" xref="S3.SS1.p3.4.4.m4.1.1.2.2.2.1.cmml">⁢</mo><mi id="S3.SS1.p3.4.4.m4.1.1.2.2.2.3" xref="S3.SS1.p3.4.4.m4.1.1.2.2.2.3.cmml">w</mi></mrow><mo id="S3.SS1.p3.4.4.m4.1.1.2.2.1" lspace="0.222em" rspace="0.222em" xref="S3.SS1.p3.4.4.m4.1.1.2.2.1.cmml">×</mo><mi id="S3.SS1.p3.4.4.m4.1.1.2.2.3" xref="S3.SS1.p3.4.4.m4.1.1.2.2.3.cmml">n</mi></mrow><mo id="S3.SS1.p3.4.4.m4.1.1.2.1" xref="S3.SS1.p3.4.4.m4.1.1.2.1.cmml">⁢</mo><mi id="S3.SS1.p3.4.4.m4.1.1.2.3" xref="S3.SS1.p3.4.4.m4.1.1.2.3.cmml">h</mi></mrow><mo id="S3.SS1.p3.4.4.m4.1.1.1" lspace="0.222em" rspace="0.222em" xref="S3.SS1.p3.4.4.m4.1.1.1.cmml">×</mo><mi id="S3.SS1.p3.4.4.m4.1.1.3" xref="S3.SS1.p3.4.4.m4.1.1.3.cmml">c</mi></mrow><annotation-xml encoding="MathML-Content" id="S3.SS1.p3.4.4.m4.1b"><apply id="S3.SS1.p3.4.4.m4.1.1.cmml" xref="S3.SS1.p3.4.4.m4.1.1"><times id="S3.SS1.p3.4.4.m4.1.1.1.cmml" xref="S3.SS1.p3.4.4.m4.1.1.1"></times><apply id="S3.SS1.p3.4.4.m4.1.1.2.cmml" xref="S3.SS1.p3.4.4.m4.1.1.2"><times id="S3.SS1.p3.4.4.m4.1.1.2.1.cmml" xref="S3.SS1.p3.4.4.m4.1.1.2.1"></times><apply id="S3.SS1.p3.4.4.m4.1.1.2.2.cmml" xref="S3.SS1.p3.4.4.m4.1.1.2.2"><times id="S3.SS1.p3.4.4.m4.1.1.2.2.1.cmml" xref="S3.SS1.p3.4.4.m4.1.1.2.2.1"></times><apply id="S3.SS1.p3.4.4.m4.1.1.2.2.2.cmml" xref="S3.SS1.p3.4.4.m4.1.1.2.2.2"><times id="S3.SS1.p3.4.4.m4.1.1.2.2.2.1.cmml" xref="S3.SS1.p3.4.4.m4.1.1.2.2.2.1"></times><ci id="S3.SS1.p3.4.4.m4.1.1.2.2.2.2.cmml" xref="S3.SS1.p3.4.4.m4.1.1.2.2.2.2">𝑛</ci><ci id="S3.SS1.p3.4.4.m4.1.1.2.2.2.3.cmml" xref="S3.SS1.p3.4.4.m4.1.1.2.2.2.3">𝑤</ci></apply><ci id="S3.SS1.p3.4.4.m4.1.1.2.2.3.cmml" xref="S3.SS1.p3.4.4.m4.1.1.2.2.3">𝑛</ci></apply><ci id="S3.SS1.p3.4.4.m4.1.1.2.3.cmml" xref="S3.SS1.p3.4.4.m4.1.1.2.3">ℎ</ci></apply><ci id="S3.SS1.p3.4.4.m4.1.1.3.cmml" xref="S3.SS1.p3.4.4.m4.1.1.3">𝑐</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS1.p3.4.4.m4.1c">nw\times nh\times c</annotation><annotation encoding="application/x-llamapun" id="S3.SS1.p3.4.4.m4.1d">italic_n italic_w × italic_n italic_h × italic_c</annotation></semantics></math>. Mathematically, the shuffling operation can be described as follows,</span></p> <table class="ltx_equation ltx_eqn_table" id="S3.E12"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="\mathcal{S}(\mathbf{T})_{x,y,z}=\mathbf{T}_{\left\lfloor\frac{x}{n}\right% \rfloor,\left\lfloor\frac{y}{n}\right\rfloor,(x\bmod n)\cdot n+(y\bmod n)+z% \cdot n^{2}}\text{,}" class="ltx_Math" display="block" id="S3.E12.m1.9"><semantics id="S3.E12.m1.9a"><mrow id="S3.E12.m1.9.10" xref="S3.E12.m1.9.10.cmml"><mrow id="S3.E12.m1.9.10.2" xref="S3.E12.m1.9.10.2.cmml"><mi class="ltx_font_mathcaligraphic" id="S3.E12.m1.9.10.2.2" xref="S3.E12.m1.9.10.2.2.cmml">𝒮</mi><mo id="S3.E12.m1.9.10.2.1" xref="S3.E12.m1.9.10.2.1.cmml">⁢</mo><msub id="S3.E12.m1.9.10.2.3" xref="S3.E12.m1.9.10.2.3.cmml"><mrow id="S3.E12.m1.9.10.2.3.2.2" xref="S3.E12.m1.9.10.2.3.cmml"><mo id="S3.E12.m1.9.10.2.3.2.2.1" 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Compared with traditional upsampling methods and the transposed convolution network <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib32" title="">32</a>]</cite>, the sub-pixel CNN has better performance and can avoid the uneven overlapping problem.</span></p> </div> </section> <section class="ltx_subsection" id="S3.SS2"> <h3 class="ltx_title ltx_title_subsection"> <span class="ltx_tag ltx_tag_subsection"><span class="ltx_text" id="S3.SS2.5.1.1">III-B</span> </span><span class="ltx_text ltx_font_italic" id="S3.SS2.6.2">Structure of The Global Information Network</span> </h3> <figure class="ltx_figure" id="S3.F6"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="465" id="S3.F6.g1" src="x6.png" width="941"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 6: </span>Structure of the global information network (a) in the semantic encoder and (b) in the semantic decoder.</figcaption> </figure> <div class="ltx_para" id="S3.SS2.p1"> <p class="ltx_p" id="S3.SS2.p1.7">The structure of the global information network is shown in Fig. <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S3.F6" title="Figure 6 ‣ III-B Structure of The Global Information Network ‣ III Transceiver Design for Proposed Semantic Communication System ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">6</span></a>. <span class="ltx_text" id="S3.SS2.p1.7.7">At the transmitter, a convolutional residual network is first utilized to extract features from both the left and right images. These extracted features are combined through direct channel concatenation, which further passes a set of convolutional layers. From the fused features, two sets of convolutional layers with different parameters are then used to separate the left and right semantic features, thereby achieving joint semantic extraction from the left and right images.<span class="ltx_text" id="S3.SS2.p1.7.7.7"> The extracted global semantic features are written as <math alttext="F_{l},F_{r}\in{\mathbb{R}^{w\times h\times f}}" class="ltx_Math" display="inline" id="S3.SS2.p1.1.1.1.m1.2"><semantics id="S3.SS2.p1.1.1.1.m1.2a"><mrow id="S3.SS2.p1.1.1.1.m1.2.2" xref="S3.SS2.p1.1.1.1.m1.2.2.cmml"><mrow id="S3.SS2.p1.1.1.1.m1.2.2.2.2" xref="S3.SS2.p1.1.1.1.m1.2.2.2.3.cmml"><msub id="S3.SS2.p1.1.1.1.m1.1.1.1.1.1" xref="S3.SS2.p1.1.1.1.m1.1.1.1.1.1.cmml"><mi id="S3.SS2.p1.1.1.1.m1.1.1.1.1.1.2" xref="S3.SS2.p1.1.1.1.m1.1.1.1.1.1.2.cmml">F</mi><mi id="S3.SS2.p1.1.1.1.m1.1.1.1.1.1.3" xref="S3.SS2.p1.1.1.1.m1.1.1.1.1.1.3.cmml">l</mi></msub><mo id="S3.SS2.p1.1.1.1.m1.2.2.2.2.3" xref="S3.SS2.p1.1.1.1.m1.2.2.2.3.cmml">,</mo><msub id="S3.SS2.p1.1.1.1.m1.2.2.2.2.2" xref="S3.SS2.p1.1.1.1.m1.2.2.2.2.2.cmml"><mi id="S3.SS2.p1.1.1.1.m1.2.2.2.2.2.2" xref="S3.SS2.p1.1.1.1.m1.2.2.2.2.2.2.cmml">F</mi><mi id="S3.SS2.p1.1.1.1.m1.2.2.2.2.2.3" xref="S3.SS2.p1.1.1.1.m1.2.2.2.2.2.3.cmml">r</mi></msub></mrow><mo id="S3.SS2.p1.1.1.1.m1.2.2.3" xref="S3.SS2.p1.1.1.1.m1.2.2.3.cmml">∈</mo><msup id="S3.SS2.p1.1.1.1.m1.2.2.4" xref="S3.SS2.p1.1.1.1.m1.2.2.4.cmml"><mi id="S3.SS2.p1.1.1.1.m1.2.2.4.2" xref="S3.SS2.p1.1.1.1.m1.2.2.4.2.cmml">ℝ</mi><mrow id="S3.SS2.p1.1.1.1.m1.2.2.4.3" xref="S3.SS2.p1.1.1.1.m1.2.2.4.3.cmml"><mi id="S3.SS2.p1.1.1.1.m1.2.2.4.3.2" xref="S3.SS2.p1.1.1.1.m1.2.2.4.3.2.cmml">w</mi><mo id="S3.SS2.p1.1.1.1.m1.2.2.4.3.1" lspace="0.222em" rspace="0.222em" xref="S3.SS2.p1.1.1.1.m1.2.2.4.3.1.cmml">×</mo><mi id="S3.SS2.p1.1.1.1.m1.2.2.4.3.3" xref="S3.SS2.p1.1.1.1.m1.2.2.4.3.3.cmml">h</mi><mo id="S3.SS2.p1.1.1.1.m1.2.2.4.3.1a" lspace="0.222em" rspace="0.222em" xref="S3.SS2.p1.1.1.1.m1.2.2.4.3.1.cmml">×</mo><mi id="S3.SS2.p1.1.1.1.m1.2.2.4.3.4" xref="S3.SS2.p1.1.1.1.m1.2.2.4.3.4.cmml">f</mi></mrow></msup></mrow><annotation-xml encoding="MathML-Content" id="S3.SS2.p1.1.1.1.m1.2b"><apply id="S3.SS2.p1.1.1.1.m1.2.2.cmml" xref="S3.SS2.p1.1.1.1.m1.2.2"><in id="S3.SS2.p1.1.1.1.m1.2.2.3.cmml" xref="S3.SS2.p1.1.1.1.m1.2.2.3"></in><list id="S3.SS2.p1.1.1.1.m1.2.2.2.3.cmml" xref="S3.SS2.p1.1.1.1.m1.2.2.2.2"><apply id="S3.SS2.p1.1.1.1.m1.1.1.1.1.1.cmml" xref="S3.SS2.p1.1.1.1.m1.1.1.1.1.1"><csymbol cd="ambiguous" id="S3.SS2.p1.1.1.1.m1.1.1.1.1.1.1.cmml" xref="S3.SS2.p1.1.1.1.m1.1.1.1.1.1">subscript</csymbol><ci id="S3.SS2.p1.1.1.1.m1.1.1.1.1.1.2.cmml" xref="S3.SS2.p1.1.1.1.m1.1.1.1.1.1.2">𝐹</ci><ci id="S3.SS2.p1.1.1.1.m1.1.1.1.1.1.3.cmml" xref="S3.SS2.p1.1.1.1.m1.1.1.1.1.1.3">𝑙</ci></apply><apply id="S3.SS2.p1.1.1.1.m1.2.2.2.2.2.cmml" xref="S3.SS2.p1.1.1.1.m1.2.2.2.2.2"><csymbol cd="ambiguous" id="S3.SS2.p1.1.1.1.m1.2.2.2.2.2.1.cmml" xref="S3.SS2.p1.1.1.1.m1.2.2.2.2.2">subscript</csymbol><ci id="S3.SS2.p1.1.1.1.m1.2.2.2.2.2.2.cmml" xref="S3.SS2.p1.1.1.1.m1.2.2.2.2.2.2">𝐹</ci><ci id="S3.SS2.p1.1.1.1.m1.2.2.2.2.2.3.cmml" xref="S3.SS2.p1.1.1.1.m1.2.2.2.2.2.3">𝑟</ci></apply></list><apply id="S3.SS2.p1.1.1.1.m1.2.2.4.cmml" xref="S3.SS2.p1.1.1.1.m1.2.2.4"><csymbol cd="ambiguous" id="S3.SS2.p1.1.1.1.m1.2.2.4.1.cmml" xref="S3.SS2.p1.1.1.1.m1.2.2.4">superscript</csymbol><ci id="S3.SS2.p1.1.1.1.m1.2.2.4.2.cmml" xref="S3.SS2.p1.1.1.1.m1.2.2.4.2">ℝ</ci><apply id="S3.SS2.p1.1.1.1.m1.2.2.4.3.cmml" xref="S3.SS2.p1.1.1.1.m1.2.2.4.3"><times id="S3.SS2.p1.1.1.1.m1.2.2.4.3.1.cmml" xref="S3.SS2.p1.1.1.1.m1.2.2.4.3.1"></times><ci id="S3.SS2.p1.1.1.1.m1.2.2.4.3.2.cmml" xref="S3.SS2.p1.1.1.1.m1.2.2.4.3.2">𝑤</ci><ci id="S3.SS2.p1.1.1.1.m1.2.2.4.3.3.cmml" xref="S3.SS2.p1.1.1.1.m1.2.2.4.3.3">ℎ</ci><ci id="S3.SS2.p1.1.1.1.m1.2.2.4.3.4.cmml" xref="S3.SS2.p1.1.1.1.m1.2.2.4.3.4">𝑓</ci></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS2.p1.1.1.1.m1.2c">F_{l},F_{r}\in{\mathbb{R}^{w\times h\times f}}</annotation><annotation encoding="application/x-llamapun" id="S3.SS2.p1.1.1.1.m1.2d">italic_F start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , italic_F start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT italic_w × italic_h × italic_f end_POSTSUPERSCRIPT</annotation></semantics></math>, where <math alttext="f" class="ltx_Math" display="inline" id="S3.SS2.p1.2.2.2.m2.1"><semantics id="S3.SS2.p1.2.2.2.m2.1a"><mi id="S3.SS2.p1.2.2.2.m2.1.1" xref="S3.SS2.p1.2.2.2.m2.1.1.cmml">f</mi><annotation-xml encoding="MathML-Content" id="S3.SS2.p1.2.2.2.m2.1b"><ci id="S3.SS2.p1.2.2.2.m2.1.1.cmml" xref="S3.SS2.p1.2.2.2.m2.1.1">𝑓</ci></annotation-xml><annotation encoding="application/x-tex" id="S3.SS2.p1.2.2.2.m2.1c">f</annotation><annotation encoding="application/x-llamapun" id="S3.SS2.p1.2.2.2.m2.1d">italic_f</annotation></semantics></math> represents the number of feature channels. 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The feature extraction and compression processes are concisely represented by operation <math alttext="T_{\gamma}(\cdot)" class="ltx_Math" display="inline" id="S3.SS2.p1.5.5.5.m5.1"><semantics id="S3.SS2.p1.5.5.5.m5.1a"><mrow id="S3.SS2.p1.5.5.5.m5.1.2" xref="S3.SS2.p1.5.5.5.m5.1.2.cmml"><msub id="S3.SS2.p1.5.5.5.m5.1.2.2" xref="S3.SS2.p1.5.5.5.m5.1.2.2.cmml"><mi id="S3.SS2.p1.5.5.5.m5.1.2.2.2" xref="S3.SS2.p1.5.5.5.m5.1.2.2.2.cmml">T</mi><mi id="S3.SS2.p1.5.5.5.m5.1.2.2.3" xref="S3.SS2.p1.5.5.5.m5.1.2.2.3.cmml">γ</mi></msub><mo id="S3.SS2.p1.5.5.5.m5.1.2.1" xref="S3.SS2.p1.5.5.5.m5.1.2.1.cmml">⁢</mo><mrow id="S3.SS2.p1.5.5.5.m5.1.2.3.2" xref="S3.SS2.p1.5.5.5.m5.1.2.cmml"><mo id="S3.SS2.p1.5.5.5.m5.1.2.3.2.1" stretchy="false" xref="S3.SS2.p1.5.5.5.m5.1.2.cmml">(</mo><mo id="S3.SS2.p1.5.5.5.m5.1.1" lspace="0em" rspace="0em" xref="S3.SS2.p1.5.5.5.m5.1.1.cmml">⋅</mo><mo id="S3.SS2.p1.5.5.5.m5.1.2.3.2.2" stretchy="false" 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and (<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S2.E4" title="In II-A The Semantic Encoder Network ‣ II System Model ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">4</span></a>).</span></span></p> </div> <div class="ltx_para" id="S3.SS2.p2"> <p class="ltx_p" id="S3.SS2.p2.1">At the receiver, the optical flow method is introduced to utilize the correlation between left and right features for semantic recovery. The optical flow, first proposed by Gibson <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib29" title="">29</a>]</cite>, describes the projection of a 3D pixel’s motion onto a 2D image plane. By calculating the optical flow between two images or feature maps, the relative motion information of the pixels between the images or feature maps can be estimated. Based on the estimated motion information, it can effectively achieve feature alignment between images or feature maps <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib33" title="">33</a>]</cite>. Thus, many optical-flow-driven methods are proposed in video super-resolution recovery <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib33" title="">33</a>]</cite> and object tracking tasks <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib34" title="">34</a>]</cite>. Based on this idea, the receiver adopts the optical flow to align the left and right features and enhance semantic recovery. Besides, a well-trained network, called SpyNet, <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib35" title="">35</a>]</cite> is introduced to perform optical flow calculations.</p> </div> <figure class="ltx_figure" id="S3.F7"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="315" id="S3.F7.g1" src="x7.png" width="477"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 7: </span>Structure of the optical-flow-driven semantic recovery module.</figcaption> </figure> <div class="ltx_para" id="S3.SS2.p3"> <p class="ltx_p" id="S3.SS2.p3.3">The received global information is first input into the SpyNet to estimate the left-to-right and right-to-left optical flow <math alttext="\left\{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle\rightarrow$}}% \over{\mathcal{O}}},\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle% \leftarrow$}}\over{\mathcal{O}}}\right\}" class="ltx_Math" display="inline" id="S3.SS2.p3.1.m1.2"><semantics id="S3.SS2.p3.1.m1.2a"><mrow id="S3.SS2.p3.1.m1.2.3.2" xref="S3.SS2.p3.1.m1.2.3.1.cmml"><mo id="S3.SS2.p3.1.m1.2.3.2.1" xref="S3.SS2.p3.1.m1.2.3.1.cmml">{</mo><mover id="S3.SS2.p3.1.m1.1.1.1" xref="S3.SS2.p3.1.m1.1.1.1a.cmml"><mi class="ltx_font_mathcaligraphic" id="S3.SS2.p3.1.m1.1.1.1.3" xref="S3.SS2.p3.1.m1.1.1.1.3.cmml">𝒪</mi><mpadded id="S3.SS2.p3.1.m1.1.1.1.1" voffset="-3.0pt" xref="S3.SS2.p3.1.m1.1.1.1.1.cmml"><mo id="S3.SS2.p3.1.m1.1.1.1.1a" mathsize="71%" stretchy="false" xref="S3.SS2.p3.1.m1.1.1.1.1.cmml">→</mo></mpadded></mover><mo id="S3.SS2.p3.1.m1.2.3.2.2" xref="S3.SS2.p3.1.m1.2.3.1.cmml">,</mo><mover id="S3.SS2.p3.1.m1.2.2.1" xref="S3.SS2.p3.1.m1.2.2.1a.cmml"><mi class="ltx_font_mathcaligraphic" id="S3.SS2.p3.1.m1.2.2.1.3" xref="S3.SS2.p3.1.m1.2.2.1.3.cmml">𝒪</mi><mpadded id="S3.SS2.p3.1.m1.2.2.1.1" voffset="-3.0pt" xref="S3.SS2.p3.1.m1.2.2.1.1.cmml"><mo id="S3.SS2.p3.1.m1.2.2.1.1a" mathsize="71%" stretchy="false" xref="S3.SS2.p3.1.m1.2.2.1.1.cmml">←</mo></mpadded></mover><mo id="S3.SS2.p3.1.m1.2.3.2.3" xref="S3.SS2.p3.1.m1.2.3.1.cmml">}</mo></mrow><annotation-xml encoding="MathML-Content" id="S3.SS2.p3.1.m1.2b"><set id="S3.SS2.p3.1.m1.2.3.1.cmml" xref="S3.SS2.p3.1.m1.2.3.2"><ci id="S3.SS2.p3.1.m1.1.1.1a.cmml" xref="S3.SS2.p3.1.m1.1.1.1"><mover id="S3.SS2.p3.1.m1.1.1.1.cmml" xref="S3.SS2.p3.1.m1.1.1.1"><mi class="ltx_font_mathcaligraphic" id="S3.SS2.p3.1.m1.1.1.1.3.cmml" xref="S3.SS2.p3.1.m1.1.1.1.3">𝒪</mi><mpadded id="S3.SS2.p3.1.m1.1.1.1.1.cmml" voffset="-3.0pt" xref="S3.SS2.p3.1.m1.1.1.1.1"><mo id="S3.SS2.p3.1.m1.1.1.1.1a.cmml" mathsize="71%" stretchy="false" xref="S3.SS2.p3.1.m1.1.1.1.1">→</mo></mpadded></mover></ci><ci id="S3.SS2.p3.1.m1.2.2.1a.cmml" xref="S3.SS2.p3.1.m1.2.2.1"><mover id="S3.SS2.p3.1.m1.2.2.1.cmml" xref="S3.SS2.p3.1.m1.2.2.1"><mi class="ltx_font_mathcaligraphic" id="S3.SS2.p3.1.m1.2.2.1.3.cmml" xref="S3.SS2.p3.1.m1.2.2.1.3">𝒪</mi><mpadded id="S3.SS2.p3.1.m1.2.2.1.1.cmml" voffset="-3.0pt" xref="S3.SS2.p3.1.m1.2.2.1.1"><mo id="S3.SS2.p3.1.m1.2.2.1.1a.cmml" mathsize="71%" stretchy="false" xref="S3.SS2.p3.1.m1.2.2.1.1">←</mo></mpadded></mover></ci></set></annotation-xml><annotation encoding="application/x-tex" id="S3.SS2.p3.1.m1.2c">\left\{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle\rightarrow$}}% \over{\mathcal{O}}},\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle% \leftarrow$}}\over{\mathcal{O}}}\right\}</annotation><annotation encoding="application/x-llamapun" id="S3.SS2.p3.1.m1.2d">{ start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG → end_ARG end_ID , start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG ← end_ARG end_ID }</annotation></semantics></math>. <span class="ltx_text" id="S3.SS2.p3.3.2">Afterward, as shown in Fig. <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S3.F7" title="Figure 7 ‣ III-B Structure of The Global Information Network ‣ III Transceiver Design for Proposed Semantic Communication System ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">7</span></a>, the optical-flow-driven recovery module is used to recover the global semantic features, which corresponds to the global information decoder network in Fig. <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S3.F6" title="Figure 6 ‣ III-B Structure of The Global Information Network ‣ III Transceiver Design for Proposed Semantic Communication System ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">6</span></a> (excluding SpyNet). 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id="S3.E13.m1.1.1.1.1.cmml" voffset="-3.0pt" xref="S3.E13.m1.1.1.1.1"><mo id="S3.E13.m1.1.1.1.1a.cmml" mathsize="71%" stretchy="false" xref="S3.E13.m1.1.1.1.1">←</mo></mpadded></mover></ci></interval><ci id="S3.E13.m1.6.6.1.4a.cmml" xref="S3.E13.m1.6.6.1.4"><mtext id="S3.E13.m1.6.6.1.4.cmml" xref="S3.E13.m1.6.6.1.4">,</mtext></ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.E13.m1.6c">\hat{F}_{l,2}={\mathcal{F}_{warp}}\left(\hat{F}_{r,1},\mathord{\buildrel{% \lower 3.0pt\hbox{$\scriptscriptstyle\leftarrow$}}\over{\mathcal{O}}}\right)% \text{,}</annotation><annotation encoding="application/x-llamapun" id="S3.E13.m1.6d">over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_l , 2 end_POSTSUBSCRIPT = caligraphic_F start_POSTSUBSCRIPT italic_w italic_a italic_r italic_p end_POSTSUBSCRIPT ( over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_r , 1 end_POSTSUBSCRIPT , start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG ← end_ARG end_ID ) ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(13)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S3.SS2.p3.18">and</p> <table class="ltx_equation ltx_eqn_table" id="S3.E14"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="\hat{F}_{r,2}={\mathcal{F}_{warp}}\left(\hat{F}_{l,1},\mathord{\buildrel{% \lower 3.0pt\hbox{$\scriptscriptstyle\rightarrow$}}\over{\mathcal{O}}}\right)% \text{,}" class="ltx_Math" display="block" id="S3.E14.m1.6"><semantics id="S3.E14.m1.6a"><mrow id="S3.E14.m1.6.6" xref="S3.E14.m1.6.6.cmml"><msub id="S3.E14.m1.6.6.3" xref="S3.E14.m1.6.6.3.cmml"><mover accent="true" id="S3.E14.m1.6.6.3.2" xref="S3.E14.m1.6.6.3.2.cmml"><mi id="S3.E14.m1.6.6.3.2.2" xref="S3.E14.m1.6.6.3.2.2.cmml">F</mi><mo id="S3.E14.m1.6.6.3.2.1" xref="S3.E14.m1.6.6.3.2.1.cmml">^</mo></mover><mrow id="S3.E14.m1.3.3.2.4" xref="S3.E14.m1.3.3.2.3.cmml"><mi id="S3.E14.m1.2.2.1.1" xref="S3.E14.m1.2.2.1.1.cmml">r</mi><mo id="S3.E14.m1.3.3.2.4.1" xref="S3.E14.m1.3.3.2.3.cmml">,</mo><mn id="S3.E14.m1.3.3.2.2" xref="S3.E14.m1.3.3.2.2.cmml">2</mn></mrow></msub><mo id="S3.E14.m1.6.6.2" xref="S3.E14.m1.6.6.2.cmml">=</mo><mrow id="S3.E14.m1.6.6.1" xref="S3.E14.m1.6.6.1.cmml"><msub id="S3.E14.m1.6.6.1.3" xref="S3.E14.m1.6.6.1.3.cmml"><mi class="ltx_font_mathcaligraphic" id="S3.E14.m1.6.6.1.3.2" xref="S3.E14.m1.6.6.1.3.2.cmml">ℱ</mi><mrow id="S3.E14.m1.6.6.1.3.3" xref="S3.E14.m1.6.6.1.3.3.cmml"><mi id="S3.E14.m1.6.6.1.3.3.2" xref="S3.E14.m1.6.6.1.3.3.2.cmml">w</mi><mo id="S3.E14.m1.6.6.1.3.3.1" xref="S3.E14.m1.6.6.1.3.3.1.cmml">⁢</mo><mi id="S3.E14.m1.6.6.1.3.3.3" xref="S3.E14.m1.6.6.1.3.3.3.cmml">a</mi><mo id="S3.E14.m1.6.6.1.3.3.1a" xref="S3.E14.m1.6.6.1.3.3.1.cmml">⁢</mo><mi id="S3.E14.m1.6.6.1.3.3.4" xref="S3.E14.m1.6.6.1.3.3.4.cmml">r</mi><mo id="S3.E14.m1.6.6.1.3.3.1b" xref="S3.E14.m1.6.6.1.3.3.1.cmml">⁢</mo><mi id="S3.E14.m1.6.6.1.3.3.5" xref="S3.E14.m1.6.6.1.3.3.5.cmml">p</mi></mrow></msub><mo id="S3.E14.m1.6.6.1.2" xref="S3.E14.m1.6.6.1.2.cmml">⁢</mo><mrow id="S3.E14.m1.6.6.1.1.1" xref="S3.E14.m1.6.6.1.1.2.cmml"><mo id="S3.E14.m1.6.6.1.1.1.2" xref="S3.E14.m1.6.6.1.1.2.cmml">(</mo><msub id="S3.E14.m1.6.6.1.1.1.1" xref="S3.E14.m1.6.6.1.1.1.1.cmml"><mover accent="true" id="S3.E14.m1.6.6.1.1.1.1.2" xref="S3.E14.m1.6.6.1.1.1.1.2.cmml"><mi id="S3.E14.m1.6.6.1.1.1.1.2.2" xref="S3.E14.m1.6.6.1.1.1.1.2.2.cmml">F</mi><mo id="S3.E14.m1.6.6.1.1.1.1.2.1" xref="S3.E14.m1.6.6.1.1.1.1.2.1.cmml">^</mo></mover><mrow id="S3.E14.m1.5.5.2.4" xref="S3.E14.m1.5.5.2.3.cmml"><mi id="S3.E14.m1.4.4.1.1" xref="S3.E14.m1.4.4.1.1.cmml">l</mi><mo id="S3.E14.m1.5.5.2.4.1" xref="S3.E14.m1.5.5.2.3.cmml">,</mo><mn id="S3.E14.m1.5.5.2.2" xref="S3.E14.m1.5.5.2.2.cmml">1</mn></mrow></msub><mo id="S3.E14.m1.6.6.1.1.1.3" xref="S3.E14.m1.6.6.1.1.2.cmml">,</mo><mover id="S3.E14.m1.1.1.1" xref="S3.E14.m1.1.1.1a.cmml"><mi class="ltx_font_mathcaligraphic" id="S3.E14.m1.1.1.1.3" xref="S3.E14.m1.1.1.1.3.cmml">𝒪</mi><mpadded id="S3.E14.m1.1.1.1.1" voffset="-3.0pt" xref="S3.E14.m1.1.1.1.1.cmml"><mo id="S3.E14.m1.1.1.1.1a" mathsize="71%" stretchy="false" xref="S3.E14.m1.1.1.1.1.cmml">→</mo></mpadded></mover><mo id="S3.E14.m1.6.6.1.1.1.4" xref="S3.E14.m1.6.6.1.1.2.cmml">)</mo></mrow><mo id="S3.E14.m1.6.6.1.2a" xref="S3.E14.m1.6.6.1.2.cmml">⁢</mo><mtext id="S3.E14.m1.6.6.1.4" xref="S3.E14.m1.6.6.1.4a.cmml">,</mtext></mrow></mrow><annotation-xml encoding="MathML-Content" id="S3.E14.m1.6b"><apply id="S3.E14.m1.6.6.cmml" xref="S3.E14.m1.6.6"><eq id="S3.E14.m1.6.6.2.cmml" xref="S3.E14.m1.6.6.2"></eq><apply id="S3.E14.m1.6.6.3.cmml" xref="S3.E14.m1.6.6.3"><csymbol cd="ambiguous" id="S3.E14.m1.6.6.3.1.cmml" xref="S3.E14.m1.6.6.3">subscript</csymbol><apply id="S3.E14.m1.6.6.3.2.cmml" xref="S3.E14.m1.6.6.3.2"><ci id="S3.E14.m1.6.6.3.2.1.cmml" xref="S3.E14.m1.6.6.3.2.1">^</ci><ci id="S3.E14.m1.6.6.3.2.2.cmml" xref="S3.E14.m1.6.6.3.2.2">𝐹</ci></apply><list id="S3.E14.m1.3.3.2.3.cmml" xref="S3.E14.m1.3.3.2.4"><ci id="S3.E14.m1.2.2.1.1.cmml" xref="S3.E14.m1.2.2.1.1">𝑟</ci><cn id="S3.E14.m1.3.3.2.2.cmml" type="integer" xref="S3.E14.m1.3.3.2.2">2</cn></list></apply><apply id="S3.E14.m1.6.6.1.cmml" xref="S3.E14.m1.6.6.1"><times id="S3.E14.m1.6.6.1.2.cmml" xref="S3.E14.m1.6.6.1.2"></times><apply id="S3.E14.m1.6.6.1.3.cmml" xref="S3.E14.m1.6.6.1.3"><csymbol cd="ambiguous" id="S3.E14.m1.6.6.1.3.1.cmml" xref="S3.E14.m1.6.6.1.3">subscript</csymbol><ci id="S3.E14.m1.6.6.1.3.2.cmml" xref="S3.E14.m1.6.6.1.3.2">ℱ</ci><apply id="S3.E14.m1.6.6.1.3.3.cmml" xref="S3.E14.m1.6.6.1.3.3"><times id="S3.E14.m1.6.6.1.3.3.1.cmml" xref="S3.E14.m1.6.6.1.3.3.1"></times><ci id="S3.E14.m1.6.6.1.3.3.2.cmml" xref="S3.E14.m1.6.6.1.3.3.2">𝑤</ci><ci id="S3.E14.m1.6.6.1.3.3.3.cmml" xref="S3.E14.m1.6.6.1.3.3.3">𝑎</ci><ci id="S3.E14.m1.6.6.1.3.3.4.cmml" xref="S3.E14.m1.6.6.1.3.3.4">𝑟</ci><ci id="S3.E14.m1.6.6.1.3.3.5.cmml" xref="S3.E14.m1.6.6.1.3.3.5">𝑝</ci></apply></apply><interval closure="open" id="S3.E14.m1.6.6.1.1.2.cmml" xref="S3.E14.m1.6.6.1.1.1"><apply id="S3.E14.m1.6.6.1.1.1.1.cmml" xref="S3.E14.m1.6.6.1.1.1.1"><csymbol cd="ambiguous" id="S3.E14.m1.6.6.1.1.1.1.1.cmml" xref="S3.E14.m1.6.6.1.1.1.1">subscript</csymbol><apply id="S3.E14.m1.6.6.1.1.1.1.2.cmml" xref="S3.E14.m1.6.6.1.1.1.1.2"><ci id="S3.E14.m1.6.6.1.1.1.1.2.1.cmml" xref="S3.E14.m1.6.6.1.1.1.1.2.1">^</ci><ci id="S3.E14.m1.6.6.1.1.1.1.2.2.cmml" xref="S3.E14.m1.6.6.1.1.1.1.2.2">𝐹</ci></apply><list id="S3.E14.m1.5.5.2.3.cmml" xref="S3.E14.m1.5.5.2.4"><ci id="S3.E14.m1.4.4.1.1.cmml" xref="S3.E14.m1.4.4.1.1">𝑙</ci><cn id="S3.E14.m1.5.5.2.2.cmml" type="integer" xref="S3.E14.m1.5.5.2.2">1</cn></list></apply><ci id="S3.E14.m1.1.1.1a.cmml" xref="S3.E14.m1.1.1.1"><mover id="S3.E14.m1.1.1.1.cmml" xref="S3.E14.m1.1.1.1"><mi class="ltx_font_mathcaligraphic" id="S3.E14.m1.1.1.1.3.cmml" xref="S3.E14.m1.1.1.1.3">𝒪</mi><mpadded id="S3.E14.m1.1.1.1.1.cmml" voffset="-3.0pt" xref="S3.E14.m1.1.1.1.1"><mo id="S3.E14.m1.1.1.1.1a.cmml" mathsize="71%" stretchy="false" xref="S3.E14.m1.1.1.1.1">→</mo></mpadded></mover></ci></interval><ci id="S3.E14.m1.6.6.1.4a.cmml" xref="S3.E14.m1.6.6.1.4"><mtext id="S3.E14.m1.6.6.1.4.cmml" xref="S3.E14.m1.6.6.1.4">,</mtext></ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.E14.m1.6c">\hat{F}_{r,2}={\mathcal{F}_{warp}}\left(\hat{F}_{l,1},\mathord{\buildrel{% \lower 3.0pt\hbox{$\scriptscriptstyle\rightarrow$}}\over{\mathcal{O}}}\right)% \text{,}</annotation><annotation encoding="application/x-llamapun" id="S3.E14.m1.6d">over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_r , 2 end_POSTSUBSCRIPT = caligraphic_F start_POSTSUBSCRIPT italic_w italic_a italic_r italic_p end_POSTSUBSCRIPT ( over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_l , 1 end_POSTSUBSCRIPT , start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG → end_ARG end_ID ) ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(14)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S3.SS2.p3.17">where <math alttext="\mathcal{F}_{warp}" class="ltx_Math" display="inline" id="S3.SS2.p3.4.m1.1"><semantics id="S3.SS2.p3.4.m1.1a"><msub id="S3.SS2.p3.4.m1.1.1" xref="S3.SS2.p3.4.m1.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="S3.SS2.p3.4.m1.1.1.2" xref="S3.SS2.p3.4.m1.1.1.2.cmml">ℱ</mi><mrow id="S3.SS2.p3.4.m1.1.1.3" xref="S3.SS2.p3.4.m1.1.1.3.cmml"><mi id="S3.SS2.p3.4.m1.1.1.3.2" xref="S3.SS2.p3.4.m1.1.1.3.2.cmml">w</mi><mo id="S3.SS2.p3.4.m1.1.1.3.1" xref="S3.SS2.p3.4.m1.1.1.3.1.cmml">⁢</mo><mi id="S3.SS2.p3.4.m1.1.1.3.3" xref="S3.SS2.p3.4.m1.1.1.3.3.cmml">a</mi><mo id="S3.SS2.p3.4.m1.1.1.3.1a" xref="S3.SS2.p3.4.m1.1.1.3.1.cmml">⁢</mo><mi id="S3.SS2.p3.4.m1.1.1.3.4" xref="S3.SS2.p3.4.m1.1.1.3.4.cmml">r</mi><mo id="S3.SS2.p3.4.m1.1.1.3.1b" xref="S3.SS2.p3.4.m1.1.1.3.1.cmml">⁢</mo><mi id="S3.SS2.p3.4.m1.1.1.3.5" xref="S3.SS2.p3.4.m1.1.1.3.5.cmml">p</mi></mrow></msub><annotation-xml encoding="MathML-Content" id="S3.SS2.p3.4.m1.1b"><apply id="S3.SS2.p3.4.m1.1.1.cmml" xref="S3.SS2.p3.4.m1.1.1"><csymbol cd="ambiguous" id="S3.SS2.p3.4.m1.1.1.1.cmml" xref="S3.SS2.p3.4.m1.1.1">subscript</csymbol><ci id="S3.SS2.p3.4.m1.1.1.2.cmml" xref="S3.SS2.p3.4.m1.1.1.2">ℱ</ci><apply id="S3.SS2.p3.4.m1.1.1.3.cmml" xref="S3.SS2.p3.4.m1.1.1.3"><times id="S3.SS2.p3.4.m1.1.1.3.1.cmml" xref="S3.SS2.p3.4.m1.1.1.3.1"></times><ci id="S3.SS2.p3.4.m1.1.1.3.2.cmml" xref="S3.SS2.p3.4.m1.1.1.3.2">𝑤</ci><ci id="S3.SS2.p3.4.m1.1.1.3.3.cmml" xref="S3.SS2.p3.4.m1.1.1.3.3">𝑎</ci><ci id="S3.SS2.p3.4.m1.1.1.3.4.cmml" xref="S3.SS2.p3.4.m1.1.1.3.4">𝑟</ci><ci id="S3.SS2.p3.4.m1.1.1.3.5.cmml" xref="S3.SS2.p3.4.m1.1.1.3.5">𝑝</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS2.p3.4.m1.1c">\mathcal{F}_{warp}</annotation><annotation encoding="application/x-llamapun" id="S3.SS2.p3.4.m1.1d">caligraphic_F start_POSTSUBSCRIPT italic_w italic_a italic_r italic_p end_POSTSUBSCRIPT</annotation></semantics></math> represents the warping operation and <math alttext="\hat{F}_{l,2},\hat{F}_{r,2}\in{\mathbb{R}^{w/m\times h/m\times 3}}" class="ltx_Math" display="inline" id="S3.SS2.p3.5.m2.6"><semantics id="S3.SS2.p3.5.m2.6a"><mrow id="S3.SS2.p3.5.m2.6.6" xref="S3.SS2.p3.5.m2.6.6.cmml"><mrow id="S3.SS2.p3.5.m2.6.6.2.2" xref="S3.SS2.p3.5.m2.6.6.2.3.cmml"><msub id="S3.SS2.p3.5.m2.5.5.1.1.1" xref="S3.SS2.p3.5.m2.5.5.1.1.1.cmml"><mover accent="true" id="S3.SS2.p3.5.m2.5.5.1.1.1.2" xref="S3.SS2.p3.5.m2.5.5.1.1.1.2.cmml"><mi id="S3.SS2.p3.5.m2.5.5.1.1.1.2.2" xref="S3.SS2.p3.5.m2.5.5.1.1.1.2.2.cmml">F</mi><mo id="S3.SS2.p3.5.m2.5.5.1.1.1.2.1" xref="S3.SS2.p3.5.m2.5.5.1.1.1.2.1.cmml">^</mo></mover><mrow id="S3.SS2.p3.5.m2.2.2.2.4" xref="S3.SS2.p3.5.m2.2.2.2.3.cmml"><mi id="S3.SS2.p3.5.m2.1.1.1.1" xref="S3.SS2.p3.5.m2.1.1.1.1.cmml">l</mi><mo id="S3.SS2.p3.5.m2.2.2.2.4.1" xref="S3.SS2.p3.5.m2.2.2.2.3.cmml">,</mo><mn id="S3.SS2.p3.5.m2.2.2.2.2" xref="S3.SS2.p3.5.m2.2.2.2.2.cmml">2</mn></mrow></msub><mo id="S3.SS2.p3.5.m2.6.6.2.2.3" xref="S3.SS2.p3.5.m2.6.6.2.3.cmml">,</mo><msub id="S3.SS2.p3.5.m2.6.6.2.2.2" xref="S3.SS2.p3.5.m2.6.6.2.2.2.cmml"><mover accent="true" id="S3.SS2.p3.5.m2.6.6.2.2.2.2" xref="S3.SS2.p3.5.m2.6.6.2.2.2.2.cmml"><mi id="S3.SS2.p3.5.m2.6.6.2.2.2.2.2" xref="S3.SS2.p3.5.m2.6.6.2.2.2.2.2.cmml">F</mi><mo id="S3.SS2.p3.5.m2.6.6.2.2.2.2.1" xref="S3.SS2.p3.5.m2.6.6.2.2.2.2.1.cmml">^</mo></mover><mrow id="S3.SS2.p3.5.m2.4.4.2.4" 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xref="S3.SS2.p3.5.m2.5.5.1.1.1"><csymbol cd="ambiguous" id="S3.SS2.p3.5.m2.5.5.1.1.1.1.cmml" xref="S3.SS2.p3.5.m2.5.5.1.1.1">subscript</csymbol><apply id="S3.SS2.p3.5.m2.5.5.1.1.1.2.cmml" xref="S3.SS2.p3.5.m2.5.5.1.1.1.2"><ci id="S3.SS2.p3.5.m2.5.5.1.1.1.2.1.cmml" xref="S3.SS2.p3.5.m2.5.5.1.1.1.2.1">^</ci><ci id="S3.SS2.p3.5.m2.5.5.1.1.1.2.2.cmml" xref="S3.SS2.p3.5.m2.5.5.1.1.1.2.2">𝐹</ci></apply><list id="S3.SS2.p3.5.m2.2.2.2.3.cmml" xref="S3.SS2.p3.5.m2.2.2.2.4"><ci id="S3.SS2.p3.5.m2.1.1.1.1.cmml" xref="S3.SS2.p3.5.m2.1.1.1.1">𝑙</ci><cn id="S3.SS2.p3.5.m2.2.2.2.2.cmml" type="integer" xref="S3.SS2.p3.5.m2.2.2.2.2">2</cn></list></apply><apply id="S3.SS2.p3.5.m2.6.6.2.2.2.cmml" xref="S3.SS2.p3.5.m2.6.6.2.2.2"><csymbol cd="ambiguous" id="S3.SS2.p3.5.m2.6.6.2.2.2.1.cmml" xref="S3.SS2.p3.5.m2.6.6.2.2.2">subscript</csymbol><apply id="S3.SS2.p3.5.m2.6.6.2.2.2.2.cmml" xref="S3.SS2.p3.5.m2.6.6.2.2.2.2"><ci id="S3.SS2.p3.5.m2.6.6.2.2.2.2.1.cmml" xref="S3.SS2.p3.5.m2.6.6.2.2.2.2.1">^</ci><ci 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id="S3.SS2.p3.5.m2.6.6.4.3.2.2.1.cmml" xref="S3.SS2.p3.5.m2.6.6.4.3.2.2.1"></times><apply id="S3.SS2.p3.5.m2.6.6.4.3.2.2.2.cmml" xref="S3.SS2.p3.5.m2.6.6.4.3.2.2.2"><divide id="S3.SS2.p3.5.m2.6.6.4.3.2.2.2.1.cmml" xref="S3.SS2.p3.5.m2.6.6.4.3.2.2.2.1"></divide><ci id="S3.SS2.p3.5.m2.6.6.4.3.2.2.2.2.cmml" xref="S3.SS2.p3.5.m2.6.6.4.3.2.2.2.2">𝑤</ci><ci id="S3.SS2.p3.5.m2.6.6.4.3.2.2.2.3.cmml" xref="S3.SS2.p3.5.m2.6.6.4.3.2.2.2.3">𝑚</ci></apply><ci id="S3.SS2.p3.5.m2.6.6.4.3.2.2.3.cmml" xref="S3.SS2.p3.5.m2.6.6.4.3.2.2.3">ℎ</ci></apply><ci id="S3.SS2.p3.5.m2.6.6.4.3.2.3.cmml" xref="S3.SS2.p3.5.m2.6.6.4.3.2.3">𝑚</ci></apply><cn id="S3.SS2.p3.5.m2.6.6.4.3.3.cmml" type="integer" xref="S3.SS2.p3.5.m2.6.6.4.3.3">3</cn></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS2.p3.5.m2.6c">\hat{F}_{l,2},\hat{F}_{r,2}\in{\mathbb{R}^{w/m\times h/m\times 3}}</annotation><annotation encoding="application/x-llamapun" id="S3.SS2.p3.5.m2.6d">over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_l , 2 end_POSTSUBSCRIPT , over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_r , 2 end_POSTSUBSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT italic_w / italic_m × italic_h / italic_m × 3 end_POSTSUPERSCRIPT</annotation></semantics></math> are the warped left and right feature maps. Note that after optical warping, left features are warped to right features and vice versa. After the warping, right features <math alttext="\hat{F}_{r,2}" class="ltx_Math" display="inline" id="S3.SS2.p3.6.m3.2"><semantics id="S3.SS2.p3.6.m3.2a"><msub id="S3.SS2.p3.6.m3.2.3" xref="S3.SS2.p3.6.m3.2.3.cmml"><mover accent="true" id="S3.SS2.p3.6.m3.2.3.2" xref="S3.SS2.p3.6.m3.2.3.2.cmml"><mi id="S3.SS2.p3.6.m3.2.3.2.2" xref="S3.SS2.p3.6.m3.2.3.2.2.cmml">F</mi><mo id="S3.SS2.p3.6.m3.2.3.2.1" xref="S3.SS2.p3.6.m3.2.3.2.1.cmml">^</mo></mover><mrow id="S3.SS2.p3.6.m3.2.2.2.4" xref="S3.SS2.p3.6.m3.2.2.2.3.cmml"><mi id="S3.SS2.p3.6.m3.1.1.1.1" xref="S3.SS2.p3.6.m3.1.1.1.1.cmml">r</mi><mo id="S3.SS2.p3.6.m3.2.2.2.4.1" xref="S3.SS2.p3.6.m3.2.2.2.3.cmml">,</mo><mn id="S3.SS2.p3.6.m3.2.2.2.2" xref="S3.SS2.p3.6.m3.2.2.2.2.cmml">2</mn></mrow></msub><annotation-xml encoding="MathML-Content" id="S3.SS2.p3.6.m3.2b"><apply id="S3.SS2.p3.6.m3.2.3.cmml" xref="S3.SS2.p3.6.m3.2.3"><csymbol cd="ambiguous" id="S3.SS2.p3.6.m3.2.3.1.cmml" xref="S3.SS2.p3.6.m3.2.3">subscript</csymbol><apply id="S3.SS2.p3.6.m3.2.3.2.cmml" xref="S3.SS2.p3.6.m3.2.3.2"><ci id="S3.SS2.p3.6.m3.2.3.2.1.cmml" xref="S3.SS2.p3.6.m3.2.3.2.1">^</ci><ci id="S3.SS2.p3.6.m3.2.3.2.2.cmml" xref="S3.SS2.p3.6.m3.2.3.2.2">𝐹</ci></apply><list id="S3.SS2.p3.6.m3.2.2.2.3.cmml" xref="S3.SS2.p3.6.m3.2.2.2.4"><ci id="S3.SS2.p3.6.m3.1.1.1.1.cmml" xref="S3.SS2.p3.6.m3.1.1.1.1">𝑟</ci><cn id="S3.SS2.p3.6.m3.2.2.2.2.cmml" type="integer" xref="S3.SS2.p3.6.m3.2.2.2.2">2</cn></list></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS2.p3.6.m3.2c">\hat{F}_{r,2}</annotation><annotation encoding="application/x-llamapun" id="S3.SS2.p3.6.m3.2d">over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_r , 2 end_POSTSUBSCRIPT</annotation></semantics></math> is concatenated with the received global information <math alttext="\hat{G}_{r}" class="ltx_Math" display="inline" id="S3.SS2.p3.7.m4.1"><semantics id="S3.SS2.p3.7.m4.1a"><msub id="S3.SS2.p3.7.m4.1.1" xref="S3.SS2.p3.7.m4.1.1.cmml"><mover accent="true" id="S3.SS2.p3.7.m4.1.1.2" xref="S3.SS2.p3.7.m4.1.1.2.cmml"><mi id="S3.SS2.p3.7.m4.1.1.2.2" xref="S3.SS2.p3.7.m4.1.1.2.2.cmml">G</mi><mo id="S3.SS2.p3.7.m4.1.1.2.1" xref="S3.SS2.p3.7.m4.1.1.2.1.cmml">^</mo></mover><mi id="S3.SS2.p3.7.m4.1.1.3" xref="S3.SS2.p3.7.m4.1.1.3.cmml">r</mi></msub><annotation-xml encoding="MathML-Content" id="S3.SS2.p3.7.m4.1b"><apply id="S3.SS2.p3.7.m4.1.1.cmml" xref="S3.SS2.p3.7.m4.1.1"><csymbol cd="ambiguous" id="S3.SS2.p3.7.m4.1.1.1.cmml" xref="S3.SS2.p3.7.m4.1.1">subscript</csymbol><apply id="S3.SS2.p3.7.m4.1.1.2.cmml" xref="S3.SS2.p3.7.m4.1.1.2"><ci id="S3.SS2.p3.7.m4.1.1.2.1.cmml" xref="S3.SS2.p3.7.m4.1.1.2.1">^</ci><ci id="S3.SS2.p3.7.m4.1.1.2.2.cmml" xref="S3.SS2.p3.7.m4.1.1.2.2">𝐺</ci></apply><ci id="S3.SS2.p3.7.m4.1.1.3.cmml" xref="S3.SS2.p3.7.m4.1.1.3">𝑟</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS2.p3.7.m4.1c">\hat{G}_{r}</annotation><annotation encoding="application/x-llamapun" id="S3.SS2.p3.7.m4.1d">over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT</annotation></semantics></math> in the feature channels and input into convolutional residual networks, obtaining new feature map <math alttext="\hat{F}_{r,3}" class="ltx_Math" display="inline" id="S3.SS2.p3.8.m5.2"><semantics id="S3.SS2.p3.8.m5.2a"><msub id="S3.SS2.p3.8.m5.2.3" xref="S3.SS2.p3.8.m5.2.3.cmml"><mover accent="true" id="S3.SS2.p3.8.m5.2.3.2" xref="S3.SS2.p3.8.m5.2.3.2.cmml"><mi id="S3.SS2.p3.8.m5.2.3.2.2" xref="S3.SS2.p3.8.m5.2.3.2.2.cmml">F</mi><mo id="S3.SS2.p3.8.m5.2.3.2.1" xref="S3.SS2.p3.8.m5.2.3.2.1.cmml">^</mo></mover><mrow id="S3.SS2.p3.8.m5.2.2.2.4" xref="S3.SS2.p3.8.m5.2.2.2.3.cmml"><mi id="S3.SS2.p3.8.m5.1.1.1.1" xref="S3.SS2.p3.8.m5.1.1.1.1.cmml">r</mi><mo id="S3.SS2.p3.8.m5.2.2.2.4.1" xref="S3.SS2.p3.8.m5.2.2.2.3.cmml">,</mo><mn id="S3.SS2.p3.8.m5.2.2.2.2" xref="S3.SS2.p3.8.m5.2.2.2.2.cmml">3</mn></mrow></msub><annotation-xml encoding="MathML-Content" id="S3.SS2.p3.8.m5.2b"><apply id="S3.SS2.p3.8.m5.2.3.cmml" xref="S3.SS2.p3.8.m5.2.3"><csymbol cd="ambiguous" id="S3.SS2.p3.8.m5.2.3.1.cmml" xref="S3.SS2.p3.8.m5.2.3">subscript</csymbol><apply id="S3.SS2.p3.8.m5.2.3.2.cmml" xref="S3.SS2.p3.8.m5.2.3.2"><ci id="S3.SS2.p3.8.m5.2.3.2.1.cmml" xref="S3.SS2.p3.8.m5.2.3.2.1">^</ci><ci id="S3.SS2.p3.8.m5.2.3.2.2.cmml" xref="S3.SS2.p3.8.m5.2.3.2.2">𝐹</ci></apply><list id="S3.SS2.p3.8.m5.2.2.2.3.cmml" xref="S3.SS2.p3.8.m5.2.2.2.4"><ci id="S3.SS2.p3.8.m5.1.1.1.1.cmml" xref="S3.SS2.p3.8.m5.1.1.1.1">𝑟</ci><cn id="S3.SS2.p3.8.m5.2.2.2.2.cmml" type="integer" xref="S3.SS2.p3.8.m5.2.2.2.2">3</cn></list></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS2.p3.8.m5.2c">\hat{F}_{r,3}</annotation><annotation encoding="application/x-llamapun" id="S3.SS2.p3.8.m5.2d">over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_r , 3 end_POSTSUBSCRIPT</annotation></semantics></math>. Meanwhile, new left feature map <math alttext="\hat{F}_{l,3}" class="ltx_Math" display="inline" id="S3.SS2.p3.9.m6.2"><semantics id="S3.SS2.p3.9.m6.2a"><msub id="S3.SS2.p3.9.m6.2.3" xref="S3.SS2.p3.9.m6.2.3.cmml"><mover accent="true" id="S3.SS2.p3.9.m6.2.3.2" xref="S3.SS2.p3.9.m6.2.3.2.cmml"><mi id="S3.SS2.p3.9.m6.2.3.2.2" xref="S3.SS2.p3.9.m6.2.3.2.2.cmml">F</mi><mo id="S3.SS2.p3.9.m6.2.3.2.1" xref="S3.SS2.p3.9.m6.2.3.2.1.cmml">^</mo></mover><mrow id="S3.SS2.p3.9.m6.2.2.2.4" xref="S3.SS2.p3.9.m6.2.2.2.3.cmml"><mi id="S3.SS2.p3.9.m6.1.1.1.1" xref="S3.SS2.p3.9.m6.1.1.1.1.cmml">l</mi><mo id="S3.SS2.p3.9.m6.2.2.2.4.1" xref="S3.SS2.p3.9.m6.2.2.2.3.cmml">,</mo><mn id="S3.SS2.p3.9.m6.2.2.2.2" xref="S3.SS2.p3.9.m6.2.2.2.2.cmml">3</mn></mrow></msub><annotation-xml encoding="MathML-Content" id="S3.SS2.p3.9.m6.2b"><apply id="S3.SS2.p3.9.m6.2.3.cmml" xref="S3.SS2.p3.9.m6.2.3"><csymbol cd="ambiguous" id="S3.SS2.p3.9.m6.2.3.1.cmml" xref="S3.SS2.p3.9.m6.2.3">subscript</csymbol><apply id="S3.SS2.p3.9.m6.2.3.2.cmml" xref="S3.SS2.p3.9.m6.2.3.2"><ci id="S3.SS2.p3.9.m6.2.3.2.1.cmml" xref="S3.SS2.p3.9.m6.2.3.2.1">^</ci><ci id="S3.SS2.p3.9.m6.2.3.2.2.cmml" xref="S3.SS2.p3.9.m6.2.3.2.2">𝐹</ci></apply><list id="S3.SS2.p3.9.m6.2.2.2.3.cmml" xref="S3.SS2.p3.9.m6.2.2.2.4"><ci id="S3.SS2.p3.9.m6.1.1.1.1.cmml" xref="S3.SS2.p3.9.m6.1.1.1.1">𝑙</ci><cn id="S3.SS2.p3.9.m6.2.2.2.2.cmml" type="integer" xref="S3.SS2.p3.9.m6.2.2.2.2">3</cn></list></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS2.p3.9.m6.2c">\hat{F}_{l,3}</annotation><annotation encoding="application/x-llamapun" id="S3.SS2.p3.9.m6.2d">over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_l , 3 end_POSTSUBSCRIPT</annotation></semantics></math> can be obtained from <math alttext="\hat{G}_{l}" class="ltx_Math" display="inline" id="S3.SS2.p3.10.m7.1"><semantics id="S3.SS2.p3.10.m7.1a"><msub id="S3.SS2.p3.10.m7.1.1" xref="S3.SS2.p3.10.m7.1.1.cmml"><mover accent="true" id="S3.SS2.p3.10.m7.1.1.2" xref="S3.SS2.p3.10.m7.1.1.2.cmml"><mi id="S3.SS2.p3.10.m7.1.1.2.2" xref="S3.SS2.p3.10.m7.1.1.2.2.cmml">G</mi><mo id="S3.SS2.p3.10.m7.1.1.2.1" xref="S3.SS2.p3.10.m7.1.1.2.1.cmml">^</mo></mover><mi id="S3.SS2.p3.10.m7.1.1.3" xref="S3.SS2.p3.10.m7.1.1.3.cmml">l</mi></msub><annotation-xml encoding="MathML-Content" id="S3.SS2.p3.10.m7.1b"><apply id="S3.SS2.p3.10.m7.1.1.cmml" xref="S3.SS2.p3.10.m7.1.1"><csymbol cd="ambiguous" id="S3.SS2.p3.10.m7.1.1.1.cmml" xref="S3.SS2.p3.10.m7.1.1">subscript</csymbol><apply id="S3.SS2.p3.10.m7.1.1.2.cmml" xref="S3.SS2.p3.10.m7.1.1.2"><ci id="S3.SS2.p3.10.m7.1.1.2.1.cmml" xref="S3.SS2.p3.10.m7.1.1.2.1">^</ci><ci id="S3.SS2.p3.10.m7.1.1.2.2.cmml" xref="S3.SS2.p3.10.m7.1.1.2.2">𝐺</ci></apply><ci id="S3.SS2.p3.10.m7.1.1.3.cmml" xref="S3.SS2.p3.10.m7.1.1.3">𝑙</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS2.p3.10.m7.1c">\hat{G}_{l}</annotation><annotation encoding="application/x-llamapun" id="S3.SS2.p3.10.m7.1d">over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT</annotation></semantics></math> and <math alttext="\hat{F}_{l,2}" class="ltx_Math" display="inline" id="S3.SS2.p3.11.m8.2"><semantics id="S3.SS2.p3.11.m8.2a"><msub id="S3.SS2.p3.11.m8.2.3" xref="S3.SS2.p3.11.m8.2.3.cmml"><mover accent="true" id="S3.SS2.p3.11.m8.2.3.2" xref="S3.SS2.p3.11.m8.2.3.2.cmml"><mi id="S3.SS2.p3.11.m8.2.3.2.2" xref="S3.SS2.p3.11.m8.2.3.2.2.cmml">F</mi><mo id="S3.SS2.p3.11.m8.2.3.2.1" xref="S3.SS2.p3.11.m8.2.3.2.1.cmml">^</mo></mover><mrow id="S3.SS2.p3.11.m8.2.2.2.4" xref="S3.SS2.p3.11.m8.2.2.2.3.cmml"><mi id="S3.SS2.p3.11.m8.1.1.1.1" xref="S3.SS2.p3.11.m8.1.1.1.1.cmml">l</mi><mo id="S3.SS2.p3.11.m8.2.2.2.4.1" xref="S3.SS2.p3.11.m8.2.2.2.3.cmml">,</mo><mn id="S3.SS2.p3.11.m8.2.2.2.2" xref="S3.SS2.p3.11.m8.2.2.2.2.cmml">2</mn></mrow></msub><annotation-xml encoding="MathML-Content" id="S3.SS2.p3.11.m8.2b"><apply id="S3.SS2.p3.11.m8.2.3.cmml" xref="S3.SS2.p3.11.m8.2.3"><csymbol cd="ambiguous" id="S3.SS2.p3.11.m8.2.3.1.cmml" xref="S3.SS2.p3.11.m8.2.3">subscript</csymbol><apply id="S3.SS2.p3.11.m8.2.3.2.cmml" xref="S3.SS2.p3.11.m8.2.3.2"><ci id="S3.SS2.p3.11.m8.2.3.2.1.cmml" xref="S3.SS2.p3.11.m8.2.3.2.1">^</ci><ci id="S3.SS2.p3.11.m8.2.3.2.2.cmml" xref="S3.SS2.p3.11.m8.2.3.2.2">𝐹</ci></apply><list id="S3.SS2.p3.11.m8.2.2.2.3.cmml" xref="S3.SS2.p3.11.m8.2.2.2.4"><ci id="S3.SS2.p3.11.m8.1.1.1.1.cmml" xref="S3.SS2.p3.11.m8.1.1.1.1">𝑙</ci><cn id="S3.SS2.p3.11.m8.2.2.2.2.cmml" type="integer" xref="S3.SS2.p3.11.m8.2.2.2.2">2</cn></list></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS2.p3.11.m8.2c">\hat{F}_{l,2}</annotation><annotation encoding="application/x-llamapun" id="S3.SS2.p3.11.m8.2d">over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_l , 2 end_POSTSUBSCRIPT</annotation></semantics></math> in the same way. Finally, feature maps <math alttext="\left\{\hat{F}_{l,1},\hat{F}_{l,3}\right\}" class="ltx_Math" display="inline" id="S3.SS2.p3.12.m9.6"><semantics id="S3.SS2.p3.12.m9.6a"><mrow id="S3.SS2.p3.12.m9.6.6.2" xref="S3.SS2.p3.12.m9.6.6.3.cmml"><mo id="S3.SS2.p3.12.m9.6.6.2.3" xref="S3.SS2.p3.12.m9.6.6.3.cmml">{</mo><msub id="S3.SS2.p3.12.m9.5.5.1.1" xref="S3.SS2.p3.12.m9.5.5.1.1.cmml"><mover accent="true" id="S3.SS2.p3.12.m9.5.5.1.1.2" xref="S3.SS2.p3.12.m9.5.5.1.1.2.cmml"><mi id="S3.SS2.p3.12.m9.5.5.1.1.2.2" xref="S3.SS2.p3.12.m9.5.5.1.1.2.2.cmml">F</mi><mo id="S3.SS2.p3.12.m9.5.5.1.1.2.1" xref="S3.SS2.p3.12.m9.5.5.1.1.2.1.cmml">^</mo></mover><mrow id="S3.SS2.p3.12.m9.2.2.2.4" xref="S3.SS2.p3.12.m9.2.2.2.3.cmml"><mi id="S3.SS2.p3.12.m9.1.1.1.1" xref="S3.SS2.p3.12.m9.1.1.1.1.cmml">l</mi><mo id="S3.SS2.p3.12.m9.2.2.2.4.1" xref="S3.SS2.p3.12.m9.2.2.2.3.cmml">,</mo><mn id="S3.SS2.p3.12.m9.2.2.2.2" xref="S3.SS2.p3.12.m9.2.2.2.2.cmml">1</mn></mrow></msub><mo id="S3.SS2.p3.12.m9.6.6.2.4" 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end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT italic_w × italic_h × 3 end_POSTSUPERSCRIPT</annotation></semantics></math>. The optical-flow module corresponds to <math alttext="T_{{\phi}}(\cdot)" class="ltx_Math" display="inline" id="S3.SS2.p3.15.2.2.m2.1"><semantics id="S3.SS2.p3.15.2.2.m2.1a"><mrow id="S3.SS2.p3.15.2.2.m2.1.2" xref="S3.SS2.p3.15.2.2.m2.1.2.cmml"><msub id="S3.SS2.p3.15.2.2.m2.1.2.2" xref="S3.SS2.p3.15.2.2.m2.1.2.2.cmml"><mi id="S3.SS2.p3.15.2.2.m2.1.2.2.2" xref="S3.SS2.p3.15.2.2.m2.1.2.2.2.cmml">T</mi><mi id="S3.SS2.p3.15.2.2.m2.1.2.2.3" xref="S3.SS2.p3.15.2.2.m2.1.2.2.3.cmml">ϕ</mi></msub><mo id="S3.SS2.p3.15.2.2.m2.1.2.1" xref="S3.SS2.p3.15.2.2.m2.1.2.1.cmml">⁢</mo><mrow id="S3.SS2.p3.15.2.2.m2.1.2.3.2" xref="S3.SS2.p3.15.2.2.m2.1.2.cmml"><mo id="S3.SS2.p3.15.2.2.m2.1.2.3.2.1" stretchy="false" xref="S3.SS2.p3.15.2.2.m2.1.2.cmml">(</mo><mo id="S3.SS2.p3.15.2.2.m2.1.1" lspace="0em" rspace="0em" xref="S3.SS2.p3.15.2.2.m2.1.1.cmml">⋅</mo><mo id="S3.SS2.p3.15.2.2.m2.1.2.3.2.2" stretchy="false" xref="S3.SS2.p3.15.2.2.m2.1.2.cmml">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="S3.SS2.p3.15.2.2.m2.1b"><apply id="S3.SS2.p3.15.2.2.m2.1.2.cmml" xref="S3.SS2.p3.15.2.2.m2.1.2"><times id="S3.SS2.p3.15.2.2.m2.1.2.1.cmml" xref="S3.SS2.p3.15.2.2.m2.1.2.1"></times><apply id="S3.SS2.p3.15.2.2.m2.1.2.2.cmml" xref="S3.SS2.p3.15.2.2.m2.1.2.2"><csymbol cd="ambiguous" id="S3.SS2.p3.15.2.2.m2.1.2.2.1.cmml" xref="S3.SS2.p3.15.2.2.m2.1.2.2">subscript</csymbol><ci id="S3.SS2.p3.15.2.2.m2.1.2.2.2.cmml" xref="S3.SS2.p3.15.2.2.m2.1.2.2.2">𝑇</ci><ci id="S3.SS2.p3.15.2.2.m2.1.2.2.3.cmml" xref="S3.SS2.p3.15.2.2.m2.1.2.2.3">italic-ϕ</ci></apply><ci id="S3.SS2.p3.15.2.2.m2.1.1.cmml" xref="S3.SS2.p3.15.2.2.m2.1.1">⋅</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS2.p3.15.2.2.m2.1c">T_{{\phi}}(\cdot)</annotation><annotation encoding="application/x-llamapun" id="S3.SS2.p3.15.2.2.m2.1d">italic_T start_POSTSUBSCRIPT italic_ϕ end_POSTSUBSCRIPT ( ⋅ )</annotation></semantics></math> in (<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S2.E9" title="In II-C The Semantic Decoder Network ‣ II System Model ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">9</span></a>), and the recovery modules are represented by operation <math alttext="T^{l}_{\chi}(\cdot)" class="ltx_Math" display="inline" id="S3.SS2.p3.16.3.3.m3.1"><semantics id="S3.SS2.p3.16.3.3.m3.1a"><mrow id="S3.SS2.p3.16.3.3.m3.1.2" xref="S3.SS2.p3.16.3.3.m3.1.2.cmml"><msubsup id="S3.SS2.p3.16.3.3.m3.1.2.2" xref="S3.SS2.p3.16.3.3.m3.1.2.2.cmml"><mi id="S3.SS2.p3.16.3.3.m3.1.2.2.2.2" xref="S3.SS2.p3.16.3.3.m3.1.2.2.2.2.cmml">T</mi><mi id="S3.SS2.p3.16.3.3.m3.1.2.2.3" xref="S3.SS2.p3.16.3.3.m3.1.2.2.3.cmml">χ</mi><mi id="S3.SS2.p3.16.3.3.m3.1.2.2.2.3" xref="S3.SS2.p3.16.3.3.m3.1.2.2.2.3.cmml">l</mi></msubsup><mo id="S3.SS2.p3.16.3.3.m3.1.2.1" xref="S3.SS2.p3.16.3.3.m3.1.2.1.cmml">⁢</mo><mrow id="S3.SS2.p3.16.3.3.m3.1.2.3.2" xref="S3.SS2.p3.16.3.3.m3.1.2.cmml"><mo id="S3.SS2.p3.16.3.3.m3.1.2.3.2.1" stretchy="false" xref="S3.SS2.p3.16.3.3.m3.1.2.cmml">(</mo><mo id="S3.SS2.p3.16.3.3.m3.1.1" lspace="0em" rspace="0em" xref="S3.SS2.p3.16.3.3.m3.1.1.cmml">⋅</mo><mo id="S3.SS2.p3.16.3.3.m3.1.2.3.2.2" stretchy="false" xref="S3.SS2.p3.16.3.3.m3.1.2.cmml">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="S3.SS2.p3.16.3.3.m3.1b"><apply id="S3.SS2.p3.16.3.3.m3.1.2.cmml" xref="S3.SS2.p3.16.3.3.m3.1.2"><times id="S3.SS2.p3.16.3.3.m3.1.2.1.cmml" xref="S3.SS2.p3.16.3.3.m3.1.2.1"></times><apply id="S3.SS2.p3.16.3.3.m3.1.2.2.cmml" xref="S3.SS2.p3.16.3.3.m3.1.2.2"><csymbol cd="ambiguous" id="S3.SS2.p3.16.3.3.m3.1.2.2.1.cmml" xref="S3.SS2.p3.16.3.3.m3.1.2.2">subscript</csymbol><apply id="S3.SS2.p3.16.3.3.m3.1.2.2.2.cmml" xref="S3.SS2.p3.16.3.3.m3.1.2.2"><csymbol cd="ambiguous" id="S3.SS2.p3.16.3.3.m3.1.2.2.2.1.cmml" xref="S3.SS2.p3.16.3.3.m3.1.2.2">superscript</csymbol><ci id="S3.SS2.p3.16.3.3.m3.1.2.2.2.2.cmml" xref="S3.SS2.p3.16.3.3.m3.1.2.2.2.2">𝑇</ci><ci id="S3.SS2.p3.16.3.3.m3.1.2.2.2.3.cmml" xref="S3.SS2.p3.16.3.3.m3.1.2.2.2.3">𝑙</ci></apply><ci id="S3.SS2.p3.16.3.3.m3.1.2.2.3.cmml" xref="S3.SS2.p3.16.3.3.m3.1.2.2.3">𝜒</ci></apply><ci id="S3.SS2.p3.16.3.3.m3.1.1.cmml" xref="S3.SS2.p3.16.3.3.m3.1.1">⋅</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS2.p3.16.3.3.m3.1c">T^{l}_{\chi}(\cdot)</annotation><annotation encoding="application/x-llamapun" id="S3.SS2.p3.16.3.3.m3.1d">italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_χ end_POSTSUBSCRIPT ( ⋅ )</annotation></semantics></math> and <math alttext="T^{r}_{\chi}(\cdot)" class="ltx_Math" display="inline" id="S3.SS2.p3.17.4.4.m4.1"><semantics id="S3.SS2.p3.17.4.4.m4.1a"><mrow id="S3.SS2.p3.17.4.4.m4.1.2" xref="S3.SS2.p3.17.4.4.m4.1.2.cmml"><msubsup id="S3.SS2.p3.17.4.4.m4.1.2.2" xref="S3.SS2.p3.17.4.4.m4.1.2.2.cmml"><mi id="S3.SS2.p3.17.4.4.m4.1.2.2.2.2" xref="S3.SS2.p3.17.4.4.m4.1.2.2.2.2.cmml">T</mi><mi id="S3.SS2.p3.17.4.4.m4.1.2.2.3" xref="S3.SS2.p3.17.4.4.m4.1.2.2.3.cmml">χ</mi><mi id="S3.SS2.p3.17.4.4.m4.1.2.2.2.3" xref="S3.SS2.p3.17.4.4.m4.1.2.2.2.3.cmml">r</mi></msubsup><mo id="S3.SS2.p3.17.4.4.m4.1.2.1" xref="S3.SS2.p3.17.4.4.m4.1.2.1.cmml">⁢</mo><mrow id="S3.SS2.p3.17.4.4.m4.1.2.3.2" xref="S3.SS2.p3.17.4.4.m4.1.2.cmml"><mo id="S3.SS2.p3.17.4.4.m4.1.2.3.2.1" stretchy="false" xref="S3.SS2.p3.17.4.4.m4.1.2.cmml">(</mo><mo id="S3.SS2.p3.17.4.4.m4.1.1" lspace="0em" rspace="0em" xref="S3.SS2.p3.17.4.4.m4.1.1.cmml">⋅</mo><mo id="S3.SS2.p3.17.4.4.m4.1.2.3.2.2" stretchy="false" xref="S3.SS2.p3.17.4.4.m4.1.2.cmml">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="S3.SS2.p3.17.4.4.m4.1b"><apply id="S3.SS2.p3.17.4.4.m4.1.2.cmml" xref="S3.SS2.p3.17.4.4.m4.1.2"><times id="S3.SS2.p3.17.4.4.m4.1.2.1.cmml" xref="S3.SS2.p3.17.4.4.m4.1.2.1"></times><apply id="S3.SS2.p3.17.4.4.m4.1.2.2.cmml" xref="S3.SS2.p3.17.4.4.m4.1.2.2"><csymbol cd="ambiguous" id="S3.SS2.p3.17.4.4.m4.1.2.2.1.cmml" xref="S3.SS2.p3.17.4.4.m4.1.2.2">subscript</csymbol><apply id="S3.SS2.p3.17.4.4.m4.1.2.2.2.cmml" xref="S3.SS2.p3.17.4.4.m4.1.2.2"><csymbol cd="ambiguous" id="S3.SS2.p3.17.4.4.m4.1.2.2.2.1.cmml" xref="S3.SS2.p3.17.4.4.m4.1.2.2">superscript</csymbol><ci id="S3.SS2.p3.17.4.4.m4.1.2.2.2.2.cmml" xref="S3.SS2.p3.17.4.4.m4.1.2.2.2.2">𝑇</ci><ci id="S3.SS2.p3.17.4.4.m4.1.2.2.2.3.cmml" xref="S3.SS2.p3.17.4.4.m4.1.2.2.2.3">𝑟</ci></apply><ci id="S3.SS2.p3.17.4.4.m4.1.2.2.3.cmml" xref="S3.SS2.p3.17.4.4.m4.1.2.2.3">𝜒</ci></apply><ci id="S3.SS2.p3.17.4.4.m4.1.1.cmml" xref="S3.SS2.p3.17.4.4.m4.1.1">⋅</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S3.SS2.p3.17.4.4.m4.1c">T^{r}_{\chi}(\cdot)</annotation><annotation encoding="application/x-llamapun" id="S3.SS2.p3.17.4.4.m4.1d">italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_χ end_POSTSUBSCRIPT ( ⋅ )</annotation></semantics></math> in (<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S2.E10" title="In II-C The Semantic Decoder Network ‣ II System Model ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">10</span></a>).</span></span></p> </div> </section> <section class="ltx_subsection" id="S3.SS3"> <h3 class="ltx_title ltx_title_subsection"> <span class="ltx_tag ltx_tag_subsection"><span class="ltx_text" id="S3.SS3.5.1.1">III-C</span> </span><span class="ltx_text ltx_font_italic" id="S3.SS3.6.2">Structure of The Fusion Network</span> </h3> <div class="ltx_para" id="S3.SS3.p1"> <p class="ltx_p" id="S3.SS3.p1.2">After the recovery network, the fusion networks combine <span class="ltx_text" id="S3.SS3.p1.2.2">the key area and the global semantic features<span class="ltx_text" id="S3.SS3.p1.2.2.2"> to generate stereo-vision images, as shown in Fig. <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S3.F8" title="Figure 8 ‣ III-C Structure of The Fusion Network ‣ III Transceiver Design for Proposed Semantic Communication System ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">8</span></a>. The residual network architecture of the fusion networks fuses <span class="ltx_text" id="S3.SS3.p1.2.2.2.2">semantic features<span class="ltx_text" id="S3.SS3.p1.2.2.2.2.2"> through multiple convolutional layers and adds features as residuals, obtaining the stereo-vision images. The recovered images are finally input into stereo RCNNs for 3D detection. 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start_POSTSUBSCRIPT italic_ν end_POSTSUBSCRIPT ( ⋅ )</annotation></semantics></math> in (<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S2.E11" title="In II-C The Semantic Decoder Network ‣ II System Model ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">11</span></a>).</span></span></span></span></p> </div> <figure class="ltx_figure" id="S3.F8"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="286" id="S3.F8.g1" src="x8.png" width="477"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 8: </span>Structure of the fusion network.</figcaption> </figure> </section> <section class="ltx_subsection" id="S3.SS4"> <h3 class="ltx_title ltx_title_subsection"> <span class="ltx_tag ltx_tag_subsection"><span class="ltx_text" id="S3.SS4.5.1.1">III-D</span> </span><span class="ltx_text ltx_font_italic" id="S3.SS4.6.2">Structure of The Channel Codec Network</span> </h3> <div class="ltx_para" id="S3.SS4.p1"> <p class="ltx_p" id="S3.SS4.p1.1">Multiple convolutional layers form both the channel encoder and the channel decoder, with an exemplary network structure given in Table <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#A1.T9" title="TABLE IX ‣ Appendix A The Parameters of The Proposed Network ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">IX</span></a> in Appendix A. The input layer dimension of the channel encoder is consistent with the compressed information dimension while the output layer dimension is adjustable to match the desired channel coding rate. Correspondingly, the channel decoder’s input and output layer dimensions are in correspondence to those of the channel encoder. Besides, the dimensions of the intermediate layers of the channel codec are determined by the design requirements.</p> </div> </section> </section> <section class="ltx_section" id="S4"> <h2 class="ltx_title ltx_title_section"> <span class="ltx_tag ltx_tag_section">IV </span><span class="ltx_text ltx_font_smallcaps" id="S4.1.1">Training Strategy</span> </h2> <div class="ltx_para" id="S4.p1"> <p class="ltx_p" id="S4.p1.1">We propose a five-step training method to train the whole network. The first four steps are used to train the semantic codec network and the last step trains the channel codec network along with the overall end-to-end fine-tuning.</p> </div> <div class="ltx_para" id="S4.p2"> <p class="ltx_p" id="S4.p2.4"><span class="ltx_text" id="S4.p2.4.1">Step 1 trains the global information network and the fusion network. The training images are sampled from the stereo-vision 3D object detection dataset and pass through the global information network and the fusion network sequentially. Since the key area information network is not trained yet, the recovered key area semantics input into the fusion network are temporarily replaced by all-zero tensors. Besides, a pre-trained SpyNet is used and frozen at the beginning of the training process to train the other part of the global information network. The parameter of the SpyNet is obtained from <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib35" title="">35</a>]</cite>. After several epochs of training, the parameter of the SpyNet is unfrozen, and the whole global information network is trained. 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italic_h italic_a italic_r end_POSTSUBSCRIPT ( bold_I , over^ start_ARG bold_I end_ARG ) = square-root start_ARG ∥ bold_I - over^ start_ARG bold_I end_ARG ∥ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT + italic_ϵ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(15)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S4.p2.3">where <math alttext="\bf{I}" class="ltx_Math" display="inline" id="S4.p2.1.m1.1"><semantics id="S4.p2.1.m1.1a"><mi id="S4.p2.1.m1.1.1" xref="S4.p2.1.m1.1.1.cmml">𝐈</mi><annotation-xml encoding="MathML-Content" id="S4.p2.1.m1.1b"><ci id="S4.p2.1.m1.1.1.cmml" xref="S4.p2.1.m1.1.1">𝐈</ci></annotation-xml><annotation encoding="application/x-tex" id="S4.p2.1.m1.1c">\bf{I}</annotation><annotation encoding="application/x-llamapun" id="S4.p2.1.m1.1d">bold_I</annotation></semantics></math> and <math alttext="\bf{\hat{I}}" class="ltx_Math" display="inline" id="S4.p2.2.m2.1"><semantics id="S4.p2.2.m2.1a"><mover accent="true" id="S4.p2.2.m2.1.1" xref="S4.p2.2.m2.1.1.cmml"><mi id="S4.p2.2.m2.1.1.2" xref="S4.p2.2.m2.1.1.2.cmml">𝐈</mi><mo id="S4.p2.2.m2.1.1.1" xref="S4.p2.2.m2.1.1.1.cmml">^</mo></mover><annotation-xml encoding="MathML-Content" id="S4.p2.2.m2.1b"><apply id="S4.p2.2.m2.1.1.cmml" xref="S4.p2.2.m2.1.1"><ci id="S4.p2.2.m2.1.1.1.cmml" xref="S4.p2.2.m2.1.1.1">^</ci><ci id="S4.p2.2.m2.1.1.2.cmml" xref="S4.p2.2.m2.1.1.2">𝐈</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S4.p2.2.m2.1c">\bf{\hat{I}}</annotation><annotation encoding="application/x-llamapun" id="S4.p2.2.m2.1d">over^ start_ARG bold_I end_ARG</annotation></semantics></math> represent the input stereo-vision images and the output recovered images, respectively, and <math alttext="\epsilon^{2}" class="ltx_Math" display="inline" id="S4.p2.3.m3.1"><semantics id="S4.p2.3.m3.1a"><msup id="S4.p2.3.m3.1.1" xref="S4.p2.3.m3.1.1.cmml"><mi id="S4.p2.3.m3.1.1.2" xref="S4.p2.3.m3.1.1.2.cmml">ϵ</mi><mn id="S4.p2.3.m3.1.1.3" xref="S4.p2.3.m3.1.1.3.cmml">2</mn></msup><annotation-xml encoding="MathML-Content" id="S4.p2.3.m3.1b"><apply id="S4.p2.3.m3.1.1.cmml" xref="S4.p2.3.m3.1.1"><csymbol cd="ambiguous" id="S4.p2.3.m3.1.1.1.cmml" xref="S4.p2.3.m3.1.1">superscript</csymbol><ci id="S4.p2.3.m3.1.1.2.cmml" xref="S4.p2.3.m3.1.1.2">italic-ϵ</ci><cn id="S4.p2.3.m3.1.1.3.cmml" type="integer" xref="S4.p2.3.m3.1.1.3">2</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="S4.p2.3.m3.1c">\epsilon^{2}</annotation><annotation encoding="application/x-llamapun" id="S4.p2.3.m3.1d">italic_ϵ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT</annotation></semantics></math> is a constant. The pseudocode of the Step 1 is provided in Algorithm <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#alg1" title="Algorithm 1 ‣ IV Training Strategy ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">1</span></a>.<span class="ltx_text" id="S4.p2.3.1"></span></p> </div> <figure class="ltx_float ltx_float_algorithm ltx_framed ltx_framed_top" id="alg1"> <figcaption class="ltx_caption"><span class="ltx_tag ltx_tag_float"><span class="ltx_text ltx_font_bold" id="alg1.2.1.1">Algorithm 1</span> </span> Training the global information network</figcaption> <div class="ltx_listing ltx_listing" id="alg1.3"> <div class="ltx_listingline" id="alg1.l1"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l1.1.1.1" style="font-size:80%;">1:</span></span> <span class="ltx_text ltx_font_bold" id="alg1.l1.2">Input:</span> The 3D vehicle detection dataset <math alttext="\mathcal{K}_{1}" class="ltx_Math" display="inline" id="alg1.l1.m1.1"><semantics id="alg1.l1.m1.1a"><msub id="alg1.l1.m1.1.1" xref="alg1.l1.m1.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="alg1.l1.m1.1.1.2" xref="alg1.l1.m1.1.1.2.cmml">𝒦</mi><mn id="alg1.l1.m1.1.1.3" xref="alg1.l1.m1.1.1.3.cmml">1</mn></msub><annotation-xml encoding="MathML-Content" id="alg1.l1.m1.1b"><apply id="alg1.l1.m1.1.1.cmml" xref="alg1.l1.m1.1.1"><csymbol cd="ambiguous" id="alg1.l1.m1.1.1.1.cmml" xref="alg1.l1.m1.1.1">subscript</csymbol><ci id="alg1.l1.m1.1.1.2.cmml" xref="alg1.l1.m1.1.1.2">𝒦</ci><cn id="alg1.l1.m1.1.1.3.cmml" type="integer" xref="alg1.l1.m1.1.1.3">1</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l1.m1.1c">\mathcal{K}_{1}</annotation><annotation encoding="application/x-llamapun" id="alg1.l1.m1.1d">caligraphic_K start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT</annotation></semantics></math>. </div> <div class="ltx_listingline" id="alg1.l2"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l2.1.1.1" style="font-size:80%;">2:</span></span> <span class="ltx_text ltx_font_bold" id="alg1.l2.2">Initialize parameters:</span> <math alttext="\gamma" class="ltx_Math" display="inline" id="alg1.l2.m1.1"><semantics id="alg1.l2.m1.1a"><mi id="alg1.l2.m1.1.1" xref="alg1.l2.m1.1.1.cmml">γ</mi><annotation-xml encoding="MathML-Content" id="alg1.l2.m1.1b"><ci id="alg1.l2.m1.1.1.cmml" xref="alg1.l2.m1.1.1">𝛾</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l2.m1.1c">\gamma</annotation><annotation encoding="application/x-llamapun" id="alg1.l2.m1.1d">italic_γ</annotation></semantics></math>, <math alttext="\varphi" class="ltx_Math" display="inline" id="alg1.l2.m2.1"><semantics id="alg1.l2.m2.1a"><mi id="alg1.l2.m2.1.1" xref="alg1.l2.m2.1.1.cmml">φ</mi><annotation-xml encoding="MathML-Content" id="alg1.l2.m2.1b"><ci id="alg1.l2.m2.1.1.cmml" xref="alg1.l2.m2.1.1">𝜑</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l2.m2.1c">\varphi</annotation><annotation encoding="application/x-llamapun" id="alg1.l2.m2.1d">italic_φ</annotation></semantics></math>, <math alttext="\phi" class="ltx_Math" display="inline" id="alg1.l2.m3.1"><semantics id="alg1.l2.m3.1a"><mi id="alg1.l2.m3.1.1" xref="alg1.l2.m3.1.1.cmml">ϕ</mi><annotation-xml encoding="MathML-Content" id="alg1.l2.m3.1b"><ci id="alg1.l2.m3.1.1.cmml" xref="alg1.l2.m3.1.1">italic-ϕ</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l2.m3.1c">\phi</annotation><annotation encoding="application/x-llamapun" id="alg1.l2.m3.1d">italic_ϕ</annotation></semantics></math>, <math alttext="\chi" class="ltx_Math" display="inline" id="alg1.l2.m4.1"><semantics id="alg1.l2.m4.1a"><mi id="alg1.l2.m4.1.1" xref="alg1.l2.m4.1.1.cmml">χ</mi><annotation-xml encoding="MathML-Content" id="alg1.l2.m4.1b"><ci id="alg1.l2.m4.1.1.cmml" xref="alg1.l2.m4.1.1">𝜒</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l2.m4.1c">\chi</annotation><annotation encoding="application/x-llamapun" id="alg1.l2.m4.1d">italic_χ</annotation></semantics></math>, <math alttext="{\nu}" class="ltx_Math" display="inline" id="alg1.l2.m5.1"><semantics id="alg1.l2.m5.1a"><mi id="alg1.l2.m5.1.1" xref="alg1.l2.m5.1.1.cmml">ν</mi><annotation-xml encoding="MathML-Content" id="alg1.l2.m5.1b"><ci id="alg1.l2.m5.1.1.cmml" xref="alg1.l2.m5.1.1">𝜈</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l2.m5.1c">{\nu}</annotation><annotation encoding="application/x-llamapun" id="alg1.l2.m5.1d">italic_ν</annotation></semantics></math>. </div> <div class="ltx_listingline" id="alg1.l3"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l3.1.1.1" style="font-size:80%;">3:</span></span> Load and freeze the pre-trained SpyNet. </div> <div class="ltx_listingline" id="alg1.l4"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l4.1.1.1" style="font-size:80%;">4:</span></span> <span class="ltx_text ltx_font_bold" id="alg1.l4.2">repeat</span> </div> <div class="ltx_listingline" id="alg1.l5"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l5.1.1.1" style="font-size:80%;">5:</span></span> Sample from dataset <math alttext="\mathcal{K}_{1}" class="ltx_Math" display="inline" id="alg1.l5.m1.1"><semantics id="alg1.l5.m1.1a"><msub id="alg1.l5.m1.1.1" xref="alg1.l5.m1.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="alg1.l5.m1.1.1.2" xref="alg1.l5.m1.1.1.2.cmml">𝒦</mi><mn id="alg1.l5.m1.1.1.3" xref="alg1.l5.m1.1.1.3.cmml">1</mn></msub><annotation-xml encoding="MathML-Content" id="alg1.l5.m1.1b"><apply id="alg1.l5.m1.1.1.cmml" xref="alg1.l5.m1.1.1"><csymbol cd="ambiguous" id="alg1.l5.m1.1.1.1.cmml" xref="alg1.l5.m1.1.1">subscript</csymbol><ci id="alg1.l5.m1.1.1.2.cmml" xref="alg1.l5.m1.1.1.2">𝒦</ci><cn id="alg1.l5.m1.1.1.3.cmml" type="integer" xref="alg1.l5.m1.1.1.3">1</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l5.m1.1c">\mathcal{K}_{1}</annotation><annotation encoding="application/x-llamapun" id="alg1.l5.m1.1d">caligraphic_K start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT</annotation></semantics></math>, obtaining the stereo-vision images <math alttext="\mathbf{I}\coloneqq\left[I_{l},I_{r}\right]" class="ltx_Math" display="inline" id="alg1.l5.m2.2"><semantics id="alg1.l5.m2.2a"><mrow id="alg1.l5.m2.2.2" xref="alg1.l5.m2.2.2.cmml"><mi id="alg1.l5.m2.2.2.4" xref="alg1.l5.m2.2.2.4.cmml">𝐈</mi><mo id="alg1.l5.m2.2.2.3" xref="alg1.l5.m2.2.2.3.cmml">≔</mo><mrow id="alg1.l5.m2.2.2.2.2" xref="alg1.l5.m2.2.2.2.3.cmml"><mo id="alg1.l5.m2.2.2.2.2.3" xref="alg1.l5.m2.2.2.2.3.cmml">[</mo><msub id="alg1.l5.m2.1.1.1.1.1" xref="alg1.l5.m2.1.1.1.1.1.cmml"><mi id="alg1.l5.m2.1.1.1.1.1.2" xref="alg1.l5.m2.1.1.1.1.1.2.cmml">I</mi><mi id="alg1.l5.m2.1.1.1.1.1.3" xref="alg1.l5.m2.1.1.1.1.1.3.cmml">l</mi></msub><mo id="alg1.l5.m2.2.2.2.2.4" xref="alg1.l5.m2.2.2.2.3.cmml">,</mo><msub id="alg1.l5.m2.2.2.2.2.2" xref="alg1.l5.m2.2.2.2.2.2.cmml"><mi id="alg1.l5.m2.2.2.2.2.2.2" xref="alg1.l5.m2.2.2.2.2.2.2.cmml">I</mi><mi id="alg1.l5.m2.2.2.2.2.2.3" xref="alg1.l5.m2.2.2.2.2.2.3.cmml">r</mi></msub><mo id="alg1.l5.m2.2.2.2.2.5" xref="alg1.l5.m2.2.2.2.3.cmml">]</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="alg1.l5.m2.2b"><apply id="alg1.l5.m2.2.2.cmml" xref="alg1.l5.m2.2.2"><ci id="alg1.l5.m2.2.2.3.cmml" xref="alg1.l5.m2.2.2.3">≔</ci><ci id="alg1.l5.m2.2.2.4.cmml" xref="alg1.l5.m2.2.2.4">𝐈</ci><interval closure="closed" id="alg1.l5.m2.2.2.2.3.cmml" xref="alg1.l5.m2.2.2.2.2"><apply id="alg1.l5.m2.1.1.1.1.1.cmml" xref="alg1.l5.m2.1.1.1.1.1"><csymbol cd="ambiguous" id="alg1.l5.m2.1.1.1.1.1.1.cmml" xref="alg1.l5.m2.1.1.1.1.1">subscript</csymbol><ci id="alg1.l5.m2.1.1.1.1.1.2.cmml" xref="alg1.l5.m2.1.1.1.1.1.2">𝐼</ci><ci id="alg1.l5.m2.1.1.1.1.1.3.cmml" xref="alg1.l5.m2.1.1.1.1.1.3">𝑙</ci></apply><apply id="alg1.l5.m2.2.2.2.2.2.cmml" xref="alg1.l5.m2.2.2.2.2.2"><csymbol cd="ambiguous" id="alg1.l5.m2.2.2.2.2.2.1.cmml" xref="alg1.l5.m2.2.2.2.2.2">subscript</csymbol><ci id="alg1.l5.m2.2.2.2.2.2.2.cmml" xref="alg1.l5.m2.2.2.2.2.2.2">𝐼</ci><ci id="alg1.l5.m2.2.2.2.2.2.3.cmml" xref="alg1.l5.m2.2.2.2.2.2.3">𝑟</ci></apply></interval></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l5.m2.2c">\mathbf{I}\coloneqq\left[I_{l},I_{r}\right]</annotation><annotation encoding="application/x-llamapun" id="alg1.l5.m2.2d">bold_I ≔ [ italic_I start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , italic_I start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ]</annotation></semantics></math> </div> <div class="ltx_listingline" id="alg1.l6"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l6.1.1.1" style="font-size:80%;">6:</span></span> Extract the semantic features: <math alttext="\left[F_{l},F_{r}\right]=T_{\gamma}\left(I_{l},I_{r}\right)" class="ltx_Math" display="inline" id="alg1.l6.m1.4"><semantics id="alg1.l6.m1.4a"><mrow id="alg1.l6.m1.4.4" xref="alg1.l6.m1.4.4.cmml"><mrow id="alg1.l6.m1.2.2.2.2" xref="alg1.l6.m1.2.2.2.3.cmml"><mo id="alg1.l6.m1.2.2.2.2.3" xref="alg1.l6.m1.2.2.2.3.cmml">[</mo><msub id="alg1.l6.m1.1.1.1.1.1" xref="alg1.l6.m1.1.1.1.1.1.cmml"><mi id="alg1.l6.m1.1.1.1.1.1.2" xref="alg1.l6.m1.1.1.1.1.1.2.cmml">F</mi><mi id="alg1.l6.m1.1.1.1.1.1.3" xref="alg1.l6.m1.1.1.1.1.1.3.cmml">l</mi></msub><mo id="alg1.l6.m1.2.2.2.2.4" xref="alg1.l6.m1.2.2.2.3.cmml">,</mo><msub id="alg1.l6.m1.2.2.2.2.2" xref="alg1.l6.m1.2.2.2.2.2.cmml"><mi id="alg1.l6.m1.2.2.2.2.2.2" xref="alg1.l6.m1.2.2.2.2.2.2.cmml">F</mi><mi id="alg1.l6.m1.2.2.2.2.2.3" xref="alg1.l6.m1.2.2.2.2.2.3.cmml">r</mi></msub><mo id="alg1.l6.m1.2.2.2.2.5" xref="alg1.l6.m1.2.2.2.3.cmml">]</mo></mrow><mo id="alg1.l6.m1.4.4.5" xref="alg1.l6.m1.4.4.5.cmml">=</mo><mrow id="alg1.l6.m1.4.4.4" xref="alg1.l6.m1.4.4.4.cmml"><msub id="alg1.l6.m1.4.4.4.4" xref="alg1.l6.m1.4.4.4.4.cmml"><mi id="alg1.l6.m1.4.4.4.4.2" xref="alg1.l6.m1.4.4.4.4.2.cmml">T</mi><mi id="alg1.l6.m1.4.4.4.4.3" xref="alg1.l6.m1.4.4.4.4.3.cmml">γ</mi></msub><mo id="alg1.l6.m1.4.4.4.3" xref="alg1.l6.m1.4.4.4.3.cmml">⁢</mo><mrow id="alg1.l6.m1.4.4.4.2.2" xref="alg1.l6.m1.4.4.4.2.3.cmml"><mo id="alg1.l6.m1.4.4.4.2.2.3" xref="alg1.l6.m1.4.4.4.2.3.cmml">(</mo><msub id="alg1.l6.m1.3.3.3.1.1.1" xref="alg1.l6.m1.3.3.3.1.1.1.cmml"><mi id="alg1.l6.m1.3.3.3.1.1.1.2" xref="alg1.l6.m1.3.3.3.1.1.1.2.cmml">I</mi><mi id="alg1.l6.m1.3.3.3.1.1.1.3" xref="alg1.l6.m1.3.3.3.1.1.1.3.cmml">l</mi></msub><mo id="alg1.l6.m1.4.4.4.2.2.4" xref="alg1.l6.m1.4.4.4.2.3.cmml">,</mo><msub id="alg1.l6.m1.4.4.4.2.2.2" xref="alg1.l6.m1.4.4.4.2.2.2.cmml"><mi id="alg1.l6.m1.4.4.4.2.2.2.2" xref="alg1.l6.m1.4.4.4.2.2.2.2.cmml">I</mi><mi id="alg1.l6.m1.4.4.4.2.2.2.3" xref="alg1.l6.m1.4.4.4.2.2.2.3.cmml">r</mi></msub><mo id="alg1.l6.m1.4.4.4.2.2.5" xref="alg1.l6.m1.4.4.4.2.3.cmml">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="alg1.l6.m1.4b"><apply id="alg1.l6.m1.4.4.cmml" xref="alg1.l6.m1.4.4"><eq id="alg1.l6.m1.4.4.5.cmml" xref="alg1.l6.m1.4.4.5"></eq><interval closure="closed" id="alg1.l6.m1.2.2.2.3.cmml" xref="alg1.l6.m1.2.2.2.2"><apply id="alg1.l6.m1.1.1.1.1.1.cmml" xref="alg1.l6.m1.1.1.1.1.1"><csymbol cd="ambiguous" id="alg1.l6.m1.1.1.1.1.1.1.cmml" xref="alg1.l6.m1.1.1.1.1.1">subscript</csymbol><ci id="alg1.l6.m1.1.1.1.1.1.2.cmml" xref="alg1.l6.m1.1.1.1.1.1.2">𝐹</ci><ci id="alg1.l6.m1.1.1.1.1.1.3.cmml" xref="alg1.l6.m1.1.1.1.1.1.3">𝑙</ci></apply><apply id="alg1.l6.m1.2.2.2.2.2.cmml" xref="alg1.l6.m1.2.2.2.2.2"><csymbol cd="ambiguous" id="alg1.l6.m1.2.2.2.2.2.1.cmml" xref="alg1.l6.m1.2.2.2.2.2">subscript</csymbol><ci id="alg1.l6.m1.2.2.2.2.2.2.cmml" xref="alg1.l6.m1.2.2.2.2.2.2">𝐹</ci><ci id="alg1.l6.m1.2.2.2.2.2.3.cmml" xref="alg1.l6.m1.2.2.2.2.2.3">𝑟</ci></apply></interval><apply id="alg1.l6.m1.4.4.4.cmml" xref="alg1.l6.m1.4.4.4"><times id="alg1.l6.m1.4.4.4.3.cmml" xref="alg1.l6.m1.4.4.4.3"></times><apply id="alg1.l6.m1.4.4.4.4.cmml" xref="alg1.l6.m1.4.4.4.4"><csymbol cd="ambiguous" id="alg1.l6.m1.4.4.4.4.1.cmml" xref="alg1.l6.m1.4.4.4.4">subscript</csymbol><ci id="alg1.l6.m1.4.4.4.4.2.cmml" xref="alg1.l6.m1.4.4.4.4.2">𝑇</ci><ci id="alg1.l6.m1.4.4.4.4.3.cmml" xref="alg1.l6.m1.4.4.4.4.3">𝛾</ci></apply><interval closure="open" id="alg1.l6.m1.4.4.4.2.3.cmml" xref="alg1.l6.m1.4.4.4.2.2"><apply id="alg1.l6.m1.3.3.3.1.1.1.cmml" xref="alg1.l6.m1.3.3.3.1.1.1"><csymbol cd="ambiguous" id="alg1.l6.m1.3.3.3.1.1.1.1.cmml" xref="alg1.l6.m1.3.3.3.1.1.1">subscript</csymbol><ci id="alg1.l6.m1.3.3.3.1.1.1.2.cmml" xref="alg1.l6.m1.3.3.3.1.1.1.2">𝐼</ci><ci id="alg1.l6.m1.3.3.3.1.1.1.3.cmml" xref="alg1.l6.m1.3.3.3.1.1.1.3">𝑙</ci></apply><apply id="alg1.l6.m1.4.4.4.2.2.2.cmml" xref="alg1.l6.m1.4.4.4.2.2.2"><csymbol cd="ambiguous" id="alg1.l6.m1.4.4.4.2.2.2.1.cmml" xref="alg1.l6.m1.4.4.4.2.2.2">subscript</csymbol><ci id="alg1.l6.m1.4.4.4.2.2.2.2.cmml" xref="alg1.l6.m1.4.4.4.2.2.2.2">𝐼</ci><ci id="alg1.l6.m1.4.4.4.2.2.2.3.cmml" xref="alg1.l6.m1.4.4.4.2.2.2.3">𝑟</ci></apply></interval></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l6.m1.4c">\left[F_{l},F_{r}\right]=T_{\gamma}\left(I_{l},I_{r}\right)</annotation><annotation encoding="application/x-llamapun" id="alg1.l6.m1.4d">[ italic_F start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , italic_F start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ] = italic_T start_POSTSUBSCRIPT italic_γ end_POSTSUBSCRIPT ( italic_I start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , italic_I start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT )</annotation></semantics></math> </div> <div class="ltx_listingline" id="alg1.l7"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l7.1.1.1" style="font-size:80%;">7:</span></span> Compress the semantic features: <math alttext="G_{l}=T^{l}_{\varphi}\left(F_{l}\right),G_{r}=T^{r}_{\varphi}\left(F_{r}\right)" class="ltx_Math" display="inline" id="alg1.l7.m1.2"><semantics id="alg1.l7.m1.2a"><mrow id="alg1.l7.m1.2.2.2" xref="alg1.l7.m1.2.2.3.cmml"><mrow id="alg1.l7.m1.1.1.1.1" xref="alg1.l7.m1.1.1.1.1.cmml"><msub id="alg1.l7.m1.1.1.1.1.3" xref="alg1.l7.m1.1.1.1.1.3.cmml"><mi id="alg1.l7.m1.1.1.1.1.3.2" xref="alg1.l7.m1.1.1.1.1.3.2.cmml">G</mi><mi id="alg1.l7.m1.1.1.1.1.3.3" xref="alg1.l7.m1.1.1.1.1.3.3.cmml">l</mi></msub><mo id="alg1.l7.m1.1.1.1.1.2" xref="alg1.l7.m1.1.1.1.1.2.cmml">=</mo><mrow id="alg1.l7.m1.1.1.1.1.1" xref="alg1.l7.m1.1.1.1.1.1.cmml"><msubsup id="alg1.l7.m1.1.1.1.1.1.3" xref="alg1.l7.m1.1.1.1.1.1.3.cmml"><mi id="alg1.l7.m1.1.1.1.1.1.3.2.2" xref="alg1.l7.m1.1.1.1.1.1.3.2.2.cmml">T</mi><mi id="alg1.l7.m1.1.1.1.1.1.3.3" xref="alg1.l7.m1.1.1.1.1.1.3.3.cmml">φ</mi><mi id="alg1.l7.m1.1.1.1.1.1.3.2.3" xref="alg1.l7.m1.1.1.1.1.1.3.2.3.cmml">l</mi></msubsup><mo id="alg1.l7.m1.1.1.1.1.1.2" xref="alg1.l7.m1.1.1.1.1.1.2.cmml">⁢</mo><mrow id="alg1.l7.m1.1.1.1.1.1.1.1" xref="alg1.l7.m1.1.1.1.1.1.1.1.1.cmml"><mo id="alg1.l7.m1.1.1.1.1.1.1.1.2" xref="alg1.l7.m1.1.1.1.1.1.1.1.1.cmml">(</mo><msub id="alg1.l7.m1.1.1.1.1.1.1.1.1" xref="alg1.l7.m1.1.1.1.1.1.1.1.1.cmml"><mi id="alg1.l7.m1.1.1.1.1.1.1.1.1.2" xref="alg1.l7.m1.1.1.1.1.1.1.1.1.2.cmml">F</mi><mi id="alg1.l7.m1.1.1.1.1.1.1.1.1.3" xref="alg1.l7.m1.1.1.1.1.1.1.1.1.3.cmml">l</mi></msub><mo id="alg1.l7.m1.1.1.1.1.1.1.1.3" xref="alg1.l7.m1.1.1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow><mo id="alg1.l7.m1.2.2.2.3" xref="alg1.l7.m1.2.2.3a.cmml">,</mo><mrow id="alg1.l7.m1.2.2.2.2" xref="alg1.l7.m1.2.2.2.2.cmml"><msub id="alg1.l7.m1.2.2.2.2.3" xref="alg1.l7.m1.2.2.2.2.3.cmml"><mi id="alg1.l7.m1.2.2.2.2.3.2" xref="alg1.l7.m1.2.2.2.2.3.2.cmml">G</mi><mi id="alg1.l7.m1.2.2.2.2.3.3" xref="alg1.l7.m1.2.2.2.2.3.3.cmml">r</mi></msub><mo id="alg1.l7.m1.2.2.2.2.2" xref="alg1.l7.m1.2.2.2.2.2.cmml">=</mo><mrow id="alg1.l7.m1.2.2.2.2.1" xref="alg1.l7.m1.2.2.2.2.1.cmml"><msubsup id="alg1.l7.m1.2.2.2.2.1.3" xref="alg1.l7.m1.2.2.2.2.1.3.cmml"><mi id="alg1.l7.m1.2.2.2.2.1.3.2.2" xref="alg1.l7.m1.2.2.2.2.1.3.2.2.cmml">T</mi><mi id="alg1.l7.m1.2.2.2.2.1.3.3" xref="alg1.l7.m1.2.2.2.2.1.3.3.cmml">φ</mi><mi id="alg1.l7.m1.2.2.2.2.1.3.2.3" xref="alg1.l7.m1.2.2.2.2.1.3.2.3.cmml">r</mi></msubsup><mo id="alg1.l7.m1.2.2.2.2.1.2" xref="alg1.l7.m1.2.2.2.2.1.2.cmml">⁢</mo><mrow id="alg1.l7.m1.2.2.2.2.1.1.1" xref="alg1.l7.m1.2.2.2.2.1.1.1.1.cmml"><mo id="alg1.l7.m1.2.2.2.2.1.1.1.2" xref="alg1.l7.m1.2.2.2.2.1.1.1.1.cmml">(</mo><msub id="alg1.l7.m1.2.2.2.2.1.1.1.1" xref="alg1.l7.m1.2.2.2.2.1.1.1.1.cmml"><mi id="alg1.l7.m1.2.2.2.2.1.1.1.1.2" xref="alg1.l7.m1.2.2.2.2.1.1.1.1.2.cmml">F</mi><mi id="alg1.l7.m1.2.2.2.2.1.1.1.1.3" xref="alg1.l7.m1.2.2.2.2.1.1.1.1.3.cmml">r</mi></msub><mo id="alg1.l7.m1.2.2.2.2.1.1.1.3" xref="alg1.l7.m1.2.2.2.2.1.1.1.1.cmml">)</mo></mrow></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="alg1.l7.m1.2b"><apply id="alg1.l7.m1.2.2.3.cmml" xref="alg1.l7.m1.2.2.2"><csymbol cd="ambiguous" id="alg1.l7.m1.2.2.3a.cmml" xref="alg1.l7.m1.2.2.2.3">formulae-sequence</csymbol><apply id="alg1.l7.m1.1.1.1.1.cmml" xref="alg1.l7.m1.1.1.1.1"><eq id="alg1.l7.m1.1.1.1.1.2.cmml" xref="alg1.l7.m1.1.1.1.1.2"></eq><apply id="alg1.l7.m1.1.1.1.1.3.cmml" xref="alg1.l7.m1.1.1.1.1.3"><csymbol cd="ambiguous" id="alg1.l7.m1.1.1.1.1.3.1.cmml" xref="alg1.l7.m1.1.1.1.1.3">subscript</csymbol><ci id="alg1.l7.m1.1.1.1.1.3.2.cmml" xref="alg1.l7.m1.1.1.1.1.3.2">𝐺</ci><ci id="alg1.l7.m1.1.1.1.1.3.3.cmml" xref="alg1.l7.m1.1.1.1.1.3.3">𝑙</ci></apply><apply id="alg1.l7.m1.1.1.1.1.1.cmml" xref="alg1.l7.m1.1.1.1.1.1"><times id="alg1.l7.m1.1.1.1.1.1.2.cmml" xref="alg1.l7.m1.1.1.1.1.1.2"></times><apply id="alg1.l7.m1.1.1.1.1.1.3.cmml" xref="alg1.l7.m1.1.1.1.1.1.3"><csymbol cd="ambiguous" id="alg1.l7.m1.1.1.1.1.1.3.1.cmml" xref="alg1.l7.m1.1.1.1.1.1.3">subscript</csymbol><apply id="alg1.l7.m1.1.1.1.1.1.3.2.cmml" 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id="alg1.l7.m1.2.2.2.2.3.1.cmml" xref="alg1.l7.m1.2.2.2.2.3">subscript</csymbol><ci id="alg1.l7.m1.2.2.2.2.3.2.cmml" xref="alg1.l7.m1.2.2.2.2.3.2">𝐺</ci><ci id="alg1.l7.m1.2.2.2.2.3.3.cmml" xref="alg1.l7.m1.2.2.2.2.3.3">𝑟</ci></apply><apply id="alg1.l7.m1.2.2.2.2.1.cmml" xref="alg1.l7.m1.2.2.2.2.1"><times id="alg1.l7.m1.2.2.2.2.1.2.cmml" xref="alg1.l7.m1.2.2.2.2.1.2"></times><apply id="alg1.l7.m1.2.2.2.2.1.3.cmml" xref="alg1.l7.m1.2.2.2.2.1.3"><csymbol cd="ambiguous" id="alg1.l7.m1.2.2.2.2.1.3.1.cmml" xref="alg1.l7.m1.2.2.2.2.1.3">subscript</csymbol><apply id="alg1.l7.m1.2.2.2.2.1.3.2.cmml" xref="alg1.l7.m1.2.2.2.2.1.3"><csymbol cd="ambiguous" id="alg1.l7.m1.2.2.2.2.1.3.2.1.cmml" xref="alg1.l7.m1.2.2.2.2.1.3">superscript</csymbol><ci id="alg1.l7.m1.2.2.2.2.1.3.2.2.cmml" xref="alg1.l7.m1.2.2.2.2.1.3.2.2">𝑇</ci><ci id="alg1.l7.m1.2.2.2.2.1.3.2.3.cmml" xref="alg1.l7.m1.2.2.2.2.1.3.2.3">𝑟</ci></apply><ci id="alg1.l7.m1.2.2.2.2.1.3.3.cmml" xref="alg1.l7.m1.2.2.2.2.1.3.3">𝜑</ci></apply><apply id="alg1.l7.m1.2.2.2.2.1.1.1.1.cmml" xref="alg1.l7.m1.2.2.2.2.1.1.1"><csymbol cd="ambiguous" id="alg1.l7.m1.2.2.2.2.1.1.1.1.1.cmml" xref="alg1.l7.m1.2.2.2.2.1.1.1">subscript</csymbol><ci id="alg1.l7.m1.2.2.2.2.1.1.1.1.2.cmml" xref="alg1.l7.m1.2.2.2.2.1.1.1.1.2">𝐹</ci><ci id="alg1.l7.m1.2.2.2.2.1.1.1.1.3.cmml" xref="alg1.l7.m1.2.2.2.2.1.1.1.1.3">𝑟</ci></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l7.m1.2c">G_{l}=T^{l}_{\varphi}\left(F_{l}\right),G_{r}=T^{r}_{\varphi}\left(F_{r}\right)</annotation><annotation encoding="application/x-llamapun" id="alg1.l7.m1.2d">italic_G start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_φ end_POSTSUBSCRIPT ( italic_F start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT ) , italic_G start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_φ end_POSTSUBSCRIPT ( italic_F start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT )</annotation></semantics></math> </div> <div class="ltx_listingline" id="alg1.l8"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l8.1.1.1" style="font-size:80%;">8:</span></span> Extract the optical flow: <math alttext="\left[{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle\rightarrow$}}% \over{\mathcal{O}}}},{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle% \leftarrow$}}\over{\mathcal{O}}}}\right]=T_{\phi}\left(\hat{G}_{l},\hat{G}_{r}\right)" class="ltx_Math" display="inline" id="alg1.l8.m1.4"><semantics id="alg1.l8.m1.4a"><mrow id="alg1.l8.m1.4.4" xref="alg1.l8.m1.4.4.cmml"><mrow id="alg1.l8.m1.4.4.4.2" xref="alg1.l8.m1.4.4.4.1.cmml"><mo id="alg1.l8.m1.4.4.4.2.1" xref="alg1.l8.m1.4.4.4.1.cmml">[</mo><mover id="alg1.l8.m1.1.1.1" xref="alg1.l8.m1.1.1.1a.cmml"><mi class="ltx_font_mathcaligraphic" id="alg1.l8.m1.1.1.1.3" xref="alg1.l8.m1.1.1.1.3.cmml">𝒪</mi><mpadded id="alg1.l8.m1.1.1.1.1" voffset="-3.0pt" xref="alg1.l8.m1.1.1.1.1.cmml"><mo id="alg1.l8.m1.1.1.1.1a" mathsize="71%" stretchy="false" xref="alg1.l8.m1.1.1.1.1.cmml">→</mo></mpadded></mover><mo id="alg1.l8.m1.4.4.4.2.2" xref="alg1.l8.m1.4.4.4.1.cmml">,</mo><mover id="alg1.l8.m1.2.2.1" xref="alg1.l8.m1.2.2.1a.cmml"><mi class="ltx_font_mathcaligraphic" id="alg1.l8.m1.2.2.1.3" xref="alg1.l8.m1.2.2.1.3.cmml">𝒪</mi><mpadded id="alg1.l8.m1.2.2.1.1" voffset="-3.0pt" xref="alg1.l8.m1.2.2.1.1.cmml"><mo id="alg1.l8.m1.2.2.1.1a" mathsize="71%" stretchy="false" xref="alg1.l8.m1.2.2.1.1.cmml">←</mo></mpadded></mover><mo id="alg1.l8.m1.4.4.4.2.3" xref="alg1.l8.m1.4.4.4.1.cmml">]</mo></mrow><mo id="alg1.l8.m1.4.4.3" xref="alg1.l8.m1.4.4.3.cmml">=</mo><mrow id="alg1.l8.m1.4.4.2" xref="alg1.l8.m1.4.4.2.cmml"><msub id="alg1.l8.m1.4.4.2.4" xref="alg1.l8.m1.4.4.2.4.cmml"><mi id="alg1.l8.m1.4.4.2.4.2" xref="alg1.l8.m1.4.4.2.4.2.cmml">T</mi><mi id="alg1.l8.m1.4.4.2.4.3" xref="alg1.l8.m1.4.4.2.4.3.cmml">ϕ</mi></msub><mo id="alg1.l8.m1.4.4.2.3" xref="alg1.l8.m1.4.4.2.3.cmml">⁢</mo><mrow id="alg1.l8.m1.4.4.2.2.2" xref="alg1.l8.m1.4.4.2.2.3.cmml"><mo id="alg1.l8.m1.4.4.2.2.2.3" xref="alg1.l8.m1.4.4.2.2.3.cmml">(</mo><msub id="alg1.l8.m1.3.3.1.1.1.1" xref="alg1.l8.m1.3.3.1.1.1.1.cmml"><mover accent="true" id="alg1.l8.m1.3.3.1.1.1.1.2" xref="alg1.l8.m1.3.3.1.1.1.1.2.cmml"><mi id="alg1.l8.m1.3.3.1.1.1.1.2.2" xref="alg1.l8.m1.3.3.1.1.1.1.2.2.cmml">G</mi><mo id="alg1.l8.m1.3.3.1.1.1.1.2.1" xref="alg1.l8.m1.3.3.1.1.1.1.2.1.cmml">^</mo></mover><mi id="alg1.l8.m1.3.3.1.1.1.1.3" xref="alg1.l8.m1.3.3.1.1.1.1.3.cmml">l</mi></msub><mo id="alg1.l8.m1.4.4.2.2.2.4" xref="alg1.l8.m1.4.4.2.2.3.cmml">,</mo><msub id="alg1.l8.m1.4.4.2.2.2.2" xref="alg1.l8.m1.4.4.2.2.2.2.cmml"><mover accent="true" id="alg1.l8.m1.4.4.2.2.2.2.2" xref="alg1.l8.m1.4.4.2.2.2.2.2.cmml"><mi id="alg1.l8.m1.4.4.2.2.2.2.2.2" xref="alg1.l8.m1.4.4.2.2.2.2.2.2.cmml">G</mi><mo id="alg1.l8.m1.4.4.2.2.2.2.2.1" xref="alg1.l8.m1.4.4.2.2.2.2.2.1.cmml">^</mo></mover><mi id="alg1.l8.m1.4.4.2.2.2.2.3" xref="alg1.l8.m1.4.4.2.2.2.2.3.cmml">r</mi></msub><mo id="alg1.l8.m1.4.4.2.2.2.5" xref="alg1.l8.m1.4.4.2.2.3.cmml">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="alg1.l8.m1.4b"><apply id="alg1.l8.m1.4.4.cmml" xref="alg1.l8.m1.4.4"><eq id="alg1.l8.m1.4.4.3.cmml" xref="alg1.l8.m1.4.4.3"></eq><interval closure="closed" id="alg1.l8.m1.4.4.4.1.cmml" xref="alg1.l8.m1.4.4.4.2"><ci id="alg1.l8.m1.1.1.1a.cmml" xref="alg1.l8.m1.1.1.1"><mover id="alg1.l8.m1.1.1.1.cmml" xref="alg1.l8.m1.1.1.1"><mi class="ltx_font_mathcaligraphic" id="alg1.l8.m1.1.1.1.3.cmml" xref="alg1.l8.m1.1.1.1.3">𝒪</mi><mpadded id="alg1.l8.m1.1.1.1.1.cmml" voffset="-3.0pt" xref="alg1.l8.m1.1.1.1.1"><mo id="alg1.l8.m1.1.1.1.1a.cmml" mathsize="71%" stretchy="false" xref="alg1.l8.m1.1.1.1.1">→</mo></mpadded></mover></ci><ci id="alg1.l8.m1.2.2.1a.cmml" xref="alg1.l8.m1.2.2.1"><mover id="alg1.l8.m1.2.2.1.cmml" xref="alg1.l8.m1.2.2.1"><mi class="ltx_font_mathcaligraphic" id="alg1.l8.m1.2.2.1.3.cmml" xref="alg1.l8.m1.2.2.1.3">𝒪</mi><mpadded id="alg1.l8.m1.2.2.1.1.cmml" voffset="-3.0pt" xref="alg1.l8.m1.2.2.1.1"><mo id="alg1.l8.m1.2.2.1.1a.cmml" mathsize="71%" stretchy="false" xref="alg1.l8.m1.2.2.1.1">←</mo></mpadded></mover></ci></interval><apply id="alg1.l8.m1.4.4.2.cmml" xref="alg1.l8.m1.4.4.2"><times id="alg1.l8.m1.4.4.2.3.cmml" xref="alg1.l8.m1.4.4.2.3"></times><apply id="alg1.l8.m1.4.4.2.4.cmml" xref="alg1.l8.m1.4.4.2.4"><csymbol cd="ambiguous" id="alg1.l8.m1.4.4.2.4.1.cmml" xref="alg1.l8.m1.4.4.2.4">subscript</csymbol><ci id="alg1.l8.m1.4.4.2.4.2.cmml" xref="alg1.l8.m1.4.4.2.4.2">𝑇</ci><ci id="alg1.l8.m1.4.4.2.4.3.cmml" xref="alg1.l8.m1.4.4.2.4.3">italic-ϕ</ci></apply><interval closure="open" id="alg1.l8.m1.4.4.2.2.3.cmml" xref="alg1.l8.m1.4.4.2.2.2"><apply id="alg1.l8.m1.3.3.1.1.1.1.cmml" xref="alg1.l8.m1.3.3.1.1.1.1"><csymbol cd="ambiguous" id="alg1.l8.m1.3.3.1.1.1.1.1.cmml" xref="alg1.l8.m1.3.3.1.1.1.1">subscript</csymbol><apply id="alg1.l8.m1.3.3.1.1.1.1.2.cmml" xref="alg1.l8.m1.3.3.1.1.1.1.2"><ci id="alg1.l8.m1.3.3.1.1.1.1.2.1.cmml" xref="alg1.l8.m1.3.3.1.1.1.1.2.1">^</ci><ci id="alg1.l8.m1.3.3.1.1.1.1.2.2.cmml" xref="alg1.l8.m1.3.3.1.1.1.1.2.2">𝐺</ci></apply><ci id="alg1.l8.m1.3.3.1.1.1.1.3.cmml" xref="alg1.l8.m1.3.3.1.1.1.1.3">𝑙</ci></apply><apply id="alg1.l8.m1.4.4.2.2.2.2.cmml" xref="alg1.l8.m1.4.4.2.2.2.2"><csymbol cd="ambiguous" id="alg1.l8.m1.4.4.2.2.2.2.1.cmml" xref="alg1.l8.m1.4.4.2.2.2.2">subscript</csymbol><apply id="alg1.l8.m1.4.4.2.2.2.2.2.cmml" xref="alg1.l8.m1.4.4.2.2.2.2.2"><ci id="alg1.l8.m1.4.4.2.2.2.2.2.1.cmml" xref="alg1.l8.m1.4.4.2.2.2.2.2.1">^</ci><ci id="alg1.l8.m1.4.4.2.2.2.2.2.2.cmml" xref="alg1.l8.m1.4.4.2.2.2.2.2.2">𝐺</ci></apply><ci id="alg1.l8.m1.4.4.2.2.2.2.3.cmml" xref="alg1.l8.m1.4.4.2.2.2.2.3">𝑟</ci></apply></interval></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l8.m1.4c">\left[{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle\rightarrow$}}% \over{\mathcal{O}}}},{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle% \leftarrow$}}\over{\mathcal{O}}}}\right]=T_{\phi}\left(\hat{G}_{l},\hat{G}_{r}\right)</annotation><annotation encoding="application/x-llamapun" id="alg1.l8.m1.4d">[ start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG → end_ARG end_ID , start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG ← end_ARG end_ID ] = italic_T start_POSTSUBSCRIPT italic_ϕ end_POSTSUBSCRIPT ( over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT )</annotation></semantics></math> </div> <div class="ltx_listingline" id="alg1.l9"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l9.1.1.1" style="font-size:80%;">9:</span></span> Recover the semantic features: <math alttext="\hat{F}_{l}=T^{l}_{\chi}\left({\mathord{\buildrel{\lower 3.0pt\hbox{$% \scriptscriptstyle\leftarrow$}}\over{\mathcal{O}}}},\hat{G}_{l},\hat{G}_{r}% \right),\hat{F}_{r}=T^{r}_{\chi}\left({\mathord{\buildrel{\lower 3.0pt\hbox{$% \scriptscriptstyle\rightarrow$}}\over{\mathcal{O}}}},\hat{G}_{r},\hat{G}_{l}\right)" class="ltx_Math" display="inline" id="alg1.l9.m1.4"><semantics id="alg1.l9.m1.4a"><mrow id="alg1.l9.m1.4.4.2" xref="alg1.l9.m1.4.4.3.cmml"><mrow id="alg1.l9.m1.3.3.1.1" xref="alg1.l9.m1.3.3.1.1.cmml"><msub id="alg1.l9.m1.3.3.1.1.4" xref="alg1.l9.m1.3.3.1.1.4.cmml"><mover accent="true" id="alg1.l9.m1.3.3.1.1.4.2" xref="alg1.l9.m1.3.3.1.1.4.2.cmml"><mi id="alg1.l9.m1.3.3.1.1.4.2.2" xref="alg1.l9.m1.3.3.1.1.4.2.2.cmml">F</mi><mo id="alg1.l9.m1.3.3.1.1.4.2.1" xref="alg1.l9.m1.3.3.1.1.4.2.1.cmml">^</mo></mover><mi id="alg1.l9.m1.3.3.1.1.4.3" xref="alg1.l9.m1.3.3.1.1.4.3.cmml">l</mi></msub><mo id="alg1.l9.m1.3.3.1.1.3" xref="alg1.l9.m1.3.3.1.1.3.cmml">=</mo><mrow id="alg1.l9.m1.3.3.1.1.2" xref="alg1.l9.m1.3.3.1.1.2.cmml"><msubsup id="alg1.l9.m1.3.3.1.1.2.4" xref="alg1.l9.m1.3.3.1.1.2.4.cmml"><mi id="alg1.l9.m1.3.3.1.1.2.4.2.2" xref="alg1.l9.m1.3.3.1.1.2.4.2.2.cmml">T</mi><mi id="alg1.l9.m1.3.3.1.1.2.4.3" xref="alg1.l9.m1.3.3.1.1.2.4.3.cmml">χ</mi><mi id="alg1.l9.m1.3.3.1.1.2.4.2.3" xref="alg1.l9.m1.3.3.1.1.2.4.2.3.cmml">l</mi></msubsup><mo id="alg1.l9.m1.3.3.1.1.2.3" xref="alg1.l9.m1.3.3.1.1.2.3.cmml">⁢</mo><mrow id="alg1.l9.m1.3.3.1.1.2.2.2" xref="alg1.l9.m1.3.3.1.1.2.2.3.cmml"><mo id="alg1.l9.m1.3.3.1.1.2.2.2.3" xref="alg1.l9.m1.3.3.1.1.2.2.3.cmml">(</mo><mover id="alg1.l9.m1.1.1.1" xref="alg1.l9.m1.1.1.1a.cmml"><mi class="ltx_font_mathcaligraphic" id="alg1.l9.m1.1.1.1.3" xref="alg1.l9.m1.1.1.1.3.cmml">𝒪</mi><mpadded id="alg1.l9.m1.1.1.1.1" voffset="-3.0pt" xref="alg1.l9.m1.1.1.1.1.cmml"><mo id="alg1.l9.m1.1.1.1.1a" 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xref="alg1.l9.m1.2.2.1.3">𝒪</mi><mpadded id="alg1.l9.m1.2.2.1.1.cmml" voffset="-3.0pt" xref="alg1.l9.m1.2.2.1.1"><mo id="alg1.l9.m1.2.2.1.1a.cmml" mathsize="71%" stretchy="false" xref="alg1.l9.m1.2.2.1.1">→</mo></mpadded></mover></ci><apply id="alg1.l9.m1.4.4.2.2.1.1.1.1.cmml" xref="alg1.l9.m1.4.4.2.2.1.1.1.1"><csymbol cd="ambiguous" id="alg1.l9.m1.4.4.2.2.1.1.1.1.1.cmml" xref="alg1.l9.m1.4.4.2.2.1.1.1.1">subscript</csymbol><apply id="alg1.l9.m1.4.4.2.2.1.1.1.1.2.cmml" xref="alg1.l9.m1.4.4.2.2.1.1.1.1.2"><ci id="alg1.l9.m1.4.4.2.2.1.1.1.1.2.1.cmml" xref="alg1.l9.m1.4.4.2.2.1.1.1.1.2.1">^</ci><ci id="alg1.l9.m1.4.4.2.2.1.1.1.1.2.2.cmml" xref="alg1.l9.m1.4.4.2.2.1.1.1.1.2.2">𝐺</ci></apply><ci id="alg1.l9.m1.4.4.2.2.1.1.1.1.3.cmml" xref="alg1.l9.m1.4.4.2.2.1.1.1.1.3">𝑟</ci></apply><apply id="alg1.l9.m1.4.4.2.2.2.2.2.2.cmml" xref="alg1.l9.m1.4.4.2.2.2.2.2.2"><csymbol cd="ambiguous" id="alg1.l9.m1.4.4.2.2.2.2.2.2.1.cmml" xref="alg1.l9.m1.4.4.2.2.2.2.2.2">subscript</csymbol><apply id="alg1.l9.m1.4.4.2.2.2.2.2.2.2.cmml" xref="alg1.l9.m1.4.4.2.2.2.2.2.2.2"><ci id="alg1.l9.m1.4.4.2.2.2.2.2.2.2.1.cmml" xref="alg1.l9.m1.4.4.2.2.2.2.2.2.2.1">^</ci><ci id="alg1.l9.m1.4.4.2.2.2.2.2.2.2.2.cmml" xref="alg1.l9.m1.4.4.2.2.2.2.2.2.2.2">𝐺</ci></apply><ci id="alg1.l9.m1.4.4.2.2.2.2.2.2.3.cmml" xref="alg1.l9.m1.4.4.2.2.2.2.2.2.3">𝑙</ci></apply></vector></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l9.m1.4c">\hat{F}_{l}=T^{l}_{\chi}\left({\mathord{\buildrel{\lower 3.0pt\hbox{$% \scriptscriptstyle\leftarrow$}}\over{\mathcal{O}}}},\hat{G}_{l},\hat{G}_{r}% \right),\hat{F}_{r}=T^{r}_{\chi}\left({\mathord{\buildrel{\lower 3.0pt\hbox{$% \scriptscriptstyle\rightarrow$}}\over{\mathcal{O}}}},\hat{G}_{r},\hat{G}_{l}\right)</annotation><annotation encoding="application/x-llamapun" id="alg1.l9.m1.4d">over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_χ end_POSTSUBSCRIPT ( start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG ← end_ARG end_ID , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ) , over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_χ end_POSTSUBSCRIPT ( start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG → end_ARG end_ID , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT )</annotation></semantics></math> </div> <div class="ltx_listingline" id="alg1.l10"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l10.2.1.1" style="font-size:80%;">10:</span></span><span class="ltx_text" id="alg1.l10.1"> Fuse the 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xref="alg1.l10.1.m1.4.4.2.2"><eq id="alg1.l10.1.m1.4.4.2.2.2.cmml" xref="alg1.l10.1.m1.4.4.2.2.2"></eq><apply id="alg1.l10.1.m1.4.4.2.2.3.cmml" xref="alg1.l10.1.m1.4.4.2.2.3"><csymbol cd="ambiguous" id="alg1.l10.1.m1.4.4.2.2.3.1.cmml" xref="alg1.l10.1.m1.4.4.2.2.3">subscript</csymbol><apply id="alg1.l10.1.m1.4.4.2.2.3.2.cmml" xref="alg1.l10.1.m1.4.4.2.2.3.2"><ci id="alg1.l10.1.m1.4.4.2.2.3.2.1.cmml" xref="alg1.l10.1.m1.4.4.2.2.3.2.1">^</ci><ci id="alg1.l10.1.m1.4.4.2.2.3.2.2.cmml" xref="alg1.l10.1.m1.4.4.2.2.3.2.2">𝐼</ci></apply><ci id="alg1.l10.1.m1.4.4.2.2.3.3.cmml" xref="alg1.l10.1.m1.4.4.2.2.3.3">𝑟</ci></apply><apply id="alg1.l10.1.m1.4.4.2.2.1.cmml" xref="alg1.l10.1.m1.4.4.2.2.1"><times id="alg1.l10.1.m1.4.4.2.2.1.2.cmml" xref="alg1.l10.1.m1.4.4.2.2.1.2"></times><apply id="alg1.l10.1.m1.4.4.2.2.1.3.cmml" xref="alg1.l10.1.m1.4.4.2.2.1.3"><csymbol cd="ambiguous" id="alg1.l10.1.m1.4.4.2.2.1.3.1.cmml" xref="alg1.l10.1.m1.4.4.2.2.1.3">subscript</csymbol><apply 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xref="alg1.l10.1.m1.4.4.2.2.1.1.1.1.2.1">^</ci><ci id="alg1.l10.1.m1.4.4.2.2.1.1.1.1.2.2.cmml" xref="alg1.l10.1.m1.4.4.2.2.1.1.1.1.2.2">𝐹</ci></apply><ci id="alg1.l10.1.m1.4.4.2.2.1.1.1.1.3.cmml" xref="alg1.l10.1.m1.4.4.2.2.1.1.1.1.3">𝑟</ci></apply></interval></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l10.1.m1.4c">\hat{I}_{l}=T^{l}_{\nu}\left(\mathbf{0},\hat{F}_{l}\right),\hat{I}_{r}=T^{r}_{% \nu}\left(\mathbf{0},\hat{F}_{r}\right)</annotation><annotation encoding="application/x-llamapun" id="alg1.l10.1.m1.4d">over^ start_ARG italic_I end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_ν end_POSTSUBSCRIPT ( bold_0 , over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT ) , over^ start_ARG italic_I end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_ν end_POSTSUBSCRIPT ( bold_0 , over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT )</annotation></semantics></math><span class="ltx_text" id="alg1.l10.1.1"> </span></span> </div> <div class="ltx_listingline" id="alg1.l11"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l11.1.1.1" style="font-size:80%;">11:</span></span> Optimize <math alttext="\gamma" class="ltx_Math" display="inline" id="alg1.l11.m1.1"><semantics id="alg1.l11.m1.1a"><mi id="alg1.l11.m1.1.1" xref="alg1.l11.m1.1.1.cmml">γ</mi><annotation-xml encoding="MathML-Content" id="alg1.l11.m1.1b"><ci id="alg1.l11.m1.1.1.cmml" xref="alg1.l11.m1.1.1">𝛾</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l11.m1.1c">\gamma</annotation><annotation encoding="application/x-llamapun" id="alg1.l11.m1.1d">italic_γ</annotation></semantics></math>, <math alttext="\varphi" class="ltx_Math" display="inline" id="alg1.l11.m2.1"><semantics id="alg1.l11.m2.1a"><mi id="alg1.l11.m2.1.1" xref="alg1.l11.m2.1.1.cmml">φ</mi><annotation-xml encoding="MathML-Content" id="alg1.l11.m2.1b"><ci id="alg1.l11.m2.1.1.cmml" xref="alg1.l11.m2.1.1">𝜑</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l11.m2.1c">\varphi</annotation><annotation encoding="application/x-llamapun" id="alg1.l11.m2.1d">italic_φ</annotation></semantics></math>, <math alttext="\chi" class="ltx_Math" display="inline" id="alg1.l11.m3.1"><semantics id="alg1.l11.m3.1a"><mi id="alg1.l11.m3.1.1" xref="alg1.l11.m3.1.1.cmml">χ</mi><annotation-xml encoding="MathML-Content" id="alg1.l11.m3.1b"><ci id="alg1.l11.m3.1.1.cmml" xref="alg1.l11.m3.1.1">𝜒</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l11.m3.1c">\chi</annotation><annotation encoding="application/x-llamapun" id="alg1.l11.m3.1d">italic_χ</annotation></semantics></math>, <math alttext="{\nu}" class="ltx_Math" display="inline" id="alg1.l11.m4.1"><semantics id="alg1.l11.m4.1a"><mi id="alg1.l11.m4.1.1" xref="alg1.l11.m4.1.1.cmml">ν</mi><annotation-xml encoding="MathML-Content" id="alg1.l11.m4.1b"><ci id="alg1.l11.m4.1.1.cmml" xref="alg1.l11.m4.1.1">𝜈</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l11.m4.1c">{\nu}</annotation><annotation encoding="application/x-llamapun" id="alg1.l11.m4.1d">italic_ν</annotation></semantics></math> with loss <math alttext="\mathcal{L}_{char}" class="ltx_Math" display="inline" id="alg1.l11.m5.1"><semantics id="alg1.l11.m5.1a"><msub id="alg1.l11.m5.1.1" xref="alg1.l11.m5.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="alg1.l11.m5.1.1.2" xref="alg1.l11.m5.1.1.2.cmml">ℒ</mi><mrow id="alg1.l11.m5.1.1.3" xref="alg1.l11.m5.1.1.3.cmml"><mi id="alg1.l11.m5.1.1.3.2" xref="alg1.l11.m5.1.1.3.2.cmml">c</mi><mo id="alg1.l11.m5.1.1.3.1" xref="alg1.l11.m5.1.1.3.1.cmml">⁢</mo><mi id="alg1.l11.m5.1.1.3.3" xref="alg1.l11.m5.1.1.3.3.cmml">h</mi><mo id="alg1.l11.m5.1.1.3.1a" xref="alg1.l11.m5.1.1.3.1.cmml">⁢</mo><mi id="alg1.l11.m5.1.1.3.4" xref="alg1.l11.m5.1.1.3.4.cmml">a</mi><mo id="alg1.l11.m5.1.1.3.1b" xref="alg1.l11.m5.1.1.3.1.cmml">⁢</mo><mi id="alg1.l11.m5.1.1.3.5" xref="alg1.l11.m5.1.1.3.5.cmml">r</mi></mrow></msub><annotation-xml encoding="MathML-Content" id="alg1.l11.m5.1b"><apply id="alg1.l11.m5.1.1.cmml" xref="alg1.l11.m5.1.1"><csymbol cd="ambiguous" id="alg1.l11.m5.1.1.1.cmml" xref="alg1.l11.m5.1.1">subscript</csymbol><ci id="alg1.l11.m5.1.1.2.cmml" xref="alg1.l11.m5.1.1.2">ℒ</ci><apply id="alg1.l11.m5.1.1.3.cmml" xref="alg1.l11.m5.1.1.3"><times id="alg1.l11.m5.1.1.3.1.cmml" xref="alg1.l11.m5.1.1.3.1"></times><ci id="alg1.l11.m5.1.1.3.2.cmml" xref="alg1.l11.m5.1.1.3.2">𝑐</ci><ci id="alg1.l11.m5.1.1.3.3.cmml" xref="alg1.l11.m5.1.1.3.3">ℎ</ci><ci id="alg1.l11.m5.1.1.3.4.cmml" xref="alg1.l11.m5.1.1.3.4">𝑎</ci><ci id="alg1.l11.m5.1.1.3.5.cmml" xref="alg1.l11.m5.1.1.3.5">𝑟</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l11.m5.1c">\mathcal{L}_{char}</annotation><annotation encoding="application/x-llamapun" id="alg1.l11.m5.1d">caligraphic_L start_POSTSUBSCRIPT italic_c italic_h italic_a italic_r end_POSTSUBSCRIPT</annotation></semantics></math> using gradient descent. </div> <div class="ltx_listingline" id="alg1.l12"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l12.1.1.1" style="font-size:80%;">12:</span></span> <span class="ltx_text ltx_font_bold" id="alg1.l12.2">until</span> Reach the preset number of repetitions. </div> <div class="ltx_listingline" id="alg1.l13"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l13.1.1.1" style="font-size:80%;">13:</span></span> Unfreeze the SpyNet. </div> <div class="ltx_listingline" id="alg1.l14"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l14.1.1.1" style="font-size:80%;">14:</span></span> <span class="ltx_text ltx_font_bold" id="alg1.l14.2">repeat</span> </div> <div class="ltx_listingline" id="alg1.l15"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l15.1.1.1" style="font-size:80%;">15:</span></span> Sample from dataset <math alttext="\mathcal{K}_{1}" class="ltx_Math" display="inline" id="alg1.l15.m1.1"><semantics id="alg1.l15.m1.1a"><msub id="alg1.l15.m1.1.1" xref="alg1.l15.m1.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="alg1.l15.m1.1.1.2" xref="alg1.l15.m1.1.1.2.cmml">𝒦</mi><mn id="alg1.l15.m1.1.1.3" xref="alg1.l15.m1.1.1.3.cmml">1</mn></msub><annotation-xml encoding="MathML-Content" id="alg1.l15.m1.1b"><apply id="alg1.l15.m1.1.1.cmml" xref="alg1.l15.m1.1.1"><csymbol cd="ambiguous" id="alg1.l15.m1.1.1.1.cmml" xref="alg1.l15.m1.1.1">subscript</csymbol><ci id="alg1.l15.m1.1.1.2.cmml" xref="alg1.l15.m1.1.1.2">𝒦</ci><cn id="alg1.l15.m1.1.1.3.cmml" type="integer" xref="alg1.l15.m1.1.1.3">1</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l15.m1.1c">\mathcal{K}_{1}</annotation><annotation encoding="application/x-llamapun" id="alg1.l15.m1.1d">caligraphic_K start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT</annotation></semantics></math>, obtaining the stereo-vision images <math alttext="\mathbf{I}\coloneqq\left[I_{l},I_{r}\right]" class="ltx_Math" display="inline" id="alg1.l15.m2.2"><semantics id="alg1.l15.m2.2a"><mrow id="alg1.l15.m2.2.2" xref="alg1.l15.m2.2.2.cmml"><mi id="alg1.l15.m2.2.2.4" xref="alg1.l15.m2.2.2.4.cmml">𝐈</mi><mo id="alg1.l15.m2.2.2.3" xref="alg1.l15.m2.2.2.3.cmml">≔</mo><mrow id="alg1.l15.m2.2.2.2.2" xref="alg1.l15.m2.2.2.2.3.cmml"><mo id="alg1.l15.m2.2.2.2.2.3" xref="alg1.l15.m2.2.2.2.3.cmml">[</mo><msub id="alg1.l15.m2.1.1.1.1.1" xref="alg1.l15.m2.1.1.1.1.1.cmml"><mi id="alg1.l15.m2.1.1.1.1.1.2" xref="alg1.l15.m2.1.1.1.1.1.2.cmml">I</mi><mi id="alg1.l15.m2.1.1.1.1.1.3" xref="alg1.l15.m2.1.1.1.1.1.3.cmml">l</mi></msub><mo id="alg1.l15.m2.2.2.2.2.4" xref="alg1.l15.m2.2.2.2.3.cmml">,</mo><msub id="alg1.l15.m2.2.2.2.2.2" xref="alg1.l15.m2.2.2.2.2.2.cmml"><mi id="alg1.l15.m2.2.2.2.2.2.2" xref="alg1.l15.m2.2.2.2.2.2.2.cmml">I</mi><mi id="alg1.l15.m2.2.2.2.2.2.3" xref="alg1.l15.m2.2.2.2.2.2.3.cmml">r</mi></msub><mo id="alg1.l15.m2.2.2.2.2.5" xref="alg1.l15.m2.2.2.2.3.cmml">]</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="alg1.l15.m2.2b"><apply id="alg1.l15.m2.2.2.cmml" xref="alg1.l15.m2.2.2"><ci id="alg1.l15.m2.2.2.3.cmml" xref="alg1.l15.m2.2.2.3">≔</ci><ci id="alg1.l15.m2.2.2.4.cmml" xref="alg1.l15.m2.2.2.4">𝐈</ci><interval closure="closed" id="alg1.l15.m2.2.2.2.3.cmml" xref="alg1.l15.m2.2.2.2.2"><apply id="alg1.l15.m2.1.1.1.1.1.cmml" xref="alg1.l15.m2.1.1.1.1.1"><csymbol cd="ambiguous" id="alg1.l15.m2.1.1.1.1.1.1.cmml" xref="alg1.l15.m2.1.1.1.1.1">subscript</csymbol><ci id="alg1.l15.m2.1.1.1.1.1.2.cmml" xref="alg1.l15.m2.1.1.1.1.1.2">𝐼</ci><ci id="alg1.l15.m2.1.1.1.1.1.3.cmml" xref="alg1.l15.m2.1.1.1.1.1.3">𝑙</ci></apply><apply id="alg1.l15.m2.2.2.2.2.2.cmml" xref="alg1.l15.m2.2.2.2.2.2"><csymbol cd="ambiguous" id="alg1.l15.m2.2.2.2.2.2.1.cmml" xref="alg1.l15.m2.2.2.2.2.2">subscript</csymbol><ci id="alg1.l15.m2.2.2.2.2.2.2.cmml" xref="alg1.l15.m2.2.2.2.2.2.2">𝐼</ci><ci id="alg1.l15.m2.2.2.2.2.2.3.cmml" xref="alg1.l15.m2.2.2.2.2.2.3">𝑟</ci></apply></interval></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l15.m2.2c">\mathbf{I}\coloneqq\left[I_{l},I_{r}\right]</annotation><annotation encoding="application/x-llamapun" id="alg1.l15.m2.2d">bold_I ≔ [ italic_I start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , italic_I start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ]</annotation></semantics></math> </div> <div class="ltx_listingline" id="alg1.l16"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l16.1.1.1" style="font-size:80%;">16:</span></span> Extract the semantic features: <math alttext="\left[F_{r},F_{l}\right]=T_{\gamma}\left(I_{r},I_{l}\right)" class="ltx_Math" display="inline" id="alg1.l16.m1.4"><semantics id="alg1.l16.m1.4a"><mrow id="alg1.l16.m1.4.4" xref="alg1.l16.m1.4.4.cmml"><mrow id="alg1.l16.m1.2.2.2.2" xref="alg1.l16.m1.2.2.2.3.cmml"><mo id="alg1.l16.m1.2.2.2.2.3" xref="alg1.l16.m1.2.2.2.3.cmml">[</mo><msub id="alg1.l16.m1.1.1.1.1.1" xref="alg1.l16.m1.1.1.1.1.1.cmml"><mi id="alg1.l16.m1.1.1.1.1.1.2" xref="alg1.l16.m1.1.1.1.1.1.2.cmml">F</mi><mi id="alg1.l16.m1.1.1.1.1.1.3" xref="alg1.l16.m1.1.1.1.1.1.3.cmml">r</mi></msub><mo id="alg1.l16.m1.2.2.2.2.4" xref="alg1.l16.m1.2.2.2.3.cmml">,</mo><msub id="alg1.l16.m1.2.2.2.2.2" xref="alg1.l16.m1.2.2.2.2.2.cmml"><mi id="alg1.l16.m1.2.2.2.2.2.2" xref="alg1.l16.m1.2.2.2.2.2.2.cmml">F</mi><mi id="alg1.l16.m1.2.2.2.2.2.3" xref="alg1.l16.m1.2.2.2.2.2.3.cmml">l</mi></msub><mo id="alg1.l16.m1.2.2.2.2.5" xref="alg1.l16.m1.2.2.2.3.cmml">]</mo></mrow><mo id="alg1.l16.m1.4.4.5" xref="alg1.l16.m1.4.4.5.cmml">=</mo><mrow id="alg1.l16.m1.4.4.4" xref="alg1.l16.m1.4.4.4.cmml"><msub id="alg1.l16.m1.4.4.4.4" xref="alg1.l16.m1.4.4.4.4.cmml"><mi id="alg1.l16.m1.4.4.4.4.2" xref="alg1.l16.m1.4.4.4.4.2.cmml">T</mi><mi id="alg1.l16.m1.4.4.4.4.3" xref="alg1.l16.m1.4.4.4.4.3.cmml">γ</mi></msub><mo id="alg1.l16.m1.4.4.4.3" xref="alg1.l16.m1.4.4.4.3.cmml">⁢</mo><mrow id="alg1.l16.m1.4.4.4.2.2" xref="alg1.l16.m1.4.4.4.2.3.cmml"><mo id="alg1.l16.m1.4.4.4.2.2.3" xref="alg1.l16.m1.4.4.4.2.3.cmml">(</mo><msub id="alg1.l16.m1.3.3.3.1.1.1" xref="alg1.l16.m1.3.3.3.1.1.1.cmml"><mi id="alg1.l16.m1.3.3.3.1.1.1.2" xref="alg1.l16.m1.3.3.3.1.1.1.2.cmml">I</mi><mi id="alg1.l16.m1.3.3.3.1.1.1.3" xref="alg1.l16.m1.3.3.3.1.1.1.3.cmml">r</mi></msub><mo id="alg1.l16.m1.4.4.4.2.2.4" xref="alg1.l16.m1.4.4.4.2.3.cmml">,</mo><msub id="alg1.l16.m1.4.4.4.2.2.2" xref="alg1.l16.m1.4.4.4.2.2.2.cmml"><mi id="alg1.l16.m1.4.4.4.2.2.2.2" xref="alg1.l16.m1.4.4.4.2.2.2.2.cmml">I</mi><mi id="alg1.l16.m1.4.4.4.2.2.2.3" xref="alg1.l16.m1.4.4.4.2.2.2.3.cmml">l</mi></msub><mo id="alg1.l16.m1.4.4.4.2.2.5" xref="alg1.l16.m1.4.4.4.2.3.cmml">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="alg1.l16.m1.4b"><apply id="alg1.l16.m1.4.4.cmml" xref="alg1.l16.m1.4.4"><eq id="alg1.l16.m1.4.4.5.cmml" xref="alg1.l16.m1.4.4.5"></eq><interval closure="closed" id="alg1.l16.m1.2.2.2.3.cmml" xref="alg1.l16.m1.2.2.2.2"><apply id="alg1.l16.m1.1.1.1.1.1.cmml" xref="alg1.l16.m1.1.1.1.1.1"><csymbol cd="ambiguous" id="alg1.l16.m1.1.1.1.1.1.1.cmml" xref="alg1.l16.m1.1.1.1.1.1">subscript</csymbol><ci id="alg1.l16.m1.1.1.1.1.1.2.cmml" xref="alg1.l16.m1.1.1.1.1.1.2">𝐹</ci><ci id="alg1.l16.m1.1.1.1.1.1.3.cmml" xref="alg1.l16.m1.1.1.1.1.1.3">𝑟</ci></apply><apply id="alg1.l16.m1.2.2.2.2.2.cmml" xref="alg1.l16.m1.2.2.2.2.2"><csymbol cd="ambiguous" id="alg1.l16.m1.2.2.2.2.2.1.cmml" xref="alg1.l16.m1.2.2.2.2.2">subscript</csymbol><ci id="alg1.l16.m1.2.2.2.2.2.2.cmml" xref="alg1.l16.m1.2.2.2.2.2.2">𝐹</ci><ci id="alg1.l16.m1.2.2.2.2.2.3.cmml" xref="alg1.l16.m1.2.2.2.2.2.3">𝑙</ci></apply></interval><apply id="alg1.l16.m1.4.4.4.cmml" xref="alg1.l16.m1.4.4.4"><times id="alg1.l16.m1.4.4.4.3.cmml" xref="alg1.l16.m1.4.4.4.3"></times><apply id="alg1.l16.m1.4.4.4.4.cmml" xref="alg1.l16.m1.4.4.4.4"><csymbol cd="ambiguous" id="alg1.l16.m1.4.4.4.4.1.cmml" xref="alg1.l16.m1.4.4.4.4">subscript</csymbol><ci id="alg1.l16.m1.4.4.4.4.2.cmml" xref="alg1.l16.m1.4.4.4.4.2">𝑇</ci><ci id="alg1.l16.m1.4.4.4.4.3.cmml" xref="alg1.l16.m1.4.4.4.4.3">𝛾</ci></apply><interval closure="open" id="alg1.l16.m1.4.4.4.2.3.cmml" xref="alg1.l16.m1.4.4.4.2.2"><apply id="alg1.l16.m1.3.3.3.1.1.1.cmml" xref="alg1.l16.m1.3.3.3.1.1.1"><csymbol cd="ambiguous" id="alg1.l16.m1.3.3.3.1.1.1.1.cmml" xref="alg1.l16.m1.3.3.3.1.1.1">subscript</csymbol><ci id="alg1.l16.m1.3.3.3.1.1.1.2.cmml" xref="alg1.l16.m1.3.3.3.1.1.1.2">𝐼</ci><ci id="alg1.l16.m1.3.3.3.1.1.1.3.cmml" xref="alg1.l16.m1.3.3.3.1.1.1.3">𝑟</ci></apply><apply id="alg1.l16.m1.4.4.4.2.2.2.cmml" xref="alg1.l16.m1.4.4.4.2.2.2"><csymbol cd="ambiguous" id="alg1.l16.m1.4.4.4.2.2.2.1.cmml" xref="alg1.l16.m1.4.4.4.2.2.2">subscript</csymbol><ci id="alg1.l16.m1.4.4.4.2.2.2.2.cmml" xref="alg1.l16.m1.4.4.4.2.2.2.2">𝐼</ci><ci id="alg1.l16.m1.4.4.4.2.2.2.3.cmml" xref="alg1.l16.m1.4.4.4.2.2.2.3">𝑙</ci></apply></interval></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l16.m1.4c">\left[F_{r},F_{l}\right]=T_{\gamma}\left(I_{r},I_{l}\right)</annotation><annotation encoding="application/x-llamapun" id="alg1.l16.m1.4d">[ italic_F start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT , italic_F start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT ] = italic_T start_POSTSUBSCRIPT italic_γ end_POSTSUBSCRIPT ( italic_I start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT , italic_I start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT )</annotation></semantics></math> </div> <div class="ltx_listingline" id="alg1.l17"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l17.1.1.1" style="font-size:80%;">17:</span></span> Compress the semantic features: <math alttext="G_{l}=T^{l}_{\varphi}\left(F_{l}\right),G_{r}=T^{r}_{\varphi}\left(F_{r}\right)" class="ltx_Math" display="inline" id="alg1.l17.m1.2"><semantics id="alg1.l17.m1.2a"><mrow id="alg1.l17.m1.2.2.2" xref="alg1.l17.m1.2.2.3.cmml"><mrow id="alg1.l17.m1.1.1.1.1" xref="alg1.l17.m1.1.1.1.1.cmml"><msub id="alg1.l17.m1.1.1.1.1.3" xref="alg1.l17.m1.1.1.1.1.3.cmml"><mi id="alg1.l17.m1.1.1.1.1.3.2" xref="alg1.l17.m1.1.1.1.1.3.2.cmml">G</mi><mi id="alg1.l17.m1.1.1.1.1.3.3" xref="alg1.l17.m1.1.1.1.1.3.3.cmml">l</mi></msub><mo id="alg1.l17.m1.1.1.1.1.2" xref="alg1.l17.m1.1.1.1.1.2.cmml">=</mo><mrow id="alg1.l17.m1.1.1.1.1.1" xref="alg1.l17.m1.1.1.1.1.1.cmml"><msubsup id="alg1.l17.m1.1.1.1.1.1.3" xref="alg1.l17.m1.1.1.1.1.1.3.cmml"><mi id="alg1.l17.m1.1.1.1.1.1.3.2.2" xref="alg1.l17.m1.1.1.1.1.1.3.2.2.cmml">T</mi><mi id="alg1.l17.m1.1.1.1.1.1.3.3" xref="alg1.l17.m1.1.1.1.1.1.3.3.cmml">φ</mi><mi id="alg1.l17.m1.1.1.1.1.1.3.2.3" xref="alg1.l17.m1.1.1.1.1.1.3.2.3.cmml">l</mi></msubsup><mo id="alg1.l17.m1.1.1.1.1.1.2" xref="alg1.l17.m1.1.1.1.1.1.2.cmml">⁢</mo><mrow id="alg1.l17.m1.1.1.1.1.1.1.1" xref="alg1.l17.m1.1.1.1.1.1.1.1.1.cmml"><mo id="alg1.l17.m1.1.1.1.1.1.1.1.2" xref="alg1.l17.m1.1.1.1.1.1.1.1.1.cmml">(</mo><msub id="alg1.l17.m1.1.1.1.1.1.1.1.1" xref="alg1.l17.m1.1.1.1.1.1.1.1.1.cmml"><mi id="alg1.l17.m1.1.1.1.1.1.1.1.1.2" xref="alg1.l17.m1.1.1.1.1.1.1.1.1.2.cmml">F</mi><mi id="alg1.l17.m1.1.1.1.1.1.1.1.1.3" xref="alg1.l17.m1.1.1.1.1.1.1.1.1.3.cmml">l</mi></msub><mo id="alg1.l17.m1.1.1.1.1.1.1.1.3" xref="alg1.l17.m1.1.1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow><mo id="alg1.l17.m1.2.2.2.3" xref="alg1.l17.m1.2.2.3a.cmml">,</mo><mrow id="alg1.l17.m1.2.2.2.2" xref="alg1.l17.m1.2.2.2.2.cmml"><msub id="alg1.l17.m1.2.2.2.2.3" xref="alg1.l17.m1.2.2.2.2.3.cmml"><mi id="alg1.l17.m1.2.2.2.2.3.2" xref="alg1.l17.m1.2.2.2.2.3.2.cmml">G</mi><mi id="alg1.l17.m1.2.2.2.2.3.3" xref="alg1.l17.m1.2.2.2.2.3.3.cmml">r</mi></msub><mo id="alg1.l17.m1.2.2.2.2.2" xref="alg1.l17.m1.2.2.2.2.2.cmml">=</mo><mrow id="alg1.l17.m1.2.2.2.2.1" xref="alg1.l17.m1.2.2.2.2.1.cmml"><msubsup id="alg1.l17.m1.2.2.2.2.1.3" xref="alg1.l17.m1.2.2.2.2.1.3.cmml"><mi id="alg1.l17.m1.2.2.2.2.1.3.2.2" xref="alg1.l17.m1.2.2.2.2.1.3.2.2.cmml">T</mi><mi id="alg1.l17.m1.2.2.2.2.1.3.3" xref="alg1.l17.m1.2.2.2.2.1.3.3.cmml">φ</mi><mi id="alg1.l17.m1.2.2.2.2.1.3.2.3" xref="alg1.l17.m1.2.2.2.2.1.3.2.3.cmml">r</mi></msubsup><mo id="alg1.l17.m1.2.2.2.2.1.2" xref="alg1.l17.m1.2.2.2.2.1.2.cmml">⁢</mo><mrow id="alg1.l17.m1.2.2.2.2.1.1.1" xref="alg1.l17.m1.2.2.2.2.1.1.1.1.cmml"><mo id="alg1.l17.m1.2.2.2.2.1.1.1.2" xref="alg1.l17.m1.2.2.2.2.1.1.1.1.cmml">(</mo><msub id="alg1.l17.m1.2.2.2.2.1.1.1.1" xref="alg1.l17.m1.2.2.2.2.1.1.1.1.cmml"><mi id="alg1.l17.m1.2.2.2.2.1.1.1.1.2" xref="alg1.l17.m1.2.2.2.2.1.1.1.1.2.cmml">F</mi><mi id="alg1.l17.m1.2.2.2.2.1.1.1.1.3" xref="alg1.l17.m1.2.2.2.2.1.1.1.1.3.cmml">r</mi></msub><mo id="alg1.l17.m1.2.2.2.2.1.1.1.3" xref="alg1.l17.m1.2.2.2.2.1.1.1.1.cmml">)</mo></mrow></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="alg1.l17.m1.2b"><apply id="alg1.l17.m1.2.2.3.cmml" xref="alg1.l17.m1.2.2.2"><csymbol cd="ambiguous" id="alg1.l17.m1.2.2.3a.cmml" xref="alg1.l17.m1.2.2.2.3">formulae-sequence</csymbol><apply id="alg1.l17.m1.1.1.1.1.cmml" xref="alg1.l17.m1.1.1.1.1"><eq id="alg1.l17.m1.1.1.1.1.2.cmml" xref="alg1.l17.m1.1.1.1.1.2"></eq><apply id="alg1.l17.m1.1.1.1.1.3.cmml" xref="alg1.l17.m1.1.1.1.1.3"><csymbol cd="ambiguous" id="alg1.l17.m1.1.1.1.1.3.1.cmml" xref="alg1.l17.m1.1.1.1.1.3">subscript</csymbol><ci id="alg1.l17.m1.1.1.1.1.3.2.cmml" xref="alg1.l17.m1.1.1.1.1.3.2">𝐺</ci><ci id="alg1.l17.m1.1.1.1.1.3.3.cmml" xref="alg1.l17.m1.1.1.1.1.3.3">𝑙</ci></apply><apply id="alg1.l17.m1.1.1.1.1.1.cmml" xref="alg1.l17.m1.1.1.1.1.1"><times id="alg1.l17.m1.1.1.1.1.1.2.cmml" xref="alg1.l17.m1.1.1.1.1.1.2"></times><apply id="alg1.l17.m1.1.1.1.1.1.3.cmml" xref="alg1.l17.m1.1.1.1.1.1.3"><csymbol cd="ambiguous" id="alg1.l17.m1.1.1.1.1.1.3.1.cmml" xref="alg1.l17.m1.1.1.1.1.1.3">subscript</csymbol><apply id="alg1.l17.m1.1.1.1.1.1.3.2.cmml" xref="alg1.l17.m1.1.1.1.1.1.3"><csymbol cd="ambiguous" id="alg1.l17.m1.1.1.1.1.1.3.2.1.cmml" xref="alg1.l17.m1.1.1.1.1.1.3">superscript</csymbol><ci id="alg1.l17.m1.1.1.1.1.1.3.2.2.cmml" xref="alg1.l17.m1.1.1.1.1.1.3.2.2">𝑇</ci><ci id="alg1.l17.m1.1.1.1.1.1.3.2.3.cmml" xref="alg1.l17.m1.1.1.1.1.1.3.2.3">𝑙</ci></apply><ci id="alg1.l17.m1.1.1.1.1.1.3.3.cmml" xref="alg1.l17.m1.1.1.1.1.1.3.3">𝜑</ci></apply><apply id="alg1.l17.m1.1.1.1.1.1.1.1.1.cmml" xref="alg1.l17.m1.1.1.1.1.1.1.1"><csymbol cd="ambiguous" id="alg1.l17.m1.1.1.1.1.1.1.1.1.1.cmml" xref="alg1.l17.m1.1.1.1.1.1.1.1">subscript</csymbol><ci id="alg1.l17.m1.1.1.1.1.1.1.1.1.2.cmml" xref="alg1.l17.m1.1.1.1.1.1.1.1.1.2">𝐹</ci><ci id="alg1.l17.m1.1.1.1.1.1.1.1.1.3.cmml" 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xref="alg1.l17.m1.2.2.2.2.1.3">superscript</csymbol><ci id="alg1.l17.m1.2.2.2.2.1.3.2.2.cmml" xref="alg1.l17.m1.2.2.2.2.1.3.2.2">𝑇</ci><ci id="alg1.l17.m1.2.2.2.2.1.3.2.3.cmml" xref="alg1.l17.m1.2.2.2.2.1.3.2.3">𝑟</ci></apply><ci id="alg1.l17.m1.2.2.2.2.1.3.3.cmml" xref="alg1.l17.m1.2.2.2.2.1.3.3">𝜑</ci></apply><apply id="alg1.l17.m1.2.2.2.2.1.1.1.1.cmml" xref="alg1.l17.m1.2.2.2.2.1.1.1"><csymbol cd="ambiguous" id="alg1.l17.m1.2.2.2.2.1.1.1.1.1.cmml" xref="alg1.l17.m1.2.2.2.2.1.1.1">subscript</csymbol><ci id="alg1.l17.m1.2.2.2.2.1.1.1.1.2.cmml" xref="alg1.l17.m1.2.2.2.2.1.1.1.1.2">𝐹</ci><ci id="alg1.l17.m1.2.2.2.2.1.1.1.1.3.cmml" xref="alg1.l17.m1.2.2.2.2.1.1.1.1.3">𝑟</ci></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l17.m1.2c">G_{l}=T^{l}_{\varphi}\left(F_{l}\right),G_{r}=T^{r}_{\varphi}\left(F_{r}\right)</annotation><annotation encoding="application/x-llamapun" id="alg1.l17.m1.2d">italic_G start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_φ end_POSTSUBSCRIPT ( italic_F start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT ) , italic_G start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_φ end_POSTSUBSCRIPT ( italic_F start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT )</annotation></semantics></math> </div> <div class="ltx_listingline" id="alg1.l18"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l18.1.1.1" style="font-size:80%;">18:</span></span> Extract the optical flow: <math alttext="\left[{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle\rightarrow$}}% \over{\mathcal{O}}}},{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle% \leftarrow$}}\over{\mathcal{O}}}}\right]=T_{\phi}\left(\hat{G}_{l},\hat{G}_{r}\right)" class="ltx_Math" display="inline" id="alg1.l18.m1.4"><semantics id="alg1.l18.m1.4a"><mrow id="alg1.l18.m1.4.4" xref="alg1.l18.m1.4.4.cmml"><mrow id="alg1.l18.m1.4.4.4.2" xref="alg1.l18.m1.4.4.4.1.cmml"><mo id="alg1.l18.m1.4.4.4.2.1" xref="alg1.l18.m1.4.4.4.1.cmml">[</mo><mover id="alg1.l18.m1.1.1.1" xref="alg1.l18.m1.1.1.1a.cmml"><mi class="ltx_font_mathcaligraphic" id="alg1.l18.m1.1.1.1.3" xref="alg1.l18.m1.1.1.1.3.cmml">𝒪</mi><mpadded id="alg1.l18.m1.1.1.1.1" voffset="-3.0pt" xref="alg1.l18.m1.1.1.1.1.cmml"><mo id="alg1.l18.m1.1.1.1.1a" mathsize="71%" stretchy="false" xref="alg1.l18.m1.1.1.1.1.cmml">→</mo></mpadded></mover><mo id="alg1.l18.m1.4.4.4.2.2" xref="alg1.l18.m1.4.4.4.1.cmml">,</mo><mover id="alg1.l18.m1.2.2.1" xref="alg1.l18.m1.2.2.1a.cmml"><mi class="ltx_font_mathcaligraphic" id="alg1.l18.m1.2.2.1.3" xref="alg1.l18.m1.2.2.1.3.cmml">𝒪</mi><mpadded id="alg1.l18.m1.2.2.1.1" voffset="-3.0pt" xref="alg1.l18.m1.2.2.1.1.cmml"><mo id="alg1.l18.m1.2.2.1.1a" mathsize="71%" stretchy="false" xref="alg1.l18.m1.2.2.1.1.cmml">←</mo></mpadded></mover><mo id="alg1.l18.m1.4.4.4.2.3" xref="alg1.l18.m1.4.4.4.1.cmml">]</mo></mrow><mo id="alg1.l18.m1.4.4.3" xref="alg1.l18.m1.4.4.3.cmml">=</mo><mrow id="alg1.l18.m1.4.4.2" xref="alg1.l18.m1.4.4.2.cmml"><msub id="alg1.l18.m1.4.4.2.4" xref="alg1.l18.m1.4.4.2.4.cmml"><mi id="alg1.l18.m1.4.4.2.4.2" xref="alg1.l18.m1.4.4.2.4.2.cmml">T</mi><mi id="alg1.l18.m1.4.4.2.4.3" xref="alg1.l18.m1.4.4.2.4.3.cmml">ϕ</mi></msub><mo id="alg1.l18.m1.4.4.2.3" xref="alg1.l18.m1.4.4.2.3.cmml">⁢</mo><mrow id="alg1.l18.m1.4.4.2.2.2" xref="alg1.l18.m1.4.4.2.2.3.cmml"><mo id="alg1.l18.m1.4.4.2.2.2.3" xref="alg1.l18.m1.4.4.2.2.3.cmml">(</mo><msub id="alg1.l18.m1.3.3.1.1.1.1" xref="alg1.l18.m1.3.3.1.1.1.1.cmml"><mover accent="true" id="alg1.l18.m1.3.3.1.1.1.1.2" xref="alg1.l18.m1.3.3.1.1.1.1.2.cmml"><mi id="alg1.l18.m1.3.3.1.1.1.1.2.2" xref="alg1.l18.m1.3.3.1.1.1.1.2.2.cmml">G</mi><mo id="alg1.l18.m1.3.3.1.1.1.1.2.1" xref="alg1.l18.m1.3.3.1.1.1.1.2.1.cmml">^</mo></mover><mi id="alg1.l18.m1.3.3.1.1.1.1.3" xref="alg1.l18.m1.3.3.1.1.1.1.3.cmml">l</mi></msub><mo id="alg1.l18.m1.4.4.2.2.2.4" xref="alg1.l18.m1.4.4.2.2.3.cmml">,</mo><msub id="alg1.l18.m1.4.4.2.2.2.2" xref="alg1.l18.m1.4.4.2.2.2.2.cmml"><mover accent="true" id="alg1.l18.m1.4.4.2.2.2.2.2" xref="alg1.l18.m1.4.4.2.2.2.2.2.cmml"><mi id="alg1.l18.m1.4.4.2.2.2.2.2.2" xref="alg1.l18.m1.4.4.2.2.2.2.2.2.cmml">G</mi><mo id="alg1.l18.m1.4.4.2.2.2.2.2.1" xref="alg1.l18.m1.4.4.2.2.2.2.2.1.cmml">^</mo></mover><mi id="alg1.l18.m1.4.4.2.2.2.2.3" xref="alg1.l18.m1.4.4.2.2.2.2.3.cmml">r</mi></msub><mo id="alg1.l18.m1.4.4.2.2.2.5" xref="alg1.l18.m1.4.4.2.2.3.cmml">)</mo></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="alg1.l18.m1.4b"><apply id="alg1.l18.m1.4.4.cmml" xref="alg1.l18.m1.4.4"><eq id="alg1.l18.m1.4.4.3.cmml" xref="alg1.l18.m1.4.4.3"></eq><interval closure="closed" id="alg1.l18.m1.4.4.4.1.cmml" xref="alg1.l18.m1.4.4.4.2"><ci id="alg1.l18.m1.1.1.1a.cmml" xref="alg1.l18.m1.1.1.1"><mover id="alg1.l18.m1.1.1.1.cmml" 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xref="alg1.l18.m1.4.4.2.2.2.2">subscript</csymbol><apply id="alg1.l18.m1.4.4.2.2.2.2.2.cmml" xref="alg1.l18.m1.4.4.2.2.2.2.2"><ci id="alg1.l18.m1.4.4.2.2.2.2.2.1.cmml" xref="alg1.l18.m1.4.4.2.2.2.2.2.1">^</ci><ci id="alg1.l18.m1.4.4.2.2.2.2.2.2.cmml" xref="alg1.l18.m1.4.4.2.2.2.2.2.2">𝐺</ci></apply><ci id="alg1.l18.m1.4.4.2.2.2.2.3.cmml" xref="alg1.l18.m1.4.4.2.2.2.2.3">𝑟</ci></apply></interval></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l18.m1.4c">\left[{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle\rightarrow$}}% \over{\mathcal{O}}}},{\mathord{\buildrel{\lower 3.0pt\hbox{$\scriptscriptstyle% \leftarrow$}}\over{\mathcal{O}}}}\right]=T_{\phi}\left(\hat{G}_{l},\hat{G}_{r}\right)</annotation><annotation encoding="application/x-llamapun" id="alg1.l18.m1.4d">[ start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG → end_ARG end_ID , start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG ← end_ARG end_ID ] = italic_T start_POSTSUBSCRIPT italic_ϕ end_POSTSUBSCRIPT ( over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT )</annotation></semantics></math> </div> <div class="ltx_listingline" id="alg1.l19"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l19.1.1.1" style="font-size:80%;">19:</span></span> Recover the semantic features: <math alttext="\hat{F}_{l}=T^{l}_{\chi}\left({\mathord{\buildrel{\lower 3.0pt\hbox{$% \scriptscriptstyle\leftarrow$}}\over{\mathcal{O}}}},\hat{G}_{l},\hat{G}_{r}% \right),\hat{F}_{r}=T^{r}_{\chi}\left({\mathord{\buildrel{\lower 3.0pt\hbox{$% \scriptscriptstyle\rightarrow$}}\over{\mathcal{O}}}},\hat{G}_{r},\hat{G}_{l}\right)" class="ltx_Math" display="inline" id="alg1.l19.m1.4"><semantics id="alg1.l19.m1.4a"><mrow id="alg1.l19.m1.4.4.2" xref="alg1.l19.m1.4.4.3.cmml"><mrow id="alg1.l19.m1.3.3.1.1" xref="alg1.l19.m1.3.3.1.1.cmml"><msub 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xref="alg1.l19.m1.4.4.2.2.1.1.1.1">subscript</csymbol><apply id="alg1.l19.m1.4.4.2.2.1.1.1.1.2.cmml" xref="alg1.l19.m1.4.4.2.2.1.1.1.1.2"><ci id="alg1.l19.m1.4.4.2.2.1.1.1.1.2.1.cmml" xref="alg1.l19.m1.4.4.2.2.1.1.1.1.2.1">^</ci><ci id="alg1.l19.m1.4.4.2.2.1.1.1.1.2.2.cmml" xref="alg1.l19.m1.4.4.2.2.1.1.1.1.2.2">𝐺</ci></apply><ci id="alg1.l19.m1.4.4.2.2.1.1.1.1.3.cmml" xref="alg1.l19.m1.4.4.2.2.1.1.1.1.3">𝑟</ci></apply><apply id="alg1.l19.m1.4.4.2.2.2.2.2.2.cmml" xref="alg1.l19.m1.4.4.2.2.2.2.2.2"><csymbol cd="ambiguous" id="alg1.l19.m1.4.4.2.2.2.2.2.2.1.cmml" xref="alg1.l19.m1.4.4.2.2.2.2.2.2">subscript</csymbol><apply id="alg1.l19.m1.4.4.2.2.2.2.2.2.2.cmml" xref="alg1.l19.m1.4.4.2.2.2.2.2.2.2"><ci id="alg1.l19.m1.4.4.2.2.2.2.2.2.2.1.cmml" xref="alg1.l19.m1.4.4.2.2.2.2.2.2.2.1">^</ci><ci id="alg1.l19.m1.4.4.2.2.2.2.2.2.2.2.cmml" xref="alg1.l19.m1.4.4.2.2.2.2.2.2.2.2">𝐺</ci></apply><ci id="alg1.l19.m1.4.4.2.2.2.2.2.2.3.cmml" xref="alg1.l19.m1.4.4.2.2.2.2.2.2.3">𝑙</ci></apply></vector></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l19.m1.4c">\hat{F}_{l}=T^{l}_{\chi}\left({\mathord{\buildrel{\lower 3.0pt\hbox{$% \scriptscriptstyle\leftarrow$}}\over{\mathcal{O}}}},\hat{G}_{l},\hat{G}_{r}% \right),\hat{F}_{r}=T^{r}_{\chi}\left({\mathord{\buildrel{\lower 3.0pt\hbox{$% \scriptscriptstyle\rightarrow$}}\over{\mathcal{O}}}},\hat{G}_{r},\hat{G}_{l}\right)</annotation><annotation encoding="application/x-llamapun" id="alg1.l19.m1.4d">over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_χ end_POSTSUBSCRIPT ( start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG ← end_ARG end_ID , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ) , over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_χ end_POSTSUBSCRIPT ( start_ID SUPERSCRIPTOP start_ARG caligraphic_O end_ARG start_ARG → end_ARG end_ID , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT , over^ start_ARG italic_G end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT )</annotation></semantics></math> </div> <div class="ltx_listingline" id="alg1.l20"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l20.2.1.1" style="font-size:80%;">20:</span></span><span class="ltx_text" id="alg1.l20.1"> Fuse the semantic features: <math alttext="\hat{I}_{l}=T^{l}_{\nu}\left(\mathbf{0},\hat{F}_{l}\right),\hat{I}_{r}=T^{r}_{% \nu}\left(\mathbf{0},\hat{F}_{r}\right)" class="ltx_Math" display="inline" id="alg1.l20.1.m1.4"><semantics id="alg1.l20.1.m1.4a"><mrow id="alg1.l20.1.m1.4.4.2" 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xref="alg1.l20.1.m1.4.4.2.2.1.3.2.2">𝑇</ci><ci id="alg1.l20.1.m1.4.4.2.2.1.3.2.3.cmml" xref="alg1.l20.1.m1.4.4.2.2.1.3.2.3">𝑟</ci></apply><ci id="alg1.l20.1.m1.4.4.2.2.1.3.3.cmml" xref="alg1.l20.1.m1.4.4.2.2.1.3.3">𝜈</ci></apply><interval closure="open" id="alg1.l20.1.m1.4.4.2.2.1.1.2.cmml" xref="alg1.l20.1.m1.4.4.2.2.1.1.1"><cn id="alg1.l20.1.m1.2.2.cmml" type="integer" xref="alg1.l20.1.m1.2.2">0</cn><apply id="alg1.l20.1.m1.4.4.2.2.1.1.1.1.cmml" xref="alg1.l20.1.m1.4.4.2.2.1.1.1.1"><csymbol cd="ambiguous" id="alg1.l20.1.m1.4.4.2.2.1.1.1.1.1.cmml" xref="alg1.l20.1.m1.4.4.2.2.1.1.1.1">subscript</csymbol><apply id="alg1.l20.1.m1.4.4.2.2.1.1.1.1.2.cmml" xref="alg1.l20.1.m1.4.4.2.2.1.1.1.1.2"><ci id="alg1.l20.1.m1.4.4.2.2.1.1.1.1.2.1.cmml" xref="alg1.l20.1.m1.4.4.2.2.1.1.1.1.2.1">^</ci><ci id="alg1.l20.1.m1.4.4.2.2.1.1.1.1.2.2.cmml" xref="alg1.l20.1.m1.4.4.2.2.1.1.1.1.2.2">𝐹</ci></apply><ci id="alg1.l20.1.m1.4.4.2.2.1.1.1.1.3.cmml" xref="alg1.l20.1.m1.4.4.2.2.1.1.1.1.3">𝑟</ci></apply></interval></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l20.1.m1.4c">\hat{I}_{l}=T^{l}_{\nu}\left(\mathbf{0},\hat{F}_{l}\right),\hat{I}_{r}=T^{r}_{% \nu}\left(\mathbf{0},\hat{F}_{r}\right)</annotation><annotation encoding="application/x-llamapun" id="alg1.l20.1.m1.4d">over^ start_ARG italic_I end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_ν end_POSTSUBSCRIPT ( bold_0 , over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT ) , over^ start_ARG italic_I end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_ν end_POSTSUBSCRIPT ( bold_0 , over^ start_ARG italic_F end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT )</annotation></semantics></math><span class="ltx_text" id="alg1.l20.1.1"> </span></span> </div> <div class="ltx_listingline" id="alg1.l21"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l21.1.1.1" style="font-size:80%;">21:</span></span> Optimize <math alttext="\gamma" class="ltx_Math" display="inline" id="alg1.l21.m1.1"><semantics id="alg1.l21.m1.1a"><mi id="alg1.l21.m1.1.1" xref="alg1.l21.m1.1.1.cmml">γ</mi><annotation-xml encoding="MathML-Content" id="alg1.l21.m1.1b"><ci id="alg1.l21.m1.1.1.cmml" xref="alg1.l21.m1.1.1">𝛾</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l21.m1.1c">\gamma</annotation><annotation encoding="application/x-llamapun" id="alg1.l21.m1.1d">italic_γ</annotation></semantics></math>, <math alttext="\varphi" class="ltx_Math" display="inline" id="alg1.l21.m2.1"><semantics id="alg1.l21.m2.1a"><mi id="alg1.l21.m2.1.1" xref="alg1.l21.m2.1.1.cmml">φ</mi><annotation-xml encoding="MathML-Content" id="alg1.l21.m2.1b"><ci id="alg1.l21.m2.1.1.cmml" xref="alg1.l21.m2.1.1">𝜑</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l21.m2.1c">\varphi</annotation><annotation encoding="application/x-llamapun" id="alg1.l21.m2.1d">italic_φ</annotation></semantics></math>, <math alttext="\phi" class="ltx_Math" display="inline" id="alg1.l21.m3.1"><semantics id="alg1.l21.m3.1a"><mi id="alg1.l21.m3.1.1" xref="alg1.l21.m3.1.1.cmml">ϕ</mi><annotation-xml encoding="MathML-Content" id="alg1.l21.m3.1b"><ci id="alg1.l21.m3.1.1.cmml" xref="alg1.l21.m3.1.1">italic-ϕ</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l21.m3.1c">\phi</annotation><annotation encoding="application/x-llamapun" id="alg1.l21.m3.1d">italic_ϕ</annotation></semantics></math>, <math alttext="\chi" class="ltx_Math" display="inline" id="alg1.l21.m4.1"><semantics id="alg1.l21.m4.1a"><mi id="alg1.l21.m4.1.1" xref="alg1.l21.m4.1.1.cmml">χ</mi><annotation-xml encoding="MathML-Content" id="alg1.l21.m4.1b"><ci id="alg1.l21.m4.1.1.cmml" xref="alg1.l21.m4.1.1">𝜒</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l21.m4.1c">\chi</annotation><annotation encoding="application/x-llamapun" id="alg1.l21.m4.1d">italic_χ</annotation></semantics></math>, <math alttext="{\nu}" class="ltx_Math" display="inline" id="alg1.l21.m5.1"><semantics id="alg1.l21.m5.1a"><mi id="alg1.l21.m5.1.1" xref="alg1.l21.m5.1.1.cmml">ν</mi><annotation-xml encoding="MathML-Content" id="alg1.l21.m5.1b"><ci id="alg1.l21.m5.1.1.cmml" xref="alg1.l21.m5.1.1">𝜈</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l21.m5.1c">{\nu}</annotation><annotation encoding="application/x-llamapun" id="alg1.l21.m5.1d">italic_ν</annotation></semantics></math> with loss <math alttext="\mathcal{L}_{char}" class="ltx_Math" display="inline" id="alg1.l21.m6.1"><semantics id="alg1.l21.m6.1a"><msub id="alg1.l21.m6.1.1" xref="alg1.l21.m6.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="alg1.l21.m6.1.1.2" xref="alg1.l21.m6.1.1.2.cmml">ℒ</mi><mrow id="alg1.l21.m6.1.1.3" xref="alg1.l21.m6.1.1.3.cmml"><mi id="alg1.l21.m6.1.1.3.2" xref="alg1.l21.m6.1.1.3.2.cmml">c</mi><mo id="alg1.l21.m6.1.1.3.1" xref="alg1.l21.m6.1.1.3.1.cmml">⁢</mo><mi id="alg1.l21.m6.1.1.3.3" xref="alg1.l21.m6.1.1.3.3.cmml">h</mi><mo id="alg1.l21.m6.1.1.3.1a" xref="alg1.l21.m6.1.1.3.1.cmml">⁢</mo><mi id="alg1.l21.m6.1.1.3.4" xref="alg1.l21.m6.1.1.3.4.cmml">a</mi><mo id="alg1.l21.m6.1.1.3.1b" xref="alg1.l21.m6.1.1.3.1.cmml">⁢</mo><mi id="alg1.l21.m6.1.1.3.5" xref="alg1.l21.m6.1.1.3.5.cmml">r</mi></mrow></msub><annotation-xml encoding="MathML-Content" id="alg1.l21.m6.1b"><apply id="alg1.l21.m6.1.1.cmml" xref="alg1.l21.m6.1.1"><csymbol cd="ambiguous" id="alg1.l21.m6.1.1.1.cmml" xref="alg1.l21.m6.1.1">subscript</csymbol><ci id="alg1.l21.m6.1.1.2.cmml" xref="alg1.l21.m6.1.1.2">ℒ</ci><apply id="alg1.l21.m6.1.1.3.cmml" xref="alg1.l21.m6.1.1.3"><times id="alg1.l21.m6.1.1.3.1.cmml" xref="alg1.l21.m6.1.1.3.1"></times><ci id="alg1.l21.m6.1.1.3.2.cmml" xref="alg1.l21.m6.1.1.3.2">𝑐</ci><ci id="alg1.l21.m6.1.1.3.3.cmml" xref="alg1.l21.m6.1.1.3.3">ℎ</ci><ci id="alg1.l21.m6.1.1.3.4.cmml" xref="alg1.l21.m6.1.1.3.4">𝑎</ci><ci id="alg1.l21.m6.1.1.3.5.cmml" xref="alg1.l21.m6.1.1.3.5">𝑟</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="alg1.l21.m6.1c">\mathcal{L}_{char}</annotation><annotation encoding="application/x-llamapun" id="alg1.l21.m6.1d">caligraphic_L start_POSTSUBSCRIPT italic_c italic_h italic_a italic_r end_POSTSUBSCRIPT</annotation></semantics></math> using gradient descent. </div> <div class="ltx_listingline" id="alg1.l22"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l22.1.1.1" style="font-size:80%;">22:</span></span> <span class="ltx_text ltx_font_bold" id="alg1.l22.2">until</span> The loss function converges </div> <div class="ltx_listingline" id="alg1.l23"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg1.l23.1.1.1" style="font-size:80%;">23:</span></span> <span class="ltx_text ltx_font_bold" id="alg1.l23.2">Return:</span> Network parameters: <math alttext="\gamma" class="ltx_Math" display="inline" id="alg1.l23.m1.1"><semantics id="alg1.l23.m1.1a"><mi id="alg1.l23.m1.1.1" xref="alg1.l23.m1.1.1.cmml">γ</mi><annotation-xml encoding="MathML-Content" id="alg1.l23.m1.1b"><ci id="alg1.l23.m1.1.1.cmml" xref="alg1.l23.m1.1.1">𝛾</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l23.m1.1c">\gamma</annotation><annotation encoding="application/x-llamapun" id="alg1.l23.m1.1d">italic_γ</annotation></semantics></math>, <math alttext="\varphi" class="ltx_Math" display="inline" id="alg1.l23.m2.1"><semantics id="alg1.l23.m2.1a"><mi id="alg1.l23.m2.1.1" xref="alg1.l23.m2.1.1.cmml">φ</mi><annotation-xml encoding="MathML-Content" id="alg1.l23.m2.1b"><ci id="alg1.l23.m2.1.1.cmml" xref="alg1.l23.m2.1.1">𝜑</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l23.m2.1c">\varphi</annotation><annotation encoding="application/x-llamapun" id="alg1.l23.m2.1d">italic_φ</annotation></semantics></math>, <math alttext="\phi" class="ltx_Math" display="inline" id="alg1.l23.m3.1"><semantics id="alg1.l23.m3.1a"><mi id="alg1.l23.m3.1.1" xref="alg1.l23.m3.1.1.cmml">ϕ</mi><annotation-xml encoding="MathML-Content" id="alg1.l23.m3.1b"><ci id="alg1.l23.m3.1.1.cmml" xref="alg1.l23.m3.1.1">italic-ϕ</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l23.m3.1c">\phi</annotation><annotation encoding="application/x-llamapun" id="alg1.l23.m3.1d">italic_ϕ</annotation></semantics></math>, <math alttext="\chi" class="ltx_Math" display="inline" id="alg1.l23.m4.1"><semantics id="alg1.l23.m4.1a"><mi id="alg1.l23.m4.1.1" xref="alg1.l23.m4.1.1.cmml">χ</mi><annotation-xml encoding="MathML-Content" id="alg1.l23.m4.1b"><ci id="alg1.l23.m4.1.1.cmml" xref="alg1.l23.m4.1.1">𝜒</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l23.m4.1c">\chi</annotation><annotation encoding="application/x-llamapun" id="alg1.l23.m4.1d">italic_χ</annotation></semantics></math>, <math alttext="{\nu}" class="ltx_Math" display="inline" id="alg1.l23.m5.1"><semantics id="alg1.l23.m5.1a"><mi id="alg1.l23.m5.1.1" xref="alg1.l23.m5.1.1.cmml">ν</mi><annotation-xml encoding="MathML-Content" id="alg1.l23.m5.1b"><ci id="alg1.l23.m5.1.1.cmml" xref="alg1.l23.m5.1.1">𝜈</ci></annotation-xml><annotation encoding="application/x-tex" id="alg1.l23.m5.1c">{\nu}</annotation><annotation encoding="application/x-llamapun" id="alg1.l23.m5.1d">italic_ν</annotation></semantics></math>. </div> </div> </figure> <div class="ltx_para" id="S4.p3"> <p class="ltx_p" id="S4.p3.3"><span class="ltx_text" id="S4.p3.3.1">Step 2 successively trains the key area information network, where the 2D detection module, i.e., the YOLOv5n network, is pre-trained and frozen. In this step, the training images are sampled from the same dataset as Step 1 and only pass through the key area information network. Similarly, the Charbonnier loss is used and can be expressed as</span></p> <table class="ltx_equation ltx_eqn_table" id="S4.E16"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="\mathcal{L}_{char}({\textbf{S}_{mask}},{\hat{\textbf{S}}_{mask}})=\sqrt{{{% \left\|{{\textbf{S}_{mask}}-{\hat{\textbf{S}}_{mask}}}\right\|}^{2}}+{\epsilon% ^{2}}}\text{,}" class="ltx_Math" display="block" id="S4.E16.m1.3"><semantics id="S4.E16.m1.3a"><mrow id="S4.E16.m1.3.3" xref="S4.E16.m1.3.3.cmml"><mrow id="S4.E16.m1.3.3.2" xref="S4.E16.m1.3.3.2.cmml"><msub id="S4.E16.m1.3.3.2.4" xref="S4.E16.m1.3.3.2.4.cmml"><mi class="ltx_font_mathcaligraphic" id="S4.E16.m1.3.3.2.4.2" xref="S4.E16.m1.3.3.2.4.2.cmml">ℒ</mi><mrow id="S4.E16.m1.3.3.2.4.3" xref="S4.E16.m1.3.3.2.4.3.cmml"><mi id="S4.E16.m1.3.3.2.4.3.2" xref="S4.E16.m1.3.3.2.4.3.2.cmml">c</mi><mo id="S4.E16.m1.3.3.2.4.3.1" 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xref="S4.E16.m1.1.1.1.3">superscript</csymbol><ci id="S4.E16.m1.1.1.1.3.2.cmml" xref="S4.E16.m1.1.1.1.3.2">italic-ϵ</ci><cn id="S4.E16.m1.1.1.1.3.3.cmml" type="integer" xref="S4.E16.m1.1.1.1.3.3">2</cn></apply></apply></apply><ci id="S4.E16.m1.3.3.4.2a.cmml" xref="S4.E16.m1.3.3.4.2"><mtext id="S4.E16.m1.3.3.4.2.cmml" xref="S4.E16.m1.3.3.4.2">,</mtext></ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S4.E16.m1.3c">\mathcal{L}_{char}({\textbf{S}_{mask}},{\hat{\textbf{S}}_{mask}})=\sqrt{{{% \left\|{{\textbf{S}_{mask}}-{\hat{\textbf{S}}_{mask}}}\right\|}^{2}}+{\epsilon% ^{2}}}\text{,}</annotation><annotation encoding="application/x-llamapun" id="S4.E16.m1.3d">caligraphic_L start_POSTSUBSCRIPT italic_c italic_h italic_a italic_r end_POSTSUBSCRIPT ( S start_POSTSUBSCRIPT italic_m italic_a italic_s italic_k end_POSTSUBSCRIPT , over^ start_ARG S end_ARG start_POSTSUBSCRIPT italic_m italic_a italic_s italic_k end_POSTSUBSCRIPT ) = square-root start_ARG ∥ S start_POSTSUBSCRIPT italic_m italic_a italic_s italic_k end_POSTSUBSCRIPT - over^ start_ARG S end_ARG start_POSTSUBSCRIPT italic_m italic_a italic_s italic_k end_POSTSUBSCRIPT ∥ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT + italic_ϵ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(16)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S4.p3.2">where <math alttext="{\mathbf{S}_{mask}}" class="ltx_Math" display="inline" id="S4.p3.1.m1.1"><semantics id="S4.p3.1.m1.1a"><msub id="S4.p3.1.m1.1.1" xref="S4.p3.1.m1.1.1.cmml"><mi id="S4.p3.1.m1.1.1.2" xref="S4.p3.1.m1.1.1.2.cmml">𝐒</mi><mrow id="S4.p3.1.m1.1.1.3" xref="S4.p3.1.m1.1.1.3.cmml"><mi id="S4.p3.1.m1.1.1.3.2" xref="S4.p3.1.m1.1.1.3.2.cmml">m</mi><mo id="S4.p3.1.m1.1.1.3.1" xref="S4.p3.1.m1.1.1.3.1.cmml">⁢</mo><mi id="S4.p3.1.m1.1.1.3.3" xref="S4.p3.1.m1.1.1.3.3.cmml">a</mi><mo id="S4.p3.1.m1.1.1.3.1a" xref="S4.p3.1.m1.1.1.3.1.cmml">⁢</mo><mi id="S4.p3.1.m1.1.1.3.4" xref="S4.p3.1.m1.1.1.3.4.cmml">s</mi><mo id="S4.p3.1.m1.1.1.3.1b" xref="S4.p3.1.m1.1.1.3.1.cmml">⁢</mo><mi id="S4.p3.1.m1.1.1.3.5" xref="S4.p3.1.m1.1.1.3.5.cmml">k</mi></mrow></msub><annotation-xml encoding="MathML-Content" id="S4.p3.1.m1.1b"><apply id="S4.p3.1.m1.1.1.cmml" xref="S4.p3.1.m1.1.1"><csymbol cd="ambiguous" id="S4.p3.1.m1.1.1.1.cmml" xref="S4.p3.1.m1.1.1">subscript</csymbol><ci id="S4.p3.1.m1.1.1.2.cmml" xref="S4.p3.1.m1.1.1.2">𝐒</ci><apply id="S4.p3.1.m1.1.1.3.cmml" xref="S4.p3.1.m1.1.1.3"><times id="S4.p3.1.m1.1.1.3.1.cmml" xref="S4.p3.1.m1.1.1.3.1"></times><ci id="S4.p3.1.m1.1.1.3.2.cmml" xref="S4.p3.1.m1.1.1.3.2">𝑚</ci><ci id="S4.p3.1.m1.1.1.3.3.cmml" xref="S4.p3.1.m1.1.1.3.3">𝑎</ci><ci id="S4.p3.1.m1.1.1.3.4.cmml" xref="S4.p3.1.m1.1.1.3.4">𝑠</ci><ci 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id="S4.p3.2.m2.1.1.3.4.cmml" xref="S4.p3.2.m2.1.1.3.4">𝑠</ci><ci id="S4.p3.2.m2.1.1.3.5.cmml" xref="S4.p3.2.m2.1.1.3.5">𝑘</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S4.p3.2.m2.1c">{\mathbf{\hat{S}}_{mask}}</annotation><annotation encoding="application/x-llamapun" id="S4.p3.2.m2.1d">over^ start_ARG bold_S end_ARG start_POSTSUBSCRIPT italic_m italic_a italic_s italic_k end_POSTSUBSCRIPT</annotation></semantics></math> represent the masked extracted semantic features at the transmitter and the masked output recovered semantic features at the receiver. The mask is created based on the position boxes of 2D detection to emphasize the neural network’s ability to focus on key areas, where the images or features outside the 2D detection boxes are deemed irrelevant. The pseudocode is shown in Algorithm <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#alg2" title="Algorithm 2 ‣ IV Training Strategy ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">2</span></a>.<span class="ltx_text" id="S4.p3.2.1"></span></p> </div> <div class="ltx_para" id="S4.p4"> <p class="ltx_p" id="S4.p4.5">In step 3, the fusion network is trained with the frozen pre-trained global and key area information networks. The training dataset is the same as the first part and the loss function is the hybrid masked Charbonnier loss given by</p> <table class="ltx_equation ltx_eqn_table" id="S4.E17"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="\mathcal{L}_{hmc}=\mathcal{L}_{char}\left({\mathbf{I}_{mask}},{\mathbf{\hat{I}% }_{mask}}\right)+\lambda\mathcal{L}_{char}\left({\bf{I}},{\bf{\hat{I}}}\right)% \text{,}" class="ltx_Math" display="block" id="S4.E17.m1.4"><semantics id="S4.E17.m1.4a"><mrow id="S4.E17.m1.4.4" xref="S4.E17.m1.4.4.cmml"><msub id="S4.E17.m1.4.4.4" xref="S4.E17.m1.4.4.4.cmml"><mi class="ltx_font_mathcaligraphic" id="S4.E17.m1.4.4.4.2" xref="S4.E17.m1.4.4.4.2.cmml">ℒ</mi><mrow id="S4.E17.m1.4.4.4.3" xref="S4.E17.m1.4.4.4.3.cmml"><mi id="S4.E17.m1.4.4.4.3.2" xref="S4.E17.m1.4.4.4.3.2.cmml">h</mi><mo id="S4.E17.m1.4.4.4.3.1" 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id="S4.E17.m1.2.2.2.cmml" xref="S4.E17.m1.2.2.2">𝐈</ci></apply></interval><ci id="S4.E17.m1.4.4.2.4.5a.cmml" xref="S4.E17.m1.4.4.2.4.5"><mtext id="S4.E17.m1.4.4.2.4.5.cmml" xref="S4.E17.m1.4.4.2.4.5">,</mtext></ci></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S4.E17.m1.4c">\mathcal{L}_{hmc}=\mathcal{L}_{char}\left({\mathbf{I}_{mask}},{\mathbf{\hat{I}% }_{mask}}\right)+\lambda\mathcal{L}_{char}\left({\bf{I}},{\bf{\hat{I}}}\right)% \text{,}</annotation><annotation encoding="application/x-llamapun" id="S4.E17.m1.4d">caligraphic_L start_POSTSUBSCRIPT italic_h italic_m italic_c end_POSTSUBSCRIPT = caligraphic_L start_POSTSUBSCRIPT italic_c italic_h italic_a italic_r end_POSTSUBSCRIPT ( bold_I start_POSTSUBSCRIPT italic_m italic_a italic_s italic_k end_POSTSUBSCRIPT , over^ start_ARG bold_I end_ARG start_POSTSUBSCRIPT italic_m italic_a italic_s italic_k end_POSTSUBSCRIPT ) + italic_λ caligraphic_L start_POSTSUBSCRIPT italic_c italic_h italic_a italic_r end_POSTSUBSCRIPT ( bold_I , over^ start_ARG bold_I end_ARG ) ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(17)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S4.p4.4">where <math alttext="{\mathbf{I}_{mask}}" class="ltx_Math" display="inline" id="S4.p4.1.m1.1"><semantics id="S4.p4.1.m1.1a"><msub id="S4.p4.1.m1.1.1" xref="S4.p4.1.m1.1.1.cmml"><mi id="S4.p4.1.m1.1.1.2" xref="S4.p4.1.m1.1.1.2.cmml">𝐈</mi><mrow id="S4.p4.1.m1.1.1.3" xref="S4.p4.1.m1.1.1.3.cmml"><mi id="S4.p4.1.m1.1.1.3.2" xref="S4.p4.1.m1.1.1.3.2.cmml">m</mi><mo id="S4.p4.1.m1.1.1.3.1" xref="S4.p4.1.m1.1.1.3.1.cmml">⁢</mo><mi id="S4.p4.1.m1.1.1.3.3" xref="S4.p4.1.m1.1.1.3.3.cmml">a</mi><mo id="S4.p4.1.m1.1.1.3.1a" xref="S4.p4.1.m1.1.1.3.1.cmml">⁢</mo><mi id="S4.p4.1.m1.1.1.3.4" xref="S4.p4.1.m1.1.1.3.4.cmml">s</mi><mo id="S4.p4.1.m1.1.1.3.1b" xref="S4.p4.1.m1.1.1.3.1.cmml">⁢</mo><mi id="S4.p4.1.m1.1.1.3.5" xref="S4.p4.1.m1.1.1.3.5.cmml">k</mi></mrow></msub><annotation-xml encoding="MathML-Content" id="S4.p4.1.m1.1b"><apply id="S4.p4.1.m1.1.1.cmml" xref="S4.p4.1.m1.1.1"><csymbol cd="ambiguous" id="S4.p4.1.m1.1.1.1.cmml" xref="S4.p4.1.m1.1.1">subscript</csymbol><ci id="S4.p4.1.m1.1.1.2.cmml" xref="S4.p4.1.m1.1.1.2">𝐈</ci><apply id="S4.p4.1.m1.1.1.3.cmml" xref="S4.p4.1.m1.1.1.3"><times id="S4.p4.1.m1.1.1.3.1.cmml" xref="S4.p4.1.m1.1.1.3.1"></times><ci id="S4.p4.1.m1.1.1.3.2.cmml" xref="S4.p4.1.m1.1.1.3.2">𝑚</ci><ci id="S4.p4.1.m1.1.1.3.3.cmml" xref="S4.p4.1.m1.1.1.3.3">𝑎</ci><ci id="S4.p4.1.m1.1.1.3.4.cmml" xref="S4.p4.1.m1.1.1.3.4">𝑠</ci><ci id="S4.p4.1.m1.1.1.3.5.cmml" xref="S4.p4.1.m1.1.1.3.5">𝑘</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S4.p4.1.m1.1c">{\mathbf{I}_{mask}}</annotation><annotation encoding="application/x-llamapun" id="S4.p4.1.m1.1d">bold_I start_POSTSUBSCRIPT italic_m italic_a italic_s italic_k end_POSTSUBSCRIPT</annotation></semantics></math> and <math alttext="{\mathbf{\hat{I}}_{mask}}" class="ltx_Math" display="inline" id="S4.p4.2.m2.1"><semantics id="S4.p4.2.m2.1a"><msub id="S4.p4.2.m2.1.1" xref="S4.p4.2.m2.1.1.cmml"><mover accent="true" id="S4.p4.2.m2.1.1.2" xref="S4.p4.2.m2.1.1.2.cmml"><mi id="S4.p4.2.m2.1.1.2.2" xref="S4.p4.2.m2.1.1.2.2.cmml">𝐈</mi><mo id="S4.p4.2.m2.1.1.2.1" xref="S4.p4.2.m2.1.1.2.1.cmml">^</mo></mover><mrow id="S4.p4.2.m2.1.1.3" xref="S4.p4.2.m2.1.1.3.cmml"><mi id="S4.p4.2.m2.1.1.3.2" xref="S4.p4.2.m2.1.1.3.2.cmml">m</mi><mo id="S4.p4.2.m2.1.1.3.1" xref="S4.p4.2.m2.1.1.3.1.cmml">⁢</mo><mi id="S4.p4.2.m2.1.1.3.3" xref="S4.p4.2.m2.1.1.3.3.cmml">a</mi><mo id="S4.p4.2.m2.1.1.3.1a" xref="S4.p4.2.m2.1.1.3.1.cmml">⁢</mo><mi id="S4.p4.2.m2.1.1.3.4" xref="S4.p4.2.m2.1.1.3.4.cmml">s</mi><mo id="S4.p4.2.m2.1.1.3.1b" xref="S4.p4.2.m2.1.1.3.1.cmml">⁢</mo><mi id="S4.p4.2.m2.1.1.3.5" xref="S4.p4.2.m2.1.1.3.5.cmml">k</mi></mrow></msub><annotation-xml encoding="MathML-Content" id="S4.p4.2.m2.1b"><apply id="S4.p4.2.m2.1.1.cmml" xref="S4.p4.2.m2.1.1"><csymbol cd="ambiguous" id="S4.p4.2.m2.1.1.1.cmml" xref="S4.p4.2.m2.1.1">subscript</csymbol><apply id="S4.p4.2.m2.1.1.2.cmml" xref="S4.p4.2.m2.1.1.2"><ci id="S4.p4.2.m2.1.1.2.1.cmml" xref="S4.p4.2.m2.1.1.2.1">^</ci><ci id="S4.p4.2.m2.1.1.2.2.cmml" xref="S4.p4.2.m2.1.1.2.2">𝐈</ci></apply><apply id="S4.p4.2.m2.1.1.3.cmml" xref="S4.p4.2.m2.1.1.3"><times id="S4.p4.2.m2.1.1.3.1.cmml" xref="S4.p4.2.m2.1.1.3.1"></times><ci id="S4.p4.2.m2.1.1.3.2.cmml" xref="S4.p4.2.m2.1.1.3.2">𝑚</ci><ci id="S4.p4.2.m2.1.1.3.3.cmml" xref="S4.p4.2.m2.1.1.3.3">𝑎</ci><ci id="S4.p4.2.m2.1.1.3.4.cmml" xref="S4.p4.2.m2.1.1.3.4">𝑠</ci><ci id="S4.p4.2.m2.1.1.3.5.cmml" xref="S4.p4.2.m2.1.1.3.5">𝑘</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S4.p4.2.m2.1c">{\mathbf{\hat{I}}_{mask}}</annotation><annotation encoding="application/x-llamapun" id="S4.p4.2.m2.1d">over^ start_ARG bold_I end_ARG start_POSTSUBSCRIPT italic_m italic_a italic_s italic_k end_POSTSUBSCRIPT</annotation></semantics></math> represent the masked input stereo-vision images and the masked output recovered images. <math alttext="\lambda" class="ltx_Math" display="inline" id="S4.p4.3.m3.1"><semantics id="S4.p4.3.m3.1a"><mi id="S4.p4.3.m3.1.1" xref="S4.p4.3.m3.1.1.cmml">λ</mi><annotation-xml encoding="MathML-Content" id="S4.p4.3.m3.1b"><ci id="S4.p4.3.m3.1.1.cmml" xref="S4.p4.3.m3.1.1">𝜆</ci></annotation-xml><annotation encoding="application/x-tex" id="S4.p4.3.m3.1c">\lambda</annotation><annotation encoding="application/x-llamapun" id="S4.p4.3.m3.1d">italic_λ</annotation></semantics></math> is a weight used to balance the recovery of the key areas and global areas <span class="ltx_text" id="S4.p4.4.1">and is set to <math alttext="0.5" class="ltx_Math" display="inline" id="S4.p4.4.1.m1.1"><semantics id="S4.p4.4.1.m1.1a"><mn id="S4.p4.4.1.m1.1.1" xref="S4.p4.4.1.m1.1.1.cmml">0.5</mn><annotation-xml encoding="MathML-Content" id="S4.p4.4.1.m1.1b"><cn id="S4.p4.4.1.m1.1.1.cmml" type="float" xref="S4.p4.4.1.m1.1.1">0.5</cn></annotation-xml><annotation encoding="application/x-tex" id="S4.p4.4.1.m1.1c">0.5</annotation><annotation encoding="application/x-llamapun" id="S4.p4.4.1.m1.1d">0.5</annotation></semantics></math> in the subsequent simulations.<span class="ltx_text" id="S4.p4.4.1.1"></span></span></p> </div> <div class="ltx_para" id="S4.p5"> <p class="ltx_p" id="S4.p5.1"><span class="ltx_text" id="S4.p5.1.1">In Step 4<span class="ltx_text" id="S4.p5.1.1.1">, the whole semantic codec except the 2D detection module is trained end-to-end for fine-tuning. <span class="ltx_text" id="S4.p5.1.1.1.1">During the initial epochs, the training function uses the hybrid masked Charbonnier loss, focusing on recovering key areas. In the final epochs, the training function switches to the Charbonnier loss, emphasizing global recovery.<span class="ltx_text" id="S4.p5.1.1.1.1.1"></span></span></span></span></p> </div> <div class="ltx_para" id="S4.p6"> <p class="ltx_p" id="S4.p6.1"><span class="ltx_text" id="S4.p6.1.1">In Step 5<span class="ltx_text" id="S4.p6.1.1.1">, the channel codec is trained with the semantic codec over the AWGN channel. The training process contains two parts. In the first part, only the channel codec is trained over the AWGN channel with inputs created by the well-trained semantic encoder, where the loss function uses the mean-squared error (MSE) loss <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib22" title="">22</a>, <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib27" title="">27</a>]</cite>. The second part jointly trains the channel codec and the semantic codec in an end-to-end fashion, where the loss function uses the Charbonnier loss.</span></span></p> </div> <figure class="ltx_float ltx_float_algorithm ltx_framed ltx_framed_top" id="alg2"> <figcaption class="ltx_caption"><span class="ltx_tag ltx_tag_float"><span class="ltx_text ltx_font_bold" id="alg2.2.1.1">Algorithm 2</span> </span> Training the key area information network</figcaption> <div class="ltx_listing ltx_listing" id="alg2.3"> <div class="ltx_listingline" id="alg2.l1"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg2.l1.1.1.1" style="font-size:80%;">1:</span></span> <span class="ltx_text ltx_font_bold" id="alg2.l1.2">Input:</span> The 3D vehicle detection dataset <math alttext="\mathcal{K}_{1}" class="ltx_Math" display="inline" id="alg2.l1.m1.1"><semantics id="alg2.l1.m1.1a"><msub id="alg2.l1.m1.1.1" xref="alg2.l1.m1.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="alg2.l1.m1.1.1.2" xref="alg2.l1.m1.1.1.2.cmml">𝒦</mi><mn id="alg2.l1.m1.1.1.3" xref="alg2.l1.m1.1.1.3.cmml">1</mn></msub><annotation-xml encoding="MathML-Content" id="alg2.l1.m1.1b"><apply id="alg2.l1.m1.1.1.cmml" xref="alg2.l1.m1.1.1"><csymbol cd="ambiguous" id="alg2.l1.m1.1.1.1.cmml" xref="alg2.l1.m1.1.1">subscript</csymbol><ci id="alg2.l1.m1.1.1.2.cmml" xref="alg2.l1.m1.1.1.2">𝒦</ci><cn id="alg2.l1.m1.1.1.3.cmml" type="integer" xref="alg2.l1.m1.1.1.3">1</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="alg2.l1.m1.1c">\mathcal{K}_{1}</annotation><annotation encoding="application/x-llamapun" id="alg2.l1.m1.1d">caligraphic_K start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT</annotation></semantics></math>. </div> <div class="ltx_listingline" id="alg2.l2"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg2.l2.1.1.1" style="font-size:80%;">2:</span></span> <span class="ltx_text ltx_font_bold" id="alg2.l2.2">Initialize parameters:</span> <math alttext="\beta" class="ltx_Math" display="inline" id="alg2.l2.m1.1"><semantics id="alg2.l2.m1.1a"><mi id="alg2.l2.m1.1.1" xref="alg2.l2.m1.1.1.cmml">β</mi><annotation-xml encoding="MathML-Content" id="alg2.l2.m1.1b"><ci id="alg2.l2.m1.1.1.cmml" xref="alg2.l2.m1.1.1">𝛽</ci></annotation-xml><annotation encoding="application/x-tex" id="alg2.l2.m1.1c">\beta</annotation><annotation encoding="application/x-llamapun" id="alg2.l2.m1.1d">italic_β</annotation></semantics></math>, <math alttext="\theta" class="ltx_Math" display="inline" id="alg2.l2.m2.1"><semantics id="alg2.l2.m2.1a"><mi id="alg2.l2.m2.1.1" xref="alg2.l2.m2.1.1.cmml">θ</mi><annotation-xml encoding="MathML-Content" id="alg2.l2.m2.1b"><ci id="alg2.l2.m2.1.1.cmml" xref="alg2.l2.m2.1.1">𝜃</ci></annotation-xml><annotation encoding="application/x-tex" id="alg2.l2.m2.1c">\theta</annotation><annotation encoding="application/x-llamapun" id="alg2.l2.m2.1d">italic_θ</annotation></semantics></math>. </div> <div class="ltx_listingline" id="alg2.l3"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg2.l3.1.1.1" style="font-size:80%;">3:</span></span> Load and freeze the 2D detection module. </div> <div class="ltx_listingline" id="alg2.l4"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg2.l4.1.1.1" style="font-size:80%;">4:</span></span> <span class="ltx_text ltx_font_bold" id="alg2.l4.2">repeat</span> </div> <div class="ltx_listingline" id="alg2.l5"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg2.l5.1.1.1" style="font-size:80%;">5:</span></span> Sample from dataset <math alttext="\mathcal{K}_{1}" class="ltx_Math" display="inline" id="alg2.l5.m1.1"><semantics id="alg2.l5.m1.1a"><msub id="alg2.l5.m1.1.1" xref="alg2.l5.m1.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="alg2.l5.m1.1.1.2" xref="alg2.l5.m1.1.1.2.cmml">𝒦</mi><mn id="alg2.l5.m1.1.1.3" xref="alg2.l5.m1.1.1.3.cmml">1</mn></msub><annotation-xml encoding="MathML-Content" id="alg2.l5.m1.1b"><apply id="alg2.l5.m1.1.1.cmml" xref="alg2.l5.m1.1.1"><csymbol cd="ambiguous" id="alg2.l5.m1.1.1.1.cmml" xref="alg2.l5.m1.1.1">subscript</csymbol><ci id="alg2.l5.m1.1.1.2.cmml" xref="alg2.l5.m1.1.1.2">𝒦</ci><cn id="alg2.l5.m1.1.1.3.cmml" type="integer" xref="alg2.l5.m1.1.1.3">1</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="alg2.l5.m1.1c">\mathcal{K}_{1}</annotation><annotation encoding="application/x-llamapun" id="alg2.l5.m1.1d">caligraphic_K start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT</annotation></semantics></math>, obtaining the stereo-vision images <math alttext="\mathbf{I}\coloneqq\left[I_{l},I_{r}\right]" class="ltx_Math" display="inline" id="alg2.l5.m2.2"><semantics id="alg2.l5.m2.2a"><mrow id="alg2.l5.m2.2.2" xref="alg2.l5.m2.2.2.cmml"><mi id="alg2.l5.m2.2.2.4" xref="alg2.l5.m2.2.2.4.cmml">𝐈</mi><mo id="alg2.l5.m2.2.2.3" xref="alg2.l5.m2.2.2.3.cmml">≔</mo><mrow id="alg2.l5.m2.2.2.2.2" xref="alg2.l5.m2.2.2.2.3.cmml"><mo id="alg2.l5.m2.2.2.2.2.3" xref="alg2.l5.m2.2.2.2.3.cmml">[</mo><msub id="alg2.l5.m2.1.1.1.1.1" xref="alg2.l5.m2.1.1.1.1.1.cmml"><mi id="alg2.l5.m2.1.1.1.1.1.2" xref="alg2.l5.m2.1.1.1.1.1.2.cmml">I</mi><mi id="alg2.l5.m2.1.1.1.1.1.3" xref="alg2.l5.m2.1.1.1.1.1.3.cmml">l</mi></msub><mo id="alg2.l5.m2.2.2.2.2.4" xref="alg2.l5.m2.2.2.2.3.cmml">,</mo><msub id="alg2.l5.m2.2.2.2.2.2" xref="alg2.l5.m2.2.2.2.2.2.cmml"><mi id="alg2.l5.m2.2.2.2.2.2.2" xref="alg2.l5.m2.2.2.2.2.2.2.cmml">I</mi><mi id="alg2.l5.m2.2.2.2.2.2.3" xref="alg2.l5.m2.2.2.2.2.2.3.cmml">r</mi></msub><mo id="alg2.l5.m2.2.2.2.2.5" xref="alg2.l5.m2.2.2.2.3.cmml">]</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="alg2.l5.m2.2b"><apply id="alg2.l5.m2.2.2.cmml" xref="alg2.l5.m2.2.2"><ci id="alg2.l5.m2.2.2.3.cmml" xref="alg2.l5.m2.2.2.3">≔</ci><ci id="alg2.l5.m2.2.2.4.cmml" xref="alg2.l5.m2.2.2.4">𝐈</ci><interval closure="closed" id="alg2.l5.m2.2.2.2.3.cmml" xref="alg2.l5.m2.2.2.2.2"><apply id="alg2.l5.m2.1.1.1.1.1.cmml" xref="alg2.l5.m2.1.1.1.1.1"><csymbol cd="ambiguous" id="alg2.l5.m2.1.1.1.1.1.1.cmml" xref="alg2.l5.m2.1.1.1.1.1">subscript</csymbol><ci id="alg2.l5.m2.1.1.1.1.1.2.cmml" xref="alg2.l5.m2.1.1.1.1.1.2">𝐼</ci><ci id="alg2.l5.m2.1.1.1.1.1.3.cmml" xref="alg2.l5.m2.1.1.1.1.1.3">𝑙</ci></apply><apply id="alg2.l5.m2.2.2.2.2.2.cmml" xref="alg2.l5.m2.2.2.2.2.2"><csymbol cd="ambiguous" id="alg2.l5.m2.2.2.2.2.2.1.cmml" xref="alg2.l5.m2.2.2.2.2.2">subscript</csymbol><ci id="alg2.l5.m2.2.2.2.2.2.2.cmml" xref="alg2.l5.m2.2.2.2.2.2.2">𝐼</ci><ci id="alg2.l5.m2.2.2.2.2.2.3.cmml" xref="alg2.l5.m2.2.2.2.2.2.3">𝑟</ci></apply></interval></apply></annotation-xml><annotation encoding="application/x-tex" id="alg2.l5.m2.2c">\mathbf{I}\coloneqq\left[I_{l},I_{r}\right]</annotation><annotation encoding="application/x-llamapun" id="alg2.l5.m2.2d">bold_I ≔ [ italic_I start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , italic_I start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT ]</annotation></semantics></math> </div> <div class="ltx_listingline" id="alg2.l6"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg2.l6.1.1.1" style="font-size:80%;">6:</span></span> Extract the key area semantic features: <math alttext="S_{l}=T^{l}_{\alpha}\left(I_{l}\right),S_{r}=T^{r}_{\alpha}\left(I_{r}\right)" class="ltx_Math" display="inline" id="alg2.l6.m1.2"><semantics id="alg2.l6.m1.2a"><mrow id="alg2.l6.m1.2.2.2" xref="alg2.l6.m1.2.2.3.cmml"><mrow id="alg2.l6.m1.1.1.1.1" xref="alg2.l6.m1.1.1.1.1.cmml"><msub id="alg2.l6.m1.1.1.1.1.3" xref="alg2.l6.m1.1.1.1.1.3.cmml"><mi id="alg2.l6.m1.1.1.1.1.3.2" xref="alg2.l6.m1.1.1.1.1.3.2.cmml">S</mi><mi id="alg2.l6.m1.1.1.1.1.3.3" xref="alg2.l6.m1.1.1.1.1.3.3.cmml">l</mi></msub><mo id="alg2.l6.m1.1.1.1.1.2" xref="alg2.l6.m1.1.1.1.1.2.cmml">=</mo><mrow id="alg2.l6.m1.1.1.1.1.1" xref="alg2.l6.m1.1.1.1.1.1.cmml"><msubsup id="alg2.l6.m1.1.1.1.1.1.3" xref="alg2.l6.m1.1.1.1.1.1.3.cmml"><mi id="alg2.l6.m1.1.1.1.1.1.3.2.2" xref="alg2.l6.m1.1.1.1.1.1.3.2.2.cmml">T</mi><mi id="alg2.l6.m1.1.1.1.1.1.3.3" xref="alg2.l6.m1.1.1.1.1.1.3.3.cmml">α</mi><mi id="alg2.l6.m1.1.1.1.1.1.3.2.3" xref="alg2.l6.m1.1.1.1.1.1.3.2.3.cmml">l</mi></msubsup><mo id="alg2.l6.m1.1.1.1.1.1.2" xref="alg2.l6.m1.1.1.1.1.1.2.cmml">⁢</mo><mrow id="alg2.l6.m1.1.1.1.1.1.1.1" xref="alg2.l6.m1.1.1.1.1.1.1.1.1.cmml"><mo id="alg2.l6.m1.1.1.1.1.1.1.1.2" xref="alg2.l6.m1.1.1.1.1.1.1.1.1.cmml">(</mo><msub id="alg2.l6.m1.1.1.1.1.1.1.1.1" xref="alg2.l6.m1.1.1.1.1.1.1.1.1.cmml"><mi id="alg2.l6.m1.1.1.1.1.1.1.1.1.2" xref="alg2.l6.m1.1.1.1.1.1.1.1.1.2.cmml">I</mi><mi id="alg2.l6.m1.1.1.1.1.1.1.1.1.3" xref="alg2.l6.m1.1.1.1.1.1.1.1.1.3.cmml">l</mi></msub><mo id="alg2.l6.m1.1.1.1.1.1.1.1.3" xref="alg2.l6.m1.1.1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow><mo id="alg2.l6.m1.2.2.2.3" xref="alg2.l6.m1.2.2.3a.cmml">,</mo><mrow id="alg2.l6.m1.2.2.2.2" xref="alg2.l6.m1.2.2.2.2.cmml"><msub id="alg2.l6.m1.2.2.2.2.3" xref="alg2.l6.m1.2.2.2.2.3.cmml"><mi id="alg2.l6.m1.2.2.2.2.3.2" xref="alg2.l6.m1.2.2.2.2.3.2.cmml">S</mi><mi id="alg2.l6.m1.2.2.2.2.3.3" xref="alg2.l6.m1.2.2.2.2.3.3.cmml">r</mi></msub><mo id="alg2.l6.m1.2.2.2.2.2" xref="alg2.l6.m1.2.2.2.2.2.cmml">=</mo><mrow id="alg2.l6.m1.2.2.2.2.1" xref="alg2.l6.m1.2.2.2.2.1.cmml"><msubsup id="alg2.l6.m1.2.2.2.2.1.3" xref="alg2.l6.m1.2.2.2.2.1.3.cmml"><mi id="alg2.l6.m1.2.2.2.2.1.3.2.2" xref="alg2.l6.m1.2.2.2.2.1.3.2.2.cmml">T</mi><mi id="alg2.l6.m1.2.2.2.2.1.3.3" xref="alg2.l6.m1.2.2.2.2.1.3.3.cmml">α</mi><mi id="alg2.l6.m1.2.2.2.2.1.3.2.3" xref="alg2.l6.m1.2.2.2.2.1.3.2.3.cmml">r</mi></msubsup><mo id="alg2.l6.m1.2.2.2.2.1.2" xref="alg2.l6.m1.2.2.2.2.1.2.cmml">⁢</mo><mrow id="alg2.l6.m1.2.2.2.2.1.1.1" xref="alg2.l6.m1.2.2.2.2.1.1.1.1.cmml"><mo id="alg2.l6.m1.2.2.2.2.1.1.1.2" xref="alg2.l6.m1.2.2.2.2.1.1.1.1.cmml">(</mo><msub id="alg2.l6.m1.2.2.2.2.1.1.1.1" xref="alg2.l6.m1.2.2.2.2.1.1.1.1.cmml"><mi id="alg2.l6.m1.2.2.2.2.1.1.1.1.2" xref="alg2.l6.m1.2.2.2.2.1.1.1.1.2.cmml">I</mi><mi id="alg2.l6.m1.2.2.2.2.1.1.1.1.3" xref="alg2.l6.m1.2.2.2.2.1.1.1.1.3.cmml">r</mi></msub><mo id="alg2.l6.m1.2.2.2.2.1.1.1.3" xref="alg2.l6.m1.2.2.2.2.1.1.1.1.cmml">)</mo></mrow></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="alg2.l6.m1.2b"><apply id="alg2.l6.m1.2.2.3.cmml" xref="alg2.l6.m1.2.2.2"><csymbol cd="ambiguous" id="alg2.l6.m1.2.2.3a.cmml" xref="alg2.l6.m1.2.2.2.3">formulae-sequence</csymbol><apply id="alg2.l6.m1.1.1.1.1.cmml" xref="alg2.l6.m1.1.1.1.1"><eq id="alg2.l6.m1.1.1.1.1.2.cmml" xref="alg2.l6.m1.1.1.1.1.2"></eq><apply id="alg2.l6.m1.1.1.1.1.3.cmml" xref="alg2.l6.m1.1.1.1.1.3"><csymbol cd="ambiguous" id="alg2.l6.m1.1.1.1.1.3.1.cmml" xref="alg2.l6.m1.1.1.1.1.3">subscript</csymbol><ci id="alg2.l6.m1.1.1.1.1.3.2.cmml" xref="alg2.l6.m1.1.1.1.1.3.2">𝑆</ci><ci id="alg2.l6.m1.1.1.1.1.3.3.cmml" xref="alg2.l6.m1.1.1.1.1.3.3">𝑙</ci></apply><apply id="alg2.l6.m1.1.1.1.1.1.cmml" xref="alg2.l6.m1.1.1.1.1.1"><times id="alg2.l6.m1.1.1.1.1.1.2.cmml" xref="alg2.l6.m1.1.1.1.1.1.2"></times><apply id="alg2.l6.m1.1.1.1.1.1.3.cmml" xref="alg2.l6.m1.1.1.1.1.1.3"><csymbol cd="ambiguous" id="alg2.l6.m1.1.1.1.1.1.3.1.cmml" xref="alg2.l6.m1.1.1.1.1.1.3">subscript</csymbol><apply id="alg2.l6.m1.1.1.1.1.1.3.2.cmml" xref="alg2.l6.m1.1.1.1.1.1.3"><csymbol cd="ambiguous" id="alg2.l6.m1.1.1.1.1.1.3.2.1.cmml" xref="alg2.l6.m1.1.1.1.1.1.3">superscript</csymbol><ci id="alg2.l6.m1.1.1.1.1.1.3.2.2.cmml" xref="alg2.l6.m1.1.1.1.1.1.3.2.2">𝑇</ci><ci id="alg2.l6.m1.1.1.1.1.1.3.2.3.cmml" xref="alg2.l6.m1.1.1.1.1.1.3.2.3">𝑙</ci></apply><ci id="alg2.l6.m1.1.1.1.1.1.3.3.cmml" xref="alg2.l6.m1.1.1.1.1.1.3.3">𝛼</ci></apply><apply id="alg2.l6.m1.1.1.1.1.1.1.1.1.cmml" xref="alg2.l6.m1.1.1.1.1.1.1.1"><csymbol cd="ambiguous" id="alg2.l6.m1.1.1.1.1.1.1.1.1.1.cmml" xref="alg2.l6.m1.1.1.1.1.1.1.1">subscript</csymbol><ci id="alg2.l6.m1.1.1.1.1.1.1.1.1.2.cmml" xref="alg2.l6.m1.1.1.1.1.1.1.1.1.2">𝐼</ci><ci id="alg2.l6.m1.1.1.1.1.1.1.1.1.3.cmml" xref="alg2.l6.m1.1.1.1.1.1.1.1.1.3">𝑙</ci></apply></apply></apply><apply id="alg2.l6.m1.2.2.2.2.cmml" xref="alg2.l6.m1.2.2.2.2"><eq id="alg2.l6.m1.2.2.2.2.2.cmml" xref="alg2.l6.m1.2.2.2.2.2"></eq><apply id="alg2.l6.m1.2.2.2.2.3.cmml" xref="alg2.l6.m1.2.2.2.2.3"><csymbol cd="ambiguous" id="alg2.l6.m1.2.2.2.2.3.1.cmml" xref="alg2.l6.m1.2.2.2.2.3">subscript</csymbol><ci id="alg2.l6.m1.2.2.2.2.3.2.cmml" xref="alg2.l6.m1.2.2.2.2.3.2">𝑆</ci><ci id="alg2.l6.m1.2.2.2.2.3.3.cmml" xref="alg2.l6.m1.2.2.2.2.3.3">𝑟</ci></apply><apply id="alg2.l6.m1.2.2.2.2.1.cmml" xref="alg2.l6.m1.2.2.2.2.1"><times id="alg2.l6.m1.2.2.2.2.1.2.cmml" xref="alg2.l6.m1.2.2.2.2.1.2"></times><apply id="alg2.l6.m1.2.2.2.2.1.3.cmml" xref="alg2.l6.m1.2.2.2.2.1.3"><csymbol cd="ambiguous" id="alg2.l6.m1.2.2.2.2.1.3.1.cmml" xref="alg2.l6.m1.2.2.2.2.1.3">subscript</csymbol><apply id="alg2.l6.m1.2.2.2.2.1.3.2.cmml" xref="alg2.l6.m1.2.2.2.2.1.3"><csymbol cd="ambiguous" id="alg2.l6.m1.2.2.2.2.1.3.2.1.cmml" xref="alg2.l6.m1.2.2.2.2.1.3">superscript</csymbol><ci id="alg2.l6.m1.2.2.2.2.1.3.2.2.cmml" xref="alg2.l6.m1.2.2.2.2.1.3.2.2">𝑇</ci><ci id="alg2.l6.m1.2.2.2.2.1.3.2.3.cmml" xref="alg2.l6.m1.2.2.2.2.1.3.2.3">𝑟</ci></apply><ci id="alg2.l6.m1.2.2.2.2.1.3.3.cmml" xref="alg2.l6.m1.2.2.2.2.1.3.3">𝛼</ci></apply><apply id="alg2.l6.m1.2.2.2.2.1.1.1.1.cmml" xref="alg2.l6.m1.2.2.2.2.1.1.1"><csymbol cd="ambiguous" id="alg2.l6.m1.2.2.2.2.1.1.1.1.1.cmml" xref="alg2.l6.m1.2.2.2.2.1.1.1">subscript</csymbol><ci id="alg2.l6.m1.2.2.2.2.1.1.1.1.2.cmml" xref="alg2.l6.m1.2.2.2.2.1.1.1.1.2">𝐼</ci><ci id="alg2.l6.m1.2.2.2.2.1.1.1.1.3.cmml" xref="alg2.l6.m1.2.2.2.2.1.1.1.1.3">𝑟</ci></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="alg2.l6.m1.2c">S_{l}=T^{l}_{\alpha}\left(I_{l}\right),S_{r}=T^{r}_{\alpha}\left(I_{r}\right)</annotation><annotation encoding="application/x-llamapun" id="alg2.l6.m1.2d">italic_S start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_α end_POSTSUBSCRIPT ( italic_I start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT ) , italic_S start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_α end_POSTSUBSCRIPT ( italic_I start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT )</annotation></semantics></math> </div> <div class="ltx_listingline" id="alg2.l7"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg2.l7.1.1.1" style="font-size:80%;">7:</span></span> Compress the key area semantic features: <math alttext="K_{l}=T^{l}_{\beta}\left(S_{l}\right),K_{r}=T^{r}_{\beta}\left(S_{r}\right)" class="ltx_Math" display="inline" id="alg2.l7.m1.2"><semantics id="alg2.l7.m1.2a"><mrow id="alg2.l7.m1.2.2.2" xref="alg2.l7.m1.2.2.3.cmml"><mrow id="alg2.l7.m1.1.1.1.1" xref="alg2.l7.m1.1.1.1.1.cmml"><msub id="alg2.l7.m1.1.1.1.1.3" xref="alg2.l7.m1.1.1.1.1.3.cmml"><mi id="alg2.l7.m1.1.1.1.1.3.2" xref="alg2.l7.m1.1.1.1.1.3.2.cmml">K</mi><mi id="alg2.l7.m1.1.1.1.1.3.3" xref="alg2.l7.m1.1.1.1.1.3.3.cmml">l</mi></msub><mo id="alg2.l7.m1.1.1.1.1.2" xref="alg2.l7.m1.1.1.1.1.2.cmml">=</mo><mrow id="alg2.l7.m1.1.1.1.1.1" xref="alg2.l7.m1.1.1.1.1.1.cmml"><msubsup id="alg2.l7.m1.1.1.1.1.1.3" xref="alg2.l7.m1.1.1.1.1.1.3.cmml"><mi id="alg2.l7.m1.1.1.1.1.1.3.2.2" xref="alg2.l7.m1.1.1.1.1.1.3.2.2.cmml">T</mi><mi id="alg2.l7.m1.1.1.1.1.1.3.3" xref="alg2.l7.m1.1.1.1.1.1.3.3.cmml">β</mi><mi id="alg2.l7.m1.1.1.1.1.1.3.2.3" xref="alg2.l7.m1.1.1.1.1.1.3.2.3.cmml">l</mi></msubsup><mo id="alg2.l7.m1.1.1.1.1.1.2" xref="alg2.l7.m1.1.1.1.1.1.2.cmml">⁢</mo><mrow id="alg2.l7.m1.1.1.1.1.1.1.1" xref="alg2.l7.m1.1.1.1.1.1.1.1.1.cmml"><mo id="alg2.l7.m1.1.1.1.1.1.1.1.2" xref="alg2.l7.m1.1.1.1.1.1.1.1.1.cmml">(</mo><msub id="alg2.l7.m1.1.1.1.1.1.1.1.1" xref="alg2.l7.m1.1.1.1.1.1.1.1.1.cmml"><mi id="alg2.l7.m1.1.1.1.1.1.1.1.1.2" xref="alg2.l7.m1.1.1.1.1.1.1.1.1.2.cmml">S</mi><mi id="alg2.l7.m1.1.1.1.1.1.1.1.1.3" xref="alg2.l7.m1.1.1.1.1.1.1.1.1.3.cmml">l</mi></msub><mo id="alg2.l7.m1.1.1.1.1.1.1.1.3" xref="alg2.l7.m1.1.1.1.1.1.1.1.1.cmml">)</mo></mrow></mrow></mrow><mo id="alg2.l7.m1.2.2.2.3" xref="alg2.l7.m1.2.2.3a.cmml">,</mo><mrow id="alg2.l7.m1.2.2.2.2" xref="alg2.l7.m1.2.2.2.2.cmml"><msub id="alg2.l7.m1.2.2.2.2.3" xref="alg2.l7.m1.2.2.2.2.3.cmml"><mi id="alg2.l7.m1.2.2.2.2.3.2" xref="alg2.l7.m1.2.2.2.2.3.2.cmml">K</mi><mi id="alg2.l7.m1.2.2.2.2.3.3" xref="alg2.l7.m1.2.2.2.2.3.3.cmml">r</mi></msub><mo id="alg2.l7.m1.2.2.2.2.2" xref="alg2.l7.m1.2.2.2.2.2.cmml">=</mo><mrow id="alg2.l7.m1.2.2.2.2.1" xref="alg2.l7.m1.2.2.2.2.1.cmml"><msubsup id="alg2.l7.m1.2.2.2.2.1.3" xref="alg2.l7.m1.2.2.2.2.1.3.cmml"><mi id="alg2.l7.m1.2.2.2.2.1.3.2.2" xref="alg2.l7.m1.2.2.2.2.1.3.2.2.cmml">T</mi><mi id="alg2.l7.m1.2.2.2.2.1.3.3" xref="alg2.l7.m1.2.2.2.2.1.3.3.cmml">β</mi><mi id="alg2.l7.m1.2.2.2.2.1.3.2.3" xref="alg2.l7.m1.2.2.2.2.1.3.2.3.cmml">r</mi></msubsup><mo id="alg2.l7.m1.2.2.2.2.1.2" xref="alg2.l7.m1.2.2.2.2.1.2.cmml">⁢</mo><mrow id="alg2.l7.m1.2.2.2.2.1.1.1" xref="alg2.l7.m1.2.2.2.2.1.1.1.1.cmml"><mo id="alg2.l7.m1.2.2.2.2.1.1.1.2" xref="alg2.l7.m1.2.2.2.2.1.1.1.1.cmml">(</mo><msub id="alg2.l7.m1.2.2.2.2.1.1.1.1" xref="alg2.l7.m1.2.2.2.2.1.1.1.1.cmml"><mi id="alg2.l7.m1.2.2.2.2.1.1.1.1.2" xref="alg2.l7.m1.2.2.2.2.1.1.1.1.2.cmml">S</mi><mi id="alg2.l7.m1.2.2.2.2.1.1.1.1.3" xref="alg2.l7.m1.2.2.2.2.1.1.1.1.3.cmml">r</mi></msub><mo id="alg2.l7.m1.2.2.2.2.1.1.1.3" xref="alg2.l7.m1.2.2.2.2.1.1.1.1.cmml">)</mo></mrow></mrow></mrow></mrow><annotation-xml encoding="MathML-Content" id="alg2.l7.m1.2b"><apply id="alg2.l7.m1.2.2.3.cmml" xref="alg2.l7.m1.2.2.2"><csymbol cd="ambiguous" id="alg2.l7.m1.2.2.3a.cmml" xref="alg2.l7.m1.2.2.2.3">formulae-sequence</csymbol><apply id="alg2.l7.m1.1.1.1.1.cmml" xref="alg2.l7.m1.1.1.1.1"><eq id="alg2.l7.m1.1.1.1.1.2.cmml" 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xref="alg2.l7.m1.1.1.1.1.1.3.2.3">𝑙</ci></apply><ci id="alg2.l7.m1.1.1.1.1.1.3.3.cmml" xref="alg2.l7.m1.1.1.1.1.1.3.3">𝛽</ci></apply><apply id="alg2.l7.m1.1.1.1.1.1.1.1.1.cmml" xref="alg2.l7.m1.1.1.1.1.1.1.1"><csymbol cd="ambiguous" id="alg2.l7.m1.1.1.1.1.1.1.1.1.1.cmml" xref="alg2.l7.m1.1.1.1.1.1.1.1">subscript</csymbol><ci id="alg2.l7.m1.1.1.1.1.1.1.1.1.2.cmml" xref="alg2.l7.m1.1.1.1.1.1.1.1.1.2">𝑆</ci><ci id="alg2.l7.m1.1.1.1.1.1.1.1.1.3.cmml" xref="alg2.l7.m1.1.1.1.1.1.1.1.1.3">𝑙</ci></apply></apply></apply><apply id="alg2.l7.m1.2.2.2.2.cmml" xref="alg2.l7.m1.2.2.2.2"><eq id="alg2.l7.m1.2.2.2.2.2.cmml" xref="alg2.l7.m1.2.2.2.2.2"></eq><apply id="alg2.l7.m1.2.2.2.2.3.cmml" xref="alg2.l7.m1.2.2.2.2.3"><csymbol cd="ambiguous" id="alg2.l7.m1.2.2.2.2.3.1.cmml" xref="alg2.l7.m1.2.2.2.2.3">subscript</csymbol><ci id="alg2.l7.m1.2.2.2.2.3.2.cmml" xref="alg2.l7.m1.2.2.2.2.3.2">𝐾</ci><ci id="alg2.l7.m1.2.2.2.2.3.3.cmml" xref="alg2.l7.m1.2.2.2.2.3.3">𝑟</ci></apply><apply id="alg2.l7.m1.2.2.2.2.1.cmml" xref="alg2.l7.m1.2.2.2.2.1"><times id="alg2.l7.m1.2.2.2.2.1.2.cmml" xref="alg2.l7.m1.2.2.2.2.1.2"></times><apply id="alg2.l7.m1.2.2.2.2.1.3.cmml" xref="alg2.l7.m1.2.2.2.2.1.3"><csymbol cd="ambiguous" id="alg2.l7.m1.2.2.2.2.1.3.1.cmml" xref="alg2.l7.m1.2.2.2.2.1.3">subscript</csymbol><apply id="alg2.l7.m1.2.2.2.2.1.3.2.cmml" xref="alg2.l7.m1.2.2.2.2.1.3"><csymbol cd="ambiguous" id="alg2.l7.m1.2.2.2.2.1.3.2.1.cmml" xref="alg2.l7.m1.2.2.2.2.1.3">superscript</csymbol><ci id="alg2.l7.m1.2.2.2.2.1.3.2.2.cmml" xref="alg2.l7.m1.2.2.2.2.1.3.2.2">𝑇</ci><ci id="alg2.l7.m1.2.2.2.2.1.3.2.3.cmml" xref="alg2.l7.m1.2.2.2.2.1.3.2.3">𝑟</ci></apply><ci id="alg2.l7.m1.2.2.2.2.1.3.3.cmml" xref="alg2.l7.m1.2.2.2.2.1.3.3">𝛽</ci></apply><apply id="alg2.l7.m1.2.2.2.2.1.1.1.1.cmml" xref="alg2.l7.m1.2.2.2.2.1.1.1"><csymbol cd="ambiguous" id="alg2.l7.m1.2.2.2.2.1.1.1.1.1.cmml" xref="alg2.l7.m1.2.2.2.2.1.1.1">subscript</csymbol><ci id="alg2.l7.m1.2.2.2.2.1.1.1.1.2.cmml" xref="alg2.l7.m1.2.2.2.2.1.1.1.1.2">𝑆</ci><ci id="alg2.l7.m1.2.2.2.2.1.1.1.1.3.cmml" xref="alg2.l7.m1.2.2.2.2.1.1.1.1.3">𝑟</ci></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="alg2.l7.m1.2c">K_{l}=T^{l}_{\beta}\left(S_{l}\right),K_{r}=T^{r}_{\beta}\left(S_{r}\right)</annotation><annotation encoding="application/x-llamapun" id="alg2.l7.m1.2d">italic_K start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_β end_POSTSUBSCRIPT ( italic_S start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT ) , italic_K start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_β end_POSTSUBSCRIPT ( italic_S start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT )</annotation></semantics></math> </div> <div class="ltx_listingline" id="alg2.l8"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg2.l8.1.1.1" style="font-size:80%;">8:</span></span> Recover the key area semantic features: <math alttext="\hat{S}_{l}=T^{l}_{\theta}\left(\hat{K}_{l}\right),\hat{S}_{r}=T^{r}_{\theta}% \left(\hat{K}_{r}\right)" class="ltx_Math" display="inline" id="alg2.l8.m1.2"><semantics id="alg2.l8.m1.2a"><mrow id="alg2.l8.m1.2.2.2" xref="alg2.l8.m1.2.2.3.cmml"><mrow id="alg2.l8.m1.1.1.1.1" xref="alg2.l8.m1.1.1.1.1.cmml"><msub id="alg2.l8.m1.1.1.1.1.3" xref="alg2.l8.m1.1.1.1.1.3.cmml"><mover accent="true" id="alg2.l8.m1.1.1.1.1.3.2" xref="alg2.l8.m1.1.1.1.1.3.2.cmml"><mi id="alg2.l8.m1.1.1.1.1.3.2.2" xref="alg2.l8.m1.1.1.1.1.3.2.2.cmml">S</mi><mo id="alg2.l8.m1.1.1.1.1.3.2.1" xref="alg2.l8.m1.1.1.1.1.3.2.1.cmml">^</mo></mover><mi id="alg2.l8.m1.1.1.1.1.3.3" xref="alg2.l8.m1.1.1.1.1.3.3.cmml">l</mi></msub><mo id="alg2.l8.m1.1.1.1.1.2" xref="alg2.l8.m1.1.1.1.1.2.cmml">=</mo><mrow id="alg2.l8.m1.1.1.1.1.1" xref="alg2.l8.m1.1.1.1.1.1.cmml"><msubsup id="alg2.l8.m1.1.1.1.1.1.3" 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xref="alg2.l8.m1.2.2.2.2.1.1.1.1.3">𝑟</ci></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="alg2.l8.m1.2c">\hat{S}_{l}=T^{l}_{\theta}\left(\hat{K}_{l}\right),\hat{S}_{r}=T^{r}_{\theta}% \left(\hat{K}_{r}\right)</annotation><annotation encoding="application/x-llamapun" id="alg2.l8.m1.2d">over^ start_ARG italic_S end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_l end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_θ end_POSTSUBSCRIPT ( over^ start_ARG italic_K end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT ) , over^ start_ARG italic_S end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT = italic_T start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_θ end_POSTSUBSCRIPT ( over^ start_ARG italic_K end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT )</annotation></semantics></math> </div> <div class="ltx_listingline" id="alg2.l9"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg2.l9.4.1.1" style="font-size:80%;">9:</span></span><span class="ltx_text" id="alg2.l9.3"> Optimize <math alttext="\beta" class="ltx_Math" display="inline" id="alg2.l9.1.m1.1"><semantics id="alg2.l9.1.m1.1a"><mi id="alg2.l9.1.m1.1.1" xref="alg2.l9.1.m1.1.1.cmml">β</mi><annotation-xml encoding="MathML-Content" id="alg2.l9.1.m1.1b"><ci id="alg2.l9.1.m1.1.1.cmml" xref="alg2.l9.1.m1.1.1">𝛽</ci></annotation-xml><annotation encoding="application/x-tex" id="alg2.l9.1.m1.1c">\beta</annotation><annotation encoding="application/x-llamapun" id="alg2.l9.1.m1.1d">italic_β</annotation></semantics></math>, <math alttext="\theta" class="ltx_Math" display="inline" id="alg2.l9.2.m2.1"><semantics id="alg2.l9.2.m2.1a"><mi id="alg2.l9.2.m2.1.1" xref="alg2.l9.2.m2.1.1.cmml">θ</mi><annotation-xml encoding="MathML-Content" id="alg2.l9.2.m2.1b"><ci id="alg2.l9.2.m2.1.1.cmml" xref="alg2.l9.2.m2.1.1">𝜃</ci></annotation-xml><annotation encoding="application/x-tex" id="alg2.l9.2.m2.1c">\theta</annotation><annotation encoding="application/x-llamapun" id="alg2.l9.2.m2.1d">italic_θ</annotation></semantics></math> with <math alttext="\mathcal{L}_{char}" class="ltx_Math" display="inline" id="alg2.l9.3.m3.1"><semantics id="alg2.l9.3.m3.1a"><msub id="alg2.l9.3.m3.1.1" xref="alg2.l9.3.m3.1.1.cmml"><mi class="ltx_font_mathcaligraphic" id="alg2.l9.3.m3.1.1.2" xref="alg2.l9.3.m3.1.1.2.cmml">ℒ</mi><mrow id="alg2.l9.3.m3.1.1.3" xref="alg2.l9.3.m3.1.1.3.cmml"><mi id="alg2.l9.3.m3.1.1.3.2" xref="alg2.l9.3.m3.1.1.3.2.cmml">c</mi><mo id="alg2.l9.3.m3.1.1.3.1" xref="alg2.l9.3.m3.1.1.3.1.cmml">⁢</mo><mi id="alg2.l9.3.m3.1.1.3.3" xref="alg2.l9.3.m3.1.1.3.3.cmml">h</mi><mo id="alg2.l9.3.m3.1.1.3.1a" xref="alg2.l9.3.m3.1.1.3.1.cmml">⁢</mo><mi id="alg2.l9.3.m3.1.1.3.4" xref="alg2.l9.3.m3.1.1.3.4.cmml">a</mi><mo id="alg2.l9.3.m3.1.1.3.1b" xref="alg2.l9.3.m3.1.1.3.1.cmml">⁢</mo><mi id="alg2.l9.3.m3.1.1.3.5" xref="alg2.l9.3.m3.1.1.3.5.cmml">r</mi></mrow></msub><annotation-xml encoding="MathML-Content" id="alg2.l9.3.m3.1b"><apply id="alg2.l9.3.m3.1.1.cmml" xref="alg2.l9.3.m3.1.1"><csymbol cd="ambiguous" id="alg2.l9.3.m3.1.1.1.cmml" xref="alg2.l9.3.m3.1.1">subscript</csymbol><ci id="alg2.l9.3.m3.1.1.2.cmml" xref="alg2.l9.3.m3.1.1.2">ℒ</ci><apply id="alg2.l9.3.m3.1.1.3.cmml" xref="alg2.l9.3.m3.1.1.3"><times id="alg2.l9.3.m3.1.1.3.1.cmml" xref="alg2.l9.3.m3.1.1.3.1"></times><ci id="alg2.l9.3.m3.1.1.3.2.cmml" xref="alg2.l9.3.m3.1.1.3.2">𝑐</ci><ci id="alg2.l9.3.m3.1.1.3.3.cmml" xref="alg2.l9.3.m3.1.1.3.3">ℎ</ci><ci id="alg2.l9.3.m3.1.1.3.4.cmml" xref="alg2.l9.3.m3.1.1.3.4">𝑎</ci><ci id="alg2.l9.3.m3.1.1.3.5.cmml" xref="alg2.l9.3.m3.1.1.3.5">𝑟</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="alg2.l9.3.m3.1c">\mathcal{L}_{char}</annotation><annotation encoding="application/x-llamapun" id="alg2.l9.3.m3.1d">caligraphic_L start_POSTSUBSCRIPT italic_c italic_h italic_a italic_r end_POSTSUBSCRIPT</annotation></semantics></math> using gradient descent.<span class="ltx_text" id="alg2.l9.3.1"> </span></span> </div> <div class="ltx_listingline" id="alg2.l10"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg2.l10.1.1.1" style="font-size:80%;">10:</span></span> <span class="ltx_text ltx_font_bold" id="alg2.l10.2">until</span> Reach the preset number of repetitions. </div> <div class="ltx_listingline" id="alg2.l11"> <span class="ltx_tag ltx_tag_listingline"><span class="ltx_text" id="alg2.l11.1.1.1" style="font-size:80%;">11:</span></span> <span class="ltx_text ltx_font_bold" id="alg2.l11.2">Return:</span> The network parameters: <math alttext="\beta" class="ltx_Math" display="inline" id="alg2.l11.m1.1"><semantics id="alg2.l11.m1.1a"><mi id="alg2.l11.m1.1.1" xref="alg2.l11.m1.1.1.cmml">β</mi><annotation-xml encoding="MathML-Content" id="alg2.l11.m1.1b"><ci id="alg2.l11.m1.1.1.cmml" xref="alg2.l11.m1.1.1">𝛽</ci></annotation-xml><annotation encoding="application/x-tex" id="alg2.l11.m1.1c">\beta</annotation><annotation encoding="application/x-llamapun" id="alg2.l11.m1.1d">italic_β</annotation></semantics></math>, <math alttext="\theta" class="ltx_Math" display="inline" id="alg2.l11.m2.1"><semantics id="alg2.l11.m2.1a"><mi id="alg2.l11.m2.1.1" xref="alg2.l11.m2.1.1.cmml">θ</mi><annotation-xml encoding="MathML-Content" id="alg2.l11.m2.1b"><ci id="alg2.l11.m2.1.1.cmml" xref="alg2.l11.m2.1.1">𝜃</ci></annotation-xml><annotation encoding="application/x-tex" id="alg2.l11.m2.1c">\theta</annotation><annotation encoding="application/x-llamapun" id="alg2.l11.m2.1d">italic_θ</annotation></semantics></math>. </div> </div> </figure> </section> <section class="ltx_section" id="S5"> <h2 class="ltx_title ltx_title_section"> <span class="ltx_tag ltx_tag_section">V </span><span class="ltx_text ltx_font_smallcaps" id="S5.1.1">Simulation Results and Discussions</span> </h2> <div class="ltx_para" id="S5.p1"> <p class="ltx_p" id="S5.p1.1">In this section, we experimentally evaluate the performance of the proposed semantic communication design for stereo-vision 3D object detection. All methods are evaluated on the KITTI 3D object detection dataset <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib36" title="">36</a>]</cite>, where 7481 training images are split into training and validation sets with roughly the same amount. The cars in the images are divided into three regimes with different levels of difficulty: easy, moderate, and hard, according to their 2D box height, occlusion, and truncation levels.</p> </div> <div class="ltx_para" id="S5.p2"> <p class="ltx_p" id="S5.p2.12">For the first set of experiments, three average compression ratios are simulated, namely <math alttext="10\times" class="ltx_math_unparsed" display="inline" id="S5.p2.1.m1.1"><semantics id="S5.p2.1.m1.1a"><mrow id="S5.p2.1.m1.1b"><mn id="S5.p2.1.m1.1.1">10</mn><mo id="S5.p2.1.m1.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.p2.1.m1.1c">10\times</annotation><annotation encoding="application/x-llamapun" id="S5.p2.1.m1.1d">10 ×</annotation></semantics></math>, <math alttext="30\times" class="ltx_math_unparsed" display="inline" id="S5.p2.2.m2.1"><semantics id="S5.p2.2.m2.1a"><mrow id="S5.p2.2.m2.1b"><mn id="S5.p2.2.m2.1.1">30</mn><mo id="S5.p2.2.m2.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.p2.2.m2.1c">30\times</annotation><annotation encoding="application/x-llamapun" id="S5.p2.2.m2.1d">30 ×</annotation></semantics></math>, and <math alttext="50\times" class="ltx_math_unparsed" display="inline" id="S5.p2.3.m3.1"><semantics id="S5.p2.3.m3.1a"><mrow id="S5.p2.3.m3.1b"><mn id="S5.p2.3.m3.1.1">50</mn><mo id="S5.p2.3.m3.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.p2.3.m3.1c">50\times</annotation><annotation encoding="application/x-llamapun" id="S5.p2.3.m3.1d">50 ×</annotation></semantics></math>, to verify the network performance at low, medium, and high compression ratios. Perfect communication is assumed between the transmitter and receiver to focus on performance evaluation of semantic encoding/decoding designs. These three compression schemes have different global and key area information compression levels<span class="ltx_note ltx_role_footnote" id="footnote2"><sup class="ltx_note_mark">2</sup><span class="ltx_note_outer"><span class="ltx_note_content"><sup class="ltx_note_mark">2</sup><span class="ltx_tag ltx_tag_note">2</span><span class="ltx_text" id="footnote2.1">Various combinations of compression ratios for key areas and global information are tested during the simulations. The combination with the best detection performance is adopted here.</span></span></span></span><span class="ltx_text" id="S5.p2.12.9">. The <math alttext="10\times" class="ltx_math_unparsed" display="inline" id="S5.p2.4.1.m1.1"><semantics id="S5.p2.4.1.m1.1a"><mrow id="S5.p2.4.1.m1.1b"><mn id="S5.p2.4.1.m1.1.1">10</mn><mo id="S5.p2.4.1.m1.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.p2.4.1.m1.1c">10\times</annotation><annotation encoding="application/x-llamapun" id="S5.p2.4.1.m1.1d">10 ×</annotation></semantics></math> scheme compresses the global information <math alttext="36\times" class="ltx_math_unparsed" display="inline" id="S5.p2.5.2.m2.1"><semantics id="S5.p2.5.2.m2.1a"><mrow id="S5.p2.5.2.m2.1b"><mn id="S5.p2.5.2.m2.1.1">36</mn><mo id="S5.p2.5.2.m2.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.p2.5.2.m2.1c">36\times</annotation><annotation encoding="application/x-llamapun" id="S5.p2.5.2.m2.1d">36 ×</annotation></semantics></math> while keeping the key area information uncompressed. The <math alttext="30\times" class="ltx_math_unparsed" display="inline" id="S5.p2.6.3.m3.1"><semantics id="S5.p2.6.3.m3.1a"><mrow id="S5.p2.6.3.m3.1b"><mn id="S5.p2.6.3.m3.1.1">30</mn><mo id="S5.p2.6.3.m3.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.p2.6.3.m3.1c">30\times</annotation><annotation encoding="application/x-llamapun" id="S5.p2.6.3.m3.1d">30 ×</annotation></semantics></math> method compresses the global information <math alttext="36\times" class="ltx_math_unparsed" display="inline" id="S5.p2.7.4.m4.1"><semantics id="S5.p2.7.4.m4.1a"><mrow id="S5.p2.7.4.m4.1b"><mn id="S5.p2.7.4.m4.1.1">36</mn><mo id="S5.p2.7.4.m4.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.p2.7.4.m4.1c">36\times</annotation><annotation encoding="application/x-llamapun" id="S5.p2.7.4.m4.1d">36 ×</annotation></semantics></math> and the key area information <math alttext="4\times" class="ltx_math_unparsed" display="inline" id="S5.p2.8.5.m5.1"><semantics id="S5.p2.8.5.m5.1a"><mrow id="S5.p2.8.5.m5.1b"><mn id="S5.p2.8.5.m5.1.1">4</mn><mo id="S5.p2.8.5.m5.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.p2.8.5.m5.1c">4\times</annotation><annotation encoding="application/x-llamapun" id="S5.p2.8.5.m5.1d">4 ×</annotation></semantics></math>. The <math alttext="50\times" class="ltx_math_unparsed" display="inline" id="S5.p2.9.6.m6.1"><semantics id="S5.p2.9.6.m6.1a"><mrow id="S5.p2.9.6.m6.1b"><mn id="S5.p2.9.6.m6.1.1">50</mn><mo id="S5.p2.9.6.m6.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.p2.9.6.m6.1c">50\times</annotation><annotation encoding="application/x-llamapun" id="S5.p2.9.6.m6.1d">50 ×</annotation></semantics></math> compression technique compresses the global information <math alttext="64\times" class="ltx_math_unparsed" display="inline" id="S5.p2.10.7.m7.1"><semantics id="S5.p2.10.7.m7.1a"><mrow id="S5.p2.10.7.m7.1b"><mn id="S5.p2.10.7.m7.1.1">64</mn><mo id="S5.p2.10.7.m7.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.p2.10.7.m7.1c">64\times</annotation><annotation encoding="application/x-llamapun" id="S5.p2.10.7.m7.1d">64 ×</annotation></semantics></math> and the key area information <math alttext="16\times" class="ltx_math_unparsed" display="inline" id="S5.p2.11.8.m8.1"><semantics id="S5.p2.11.8.m8.1a"><mrow id="S5.p2.11.8.m8.1b"><mn id="S5.p2.11.8.m8.1.1">16</mn><mo id="S5.p2.11.8.m8.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.p2.11.8.m8.1c">16\times</annotation><annotation encoding="application/x-llamapun" id="S5.p2.11.8.m8.1d">16 ×</annotation></semantics></math>. Correspondingly, the model parameters of the proposed network will also be adjusted. <span class="ltx_text" id="S5.p2.12.9.1">For the second set of experiments, the <math alttext="30\times" class="ltx_math_unparsed" display="inline" id="S5.p2.12.9.1.m1.1"><semantics id="S5.p2.12.9.1.m1.1a"><mrow id="S5.p2.12.9.1.m1.1b"><mn id="S5.p2.12.9.1.m1.1.1">30</mn><mo id="S5.p2.12.9.1.m1.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.p2.12.9.1.m1.1c">30\times</annotation><annotation encoding="application/x-llamapun" id="S5.p2.12.9.1.m1.1d">30 ×</annotation></semantics></math> source compression scheme is adopted to evaluate the proposed channel codec under AWGN and Rayleigh channels at different SNR levels, ranging from 6 to 18 dB. For the third set of experiments, the proposed semantic communication system is compared with other source-channel coding algorithms over AWGN channels with varying SNRs to evaluate the joint performance of semantic coding and channel coding in the proposed system.<span class="ltx_text" id="S5.p2.12.9.1.1"></span></span></span></p> </div> <div class="ltx_para" id="S5.p3"> <p class="ltx_p" id="S5.p3.1">The following benchmarks are investigated for performance comparison.</p> <ul class="ltx_itemize" id="S5.I1"> <li class="ltx_item" id="S5.I1.ix1" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item"><math alttext="\bullet" class="ltx_Math" display="inline" id="S5.I1.ix1.1.1.m1.1"><semantics id="S5.I1.ix1.1.1.m1.1b"><mo id="S5.I1.ix1.1.1.m1.1.1" xref="S5.I1.ix1.1.1.m1.1.1.cmml">∙</mo><annotation-xml encoding="MathML-Content" id="S5.I1.ix1.1.1.m1.1c"><ci id="S5.I1.ix1.1.1.m1.1.1.cmml" xref="S5.I1.ix1.1.1.m1.1.1">∙</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.I1.ix1.1.1.m1.1d">\bullet</annotation><annotation encoding="application/x-llamapun" id="S5.I1.ix1.1.1.m1.1e">∙</annotation></semantics></math></span> <div class="ltx_para" id="S5.I1.ix1.p1"> <p class="ltx_p" id="S5.I1.ix1.p1.3"><em class="ltx_emph ltx_font_bold ltx_font_italic" id="S5.I1.ix1.p1.3.4" style="color:#000000;">Benchmarks for the first set of experiments:</em><span class="ltx_text" id="S5.I1.ix1.p1.3.3"> We use standard image compression algorithms as benchmarks, including JPEG, JPEG2000, the Super-Resolution Convolutional Neural Network (SRCNN) <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib37" title="">37</a>]</cite>, and the Epipolar Cross-Attention Stereo Image Compression (ECSIC) network <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib38" title="">38</a>]</cite>. All neural network outputs (except for ECSIC) are quantized to 8-bit and maintain average compression ratios of 10<math alttext="\times" class="ltx_Math" display="inline" id="S5.I1.ix1.p1.1.1.m1.1"><semantics id="S5.I1.ix1.p1.1.1.m1.1a"><mo id="S5.I1.ix1.p1.1.1.m1.1.1" xref="S5.I1.ix1.p1.1.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.I1.ix1.p1.1.1.m1.1b"><times id="S5.I1.ix1.p1.1.1.m1.1.1.cmml" xref="S5.I1.ix1.p1.1.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.I1.ix1.p1.1.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.I1.ix1.p1.1.1.m1.1d">×</annotation></semantics></math>, 30<math alttext="\times" class="ltx_Math" display="inline" id="S5.I1.ix1.p1.2.2.m2.1"><semantics id="S5.I1.ix1.p1.2.2.m2.1a"><mo id="S5.I1.ix1.p1.2.2.m2.1.1" xref="S5.I1.ix1.p1.2.2.m2.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.I1.ix1.p1.2.2.m2.1b"><times id="S5.I1.ix1.p1.2.2.m2.1.1.cmml" xref="S5.I1.ix1.p1.2.2.m2.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.I1.ix1.p1.2.2.m2.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.I1.ix1.p1.2.2.m2.1d">×</annotation></semantics></math>, and 50<math alttext="\times" class="ltx_Math" display="inline" id="S5.I1.ix1.p1.3.3.m3.1"><semantics id="S5.I1.ix1.p1.3.3.m3.1a"><mo id="S5.I1.ix1.p1.3.3.m3.1.1" xref="S5.I1.ix1.p1.3.3.m3.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.I1.ix1.p1.3.3.m3.1b"><times id="S5.I1.ix1.p1.3.3.m3.1.1.cmml" xref="S5.I1.ix1.p1.3.3.m3.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.I1.ix1.p1.3.3.m3.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.I1.ix1.p1.3.3.m3.1d">×</annotation></semantics></math> by adjusting the output dimensions.<span class="ltx_text" id="S5.I1.ix1.p1.3.3.1"></span></span></p> </div> </li> <li class="ltx_item" id="S5.I1.ix2" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item"><math alttext="\bullet" class="ltx_Math" display="inline" id="S5.I1.ix2.1.1.m1.1"><semantics id="S5.I1.ix2.1.1.m1.1b"><mo id="S5.I1.ix2.1.1.m1.1.1" xref="S5.I1.ix2.1.1.m1.1.1.cmml">∙</mo><annotation-xml encoding="MathML-Content" id="S5.I1.ix2.1.1.m1.1c"><ci id="S5.I1.ix2.1.1.m1.1.1.cmml" xref="S5.I1.ix2.1.1.m1.1.1">∙</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.I1.ix2.1.1.m1.1d">\bullet</annotation><annotation encoding="application/x-llamapun" id="S5.I1.ix2.1.1.m1.1e">∙</annotation></semantics></math></span> <div class="ltx_para" id="S5.I1.ix2.p1"> <p class="ltx_p" id="S5.I1.ix2.p1.1"><em class="ltx_emph ltx_font_bold ltx_font_italic" id="S5.I1.ix2.p1.1.1" style="color:#000000;">Benchmarks for the second set of experiments:</em> Based on the semantic codec network with a <math alttext="30\times" class="ltx_math_unparsed" display="inline" id="S5.I1.ix2.p1.1.m1.1"><semantics id="S5.I1.ix2.p1.1.m1.1a"><mrow id="S5.I1.ix2.p1.1.m1.1b"><mn id="S5.I1.ix2.p1.1.m1.1.1">30</mn><mo id="S5.I1.ix2.p1.1.m1.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.I1.ix2.p1.1.m1.1c">30\times</annotation><annotation encoding="application/x-llamapun" id="S5.I1.ix2.p1.1.m1.1d">30 ×</annotation></semantics></math> compression ratio, we compare the proposed channel codec network with two traditional transmission schemes, i.e., the 2/3 rate LDPC code with a 64QAM modulation and the 1/2 rate LDPC code with 256QAM modulation. Please note that these two traditional schemes will deliver the same number of source bits and we also adjust the network dimensions of the proposed method such that they all have the same channel uses for fair comparison.</p> </div> </li> <li class="ltx_item" id="S5.I1.ix3" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item"><math alttext="\bullet" class="ltx_Math" display="inline" id="S5.I1.ix3.1.1.m1.1"><semantics id="S5.I1.ix3.1.1.m1.1b"><mo id="S5.I1.ix3.1.1.m1.1.1" xref="S5.I1.ix3.1.1.m1.1.1.cmml">∙</mo><annotation-xml encoding="MathML-Content" id="S5.I1.ix3.1.1.m1.1c"><ci id="S5.I1.ix3.1.1.m1.1.1.cmml" xref="S5.I1.ix3.1.1.m1.1.1">∙</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.I1.ix3.1.1.m1.1d">\bullet</annotation><annotation encoding="application/x-llamapun" id="S5.I1.ix3.1.1.m1.1e">∙</annotation></semantics></math></span> <div class="ltx_para" id="S5.I1.ix3.p1"> <p class="ltx_p" id="S5.I1.ix3.p1.1"><em class="ltx_emph ltx_font_bold ltx_font_italic" id="S5.I1.ix3.p1.1.2" style="color:#000000;">Benchmarks for the third set of experiments:</em><span class="ltx_text" id="S5.I1.ix3.p1.1.1"> We adopt the same settings as the second set of experiments for the proposed method. The comparison approaches employ JPEG, JPEG2000, and ECSIC with <math alttext="30\times" class="ltx_math_unparsed" display="inline" id="S5.I1.ix3.p1.1.1.m1.1"><semantics id="S5.I1.ix3.p1.1.1.m1.1a"><mrow id="S5.I1.ix3.p1.1.1.m1.1b"><mn id="S5.I1.ix3.p1.1.1.m1.1.1">30</mn><mo id="S5.I1.ix3.p1.1.1.m1.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.I1.ix3.p1.1.1.m1.1c">30\times</annotation><annotation encoding="application/x-llamapun" id="S5.I1.ix3.p1.1.1.m1.1d">30 ×</annotation></semantics></math> compression as the source coding methods, along with two channel-coding and modulation schemes: 2/3 rate LDPC code with 64QAM modulation and 1/2 rate LDPC code with 256QAM modulation.<span class="ltx_text" id="S5.I1.ix3.p1.1.1.1"></span></span></p> </div> </li> </ul> </div> <div class="ltx_para" id="S5.p4"> <p class="ltx_p" id="S5.p4.1">Additionally, Appendixes A and B provide more details on network parameters and training settings for the proposed network.</p> </div> <section class="ltx_subsection" id="S5.SS1"> <h3 class="ltx_title ltx_title_subsection"> <span class="ltx_tag ltx_tag_subsection"><span class="ltx_text" id="S5.SS1.5.1.1">V-A</span> </span><span class="ltx_text ltx_font_italic" id="S5.SS1.6.2">Performance Metrics</span> </h3> <div class="ltx_para" id="S5.SS1.p1"> <p class="ltx_p" id="S5.SS1.p1.1">The peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) metrics are utilized to evaluate the image recovery performance. The PSNR and SSIM of the images inside and outside the key area boxes are calculated, respectively. The 2D average precision (AP) and the 3D AP metrics are also compared in the experiments to assess the detection accuracy of the proposed approach. These metrics are described in detail subsequently.</p> </div> <div class="ltx_para" id="S5.SS1.p2"> <p class="ltx_p" id="S5.SS1.p2.2">The PSNR calculates the MSE between two images to measure their difference. A higher PSNR indicates higher image similarity. Given an original image <math alttext="I" class="ltx_Math" display="inline" id="S5.SS1.p2.1.m1.1"><semantics id="S5.SS1.p2.1.m1.1a"><mi id="S5.SS1.p2.1.m1.1.1" xref="S5.SS1.p2.1.m1.1.1.cmml">I</mi><annotation-xml encoding="MathML-Content" id="S5.SS1.p2.1.m1.1b"><ci id="S5.SS1.p2.1.m1.1.1.cmml" xref="S5.SS1.p2.1.m1.1.1">𝐼</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p2.1.m1.1c">I</annotation><annotation encoding="application/x-llamapun" id="S5.SS1.p2.1.m1.1d">italic_I</annotation></semantics></math> and a recovered image <math alttext="\hat{I}" class="ltx_Math" display="inline" id="S5.SS1.p2.2.m2.1"><semantics id="S5.SS1.p2.2.m2.1a"><mover accent="true" id="S5.SS1.p2.2.m2.1.1" xref="S5.SS1.p2.2.m2.1.1.cmml"><mi id="S5.SS1.p2.2.m2.1.1.2" xref="S5.SS1.p2.2.m2.1.1.2.cmml">I</mi><mo id="S5.SS1.p2.2.m2.1.1.1" xref="S5.SS1.p2.2.m2.1.1.1.cmml">^</mo></mover><annotation-xml encoding="MathML-Content" id="S5.SS1.p2.2.m2.1b"><apply id="S5.SS1.p2.2.m2.1.1.cmml" xref="S5.SS1.p2.2.m2.1.1"><ci id="S5.SS1.p2.2.m2.1.1.1.cmml" xref="S5.SS1.p2.2.m2.1.1.1">^</ci><ci id="S5.SS1.p2.2.m2.1.1.2.cmml" xref="S5.SS1.p2.2.m2.1.1.2">𝐼</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p2.2.m2.1c">\hat{I}</annotation><annotation encoding="application/x-llamapun" id="S5.SS1.p2.2.m2.1d">over^ start_ARG italic_I end_ARG</annotation></semantics></math>, the PSNR is defined as</p> <table class="ltx_equation ltx_eqn_table" id="S5.E18"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="\text{PSNR}=20\cdot{\log_{10}}\left({\frac{{{\mathcal{F}_{\max}}\left(I\right)% }}{{{\mathcal{F}_{mse}}\left({I,\hat{I}}\right)}}}\right)\text{,}" class="ltx_Math" display="block" id="S5.E18.m1.4"><semantics id="S5.E18.m1.4a"><mrow id="S5.E18.m1.4.4" xref="S5.E18.m1.4.4.cmml"><mtext id="S5.E18.m1.4.4.3" xref="S5.E18.m1.4.4.3a.cmml">PSNR</mtext><mo id="S5.E18.m1.4.4.2" xref="S5.E18.m1.4.4.2.cmml">=</mo><mrow id="S5.E18.m1.4.4.1" xref="S5.E18.m1.4.4.1.cmml"><mrow id="S5.E18.m1.4.4.1.1" xref="S5.E18.m1.4.4.1.1.cmml"><mn id="S5.E18.m1.4.4.1.1.3" xref="S5.E18.m1.4.4.1.1.3.cmml">20</mn><mo id="S5.E18.m1.4.4.1.1.2" lspace="0.222em" rspace="0.222em" xref="S5.E18.m1.4.4.1.1.2.cmml">⋅</mo><mrow id="S5.E18.m1.4.4.1.1.1.1" xref="S5.E18.m1.4.4.1.1.1.2.cmml"><msub id="S5.E18.m1.4.4.1.1.1.1.1" xref="S5.E18.m1.4.4.1.1.1.1.1.cmml"><mi id="S5.E18.m1.4.4.1.1.1.1.1.2" xref="S5.E18.m1.4.4.1.1.1.1.1.2.cmml">log</mi><mn id="S5.E18.m1.4.4.1.1.1.1.1.3" xref="S5.E18.m1.4.4.1.1.1.1.1.3.cmml">10</mn></msub><mo id="S5.E18.m1.4.4.1.1.1.1a" xref="S5.E18.m1.4.4.1.1.1.2.cmml">⁡</mo><mrow id="S5.E18.m1.4.4.1.1.1.1.2" xref="S5.E18.m1.4.4.1.1.1.2.cmml"><mo id="S5.E18.m1.4.4.1.1.1.1.2.1" xref="S5.E18.m1.4.4.1.1.1.2.cmml">(</mo><mfrac id="S5.E18.m1.3.3" xref="S5.E18.m1.3.3.cmml"><mrow id="S5.E18.m1.1.1.1" xref="S5.E18.m1.1.1.1.cmml"><msub id="S5.E18.m1.1.1.1.3" xref="S5.E18.m1.1.1.1.3.cmml"><mi class="ltx_font_mathcaligraphic" id="S5.E18.m1.1.1.1.3.2" xref="S5.E18.m1.1.1.1.3.2.cmml">ℱ</mi><mi id="S5.E18.m1.1.1.1.3.3" xref="S5.E18.m1.1.1.1.3.3.cmml">max</mi></msub><mo id="S5.E18.m1.1.1.1.2" xref="S5.E18.m1.1.1.1.2.cmml">⁢</mo><mrow id="S5.E18.m1.1.1.1.4.2" xref="S5.E18.m1.1.1.1.cmml"><mo id="S5.E18.m1.1.1.1.4.2.1" xref="S5.E18.m1.1.1.1.cmml">(</mo><mi id="S5.E18.m1.1.1.1.1" xref="S5.E18.m1.1.1.1.1.cmml">I</mi><mo id="S5.E18.m1.1.1.1.4.2.2" xref="S5.E18.m1.1.1.1.cmml">)</mo></mrow></mrow><mrow id="S5.E18.m1.3.3.3" xref="S5.E18.m1.3.3.3.cmml"><msub id="S5.E18.m1.3.3.3.4" xref="S5.E18.m1.3.3.3.4.cmml"><mi class="ltx_font_mathcaligraphic" id="S5.E18.m1.3.3.3.4.2" xref="S5.E18.m1.3.3.3.4.2.cmml">ℱ</mi><mrow id="S5.E18.m1.3.3.3.4.3" xref="S5.E18.m1.3.3.3.4.3.cmml"><mi id="S5.E18.m1.3.3.3.4.3.2" xref="S5.E18.m1.3.3.3.4.3.2.cmml">m</mi><mo id="S5.E18.m1.3.3.3.4.3.1" xref="S5.E18.m1.3.3.3.4.3.1.cmml">⁢</mo><mi id="S5.E18.m1.3.3.3.4.3.3" xref="S5.E18.m1.3.3.3.4.3.3.cmml">s</mi><mo id="S5.E18.m1.3.3.3.4.3.1a" xref="S5.E18.m1.3.3.3.4.3.1.cmml">⁢</mo><mi id="S5.E18.m1.3.3.3.4.3.4" xref="S5.E18.m1.3.3.3.4.3.4.cmml">e</mi></mrow></msub><mo id="S5.E18.m1.3.3.3.3" xref="S5.E18.m1.3.3.3.3.cmml">⁢</mo><mrow id="S5.E18.m1.3.3.3.5.2" xref="S5.E18.m1.3.3.3.5.1.cmml"><mo id="S5.E18.m1.3.3.3.5.2.1" xref="S5.E18.m1.3.3.3.5.1.cmml">(</mo><mi id="S5.E18.m1.2.2.2.1" xref="S5.E18.m1.2.2.2.1.cmml">I</mi><mo id="S5.E18.m1.3.3.3.5.2.2" xref="S5.E18.m1.3.3.3.5.1.cmml">,</mo><mover accent="true" id="S5.E18.m1.3.3.3.2" xref="S5.E18.m1.3.3.3.2.cmml"><mi id="S5.E18.m1.3.3.3.2.2" xref="S5.E18.m1.3.3.3.2.2.cmml">I</mi><mo id="S5.E18.m1.3.3.3.2.1" xref="S5.E18.m1.3.3.3.2.1.cmml">^</mo></mover><mo id="S5.E18.m1.3.3.3.5.2.3" xref="S5.E18.m1.3.3.3.5.1.cmml">)</mo></mrow></mrow></mfrac><mo id="S5.E18.m1.4.4.1.1.1.1.2.2" xref="S5.E18.m1.4.4.1.1.1.2.cmml">)</mo></mrow></mrow></mrow><mo id="S5.E18.m1.4.4.1.2" xref="S5.E18.m1.4.4.1.2.cmml">⁢</mo><mtext id="S5.E18.m1.4.4.1.3" xref="S5.E18.m1.4.4.1.3a.cmml">,</mtext></mrow></mrow><annotation-xml encoding="MathML-Content" id="S5.E18.m1.4b"><apply id="S5.E18.m1.4.4.cmml" xref="S5.E18.m1.4.4"><eq id="S5.E18.m1.4.4.2.cmml" xref="S5.E18.m1.4.4.2"></eq><ci id="S5.E18.m1.4.4.3a.cmml" xref="S5.E18.m1.4.4.3"><mtext id="S5.E18.m1.4.4.3.cmml" xref="S5.E18.m1.4.4.3">PSNR</mtext></ci><apply id="S5.E18.m1.4.4.1.cmml" xref="S5.E18.m1.4.4.1"><times id="S5.E18.m1.4.4.1.2.cmml" xref="S5.E18.m1.4.4.1.2"></times><apply id="S5.E18.m1.4.4.1.1.cmml" xref="S5.E18.m1.4.4.1.1"><ci id="S5.E18.m1.4.4.1.1.2.cmml" xref="S5.E18.m1.4.4.1.1.2">⋅</ci><cn id="S5.E18.m1.4.4.1.1.3.cmml" type="integer" xref="S5.E18.m1.4.4.1.1.3">20</cn><apply id="S5.E18.m1.4.4.1.1.1.2.cmml" xref="S5.E18.m1.4.4.1.1.1.1"><apply id="S5.E18.m1.4.4.1.1.1.1.1.cmml" xref="S5.E18.m1.4.4.1.1.1.1.1"><csymbol cd="ambiguous" id="S5.E18.m1.4.4.1.1.1.1.1.1.cmml" xref="S5.E18.m1.4.4.1.1.1.1.1">subscript</csymbol><log id="S5.E18.m1.4.4.1.1.1.1.1.2.cmml" xref="S5.E18.m1.4.4.1.1.1.1.1.2"></log><cn id="S5.E18.m1.4.4.1.1.1.1.1.3.cmml" type="integer" xref="S5.E18.m1.4.4.1.1.1.1.1.3">10</cn></apply><apply id="S5.E18.m1.3.3.cmml" xref="S5.E18.m1.3.3"><divide id="S5.E18.m1.3.3.4.cmml" xref="S5.E18.m1.3.3"></divide><apply id="S5.E18.m1.1.1.1.cmml" xref="S5.E18.m1.1.1.1"><times id="S5.E18.m1.1.1.1.2.cmml" xref="S5.E18.m1.1.1.1.2"></times><apply id="S5.E18.m1.1.1.1.3.cmml" xref="S5.E18.m1.1.1.1.3"><csymbol cd="ambiguous" id="S5.E18.m1.1.1.1.3.1.cmml" xref="S5.E18.m1.1.1.1.3">subscript</csymbol><ci id="S5.E18.m1.1.1.1.3.2.cmml" xref="S5.E18.m1.1.1.1.3.2">ℱ</ci><max id="S5.E18.m1.1.1.1.3.3.cmml" xref="S5.E18.m1.1.1.1.3.3"></max></apply><ci id="S5.E18.m1.1.1.1.1.cmml" xref="S5.E18.m1.1.1.1.1">𝐼</ci></apply><apply id="S5.E18.m1.3.3.3.cmml" xref="S5.E18.m1.3.3.3"><times id="S5.E18.m1.3.3.3.3.cmml" xref="S5.E18.m1.3.3.3.3"></times><apply id="S5.E18.m1.3.3.3.4.cmml" xref="S5.E18.m1.3.3.3.4"><csymbol cd="ambiguous" id="S5.E18.m1.3.3.3.4.1.cmml" xref="S5.E18.m1.3.3.3.4">subscript</csymbol><ci id="S5.E18.m1.3.3.3.4.2.cmml" xref="S5.E18.m1.3.3.3.4.2">ℱ</ci><apply id="S5.E18.m1.3.3.3.4.3.cmml" xref="S5.E18.m1.3.3.3.4.3"><times id="S5.E18.m1.3.3.3.4.3.1.cmml" xref="S5.E18.m1.3.3.3.4.3.1"></times><ci id="S5.E18.m1.3.3.3.4.3.2.cmml" xref="S5.E18.m1.3.3.3.4.3.2">𝑚</ci><ci id="S5.E18.m1.3.3.3.4.3.3.cmml" xref="S5.E18.m1.3.3.3.4.3.3">𝑠</ci><ci id="S5.E18.m1.3.3.3.4.3.4.cmml" xref="S5.E18.m1.3.3.3.4.3.4">𝑒</ci></apply></apply><interval closure="open" id="S5.E18.m1.3.3.3.5.1.cmml" xref="S5.E18.m1.3.3.3.5.2"><ci id="S5.E18.m1.2.2.2.1.cmml" xref="S5.E18.m1.2.2.2.1">𝐼</ci><apply id="S5.E18.m1.3.3.3.2.cmml" xref="S5.E18.m1.3.3.3.2"><ci id="S5.E18.m1.3.3.3.2.1.cmml" xref="S5.E18.m1.3.3.3.2.1">^</ci><ci id="S5.E18.m1.3.3.3.2.2.cmml" xref="S5.E18.m1.3.3.3.2.2">𝐼</ci></apply></interval></apply></apply></apply></apply><ci id="S5.E18.m1.4.4.1.3a.cmml" xref="S5.E18.m1.4.4.1.3"><mtext id="S5.E18.m1.4.4.1.3.cmml" xref="S5.E18.m1.4.4.1.3">,</mtext></ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S5.E18.m1.4c">\text{PSNR}=20\cdot{\log_{10}}\left({\frac{{{\mathcal{F}_{\max}}\left(I\right)% }}{{{\mathcal{F}_{mse}}\left({I,\hat{I}}\right)}}}\right)\text{,}</annotation><annotation encoding="application/x-llamapun" id="S5.E18.m1.4d">PSNR = 20 ⋅ roman_log start_POSTSUBSCRIPT 10 end_POSTSUBSCRIPT ( divide start_ARG caligraphic_F start_POSTSUBSCRIPT roman_max end_POSTSUBSCRIPT ( italic_I ) end_ARG start_ARG caligraphic_F start_POSTSUBSCRIPT italic_m italic_s italic_e end_POSTSUBSCRIPT ( italic_I , over^ start_ARG italic_I end_ARG ) end_ARG ) ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(18)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S5.SS1.p2.4">where <math alttext="{\mathcal{F}_{\max}}\left(I\right)" class="ltx_Math" display="inline" id="S5.SS1.p2.3.m1.1"><semantics id="S5.SS1.p2.3.m1.1a"><mrow id="S5.SS1.p2.3.m1.1.2" xref="S5.SS1.p2.3.m1.1.2.cmml"><msub id="S5.SS1.p2.3.m1.1.2.2" xref="S5.SS1.p2.3.m1.1.2.2.cmml"><mi class="ltx_font_mathcaligraphic" id="S5.SS1.p2.3.m1.1.2.2.2" xref="S5.SS1.p2.3.m1.1.2.2.2.cmml">ℱ</mi><mi id="S5.SS1.p2.3.m1.1.2.2.3" xref="S5.SS1.p2.3.m1.1.2.2.3.cmml">max</mi></msub><mo id="S5.SS1.p2.3.m1.1.2.1" xref="S5.SS1.p2.3.m1.1.2.1.cmml">⁢</mo><mrow id="S5.SS1.p2.3.m1.1.2.3.2" xref="S5.SS1.p2.3.m1.1.2.cmml"><mo id="S5.SS1.p2.3.m1.1.2.3.2.1" xref="S5.SS1.p2.3.m1.1.2.cmml">(</mo><mi id="S5.SS1.p2.3.m1.1.1" xref="S5.SS1.p2.3.m1.1.1.cmml">I</mi><mo id="S5.SS1.p2.3.m1.1.2.3.2.2" xref="S5.SS1.p2.3.m1.1.2.cmml">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="S5.SS1.p2.3.m1.1b"><apply id="S5.SS1.p2.3.m1.1.2.cmml" xref="S5.SS1.p2.3.m1.1.2"><times id="S5.SS1.p2.3.m1.1.2.1.cmml" xref="S5.SS1.p2.3.m1.1.2.1"></times><apply id="S5.SS1.p2.3.m1.1.2.2.cmml" xref="S5.SS1.p2.3.m1.1.2.2"><csymbol cd="ambiguous" id="S5.SS1.p2.3.m1.1.2.2.1.cmml" xref="S5.SS1.p2.3.m1.1.2.2">subscript</csymbol><ci id="S5.SS1.p2.3.m1.1.2.2.2.cmml" xref="S5.SS1.p2.3.m1.1.2.2.2">ℱ</ci><max id="S5.SS1.p2.3.m1.1.2.2.3.cmml" xref="S5.SS1.p2.3.m1.1.2.2.3"></max></apply><ci id="S5.SS1.p2.3.m1.1.1.cmml" xref="S5.SS1.p2.3.m1.1.1">𝐼</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p2.3.m1.1c">{\mathcal{F}_{\max}}\left(I\right)</annotation><annotation encoding="application/x-llamapun" id="S5.SS1.p2.3.m1.1d">caligraphic_F start_POSTSUBSCRIPT roman_max end_POSTSUBSCRIPT ( italic_I )</annotation></semantics></math> is the maximum pixel value of the image, <math alttext="{\mathcal{F}_{mse}}\left({I,\hat{I}}\right)" class="ltx_Math" display="inline" id="S5.SS1.p2.4.m2.2"><semantics id="S5.SS1.p2.4.m2.2a"><mrow id="S5.SS1.p2.4.m2.2.3" xref="S5.SS1.p2.4.m2.2.3.cmml"><msub id="S5.SS1.p2.4.m2.2.3.2" xref="S5.SS1.p2.4.m2.2.3.2.cmml"><mi class="ltx_font_mathcaligraphic" id="S5.SS1.p2.4.m2.2.3.2.2" xref="S5.SS1.p2.4.m2.2.3.2.2.cmml">ℱ</mi><mrow id="S5.SS1.p2.4.m2.2.3.2.3" xref="S5.SS1.p2.4.m2.2.3.2.3.cmml"><mi id="S5.SS1.p2.4.m2.2.3.2.3.2" xref="S5.SS1.p2.4.m2.2.3.2.3.2.cmml">m</mi><mo id="S5.SS1.p2.4.m2.2.3.2.3.1" xref="S5.SS1.p2.4.m2.2.3.2.3.1.cmml">⁢</mo><mi id="S5.SS1.p2.4.m2.2.3.2.3.3" xref="S5.SS1.p2.4.m2.2.3.2.3.3.cmml">s</mi><mo id="S5.SS1.p2.4.m2.2.3.2.3.1a" xref="S5.SS1.p2.4.m2.2.3.2.3.1.cmml">⁢</mo><mi id="S5.SS1.p2.4.m2.2.3.2.3.4" xref="S5.SS1.p2.4.m2.2.3.2.3.4.cmml">e</mi></mrow></msub><mo id="S5.SS1.p2.4.m2.2.3.1" xref="S5.SS1.p2.4.m2.2.3.1.cmml">⁢</mo><mrow id="S5.SS1.p2.4.m2.2.3.3.2" xref="S5.SS1.p2.4.m2.2.3.3.1.cmml"><mo id="S5.SS1.p2.4.m2.2.3.3.2.1" 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italic_e end_POSTSUBSCRIPT ( italic_I , over^ start_ARG italic_I end_ARG )</annotation></semantics></math> represents the MSE between the original and recovered images.</p> </div> <div class="ltx_para" id="S5.SS1.p3"> <p class="ltx_p" id="S5.SS1.p3.14">The SSIM metric <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib39" title="">39</a>]</cite> is more focused on capturing edge and texture similarities, which are essential for mimicking human perception. It calculates the SSIM score by segmenting the image into smaller blocks and evaluating each block’s luminance, contrast, and structure scores. The SSIM score can be expressed as</p> <table class="ltx_equation ltx_eqn_table" id="S5.E19"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_eqn_cell ltx_align_center"><math alttext="\text{SSIM}=\frac{1}{N}\sum\nolimits_{n=1}^{N}{S_{l,n}\times S_{c,n}\times S_{% s,n}}\text{,}" class="ltx_Math" display="block" id="S5.E19.m1.6"><semantics id="S5.E19.m1.6a"><mrow id="S5.E19.m1.6.7" xref="S5.E19.m1.6.7.cmml"><mtext id="S5.E19.m1.6.7.2" xref="S5.E19.m1.6.7.2a.cmml">SSIM</mtext><mo id="S5.E19.m1.6.7.1" xref="S5.E19.m1.6.7.1.cmml">=</mo><mrow id="S5.E19.m1.6.7.3" xref="S5.E19.m1.6.7.3.cmml"><mfrac id="S5.E19.m1.6.7.3.2" xref="S5.E19.m1.6.7.3.2.cmml"><mn id="S5.E19.m1.6.7.3.2.2" xref="S5.E19.m1.6.7.3.2.2.cmml">1</mn><mi id="S5.E19.m1.6.7.3.2.3" xref="S5.E19.m1.6.7.3.2.3.cmml">N</mi></mfrac><mo id="S5.E19.m1.6.7.3.1" xref="S5.E19.m1.6.7.3.1.cmml">⁢</mo><mrow id="S5.E19.m1.6.7.3.3" 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id="S5.E19.m1.4.4.2.3.cmml" xref="S5.E19.m1.4.4.2.4"><ci id="S5.E19.m1.3.3.1.1.cmml" xref="S5.E19.m1.3.3.1.1">𝑐</ci><ci id="S5.E19.m1.4.4.2.2.cmml" xref="S5.E19.m1.4.4.2.2">𝑛</ci></list></apply><apply id="S5.E19.m1.6.7.3.3.2.2.4.cmml" xref="S5.E19.m1.6.7.3.3.2.2.4"><csymbol cd="ambiguous" id="S5.E19.m1.6.7.3.3.2.2.4.1.cmml" xref="S5.E19.m1.6.7.3.3.2.2.4">subscript</csymbol><ci id="S5.E19.m1.6.7.3.3.2.2.4.2.cmml" xref="S5.E19.m1.6.7.3.3.2.2.4.2">𝑆</ci><list id="S5.E19.m1.6.6.2.3.cmml" xref="S5.E19.m1.6.6.2.4"><ci id="S5.E19.m1.5.5.1.1.cmml" xref="S5.E19.m1.5.5.1.1">𝑠</ci><ci id="S5.E19.m1.6.6.2.2.cmml" xref="S5.E19.m1.6.6.2.2">𝑛</ci></list></apply></apply><ci id="S5.E19.m1.6.7.3.3.2.3a.cmml" xref="S5.E19.m1.6.7.3.3.2.3"><mtext id="S5.E19.m1.6.7.3.3.2.3.cmml" xref="S5.E19.m1.6.7.3.3.2.3">,</mtext></ci></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S5.E19.m1.6c">\text{SSIM}=\frac{1}{N}\sum\nolimits_{n=1}^{N}{S_{l,n}\times S_{c,n}\times S_{% s,n}}\text{,}</annotation><annotation encoding="application/x-llamapun" id="S5.E19.m1.6d">SSIM = divide start_ARG 1 end_ARG start_ARG italic_N end_ARG ∑ start_POSTSUBSCRIPT italic_n = 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_N end_POSTSUPERSCRIPT italic_S start_POSTSUBSCRIPT italic_l , italic_n end_POSTSUBSCRIPT × italic_S start_POSTSUBSCRIPT italic_c , italic_n end_POSTSUBSCRIPT × italic_S start_POSTSUBSCRIPT italic_s , italic_n end_POSTSUBSCRIPT ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(19)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S5.SS1.p3.5">where <math alttext="N" class="ltx_Math" display="inline" id="S5.SS1.p3.1.m1.1"><semantics id="S5.SS1.p3.1.m1.1a"><mi id="S5.SS1.p3.1.m1.1.1" xref="S5.SS1.p3.1.m1.1.1.cmml">N</mi><annotation-xml encoding="MathML-Content" id="S5.SS1.p3.1.m1.1b"><ci id="S5.SS1.p3.1.m1.1.1.cmml" xref="S5.SS1.p3.1.m1.1.1">𝑁</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p3.1.m1.1c">N</annotation><annotation encoding="application/x-llamapun" id="S5.SS1.p3.1.m1.1d">italic_N</annotation></semantics></math> is the total number of blocks, and <math alttext="S_{l,n}" class="ltx_Math" display="inline" id="S5.SS1.p3.2.m2.2"><semantics id="S5.SS1.p3.2.m2.2a"><msub id="S5.SS1.p3.2.m2.2.3" xref="S5.SS1.p3.2.m2.2.3.cmml"><mi id="S5.SS1.p3.2.m2.2.3.2" xref="S5.SS1.p3.2.m2.2.3.2.cmml">S</mi><mrow id="S5.SS1.p3.2.m2.2.2.2.4" xref="S5.SS1.p3.2.m2.2.2.2.3.cmml"><mi id="S5.SS1.p3.2.m2.1.1.1.1" xref="S5.SS1.p3.2.m2.1.1.1.1.cmml">l</mi><mo id="S5.SS1.p3.2.m2.2.2.2.4.1" xref="S5.SS1.p3.2.m2.2.2.2.3.cmml">,</mo><mi id="S5.SS1.p3.2.m2.2.2.2.2" xref="S5.SS1.p3.2.m2.2.2.2.2.cmml">n</mi></mrow></msub><annotation-xml encoding="MathML-Content" id="S5.SS1.p3.2.m2.2b"><apply id="S5.SS1.p3.2.m2.2.3.cmml" xref="S5.SS1.p3.2.m2.2.3"><csymbol cd="ambiguous" id="S5.SS1.p3.2.m2.2.3.1.cmml" xref="S5.SS1.p3.2.m2.2.3">subscript</csymbol><ci id="S5.SS1.p3.2.m2.2.3.2.cmml" xref="S5.SS1.p3.2.m2.2.3.2">𝑆</ci><list id="S5.SS1.p3.2.m2.2.2.2.3.cmml" xref="S5.SS1.p3.2.m2.2.2.2.4"><ci id="S5.SS1.p3.2.m2.1.1.1.1.cmml" xref="S5.SS1.p3.2.m2.1.1.1.1">𝑙</ci><ci id="S5.SS1.p3.2.m2.2.2.2.2.cmml" xref="S5.SS1.p3.2.m2.2.2.2.2">𝑛</ci></list></apply></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p3.2.m2.2c">S_{l,n}</annotation><annotation encoding="application/x-llamapun" id="S5.SS1.p3.2.m2.2d">italic_S start_POSTSUBSCRIPT italic_l , italic_n end_POSTSUBSCRIPT</annotation></semantics></math>, <math alttext="S_{c,n}" class="ltx_Math" display="inline" id="S5.SS1.p3.3.m3.2"><semantics id="S5.SS1.p3.3.m3.2a"><msub id="S5.SS1.p3.3.m3.2.3" xref="S5.SS1.p3.3.m3.2.3.cmml"><mi id="S5.SS1.p3.3.m3.2.3.2" xref="S5.SS1.p3.3.m3.2.3.2.cmml">S</mi><mrow id="S5.SS1.p3.3.m3.2.2.2.4" xref="S5.SS1.p3.3.m3.2.2.2.3.cmml"><mi id="S5.SS1.p3.3.m3.1.1.1.1" xref="S5.SS1.p3.3.m3.1.1.1.1.cmml">c</mi><mo id="S5.SS1.p3.3.m3.2.2.2.4.1" xref="S5.SS1.p3.3.m3.2.2.2.3.cmml">,</mo><mi id="S5.SS1.p3.3.m3.2.2.2.2" xref="S5.SS1.p3.3.m3.2.2.2.2.cmml">n</mi></mrow></msub><annotation-xml encoding="MathML-Content" id="S5.SS1.p3.3.m3.2b"><apply id="S5.SS1.p3.3.m3.2.3.cmml" xref="S5.SS1.p3.3.m3.2.3"><csymbol cd="ambiguous" id="S5.SS1.p3.3.m3.2.3.1.cmml" xref="S5.SS1.p3.3.m3.2.3">subscript</csymbol><ci id="S5.SS1.p3.3.m3.2.3.2.cmml" xref="S5.SS1.p3.3.m3.2.3.2">𝑆</ci><list id="S5.SS1.p3.3.m3.2.2.2.3.cmml" xref="S5.SS1.p3.3.m3.2.2.2.4"><ci id="S5.SS1.p3.3.m3.1.1.1.1.cmml" xref="S5.SS1.p3.3.m3.1.1.1.1">𝑐</ci><ci id="S5.SS1.p3.3.m3.2.2.2.2.cmml" xref="S5.SS1.p3.3.m3.2.2.2.2">𝑛</ci></list></apply></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p3.3.m3.2c">S_{c,n}</annotation><annotation encoding="application/x-llamapun" id="S5.SS1.p3.3.m3.2d">italic_S start_POSTSUBSCRIPT italic_c , italic_n end_POSTSUBSCRIPT</annotation></semantics></math>, <math alttext="S_{s,n}" class="ltx_Math" display="inline" id="S5.SS1.p3.4.m4.2"><semantics id="S5.SS1.p3.4.m4.2a"><msub id="S5.SS1.p3.4.m4.2.3" xref="S5.SS1.p3.4.m4.2.3.cmml"><mi id="S5.SS1.p3.4.m4.2.3.2" xref="S5.SS1.p3.4.m4.2.3.2.cmml">S</mi><mrow id="S5.SS1.p3.4.m4.2.2.2.4" xref="S5.SS1.p3.4.m4.2.2.2.3.cmml"><mi id="S5.SS1.p3.4.m4.1.1.1.1" xref="S5.SS1.p3.4.m4.1.1.1.1.cmml">s</mi><mo id="S5.SS1.p3.4.m4.2.2.2.4.1" xref="S5.SS1.p3.4.m4.2.2.2.3.cmml">,</mo><mi id="S5.SS1.p3.4.m4.2.2.2.2" xref="S5.SS1.p3.4.m4.2.2.2.2.cmml">n</mi></mrow></msub><annotation-xml encoding="MathML-Content" id="S5.SS1.p3.4.m4.2b"><apply id="S5.SS1.p3.4.m4.2.3.cmml" xref="S5.SS1.p3.4.m4.2.3"><csymbol cd="ambiguous" id="S5.SS1.p3.4.m4.2.3.1.cmml" xref="S5.SS1.p3.4.m4.2.3">subscript</csymbol><ci id="S5.SS1.p3.4.m4.2.3.2.cmml" xref="S5.SS1.p3.4.m4.2.3.2">𝑆</ci><list id="S5.SS1.p3.4.m4.2.2.2.3.cmml" xref="S5.SS1.p3.4.m4.2.2.2.4"><ci id="S5.SS1.p3.4.m4.1.1.1.1.cmml" xref="S5.SS1.p3.4.m4.1.1.1.1">𝑠</ci><ci id="S5.SS1.p3.4.m4.2.2.2.2.cmml" xref="S5.SS1.p3.4.m4.2.2.2.2">𝑛</ci></list></apply></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p3.4.m4.2c">S_{s,n}</annotation><annotation encoding="application/x-llamapun" id="S5.SS1.p3.4.m4.2d">italic_S start_POSTSUBSCRIPT italic_s , italic_n end_POSTSUBSCRIPT</annotation></semantics></math> represent the luminance, contrast, and structure scores of the <math alttext="n" class="ltx_Math" display="inline" id="S5.SS1.p3.5.m5.1"><semantics id="S5.SS1.p3.5.m5.1a"><mi id="S5.SS1.p3.5.m5.1.1" xref="S5.SS1.p3.5.m5.1.1.cmml">n</mi><annotation-xml encoding="MathML-Content" id="S5.SS1.p3.5.m5.1b"><ci id="S5.SS1.p3.5.m5.1.1.cmml" xref="S5.SS1.p3.5.m5.1.1">𝑛</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p3.5.m5.1c">n</annotation><annotation encoding="application/x-llamapun" id="S5.SS1.p3.5.m5.1d">italic_n</annotation></semantics></math>th block, respectively, and can be expressed as</p> <table class="ltx_equationgroup ltx_eqn_align ltx_eqn_table" id="A2.EGx1"> <tbody id="S5.E23"><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_center_padleft"></td> <td class="ltx_td ltx_align_right ltx_eqn_cell"><math alttext="\displaystyle\left\{{\begin{array}[]{*{20}{l}}{S_{l}=\frac{{2{\mu_{x}}{\mu_{y}% }}}{{\mu_{x}^{2}+\mu_{y}^{2}}}}\text{,}\\ {S_{c}=\frac{{2{\sigma_{x}}{\sigma_{y}}}}{{\sigma_{x}^{2}+\sigma_{y}^{2}}}}% \text{,}\\ {S_{s}=\frac{{{\sigma_{xy}}}}{{{\sigma_{x}}{\sigma_{y}}}}}\text{,}\\ \end{array}}\right." class="ltx_Math" display="inline" id="S5.E23.m1.1"><semantics id="S5.E23.m1.1a"><mrow id="S5.E23.m1.1.2.2" xref="S5.E23.m1.1.2.1.cmml"><mo id="S5.E23.m1.1.2.2.1" xref="S5.E23.m1.1.2.1.1.cmml">{</mo><mtable columnspacing="5pt" id="S5.E23.m1.1.1" rowspacing="0pt" xref="S5.E23.m1.1.1.cmml"><mtr id="S5.E23.m1.1.1a" xref="S5.E23.m1.1.1.cmml"><mtd class="ltx_align_left" columnalign="left" id="S5.E23.m1.1.1b" xref="S5.E23.m1.1.1.cmml"><mrow id="S5.E20.1.1" xref="S5.E20.1.1.cmml"><msub id="S5.E20.1.1.2" xref="S5.E20.1.1.2.cmml"><mi id="S5.E20.1.1.2.2" xref="S5.E20.1.1.2.2.cmml">S</mi><mi id="S5.E20.1.1.2.3" xref="S5.E20.1.1.2.3.cmml">l</mi></msub><mo id="S5.E20.1.1.1" xref="S5.E20.1.1.1.cmml">=</mo><mrow id="S5.E20.1.1.3" xref="S5.E20.1.1.3.cmml"><mfrac id="S5.E20.1.1.3.2" xref="S5.E20.1.1.3.2.cmml"><mrow id="S5.E20.1.1.3.2.2" xref="S5.E20.1.1.3.2.2.cmml"><mn id="S5.E20.1.1.3.2.2.2" xref="S5.E20.1.1.3.2.2.2.cmml">2</mn><mo id="S5.E20.1.1.3.2.2.1" xref="S5.E20.1.1.3.2.2.1.cmml">⁢</mo><msub id="S5.E20.1.1.3.2.2.3" xref="S5.E20.1.1.3.2.2.3.cmml"><mi id="S5.E20.1.1.3.2.2.3.2" xref="S5.E20.1.1.3.2.2.3.2.cmml">μ</mi><mi id="S5.E20.1.1.3.2.2.3.3" xref="S5.E20.1.1.3.2.2.3.3.cmml">x</mi></msub><mo id="S5.E20.1.1.3.2.2.1a" xref="S5.E20.1.1.3.2.2.1.cmml">⁢</mo><msub id="S5.E20.1.1.3.2.2.4" xref="S5.E20.1.1.3.2.2.4.cmml"><mi id="S5.E20.1.1.3.2.2.4.2" xref="S5.E20.1.1.3.2.2.4.2.cmml">μ</mi><mi id="S5.E20.1.1.3.2.2.4.3" xref="S5.E20.1.1.3.2.2.4.3.cmml">y</mi></msub></mrow><mrow id="S5.E20.1.1.3.2.3" xref="S5.E20.1.1.3.2.3.cmml"><msubsup id="S5.E20.1.1.3.2.3.2" xref="S5.E20.1.1.3.2.3.2.cmml"><mi id="S5.E20.1.1.3.2.3.2.2.2" xref="S5.E20.1.1.3.2.3.2.2.2.cmml">μ</mi><mi id="S5.E20.1.1.3.2.3.2.2.3" xref="S5.E20.1.1.3.2.3.2.2.3.cmml">x</mi><mn id="S5.E20.1.1.3.2.3.2.3" xref="S5.E20.1.1.3.2.3.2.3.cmml">2</mn></msubsup><mo id="S5.E20.1.1.3.2.3.1" xref="S5.E20.1.1.3.2.3.1.cmml">+</mo><msubsup id="S5.E20.1.1.3.2.3.3" xref="S5.E20.1.1.3.2.3.3.cmml"><mi id="S5.E20.1.1.3.2.3.3.2.2" xref="S5.E20.1.1.3.2.3.3.2.2.cmml">μ</mi><mi id="S5.E20.1.1.3.2.3.3.2.3" xref="S5.E20.1.1.3.2.3.3.2.3.cmml">y</mi><mn id="S5.E20.1.1.3.2.3.3.3" xref="S5.E20.1.1.3.2.3.3.3.cmml">2</mn></msubsup></mrow></mfrac><mo id="S5.E20.1.1.3.1" xref="S5.E20.1.1.3.1.cmml">⁢</mo><mtext id="S5.E20.1.1.3.3" xref="S5.E20.1.1.3.3a.cmml">,</mtext></mrow></mrow></mtd><mtd id="S5.E23.m1.1.1c" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1d" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1e" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1f" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1g" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1h" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1i" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1j" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1k" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1l" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1m" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1n" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1o" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1p" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1q" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1r" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1s" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1t" xref="S5.E23.m1.1.1.cmml"></mtd><mtd id="S5.E23.m1.1.1u" xref="S5.E23.m1.1.1.cmml"></mtd></mtr><mtr id="S5.E23.m1.1.1v" xref="S5.E23.m1.1.1.cmml"><mtd class="ltx_align_left" columnalign="left" id="S5.E23.m1.1.1w" xref="S5.E23.m1.1.1.cmml"><mrow id="S5.E21.1.1" xref="S5.E21.1.1.cmml"><msub id="S5.E21.1.1.2" xref="S5.E21.1.1.2.cmml"><mi id="S5.E21.1.1.2.2" xref="S5.E21.1.1.2.2.cmml">S</mi><mi id="S5.E21.1.1.2.3" xref="S5.E21.1.1.2.3.cmml">c</mi></msub><mo id="S5.E21.1.1.1" xref="S5.E21.1.1.1.cmml">=</mo><mrow id="S5.E21.1.1.3" xref="S5.E21.1.1.3.cmml"><mfrac id="S5.E21.1.1.3.2" xref="S5.E21.1.1.3.2.cmml"><mrow id="S5.E21.1.1.3.2.2" xref="S5.E21.1.1.3.2.2.cmml"><mn id="S5.E21.1.1.3.2.2.2" xref="S5.E21.1.1.3.2.2.2.cmml">2</mn><mo id="S5.E21.1.1.3.2.2.1" xref="S5.E21.1.1.3.2.2.1.cmml">⁢</mo><msub id="S5.E21.1.1.3.2.2.3" xref="S5.E21.1.1.3.2.2.3.cmml"><mi id="S5.E21.1.1.3.2.2.3.2" xref="S5.E21.1.1.3.2.2.3.2.cmml">σ</mi><mi id="S5.E21.1.1.3.2.2.3.3" xref="S5.E21.1.1.3.2.2.3.3.cmml">x</mi></msub><mo id="S5.E21.1.1.3.2.2.1a" xref="S5.E21.1.1.3.2.2.1.cmml">⁢</mo><msub id="S5.E21.1.1.3.2.2.4" xref="S5.E21.1.1.3.2.2.4.cmml"><mi id="S5.E21.1.1.3.2.2.4.2" xref="S5.E21.1.1.3.2.2.4.2.cmml">σ</mi><mi id="S5.E21.1.1.3.2.2.4.3" xref="S5.E21.1.1.3.2.2.4.3.cmml">y</mi></msub></mrow><mrow id="S5.E21.1.1.3.2.3" xref="S5.E21.1.1.3.2.3.cmml"><msubsup id="S5.E21.1.1.3.2.3.2" xref="S5.E21.1.1.3.2.3.2.cmml"><mi id="S5.E21.1.1.3.2.3.2.2.2" xref="S5.E21.1.1.3.2.3.2.2.2.cmml">σ</mi><mi id="S5.E21.1.1.3.2.3.2.2.3" xref="S5.E21.1.1.3.2.3.2.2.3.cmml">x</mi><mn id="S5.E21.1.1.3.2.3.2.3" xref="S5.E21.1.1.3.2.3.2.3.cmml">2</mn></msubsup><mo id="S5.E21.1.1.3.2.3.1" xref="S5.E21.1.1.3.2.3.1.cmml">+</mo><msubsup id="S5.E21.1.1.3.2.3.3" xref="S5.E21.1.1.3.2.3.3.cmml"><mi id="S5.E21.1.1.3.2.3.3.2.2" xref="S5.E21.1.1.3.2.3.3.2.2.cmml">σ</mi><mi id="S5.E21.1.1.3.2.3.3.2.3" xref="S5.E21.1.1.3.2.3.3.2.3.cmml">y</mi><mn id="S5.E21.1.1.3.2.3.3.3" 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xref="S5.E23.m1.1.1">missing-subexpression</csymbol></cerror></matrixrow></matrix></apply></annotation-xml><annotation encoding="application/x-tex" id="S5.E23.m1.1c">\displaystyle\left\{{\begin{array}[]{*{20}{l}}{S_{l}=\frac{{2{\mu_{x}}{\mu_{y}% }}}{{\mu_{x}^{2}+\mu_{y}^{2}}}}\text{,}\\ {S_{c}=\frac{{2{\sigma_{x}}{\sigma_{y}}}}{{\sigma_{x}^{2}+\sigma_{y}^{2}}}}% \text{,}\\ {S_{s}=\frac{{{\sigma_{xy}}}}{{{\sigma_{x}}{\sigma_{y}}}}}\text{,}\\ \end{array}}\right.</annotation><annotation encoding="application/x-llamapun" id="S5.E23.m1.1d">{ start_ARRAY start_ROW start_CELL italic_S start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT = divide start_ARG 2 italic_μ start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT italic_μ start_POSTSUBSCRIPT italic_y end_POSTSUBSCRIPT end_ARG start_ARG italic_μ start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT + italic_μ start_POSTSUBSCRIPT italic_y end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW start_ROW start_CELL italic_S start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT = divide start_ARG 2 italic_σ start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT italic_σ start_POSTSUBSCRIPT italic_y end_POSTSUBSCRIPT end_ARG start_ARG italic_σ start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT + italic_σ start_POSTSUBSCRIPT italic_y end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW start_ROW start_CELL italic_S start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT = divide start_ARG italic_σ start_POSTSUBSCRIPT italic_x italic_y end_POSTSUBSCRIPT end_ARG start_ARG italic_σ start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT italic_σ start_POSTSUBSCRIPT italic_y end_POSTSUBSCRIPT end_ARG , end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL start_CELL end_CELL end_ROW end_ARRAY</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_center_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(23)</span></td> </tr></tbody> </table> <p class="ltx_p" id="S5.SS1.p3.13">where <math alttext="x" class="ltx_Math" display="inline" id="S5.SS1.p3.6.m1.1"><semantics id="S5.SS1.p3.6.m1.1a"><mi id="S5.SS1.p3.6.m1.1.1" xref="S5.SS1.p3.6.m1.1.1.cmml">x</mi><annotation-xml encoding="MathML-Content" id="S5.SS1.p3.6.m1.1b"><ci id="S5.SS1.p3.6.m1.1.1.cmml" xref="S5.SS1.p3.6.m1.1.1">𝑥</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p3.6.m1.1c">x</annotation><annotation encoding="application/x-llamapun" id="S5.SS1.p3.6.m1.1d">italic_x</annotation></semantics></math> and <math alttext="y" class="ltx_Math" display="inline" id="S5.SS1.p3.7.m2.1"><semantics id="S5.SS1.p3.7.m2.1a"><mi id="S5.SS1.p3.7.m2.1.1" xref="S5.SS1.p3.7.m2.1.1.cmml">y</mi><annotation-xml encoding="MathML-Content" id="S5.SS1.p3.7.m2.1b"><ci id="S5.SS1.p3.7.m2.1.1.cmml" xref="S5.SS1.p3.7.m2.1.1">𝑦</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p3.7.m2.1c">y</annotation><annotation encoding="application/x-llamapun" id="S5.SS1.p3.7.m2.1d">italic_y</annotation></semantics></math> represent the blocks of the original and recovered images, <math alttext="\mu_{x}" class="ltx_Math" display="inline" id="S5.SS1.p3.8.m3.1"><semantics id="S5.SS1.p3.8.m3.1a"><msub id="S5.SS1.p3.8.m3.1.1" xref="S5.SS1.p3.8.m3.1.1.cmml"><mi id="S5.SS1.p3.8.m3.1.1.2" xref="S5.SS1.p3.8.m3.1.1.2.cmml">μ</mi><mi id="S5.SS1.p3.8.m3.1.1.3" xref="S5.SS1.p3.8.m3.1.1.3.cmml">x</mi></msub><annotation-xml encoding="MathML-Content" id="S5.SS1.p3.8.m3.1b"><apply id="S5.SS1.p3.8.m3.1.1.cmml" xref="S5.SS1.p3.8.m3.1.1"><csymbol cd="ambiguous" id="S5.SS1.p3.8.m3.1.1.1.cmml" xref="S5.SS1.p3.8.m3.1.1">subscript</csymbol><ci id="S5.SS1.p3.8.m3.1.1.2.cmml" xref="S5.SS1.p3.8.m3.1.1.2">𝜇</ci><ci id="S5.SS1.p3.8.m3.1.1.3.cmml" xref="S5.SS1.p3.8.m3.1.1.3">𝑥</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p3.8.m3.1c">\mu_{x}</annotation><annotation encoding="application/x-llamapun" id="S5.SS1.p3.8.m3.1d">italic_μ start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT</annotation></semantics></math> and <math alttext="\sigma_{x}" class="ltx_Math" display="inline" id="S5.SS1.p3.9.m4.1"><semantics id="S5.SS1.p3.9.m4.1a"><msub id="S5.SS1.p3.9.m4.1.1" xref="S5.SS1.p3.9.m4.1.1.cmml"><mi id="S5.SS1.p3.9.m4.1.1.2" xref="S5.SS1.p3.9.m4.1.1.2.cmml">σ</mi><mi id="S5.SS1.p3.9.m4.1.1.3" xref="S5.SS1.p3.9.m4.1.1.3.cmml">x</mi></msub><annotation-xml encoding="MathML-Content" id="S5.SS1.p3.9.m4.1b"><apply id="S5.SS1.p3.9.m4.1.1.cmml" xref="S5.SS1.p3.9.m4.1.1"><csymbol cd="ambiguous" id="S5.SS1.p3.9.m4.1.1.1.cmml" xref="S5.SS1.p3.9.m4.1.1">subscript</csymbol><ci id="S5.SS1.p3.9.m4.1.1.2.cmml" xref="S5.SS1.p3.9.m4.1.1.2">𝜎</ci><ci id="S5.SS1.p3.9.m4.1.1.3.cmml" xref="S5.SS1.p3.9.m4.1.1.3">𝑥</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p3.9.m4.1c">\sigma_{x}</annotation><annotation encoding="application/x-llamapun" id="S5.SS1.p3.9.m4.1d">italic_σ start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT</annotation></semantics></math> represent the average and the variance of <math alttext="x" class="ltx_Math" display="inline" id="S5.SS1.p3.10.m5.1"><semantics id="S5.SS1.p3.10.m5.1a"><mi id="S5.SS1.p3.10.m5.1.1" xref="S5.SS1.p3.10.m5.1.1.cmml">x</mi><annotation-xml encoding="MathML-Content" id="S5.SS1.p3.10.m5.1b"><ci id="S5.SS1.p3.10.m5.1.1.cmml" xref="S5.SS1.p3.10.m5.1.1">𝑥</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p3.10.m5.1c">x</annotation><annotation encoding="application/x-llamapun" id="S5.SS1.p3.10.m5.1d">italic_x</annotation></semantics></math>, and <math alttext="\sigma_{xy}" class="ltx_Math" display="inline" id="S5.SS1.p3.11.m6.1"><semantics id="S5.SS1.p3.11.m6.1a"><msub id="S5.SS1.p3.11.m6.1.1" xref="S5.SS1.p3.11.m6.1.1.cmml"><mi id="S5.SS1.p3.11.m6.1.1.2" xref="S5.SS1.p3.11.m6.1.1.2.cmml">σ</mi><mrow id="S5.SS1.p3.11.m6.1.1.3" xref="S5.SS1.p3.11.m6.1.1.3.cmml"><mi id="S5.SS1.p3.11.m6.1.1.3.2" xref="S5.SS1.p3.11.m6.1.1.3.2.cmml">x</mi><mo id="S5.SS1.p3.11.m6.1.1.3.1" xref="S5.SS1.p3.11.m6.1.1.3.1.cmml">⁢</mo><mi id="S5.SS1.p3.11.m6.1.1.3.3" xref="S5.SS1.p3.11.m6.1.1.3.3.cmml">y</mi></mrow></msub><annotation-xml encoding="MathML-Content" id="S5.SS1.p3.11.m6.1b"><apply id="S5.SS1.p3.11.m6.1.1.cmml" xref="S5.SS1.p3.11.m6.1.1"><csymbol cd="ambiguous" id="S5.SS1.p3.11.m6.1.1.1.cmml" xref="S5.SS1.p3.11.m6.1.1">subscript</csymbol><ci id="S5.SS1.p3.11.m6.1.1.2.cmml" xref="S5.SS1.p3.11.m6.1.1.2">𝜎</ci><apply id="S5.SS1.p3.11.m6.1.1.3.cmml" xref="S5.SS1.p3.11.m6.1.1.3"><times id="S5.SS1.p3.11.m6.1.1.3.1.cmml" xref="S5.SS1.p3.11.m6.1.1.3.1"></times><ci id="S5.SS1.p3.11.m6.1.1.3.2.cmml" xref="S5.SS1.p3.11.m6.1.1.3.2">𝑥</ci><ci id="S5.SS1.p3.11.m6.1.1.3.3.cmml" xref="S5.SS1.p3.11.m6.1.1.3.3">𝑦</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p3.11.m6.1c">\sigma_{xy}</annotation><annotation encoding="application/x-llamapun" id="S5.SS1.p3.11.m6.1d">italic_σ start_POSTSUBSCRIPT italic_x italic_y end_POSTSUBSCRIPT</annotation></semantics></math> represents the covariance of <math alttext="x" class="ltx_Math" display="inline" id="S5.SS1.p3.12.m7.1"><semantics id="S5.SS1.p3.12.m7.1a"><mi id="S5.SS1.p3.12.m7.1.1" xref="S5.SS1.p3.12.m7.1.1.cmml">x</mi><annotation-xml encoding="MathML-Content" id="S5.SS1.p3.12.m7.1b"><ci id="S5.SS1.p3.12.m7.1.1.cmml" xref="S5.SS1.p3.12.m7.1.1">𝑥</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p3.12.m7.1c">x</annotation><annotation encoding="application/x-llamapun" id="S5.SS1.p3.12.m7.1d">italic_x</annotation></semantics></math> and <math alttext="y" class="ltx_Math" display="inline" id="S5.SS1.p3.13.m8.1"><semantics id="S5.SS1.p3.13.m8.1a"><mi id="S5.SS1.p3.13.m8.1.1" xref="S5.SS1.p3.13.m8.1.1.cmml">y</mi><annotation-xml encoding="MathML-Content" id="S5.SS1.p3.13.m8.1b"><ci id="S5.SS1.p3.13.m8.1.1.cmml" xref="S5.SS1.p3.13.m8.1.1">𝑦</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.SS1.p3.13.m8.1c">y</annotation><annotation encoding="application/x-llamapun" id="S5.SS1.p3.13.m8.1d">italic_y</annotation></semantics></math>. The SSIM score ranges from 0 to 1, with higher values indicating better image recovery.</p> </div> <div class="ltx_para" id="S5.SS1.p4"> <p class="ltx_p" id="S5.SS1.p4.1"><span class="ltx_text" id="S5.SS1.p4.1.1">Furthermore, 2D, 3D, and bird’s-eye view (BV) AP metrics are adopted to evaluate the system’s performance in object detection. According to the system model, after the stereo-vision image pairs are recovered, they are fed into a well-trained 3D detection network, i.e., Stereo-RCNN, for 2D and 3D detection. Based on the recovered image pairs, basic 2D detection is first conducted for each image by the Stereo-RCNN, and the 2D detection results from each image are then combined to estimate the 3D bounding boxes of objects, achieving 3D detection. By comparing the output detection results of Stereo-RCNN with the ground-truth boxes, the 2D, 3D, and BV AP metrics are calculated. It is worth noting that, in 2D detection, only the 2D detection boxes, whose maximum intersection over union (IoU) with the ground-truth boxes is larger than the preset threshold, are considered true positives <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib28" title="">28</a>]</cite>.<span class="ltx_text" id="S5.SS1.p4.1.1.1"> However, in 3D detection, the estimated 3D box will be regarded as true positives only if the left and right detection boxes meet the IoU threshold conditions simultaneously and the selected left and right ground truth boxes belong to the same object <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#bib.bib28" title="">28</a>]</cite>. For 2D, 3D, and BV detection, AP ranges from 0 to 100. A higher AP indicates higher detection accuracy. In this simulation, we set the IoU threshold to 0.5 and use the official program approved by KITTI to calculate the detected AP value<span class="ltx_note ltx_role_footnote" id="footnote3"><sup class="ltx_note_mark">3</sup><span class="ltx_note_outer"><span class="ltx_note_content"><sup class="ltx_note_mark">3</sup><span class="ltx_tag ltx_tag_note">3</span>https://www.cvlibs.net/datasets/kitti</span></span></span>.</span></span></p> </div> </section> <section class="ltx_subsection" id="S5.SS2"> <h3 class="ltx_title ltx_title_subsection"> <span class="ltx_tag ltx_tag_subsection"><span class="ltx_text" id="S5.SS2.5.1.1">V-B</span> </span><span class="ltx_text ltx_font_italic" id="S5.SS2.6.2">Simulation Results</span> </h3> <figure class="ltx_table" id="S5.T1"> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_table">TABLE I: </span>Recovery Performance Under Different Compression Ratios</figcaption><div class="ltx_flex_figure"> <div class="ltx_flex_cell ltx_flex_size_1"> <table class="ltx_tabular ltx_centering ltx_figure_panel ltx_guessed_headers ltx_align_middle" id="S5.T1.16"> <thead class="ltx_thead"> <tr class="ltx_tr" id="S5.T1.4.4"> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" id="S5.T1.4.4.5" style="padding:2pt 5.0pt;">Method</th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" id="S5.T1.1.1.1" style="padding:2pt 5.0pt;">PSNR<sup class="ltx_sup" id="S5.T1.1.1.1.1">g</sup> <math alttext="\uparrow" class="ltx_Math" display="inline" id="S5.T1.1.1.1.m1.1"><semantics id="S5.T1.1.1.1.m1.1a"><mo id="S5.T1.1.1.1.m1.1.1" stretchy="false" xref="S5.T1.1.1.1.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S5.T1.1.1.1.m1.1b"><ci id="S5.T1.1.1.1.m1.1.1.cmml" xref="S5.T1.1.1.1.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.T1.1.1.1.m1.1c">\uparrow</annotation><annotation encoding="application/x-llamapun" id="S5.T1.1.1.1.m1.1d">↑</annotation></semantics></math> </th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" id="S5.T1.2.2.2" style="padding:2pt 5.0pt;">PSNR<sup class="ltx_sup" id="S5.T1.2.2.2.1">k</sup> <math alttext="\uparrow" class="ltx_Math" display="inline" id="S5.T1.2.2.2.m1.1"><semantics id="S5.T1.2.2.2.m1.1a"><mo id="S5.T1.2.2.2.m1.1.1" stretchy="false" xref="S5.T1.2.2.2.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S5.T1.2.2.2.m1.1b"><ci id="S5.T1.2.2.2.m1.1.1.cmml" xref="S5.T1.2.2.2.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.T1.2.2.2.m1.1c">\uparrow</annotation><annotation encoding="application/x-llamapun" id="S5.T1.2.2.2.m1.1d">↑</annotation></semantics></math> </th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" id="S5.T1.3.3.3" style="padding:2pt 5.0pt;">SSIM<sup class="ltx_sup" id="S5.T1.3.3.3.1">g</sup> <math alttext="\uparrow" class="ltx_Math" display="inline" id="S5.T1.3.3.3.m1.1"><semantics id="S5.T1.3.3.3.m1.1a"><mo id="S5.T1.3.3.3.m1.1.1" stretchy="false" xref="S5.T1.3.3.3.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S5.T1.3.3.3.m1.1b"><ci id="S5.T1.3.3.3.m1.1.1.cmml" xref="S5.T1.3.3.3.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.T1.3.3.3.m1.1c">\uparrow</annotation><annotation encoding="application/x-llamapun" id="S5.T1.3.3.3.m1.1d">↑</annotation></semantics></math> </th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T1.4.4.4" style="padding:2pt 5.0pt;">SSIM<sup class="ltx_sup" id="S5.T1.4.4.4.1">k</sup> <math alttext="\uparrow" class="ltx_Math" display="inline" id="S5.T1.4.4.4.m1.1"><semantics id="S5.T1.4.4.4.m1.1a"><mo id="S5.T1.4.4.4.m1.1.1" stretchy="false" xref="S5.T1.4.4.4.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S5.T1.4.4.4.m1.1b"><ci id="S5.T1.4.4.4.m1.1.1.cmml" xref="S5.T1.4.4.4.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.T1.4.4.4.m1.1c">\uparrow</annotation><annotation encoding="application/x-llamapun" id="S5.T1.4.4.4.m1.1d">↑</annotation></semantics></math> </th> </tr> </thead> <tbody class="ltx_tbody"> <tr class="ltx_tr" id="S5.T1.5.5"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" id="S5.T1.5.5.1" style="padding:2pt 5.0pt;">Proposed Method (10<math alttext="\times" class="ltx_Math" display="inline" id="S5.T1.5.5.1.m1.1"><semantics id="S5.T1.5.5.1.m1.1a"><mo id="S5.T1.5.5.1.m1.1.1" xref="S5.T1.5.5.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T1.5.5.1.m1.1b"><times id="S5.T1.5.5.1.m1.1.1.cmml" xref="S5.T1.5.5.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T1.5.5.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T1.5.5.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T1.5.5.2" style="padding:2pt 5.0pt;">27.01dB</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T1.5.5.3" style="padding:2pt 5.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T1.5.5.3.1">45.12dB</span></td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T1.5.5.4" style="padding:2pt 5.0pt;">0.83</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T1.5.5.5" style="padding:2pt 5.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T1.5.5.5.1">0.99</span></td> </tr> <tr class="ltx_tr" id="S5.T1.6.6"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T1.6.6.1" style="padding:2pt 5.0pt;">JPEG (10<math alttext="\times" class="ltx_Math" display="inline" id="S5.T1.6.6.1.m1.1"><semantics id="S5.T1.6.6.1.m1.1a"><mo id="S5.T1.6.6.1.m1.1.1" xref="S5.T1.6.6.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T1.6.6.1.m1.1b"><times id="S5.T1.6.6.1.m1.1.1.cmml" xref="S5.T1.6.6.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T1.6.6.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T1.6.6.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.6.6.2" style="padding:2pt 5.0pt;">28.45dB</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.6.6.3" style="padding:2pt 5.0pt;">29.09dB</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.6.6.4" style="padding:2pt 5.0pt;">0.89</td> <td class="ltx_td ltx_align_center" id="S5.T1.6.6.5" style="padding:2pt 5.0pt;">0.93</td> </tr> <tr class="ltx_tr" id="S5.T1.7.7"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T1.7.7.1" style="padding:2pt 5.0pt;">JPEG2000 (10<math alttext="\times" class="ltx_Math" display="inline" id="S5.T1.7.7.1.m1.1"><semantics id="S5.T1.7.7.1.m1.1a"><mo id="S5.T1.7.7.1.m1.1.1" xref="S5.T1.7.7.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T1.7.7.1.m1.1b"><times id="S5.T1.7.7.1.m1.1.1.cmml" xref="S5.T1.7.7.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T1.7.7.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T1.7.7.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.7.7.2" style="padding:2pt 5.0pt;">28.31dB</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.7.7.3" style="padding:2pt 5.0pt;">27.52dB</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.7.7.4" style="padding:2pt 5.0pt;">0.86</td> <td class="ltx_td ltx_align_center" id="S5.T1.7.7.5" style="padding:2pt 5.0pt;">0.87</td> </tr> <tr class="ltx_tr" id="S5.T1.8.8"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T1.8.8.1" style="padding:2pt 5.0pt;">SRCNN (10<math alttext="\times" class="ltx_Math" display="inline" id="S5.T1.8.8.1.m1.1"><semantics id="S5.T1.8.8.1.m1.1a"><mo id="S5.T1.8.8.1.m1.1.1" xref="S5.T1.8.8.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T1.8.8.1.m1.1b"><times id="S5.T1.8.8.1.m1.1.1.cmml" xref="S5.T1.8.8.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T1.8.8.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T1.8.8.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.8.8.2" style="padding:2pt 5.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T1.8.8.2.1">29.03dB</span></td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.8.8.3" style="padding:2pt 5.0pt;">28.32dB</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.8.8.4" style="padding:2pt 5.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T1.8.8.4.1">0.89</span></td> <td class="ltx_td ltx_align_center" id="S5.T1.8.8.5" style="padding:2pt 5.0pt;">0.90</td> </tr> <tr class="ltx_tr" id="S5.T1.9.9"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" id="S5.T1.9.9.1" style="padding:2pt 5.0pt;">Proposed Method (30<math alttext="\times" class="ltx_Math" display="inline" id="S5.T1.9.9.1.m1.1"><semantics id="S5.T1.9.9.1.m1.1a"><mo id="S5.T1.9.9.1.m1.1.1" xref="S5.T1.9.9.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T1.9.9.1.m1.1b"><times id="S5.T1.9.9.1.m1.1.1.cmml" xref="S5.T1.9.9.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T1.9.9.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T1.9.9.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T1.9.9.2" style="padding:2pt 5.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T1.9.9.2.1">26.75dB</span></td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T1.9.9.3" style="padding:2pt 5.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T1.9.9.3.1">27.21dB</span></td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T1.9.9.4" style="padding:2pt 5.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T1.9.9.4.1">0.83</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T1.9.9.5" style="padding:2pt 5.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T1.9.9.5.1">0.92</span></td> </tr> <tr class="ltx_tr" id="S5.T1.10.10"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T1.10.10.1" style="padding:2pt 5.0pt;">JPEG (30<math alttext="\times" class="ltx_Math" display="inline" id="S5.T1.10.10.1.m1.1"><semantics id="S5.T1.10.10.1.m1.1a"><mo id="S5.T1.10.10.1.m1.1.1" xref="S5.T1.10.10.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T1.10.10.1.m1.1b"><times id="S5.T1.10.10.1.m1.1.1.cmml" xref="S5.T1.10.10.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T1.10.10.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T1.10.10.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.10.10.2" style="padding:2pt 5.0pt;">26.17dB</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.10.10.3" style="padding:2pt 5.0pt;">25.50dB</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.10.10.4" style="padding:2pt 5.0pt;">0.81</td> <td class="ltx_td ltx_align_center" id="S5.T1.10.10.5" style="padding:2pt 5.0pt;">0.84</td> </tr> <tr class="ltx_tr" id="S5.T1.11.11"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T1.11.11.1" style="padding:2pt 5.0pt;">JPEG2000 (30<math alttext="\times" class="ltx_Math" display="inline" id="S5.T1.11.11.1.m1.1"><semantics id="S5.T1.11.11.1.m1.1a"><mo id="S5.T1.11.11.1.m1.1.1" xref="S5.T1.11.11.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T1.11.11.1.m1.1b"><times id="S5.T1.11.11.1.m1.1.1.cmml" xref="S5.T1.11.11.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T1.11.11.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T1.11.11.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.11.11.2" style="padding:2pt 5.0pt;">26.07dB</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.11.11.3" style="padding:2pt 5.0pt;">24.93dB</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.11.11.4" style="padding:2pt 5.0pt;">0.78</td> <td class="ltx_td ltx_align_center" id="S5.T1.11.11.5" style="padding:2pt 5.0pt;">0.78</td> </tr> <tr class="ltx_tr" id="S5.T1.12.12"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T1.12.12.1" style="padding:2pt 5.0pt;">SRCNN (30<math alttext="\times" class="ltx_Math" display="inline" id="S5.T1.12.12.1.m1.1"><semantics id="S5.T1.12.12.1.m1.1a"><mo id="S5.T1.12.12.1.m1.1.1" xref="S5.T1.12.12.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T1.12.12.1.m1.1b"><times id="S5.T1.12.12.1.m1.1.1.cmml" xref="S5.T1.12.12.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T1.12.12.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T1.12.12.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.12.12.2" style="padding:2pt 5.0pt;">25.84dB</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.12.12.3" style="padding:2pt 5.0pt;">23.56dB</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.12.12.4" style="padding:2pt 5.0pt;">0.79</td> <td class="ltx_td ltx_align_center" id="S5.T1.12.12.5" style="padding:2pt 5.0pt;">0.76</td> </tr> <tr class="ltx_tr" id="S5.T1.13.13"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" id="S5.T1.13.13.1" style="padding:2pt 5.0pt;">Proposed Method (50<math alttext="\times" class="ltx_Math" display="inline" id="S5.T1.13.13.1.m1.1"><semantics id="S5.T1.13.13.1.m1.1a"><mo id="S5.T1.13.13.1.m1.1.1" xref="S5.T1.13.13.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T1.13.13.1.m1.1b"><times id="S5.T1.13.13.1.m1.1.1.cmml" xref="S5.T1.13.13.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T1.13.13.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T1.13.13.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T1.13.13.2" style="padding:2pt 5.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T1.13.13.2.1">25.30dB</span></td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T1.13.13.3" style="padding:2pt 5.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T1.13.13.3.1">23.23dB</span></td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T1.13.13.4" style="padding:2pt 5.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T1.13.13.4.1">0.77</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T1.13.13.5" style="padding:2pt 5.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T1.13.13.5.1">0.81</span></td> </tr> <tr class="ltx_tr" id="S5.T1.14.14"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T1.14.14.1" style="padding:2pt 5.0pt;">JPEG (50<math alttext="\times" class="ltx_Math" display="inline" id="S5.T1.14.14.1.m1.1"><semantics id="S5.T1.14.14.1.m1.1a"><mo id="S5.T1.14.14.1.m1.1.1" xref="S5.T1.14.14.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T1.14.14.1.m1.1b"><times id="S5.T1.14.14.1.m1.1.1.cmml" xref="S5.T1.14.14.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T1.14.14.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T1.14.14.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.14.14.2" style="padding:2pt 5.0pt;">25.27dB</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.14.14.3" style="padding:2pt 5.0pt;">23.05dB</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.14.14.4" style="padding:2pt 5.0pt;">0.75</td> <td class="ltx_td ltx_align_center" id="S5.T1.14.14.5" style="padding:2pt 5.0pt;">0.76</td> </tr> <tr class="ltx_tr" id="S5.T1.15.15"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T1.15.15.1" style="padding:2pt 5.0pt;">JPEG2000 (50<math alttext="\times" class="ltx_Math" display="inline" id="S5.T1.15.15.1.m1.1"><semantics id="S5.T1.15.15.1.m1.1a"><mo id="S5.T1.15.15.1.m1.1.1" xref="S5.T1.15.15.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T1.15.15.1.m1.1b"><times id="S5.T1.15.15.1.m1.1.1.cmml" xref="S5.T1.15.15.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T1.15.15.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T1.15.15.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.15.15.2" style="padding:2pt 5.0pt;">25.05dB</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.15.15.3" style="padding:2pt 5.0pt;">21.92dB</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T1.15.15.4" style="padding:2pt 5.0pt;">0.73</td> <td class="ltx_td ltx_align_center" id="S5.T1.15.15.5" style="padding:2pt 5.0pt;">0.72</td> </tr> <tr class="ltx_tr" id="S5.T1.16.16"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_b ltx_border_r" id="S5.T1.16.16.1" style="padding:2pt 5.0pt;">SRCNN (50<math alttext="\times" class="ltx_Math" display="inline" id="S5.T1.16.16.1.m1.1"><semantics id="S5.T1.16.16.1.m1.1a"><mo id="S5.T1.16.16.1.m1.1.1" xref="S5.T1.16.16.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T1.16.16.1.m1.1b"><times id="S5.T1.16.16.1.m1.1.1.cmml" xref="S5.T1.16.16.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T1.16.16.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T1.16.16.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="S5.T1.16.16.2" style="padding:2pt 5.0pt;">24.26dB</td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="S5.T1.16.16.3" style="padding:2pt 5.0pt;">20.93dB</td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="S5.T1.16.16.4" style="padding:2pt 5.0pt;">0.74</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T1.16.16.5" style="padding:2pt 5.0pt;">0.69</td> </tr> </tbody> </table> </div> <div class="ltx_flex_break"></div> <div class="ltx_flex_cell ltx_flex_size_1"> <ul class="ltx_itemize ltx_centering ltx_figure_panel" id="S5.I2"> <li class="ltx_item" id="S5.I2.i1" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item">•</span> <div class="ltx_para" id="S5.I2.i1.p1"> <p class="ltx_p" id="S5.I2.i1.p1.1"><span class="ltx_text" id="S5.I2.i1.p1.1.1" style="font-size:80%;">g: the PSNR or SSIM score for the global area.</span></p> </div> </li> <li class="ltx_item" id="S5.I2.i2" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item">•</span> <div class="ltx_para" id="S5.I2.i2.p1"> <p class="ltx_p" id="S5.I2.i2.p1.1"><span class="ltx_text" id="S5.I2.i2.p1.1.1" style="font-size:80%;">k: the PSNR or SSIM score for the key areas.</span></p> </div> </li> </ul> </div> </div> </figure> <div class="ltx_para" id="S5.SS2.p1"> <p class="ltx_p" id="S5.SS2.p1.1">For the first set of experiments, Table <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.T1" title="TABLE I ‣ V-B Simulation Results ‣ V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">I</span></a> shows the average PSNR and SSIM scores for different compression ratios across the evaluated methods, where the scores of the key areas (the areas inside the semantic boxes) and the global areas (the whole images) are presented, respectively. All methods use the same validation dataset and transmit similar amounts of data on average. The table shows that the proposed method performs best in key area recovery under the three compression ratios, especially in the SSIM metric. Regarding global performance, the proposed compression scheme performs closely to other algorithms and is slightly better for the medium and high compression ratios.</p> </div> <figure class="ltx_figure" id="S5.F9"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="619" id="S5.F9.g1" src="x9.png" width="941"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 9: </span>Image recovery results of the proposed method in different areas under different compression ratios.</figcaption> </figure> <figure class="ltx_figure" id="S5.F10"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="322" id="S5.F10.g1" src="x10.png" width="941"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 10: </span>Image recovery results of different methods under <math alttext="50\times" class="ltx_math_unparsed" display="inline" id="S5.F10.2.m1.1"><semantics id="S5.F10.2.m1.1b"><mrow id="S5.F10.2.m1.1c"><mn id="S5.F10.2.m1.1.1">50</mn><mo id="S5.F10.2.m1.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.F10.2.m1.1d">50\times</annotation><annotation encoding="application/x-llamapun" id="S5.F10.2.m1.1e">50 ×</annotation></semantics></math> compression ratio.</figcaption> </figure> <div class="ltx_para" id="S5.SS2.p2"> <p class="ltx_p" id="S5.SS2.p2.1">The image recovery results of the proposed method for different compression ratios in key and global areas are shown in Fig. <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.F9" title="Figure 9 ‣ V-B Simulation Results ‣ V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">9</span></a>. <span class="ltx_text" id="S5.SS2.p2.1.1">The area marked by a solid red box represents the sampled key region, whereas the area enclosed by a dotted red box is considered the sampled other region. By comparing the selected samples from the key and other regions, it can be seen that objects in the key areas retain more distinct outlines and details, although all image qualities decrease as the compression ratio gets higher. Besides, Fig. <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.F10" title="Figure 10 ‣ V-B Simulation Results ‣ V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">10</span></a> presents an example of the recovered images for various methods under the <math alttext="50\times" class="ltx_math_unparsed" display="inline" id="S5.SS2.p2.1.1.m1.1"><semantics id="S5.SS2.p2.1.1.m1.1a"><mrow id="S5.SS2.p2.1.1.m1.1b"><mn id="S5.SS2.p2.1.1.m1.1.1">50</mn><mo id="S5.SS2.p2.1.1.m1.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.SS2.p2.1.1.m1.1c">50\times</annotation><annotation encoding="application/x-llamapun" id="S5.SS2.p2.1.1.m1.1d">50 ×</annotation></semantics></math> compression ratio.<span class="ltx_text" id="S5.SS2.p2.1.1.1"></span></span></p> </div> <div class="ltx_para" id="S5.SS2.p3"> <p class="ltx_p" id="S5.SS2.p3.2">Continuing with the first set of experiments, the 2D and 3D detection performance in terms of the AP metic with different compression ratios across the evaluated methods is presented in Table <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.T2" title="TABLE II ‣ V-B Simulation Results ‣ V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">II</span></a>. From Table <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.T2" title="TABLE II ‣ V-B Simulation Results ‣ V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">II</span></a>, when compression rates are low, i.e., <math alttext="10\times" class="ltx_math_unparsed" display="inline" id="S5.SS2.p3.1.m1.1"><semantics id="S5.SS2.p3.1.m1.1a"><mrow id="S5.SS2.p3.1.m1.1b"><mn id="S5.SS2.p3.1.m1.1.1">10</mn><mo id="S5.SS2.p3.1.m1.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.SS2.p3.1.m1.1c">10\times</annotation><annotation encoding="application/x-llamapun" id="S5.SS2.p3.1.m1.1d">10 ×</annotation></semantics></math> compression, the detection performance of all methods is close to that of using the original image directly. This suggests that excessive clarity does not necessarily lead to improved detection accuracy. <span class="ltx_text" id="S5.SS2.p3.2.1">For medium and high compression rates, the proposed method outperforms all others in 2D and 3D detection metrics, including 2D AP on the left and right images, AP on the bird’s eye view, and 3D AP. When the compression rate is <math alttext="30\times" class="ltx_math_unparsed" display="inline" id="S5.SS2.p3.2.1.m1.1"><semantics id="S5.SS2.p3.2.1.m1.1a"><mrow id="S5.SS2.p3.2.1.m1.1b"><mn id="S5.SS2.p3.2.1.m1.1.1">30</mn><mo id="S5.SS2.p3.2.1.m1.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.SS2.p3.2.1.m1.1c">30\times</annotation><annotation encoding="application/x-llamapun" id="S5.SS2.p3.2.1.m1.1d">30 ×</annotation></semantics></math>, the image recovered by the proposed method has a detection performance similar to the original image for objects in easy and moderate regimes. For objects under the hard regime, the proposed algorithm outperforms other algorithms significantly in 3D detection. Despite achieving a compression ratio of 50 times, the proposed method can still perform similarly to the uncompressed case for objects in easy regimes in terms of 2D AP. Moreover, the proposed algorithm shows slight advantages over the ECSIC method while significantly outperforming other algorithms.<span class="ltx_text" id="S5.SS2.p3.2.1.1"></span></span></p> </div> <figure class="ltx_table" id="S5.T2"> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_table">TABLE II: </span>Detection Performance Under Different Compression Ratios</figcaption> <table class="ltx_tabular ltx_centering ltx_guessed_headers ltx_align_middle" id="S5.T2.19"> <thead class="ltx_thead"> <tr class="ltx_tr" id="S5.T2.19.20.1"> <th class="ltx_td ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" id="S5.T2.19.20.1.1" style="padding:2pt 7.0pt;"></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" colspan="6" id="S5.T2.19.20.1.2" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.20.1.2.1">2D object detection</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" colspan="6" id="S5.T2.19.20.1.3" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.20.1.3.1">3D object detection</span></th> </tr> <tr class="ltx_tr" id="S5.T2.4.4"> <th class="ltx_td ltx_th ltx_th_column ltx_th_row ltx_border_r" id="S5.T2.4.4.5" style="padding:2pt 7.0pt;"></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" colspan="3" id="S5.T2.1.1.1" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.1.1.1.1">AP on left images <math alttext="\uparrow" class="ltx_Math" display="inline" id="S5.T2.1.1.1.1.m1.1"><semantics id="S5.T2.1.1.1.1.m1.1a"><mo id="S5.T2.1.1.1.1.m1.1.1" stretchy="false" xref="S5.T2.1.1.1.1.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S5.T2.1.1.1.1.m1.1b"><ci id="S5.T2.1.1.1.1.m1.1.1.cmml" xref="S5.T2.1.1.1.1.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.1.1.1.1.m1.1c">\uparrow</annotation><annotation encoding="application/x-llamapun" id="S5.T2.1.1.1.1.m1.1d">↑</annotation></semantics></math></span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" colspan="3" id="S5.T2.2.2.2" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.2.2.2.1">AP on right images <math alttext="\uparrow" class="ltx_Math" display="inline" id="S5.T2.2.2.2.1.m1.1"><semantics id="S5.T2.2.2.2.1.m1.1a"><mo id="S5.T2.2.2.2.1.m1.1.1" stretchy="false" xref="S5.T2.2.2.2.1.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S5.T2.2.2.2.1.m1.1b"><ci id="S5.T2.2.2.2.1.m1.1.1.cmml" xref="S5.T2.2.2.2.1.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.2.2.2.1.m1.1c">\uparrow</annotation><annotation encoding="application/x-llamapun" id="S5.T2.2.2.2.1.m1.1d">↑</annotation></semantics></math></span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" colspan="3" id="S5.T2.3.3.3" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.3.3.3.1">AP on bird’s-eye view <math alttext="\uparrow" class="ltx_Math" display="inline" id="S5.T2.3.3.3.1.m1.1"><semantics id="S5.T2.3.3.3.1.m1.1a"><mo id="S5.T2.3.3.3.1.m1.1.1" stretchy="false" xref="S5.T2.3.3.3.1.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S5.T2.3.3.3.1.m1.1b"><ci id="S5.T2.3.3.3.1.m1.1.1.cmml" xref="S5.T2.3.3.3.1.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.3.3.3.1.m1.1c">\uparrow</annotation><annotation encoding="application/x-llamapun" id="S5.T2.3.3.3.1.m1.1d">↑</annotation></semantics></math></span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" colspan="3" id="S5.T2.4.4.4" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.4.4.4.1">AP for 3D detection <math alttext="\uparrow" class="ltx_Math" display="inline" id="S5.T2.4.4.4.1.m1.1"><semantics id="S5.T2.4.4.4.1.m1.1a"><mo id="S5.T2.4.4.4.1.m1.1.1" stretchy="false" xref="S5.T2.4.4.4.1.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S5.T2.4.4.4.1.m1.1b"><ci id="S5.T2.4.4.4.1.m1.1.1.cmml" xref="S5.T2.4.4.4.1.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.4.4.4.1.m1.1c">\uparrow</annotation><annotation encoding="application/x-llamapun" id="S5.T2.4.4.4.1.m1.1d">↑</annotation></semantics></math></span></th> </tr> <tr class="ltx_tr" id="S5.T2.19.21.2"> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_th_row ltx_border_r" id="S5.T2.19.21.2.1" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.21.2.1.1">Method</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.21.2.2" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.21.2.2.1">Easy</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.21.2.3" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.21.2.3.1">Mode</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" id="S5.T2.19.21.2.4" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.21.2.4.1">Hard</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.21.2.5" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.21.2.5.1">Easy</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.21.2.6" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.21.2.6.1">Mode</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" id="S5.T2.19.21.2.7" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.21.2.7.1">Hard</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.21.2.8" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.21.2.8.1">Easy</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.21.2.9" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.21.2.9.1">Mode</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" id="S5.T2.19.21.2.10" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.21.2.10.1">Hard</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.21.2.11" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.21.2.11.1">Easy</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.21.2.12" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.21.2.12.1">Mode</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.21.2.13" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.21.2.13.1">Hard</span></th> </tr> <tr class="ltx_tr" id="S5.T2.19.22.3"> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" id="S5.T2.19.22.3.1" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.22.3.1.1">Original Image</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.22.3.2" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.22.3.2.1">99.88</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.22.3.3" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.22.3.3.1">90.89</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" id="S5.T2.19.22.3.4" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.22.3.4.1">81.80</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.22.3.5" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.22.3.5.1">99.72</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.22.3.6" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.22.3.6.1">90.58</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" id="S5.T2.19.22.3.7" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.22.3.7.1">81.38</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.22.3.8" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.22.3.8.1">73.33</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.22.3.9" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.22.3.9.1">47.26</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" id="S5.T2.19.22.3.10" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.22.3.10.1">40.94</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.22.3.11" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.22.3.11.1">65.72</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.22.3.12" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.22.3.12.1">45.60</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T2.19.22.3.13" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.22.3.13.1">39.39</span></th> </tr> </thead> <tbody class="ltx_tbody"> <tr class="ltx_tr" id="S5.T2.5.5"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" id="S5.T2.5.5.1" style="padding:2pt 7.0pt;">Proposed Method (10<math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.5.5.1.m1.1"><semantics id="S5.T2.5.5.1.m1.1a"><mo id="S5.T2.5.5.1.m1.1.1" xref="S5.T2.5.5.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.5.5.1.m1.1b"><times id="S5.T2.5.5.1.m1.1.1.cmml" xref="S5.T2.5.5.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.5.5.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.5.5.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.5.5.2" style="padding:2pt 7.0pt;">99.85</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.5.5.3" style="padding:2pt 7.0pt;">90.88</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T2.5.5.4" style="padding:2pt 7.0pt;">81.75</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.5.5.5" style="padding:2pt 7.0pt;">99.66</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.5.5.6" style="padding:2pt 7.0pt;">90.57</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T2.5.5.7" style="padding:2pt 7.0pt;">81.36</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.5.5.8" style="padding:2pt 7.0pt;">73.22</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.5.5.9" style="padding:2pt 7.0pt;">47.16</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T2.5.5.10" style="padding:2pt 7.0pt;">39.98</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.5.5.11" style="padding:2pt 7.0pt;">64.94</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.5.5.12" style="padding:2pt 7.0pt;">45.20</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.5.5.13" style="padding:2pt 7.0pt;">39.01</td> </tr> <tr class="ltx_tr" id="S5.T2.6.6"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T2.6.6.1" style="padding:2pt 7.0pt;">JPEG (10<math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.6.6.1.m1.1"><semantics id="S5.T2.6.6.1.m1.1a"><mo id="S5.T2.6.6.1.m1.1.1" xref="S5.T2.6.6.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.6.6.1.m1.1b"><times id="S5.T2.6.6.1.m1.1.1.cmml" xref="S5.T2.6.6.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.6.6.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.6.6.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center" id="S5.T2.6.6.2" style="padding:2pt 7.0pt;">99.79</td> <td class="ltx_td ltx_align_center" id="S5.T2.6.6.3" style="padding:2pt 7.0pt;">90.87</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.6.6.4" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.6.6.4.1">81.78</span></td> <td class="ltx_td ltx_align_center" id="S5.T2.6.6.5" style="padding:2pt 7.0pt;">99.68</td> <td class="ltx_td ltx_align_center" id="S5.T2.6.6.6" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.6.6.6.1">90.58</span></td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.6.6.7" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.6.6.7.1">81.38</span></td> <td class="ltx_td ltx_align_center" id="S5.T2.6.6.8" style="padding:2pt 7.0pt;">73.20</td> <td class="ltx_td ltx_align_center" id="S5.T2.6.6.9" style="padding:2pt 7.0pt;">47.15</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.6.6.10" style="padding:2pt 7.0pt;">39.43</td> <td class="ltx_td ltx_align_center" id="S5.T2.6.6.11" style="padding:2pt 7.0pt;">64.31</td> <td class="ltx_td ltx_align_center" id="S5.T2.6.6.12" style="padding:2pt 7.0pt;">45.18</td> <td class="ltx_td ltx_align_center" id="S5.T2.6.6.13" style="padding:2pt 7.0pt;">38.74</td> </tr> <tr class="ltx_tr" id="S5.T2.7.7"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T2.7.7.1" style="padding:2pt 7.0pt;">JPEG2000 (10<math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.7.7.1.m1.1"><semantics id="S5.T2.7.7.1.m1.1a"><mo id="S5.T2.7.7.1.m1.1.1" xref="S5.T2.7.7.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.7.7.1.m1.1b"><times id="S5.T2.7.7.1.m1.1.1.cmml" xref="S5.T2.7.7.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.7.7.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.7.7.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center" id="S5.T2.7.7.2" style="padding:2pt 7.0pt;">99.78</td> <td class="ltx_td ltx_align_center" id="S5.T2.7.7.3" style="padding:2pt 7.0pt;">90.87</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.7.7.4" style="padding:2pt 7.0pt;">81.73</td> <td class="ltx_td ltx_align_center" id="S5.T2.7.7.5" style="padding:2pt 7.0pt;">99.68</td> <td class="ltx_td ltx_align_center" id="S5.T2.7.7.6" style="padding:2pt 7.0pt;">90.58</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.7.7.7" style="padding:2pt 7.0pt;">81.34</td> <td class="ltx_td ltx_align_center" id="S5.T2.7.7.8" style="padding:2pt 7.0pt;">73.26</td> <td class="ltx_td ltx_align_center" id="S5.T2.7.7.9" style="padding:2pt 7.0pt;">47.19</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.7.7.10" style="padding:2pt 7.0pt;">39.13</td> <td class="ltx_td ltx_align_center" id="S5.T2.7.7.11" style="padding:2pt 7.0pt;">64.46</td> <td class="ltx_td ltx_align_center" id="S5.T2.7.7.12" style="padding:2pt 7.0pt;">44.67</td> <td class="ltx_td ltx_align_center" id="S5.T2.7.7.13" style="padding:2pt 7.0pt;">38.51</td> </tr> <tr class="ltx_tr" id="S5.T2.8.8"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T2.8.8.1" style="padding:2pt 7.0pt;">SRCNN (10<math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.8.8.1.m1.1"><semantics id="S5.T2.8.8.1.m1.1a"><mo id="S5.T2.8.8.1.m1.1.1" xref="S5.T2.8.8.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.8.8.1.m1.1b"><times id="S5.T2.8.8.1.m1.1.1.cmml" xref="S5.T2.8.8.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.8.8.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.8.8.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center" id="S5.T2.8.8.2" style="padding:2pt 7.0pt;">99.85</td> <td class="ltx_td ltx_align_center" id="S5.T2.8.8.3" style="padding:2pt 7.0pt;">90.87</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.8.8.4" style="padding:2pt 7.0pt;">81.74</td> <td class="ltx_td ltx_align_center" id="S5.T2.8.8.5" style="padding:2pt 7.0pt;">98.80</td> <td class="ltx_td ltx_align_center" id="S5.T2.8.8.6" style="padding:2pt 7.0pt;">89.52</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.8.8.7" style="padding:2pt 7.0pt;">80.46</td> <td class="ltx_td ltx_align_center" id="S5.T2.8.8.8" style="padding:2pt 7.0pt;">73.20</td> <td class="ltx_td ltx_align_center" id="S5.T2.8.8.9" style="padding:2pt 7.0pt;">47.18</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.8.8.10" style="padding:2pt 7.0pt;">40.80</td> <td class="ltx_td ltx_align_center" id="S5.T2.8.8.11" style="padding:2pt 7.0pt;">64.54</td> <td class="ltx_td ltx_align_center" id="S5.T2.8.8.12" style="padding:2pt 7.0pt;">45.45</td> <td class="ltx_td ltx_align_center" id="S5.T2.8.8.13" style="padding:2pt 7.0pt;">39.06</td> </tr> <tr class="ltx_tr" id="S5.T2.9.9"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T2.9.9.1" style="padding:2pt 7.0pt;">ECSIC (10<math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.9.9.1.m1.1"><semantics id="S5.T2.9.9.1.m1.1a"><mo id="S5.T2.9.9.1.m1.1.1" xref="S5.T2.9.9.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.9.9.1.m1.1b"><times id="S5.T2.9.9.1.m1.1.1.cmml" xref="S5.T2.9.9.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.9.9.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.9.9.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center" id="S5.T2.9.9.2" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.9.9.2.1">99.86</span></td> <td class="ltx_td ltx_align_center" id="S5.T2.9.9.3" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.9.9.3.1">90.88</span></td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.9.9.4" style="padding:2pt 7.0pt;">81.78</td> <td class="ltx_td ltx_align_center" id="S5.T2.9.9.5" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.9.9.5.1">99.70</span></td> <td class="ltx_td ltx_align_center" id="S5.T2.9.9.6" style="padding:2pt 7.0pt;">90.58</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.9.9.7" style="padding:2pt 7.0pt;">81.37</td> <td class="ltx_td ltx_align_center" id="S5.T2.9.9.8" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.9.9.8.1">73.30</span></td> <td class="ltx_td ltx_align_center" id="S5.T2.9.9.9" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.9.9.9.1">47.20</span></td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.9.9.10" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.9.9.10.1">40.81</span></td> <td class="ltx_td ltx_align_center" id="S5.T2.9.9.11" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.9.9.11.1">65.44</span></td> <td class="ltx_td ltx_align_center" id="S5.T2.9.9.12" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.9.9.12.1">45.53</span></td> <td class="ltx_td ltx_align_center" id="S5.T2.9.9.13" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.9.9.13.1">39.26</span></td> </tr> <tr class="ltx_tr" id="S5.T2.10.10"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" id="S5.T2.10.10.1" style="padding:2pt 7.0pt;">Proposed Method (30<math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.10.10.1.m1.1"><semantics id="S5.T2.10.10.1.m1.1a"><mo id="S5.T2.10.10.1.m1.1.1" xref="S5.T2.10.10.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.10.10.1.m1.1b"><times id="S5.T2.10.10.1.m1.1.1.cmml" xref="S5.T2.10.10.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.10.10.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.10.10.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.10.10.2" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.10.10.2.1">99.79</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.10.10.3" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.10.10.3.1">90.86</span></td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T2.10.10.4" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.10.10.4.1">79.71</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.10.10.5" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.10.10.5.1">99.61</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.10.10.6" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.10.10.6.1">90.56</span></td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T2.10.10.7" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.10.10.7.1">79.35</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.10.10.8" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.10.10.8.1">71.06</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.10.10.9" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.10.10.9.1">46.72</span></td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T2.10.10.10" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.10.10.10.1">39.28</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.10.10.11" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.10.10.11.1">64.60</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.10.10.12" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.10.10.12.1">44.38</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.10.10.13" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.10.10.13.1">37.12</span></td> </tr> <tr class="ltx_tr" id="S5.T2.11.11"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T2.11.11.1" style="padding:2pt 7.0pt;">JPEG (30<math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.11.11.1.m1.1"><semantics id="S5.T2.11.11.1.m1.1a"><mo id="S5.T2.11.11.1.m1.1.1" xref="S5.T2.11.11.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.11.11.1.m1.1b"><times id="S5.T2.11.11.1.m1.1.1.cmml" xref="S5.T2.11.11.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.11.11.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.11.11.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center" id="S5.T2.11.11.2" style="padding:2pt 7.0pt;">90.89</td> <td class="ltx_td ltx_align_center" id="S5.T2.11.11.3" style="padding:2pt 7.0pt;">89.76</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.11.11.4" style="padding:2pt 7.0pt;">72.69</td> <td class="ltx_td ltx_align_center" id="S5.T2.11.11.5" style="padding:2pt 7.0pt;">90.71</td> <td class="ltx_td ltx_align_center" id="S5.T2.11.11.6" style="padding:2pt 7.0pt;">89.25</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.11.11.7" style="padding:2pt 7.0pt;">72.21</td> <td class="ltx_td ltx_align_center" id="S5.T2.11.11.8" style="padding:2pt 7.0pt;">65.26</td> <td class="ltx_td ltx_align_center" id="S5.T2.11.11.9" style="padding:2pt 7.0pt;">45.80</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.11.11.10" style="padding:2pt 7.0pt;">35.22</td> <td class="ltx_td ltx_align_center" id="S5.T2.11.11.11" style="padding:2pt 7.0pt;">61.07</td> <td class="ltx_td ltx_align_center" id="S5.T2.11.11.12" style="padding:2pt 7.0pt;">39.60</td> <td class="ltx_td ltx_align_center" id="S5.T2.11.11.13" style="padding:2pt 7.0pt;">33.49</td> </tr> <tr class="ltx_tr" id="S5.T2.12.12"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T2.12.12.1" style="padding:2pt 7.0pt;">JPEG2000 (30<math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.12.12.1.m1.1"><semantics id="S5.T2.12.12.1.m1.1a"><mo id="S5.T2.12.12.1.m1.1.1" xref="S5.T2.12.12.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.12.12.1.m1.1b"><times id="S5.T2.12.12.1.m1.1.1.cmml" xref="S5.T2.12.12.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.12.12.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.12.12.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center" id="S5.T2.12.12.2" style="padding:2pt 7.0pt;">90.79</td> <td class="ltx_td ltx_align_center" id="S5.T2.12.12.3" style="padding:2pt 7.0pt;">81.67</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.12.12.4" style="padding:2pt 7.0pt;">72.55</td> <td class="ltx_td ltx_align_center" id="S5.T2.12.12.5" style="padding:2pt 7.0pt;">89.48</td> <td class="ltx_td ltx_align_center" id="S5.T2.12.12.6" style="padding:2pt 7.0pt;">79.98</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.12.12.7" style="padding:2pt 7.0pt;">71.93</td> <td class="ltx_td ltx_align_center" id="S5.T2.12.12.8" style="padding:2pt 7.0pt;">63.84</td> <td class="ltx_td ltx_align_center" id="S5.T2.12.12.9" style="padding:2pt 7.0pt;">40.76</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.12.12.10" style="padding:2pt 7.0pt;">34.25</td> <td class="ltx_td ltx_align_center" id="S5.T2.12.12.11" style="padding:2pt 7.0pt;">55.06</td> <td class="ltx_td ltx_align_center" id="S5.T2.12.12.12" style="padding:2pt 7.0pt;">37.56</td> <td class="ltx_td ltx_align_center" id="S5.T2.12.12.13" style="padding:2pt 7.0pt;">31.76</td> </tr> <tr class="ltx_tr" id="S5.T2.13.13"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T2.13.13.1" style="padding:2pt 7.0pt;">SRCNN (30<math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.13.13.1.m1.1"><semantics id="S5.T2.13.13.1.m1.1a"><mo id="S5.T2.13.13.1.m1.1.1" xref="S5.T2.13.13.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.13.13.1.m1.1b"><times id="S5.T2.13.13.1.m1.1.1.cmml" xref="S5.T2.13.13.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.13.13.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.13.13.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center" id="S5.T2.13.13.2" style="padding:2pt 7.0pt;">90.73</td> <td class="ltx_td ltx_align_center" id="S5.T2.13.13.3" style="padding:2pt 7.0pt;">81.35</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.13.13.4" style="padding:2pt 7.0pt;">63.40</td> <td class="ltx_td ltx_align_center" id="S5.T2.13.13.5" style="padding:2pt 7.0pt;">88.24</td> <td class="ltx_td ltx_align_center" id="S5.T2.13.13.6" style="padding:2pt 7.0pt;">77.28</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.13.13.7" style="padding:2pt 7.0pt;">60.28</td> <td class="ltx_td ltx_align_center" id="S5.T2.13.13.8" style="padding:2pt 7.0pt;">65.18</td> <td class="ltx_td ltx_align_center" id="S5.T2.13.13.9" style="padding:2pt 7.0pt;">42.60</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.13.13.10" style="padding:2pt 7.0pt;">35.47</td> <td class="ltx_td ltx_align_center" id="S5.T2.13.13.11" style="padding:2pt 7.0pt;">55.77</td> <td class="ltx_td ltx_align_center" id="S5.T2.13.13.12" style="padding:2pt 7.0pt;">34.89</td> <td class="ltx_td ltx_align_center" id="S5.T2.13.13.13" style="padding:2pt 7.0pt;">28.33</td> </tr> <tr class="ltx_tr" id="S5.T2.14.14"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T2.14.14.1" style="padding:2pt 7.0pt;">ECSIC (30<math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.14.14.1.m1.1"><semantics id="S5.T2.14.14.1.m1.1a"><mo id="S5.T2.14.14.1.m1.1.1" xref="S5.T2.14.14.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.14.14.1.m1.1b"><times id="S5.T2.14.14.1.m1.1.1.cmml" xref="S5.T2.14.14.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.14.14.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.14.14.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center" id="S5.T2.14.14.2" style="padding:2pt 7.0pt;">99.74</td> <td class="ltx_td ltx_align_center" id="S5.T2.14.14.3" style="padding:2pt 7.0pt;">90.78</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.14.14.4" style="padding:2pt 7.0pt;">79.58</td> <td class="ltx_td ltx_align_center" id="S5.T2.14.14.5" style="padding:2pt 7.0pt;">99.54</td> <td class="ltx_td ltx_align_center" id="S5.T2.14.14.6" style="padding:2pt 7.0pt;">90.37</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.14.14.7" style="padding:2pt 7.0pt;">79.09</td> <td class="ltx_td ltx_align_center" id="S5.T2.14.14.8" style="padding:2pt 7.0pt;">68.82</td> <td class="ltx_td ltx_align_center" id="S5.T2.14.14.9" style="padding:2pt 7.0pt;">44.28</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.14.14.10" style="padding:2pt 7.0pt;">37.39</td> <td class="ltx_td ltx_align_center" id="S5.T2.14.14.11" style="padding:2pt 7.0pt;">62.68</td> <td class="ltx_td ltx_align_center" id="S5.T2.14.14.12" style="padding:2pt 7.0pt;">43.49</td> <td class="ltx_td ltx_align_center" id="S5.T2.14.14.13" style="padding:2pt 7.0pt;">35.41</td> </tr> <tr class="ltx_tr" id="S5.T2.15.15"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" id="S5.T2.15.15.1" style="padding:2pt 7.0pt;">Proposed Method (50<math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.15.15.1.m1.1"><semantics id="S5.T2.15.15.1.m1.1a"><mo id="S5.T2.15.15.1.m1.1.1" xref="S5.T2.15.15.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.15.15.1.m1.1b"><times id="S5.T2.15.15.1.m1.1.1.cmml" xref="S5.T2.15.15.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.15.15.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.15.15.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.15.15.2" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.15.15.2.1">99.67</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.15.15.3" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.15.15.3.1">81.88</span></td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T2.15.15.4" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.15.15.4.1">72.66</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.15.15.5" style="padding:2pt 7.0pt;">99.13</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.15.15.6" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.15.15.6.1">80.85</span></td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T2.15.15.7" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.15.15.7.1">71.71</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.15.15.8" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.15.15.8.1">65.25</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.15.15.9" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.15.15.9.1">42.79</span></td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T2.15.15.10" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.15.15.10.1">35.87</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.15.15.11" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.15.15.11.1">60.95</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.15.15.12" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.15.15.12.1">40.24</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T2.15.15.13" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.15.15.13.1">33.33</span></td> </tr> <tr class="ltx_tr" id="S5.T2.16.16"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T2.16.16.1" style="padding:2pt 7.0pt;">JPEG (50<math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.16.16.1.m1.1"><semantics id="S5.T2.16.16.1.m1.1a"><mo id="S5.T2.16.16.1.m1.1.1" xref="S5.T2.16.16.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.16.16.1.m1.1b"><times id="S5.T2.16.16.1.m1.1.1.cmml" xref="S5.T2.16.16.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.16.16.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.16.16.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center" id="S5.T2.16.16.2" style="padding:2pt 7.0pt;">71.58</td> <td class="ltx_td ltx_align_center" id="S5.T2.16.16.3" style="padding:2pt 7.0pt;">62.74</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.16.16.4" style="padding:2pt 7.0pt;">53.78</td> <td class="ltx_td ltx_align_center" id="S5.T2.16.16.5" style="padding:2pt 7.0pt;">70.38</td> <td class="ltx_td ltx_align_center" id="S5.T2.16.16.6" style="padding:2pt 7.0pt;">61.19</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.16.16.7" style="padding:2pt 7.0pt;">52.37</td> <td class="ltx_td ltx_align_center" id="S5.T2.16.16.8" style="padding:2pt 7.0pt;">40.49</td> <td class="ltx_td ltx_align_center" id="S5.T2.16.16.9" style="padding:2pt 7.0pt;">26.60</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.16.16.10" style="padding:2pt 7.0pt;">25.66</td> <td class="ltx_td ltx_align_center" id="S5.T2.16.16.11" style="padding:2pt 7.0pt;">36.92</td> <td class="ltx_td ltx_align_center" id="S5.T2.16.16.12" style="padding:2pt 7.0pt;">24.50</td> <td class="ltx_td ltx_align_center" id="S5.T2.16.16.13" style="padding:2pt 7.0pt;">19.59</td> </tr> <tr class="ltx_tr" id="S5.T2.17.17"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T2.17.17.1" style="padding:2pt 7.0pt;">JPEG2000 (50<math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.17.17.1.m1.1"><semantics id="S5.T2.17.17.1.m1.1a"><mo id="S5.T2.17.17.1.m1.1.1" xref="S5.T2.17.17.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.17.17.1.m1.1b"><times id="S5.T2.17.17.1.m1.1.1.cmml" xref="S5.T2.17.17.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.17.17.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.17.17.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center" id="S5.T2.17.17.2" style="padding:2pt 7.0pt;">81.05</td> <td class="ltx_td ltx_align_center" id="S5.T2.17.17.3" style="padding:2pt 7.0pt;">71.78</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.17.17.4" style="padding:2pt 7.0pt;">62.73</td> <td class="ltx_td ltx_align_center" id="S5.T2.17.17.5" style="padding:2pt 7.0pt;">77.65</td> <td class="ltx_td ltx_align_center" id="S5.T2.17.17.6" style="padding:2pt 7.0pt;">67.78</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.17.17.7" style="padding:2pt 7.0pt;">59.01</td> <td class="ltx_td ltx_align_center" id="S5.T2.17.17.8" style="padding:2pt 7.0pt;">45.37</td> <td class="ltx_td ltx_align_center" id="S5.T2.17.17.9" style="padding:2pt 7.0pt;">30.14</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.17.17.10" style="padding:2pt 7.0pt;">24.56</td> <td class="ltx_td ltx_align_center" id="S5.T2.17.17.11" style="padding:2pt 7.0pt;">35.44</td> <td class="ltx_td ltx_align_center" id="S5.T2.17.17.12" style="padding:2pt 7.0pt;">22.46</td> <td class="ltx_td ltx_align_center" id="S5.T2.17.17.13" style="padding:2pt 7.0pt;">17.42</td> </tr> <tr class="ltx_tr" id="S5.T2.18.18"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T2.18.18.1" style="padding:2pt 7.0pt;">SRCNN (50<math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.18.18.1.m1.1"><semantics id="S5.T2.18.18.1.m1.1a"><mo id="S5.T2.18.18.1.m1.1.1" xref="S5.T2.18.18.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.18.18.1.m1.1b"><times id="S5.T2.18.18.1.m1.1.1.cmml" xref="S5.T2.18.18.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.18.18.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.18.18.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center" id="S5.T2.18.18.2" style="padding:2pt 7.0pt;">80.14</td> <td class="ltx_td ltx_align_center" id="S5.T2.18.18.3" style="padding:2pt 7.0pt;">62.40</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.18.18.4" style="padding:2pt 7.0pt;">53.43</td> <td class="ltx_td ltx_align_center" id="S5.T2.18.18.5" style="padding:2pt 7.0pt;">76.35</td> <td class="ltx_td ltx_align_center" id="S5.T2.18.18.6" style="padding:2pt 7.0pt;">57.99</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.18.18.7" style="padding:2pt 7.0pt;">49.37</td> <td class="ltx_td ltx_align_center" id="S5.T2.18.18.8" style="padding:2pt 7.0pt;">42.26</td> <td class="ltx_td ltx_align_center" id="S5.T2.18.18.9" style="padding:2pt 7.0pt;">25.11</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T2.18.18.10" style="padding:2pt 7.0pt;">20.09</td> <td class="ltx_td ltx_align_center" id="S5.T2.18.18.11" style="padding:2pt 7.0pt;">30.99</td> <td class="ltx_td ltx_align_center" id="S5.T2.18.18.12" style="padding:2pt 7.0pt;">19.53</td> <td class="ltx_td ltx_align_center" id="S5.T2.18.18.13" style="padding:2pt 7.0pt;">15.51</td> </tr> <tr class="ltx_tr" id="S5.T2.19.19"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_b ltx_border_r" id="S5.T2.19.19.1" style="padding:2pt 7.0pt;">ECSIC (50<math alttext="\times" class="ltx_Math" display="inline" id="S5.T2.19.19.1.m1.1"><semantics id="S5.T2.19.19.1.m1.1a"><mo id="S5.T2.19.19.1.m1.1.1" xref="S5.T2.19.19.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="S5.T2.19.19.1.m1.1b"><times id="S5.T2.19.19.1.m1.1.1.cmml" xref="S5.T2.19.19.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="S5.T2.19.19.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="S5.T2.19.19.1.m1.1d">×</annotation></semantics></math>)</th> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T2.19.19.2" style="padding:2pt 7.0pt;">99.65</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T2.19.19.3" style="padding:2pt 7.0pt;">81.83</td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="S5.T2.19.19.4" style="padding:2pt 7.0pt;">72.62</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T2.19.19.5" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T2.19.19.5.1">99.14</span></td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T2.19.19.6" style="padding:2pt 7.0pt;">80.07</td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="S5.T2.19.19.7" style="padding:2pt 7.0pt;">71.60</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T2.19.19.8" style="padding:2pt 7.0pt;">64.33</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T2.19.19.9" style="padding:2pt 7.0pt;">42.56</td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="S5.T2.19.19.10" style="padding:2pt 7.0pt;">35.63</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T2.19.19.11" style="padding:2pt 7.0pt;">60.18</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T2.19.19.12" style="padding:2pt 7.0pt;">39.89</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T2.19.19.13" style="padding:2pt 7.0pt;">32.64</td> </tr> </tbody> </table> </figure> <div class="ltx_para" id="S5.SS2.p4"> <p class="ltx_p" id="S5.SS2.p4.1">For the second set of experiments, based on the <math alttext="30\times" class="ltx_math_unparsed" display="inline" id="S5.SS2.p4.1.m1.1"><semantics id="S5.SS2.p4.1.m1.1a"><mrow id="S5.SS2.p4.1.m1.1b"><mn id="S5.SS2.p4.1.m1.1.1">30</mn><mo id="S5.SS2.p4.1.m1.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.SS2.p4.1.m1.1c">30\times</annotation><annotation encoding="application/x-llamapun" id="S5.SS2.p4.1.m1.1d">30 ×</annotation></semantics></math> compression semantic codec, the proposed channel codec is compared with traditional channel coding and modulation schemes over AWGN and Rayleigh fading channels. <span class="ltx_text" id="S5.SS2.p4.1.1">In the Rayleigh fading scenario, perfect channel estimation and the zero-forcing equalization algorithm are assumed.<span class="ltx_text" id="S5.SS2.p4.1.1.1"> Fig.<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.F11" title="Figure 11 ‣ V-B Simulation Results ‣ V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">11</span></a> and Fig.<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.F12" title="Figure 12 ‣ V-B Simulation Results ‣ V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">12</span></a> show the 3D AP results of all methods for different difficulty regimes over AWGN and Rayleigh fading channels, respectively. The traditional schemes use the 2/3 rate LDPC code with 64QAM modulation and the 1/2 rate LDPC code with 256QAM modulation. The output of the semantic codec is quantized to 6-bit. To ensure a fair comparison, the average amount of transferred data remains consistent across all methods. The figures show that the proposed channel codec significantly outperforms the conventional approaches at various SNRs in detection performance over AWGN and Rayleigh fading channels, especially in the low SNR regime.</span></span></p> </div> <figure class="ltx_figure" id="S5.F11"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="204" id="S5.F11.g1" src="extracted/6213374/figure/fig11.png" width="678"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 11: </span>The 3D AP results versus SNR on the AWGN channel for (a) easy, (b) moderate and (c) hard regimes.</figcaption> </figure> <figure class="ltx_figure" id="S5.F12"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="204" id="S5.F12.g1" src="extracted/6213374/figure/a1.png" width="678"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 12: </span>The 3D AP results versus SNR on the Rayleigh fading channel for (a) easy, (b) moderate and (c) hard regimes.</figcaption> </figure> <div class="ltx_para" id="S5.SS2.p5"> <p class="ltx_p" id="S5.SS2.p5.1"><span class="ltx_text" id="S5.SS2.p5.1.1">For the third set of experiments, we evaluate the performance of the proposed semantic communication system compared with other source-channel coding algorithms under AWGN channels at varying SNR levels. The proposed method uses the same settings as in the second set of experiments. The comparison schemes adopt <math alttext="30\times" class="ltx_math_unparsed" display="inline" id="S5.SS2.p5.1.1.m1.1"><semantics id="S5.SS2.p5.1.1.m1.1a"><mrow id="S5.SS2.p5.1.1.m1.1b"><mn id="S5.SS2.p5.1.1.m1.1.1">30</mn><mo id="S5.SS2.p5.1.1.m1.1.2" lspace="0.222em">×</mo></mrow><annotation encoding="application/x-tex" id="S5.SS2.p5.1.1.m1.1c">30\times</annotation><annotation encoding="application/x-llamapun" id="S5.SS2.p5.1.1.m1.1d">30 ×</annotation></semantics></math> compressed JPEG, JPEG2000, and ECSIC as source encoding methods, along with two channel coding and modulation methods: the 2/3 rate LDPC code with 64QAM modulation and the 1/2 rate LDPC code with 256QAM modulation. For consistency, all methods transfer the same amount of data. Fig. <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.F13" title="Figure 13 ‣ V-B Simulation Results ‣ V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">13</span></a> illustrates the performance results of the proposed system and comparison methods across different difficulty regimes. The results demonstrate that the proposed semantic communication system offers superior performance over traditional source-channel coding methods at various SNR levels.<span class="ltx_text" id="S5.SS2.p5.1.1.1"></span></span></p> </div> <figure class="ltx_figure" id="S5.F13"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="212" id="S5.F13.g1" src="extracted/6213374/figure/a2.png" width="678"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 13: </span>Performance comparison between the proposed semantic communication system and other source-channel coding methods on the AWGN channel for (a) easy, (b) moderate, and (c) hard regimes.</figcaption> </figure> </section> <section class="ltx_subsection" id="S5.SS3"> <h3 class="ltx_title ltx_title_subsection"> <span class="ltx_tag ltx_tag_subsection"><span class="ltx_text" id="S5.SS3.5.1.1">V-C</span> </span><span class="ltx_text ltx_font_italic" id="S5.SS3.6.2">Ablation Study</span> </h3> <div class="ltx_para" id="S5.SS3.p1"> <p class="ltx_p" id="S5.SS3.p1.1">We conduct an ablation study on the proposed network to evaluate the impact of the key area and global information networks on the object detection results, where two networks are separated and work independently. The network separation is simulated by setting the output of the inactive network to zero. For instance, when the global information network is set to work, the output of the key area information network is zero, and vice versa. Besides, the key area and global information are compressed to the same amount to ensure fairness in the experiment. The simulation results of the ablation study are shown in Table <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.T3" title="TABLE III ‣ V-C Ablation Study ‣ V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">III</span></a>.</p> </div> <figure class="ltx_table" id="S5.T3"> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_table">TABLE III: </span>The Detection Results for The Ablation Study</figcaption><div class="ltx_flex_figure"> <div class="ltx_flex_cell ltx_flex_size_1"> <table class="ltx_tabular ltx_centering ltx_figure_panel ltx_guessed_headers ltx_align_middle" id="S5.T3.4"> <thead class="ltx_thead"> <tr class="ltx_tr" id="S5.T3.4.5.1"> <th class="ltx_td ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" id="S5.T3.4.5.1.1" style="padding:2pt 7.0pt;"></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" colspan="6" id="S5.T3.4.5.1.2" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.5.1.2.1">2D object detection</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" colspan="6" id="S5.T3.4.5.1.3" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.5.1.3.1">3D object detection</span></th> </tr> <tr class="ltx_tr" id="S5.T3.4.4"> <th class="ltx_td ltx_th ltx_th_column ltx_th_row ltx_border_r" id="S5.T3.4.4.5" style="padding:2pt 7.0pt;"></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" colspan="3" id="S5.T3.1.1.1" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.1.1.1.1">AP on left images <math alttext="\uparrow" class="ltx_Math" display="inline" id="S5.T3.1.1.1.1.m1.1"><semantics id="S5.T3.1.1.1.1.m1.1a"><mo id="S5.T3.1.1.1.1.m1.1.1" stretchy="false" xref="S5.T3.1.1.1.1.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S5.T3.1.1.1.1.m1.1b"><ci id="S5.T3.1.1.1.1.m1.1.1.cmml" xref="S5.T3.1.1.1.1.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.T3.1.1.1.1.m1.1c">\uparrow</annotation><annotation encoding="application/x-llamapun" id="S5.T3.1.1.1.1.m1.1d">↑</annotation></semantics></math></span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" colspan="3" id="S5.T3.2.2.2" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.2.2.2.1">AP on right images <math alttext="\uparrow" class="ltx_Math" display="inline" id="S5.T3.2.2.2.1.m1.1"><semantics id="S5.T3.2.2.2.1.m1.1a"><mo id="S5.T3.2.2.2.1.m1.1.1" stretchy="false" xref="S5.T3.2.2.2.1.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S5.T3.2.2.2.1.m1.1b"><ci id="S5.T3.2.2.2.1.m1.1.1.cmml" xref="S5.T3.2.2.2.1.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.T3.2.2.2.1.m1.1c">\uparrow</annotation><annotation encoding="application/x-llamapun" id="S5.T3.2.2.2.1.m1.1d">↑</annotation></semantics></math></span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" colspan="3" id="S5.T3.3.3.3" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.3.3.3.1">AP on bird’s-eye view <math alttext="\uparrow" class="ltx_Math" display="inline" id="S5.T3.3.3.3.1.m1.1"><semantics id="S5.T3.3.3.3.1.m1.1a"><mo id="S5.T3.3.3.3.1.m1.1.1" stretchy="false" xref="S5.T3.3.3.3.1.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S5.T3.3.3.3.1.m1.1b"><ci id="S5.T3.3.3.3.1.m1.1.1.cmml" xref="S5.T3.3.3.3.1.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.T3.3.3.3.1.m1.1c">\uparrow</annotation><annotation encoding="application/x-llamapun" id="S5.T3.3.3.3.1.m1.1d">↑</annotation></semantics></math></span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" colspan="3" id="S5.T3.4.4.4" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.4.4.1">AP for 3D detection <math alttext="\uparrow" class="ltx_Math" display="inline" id="S5.T3.4.4.4.1.m1.1"><semantics id="S5.T3.4.4.4.1.m1.1a"><mo id="S5.T3.4.4.4.1.m1.1.1" stretchy="false" xref="S5.T3.4.4.4.1.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S5.T3.4.4.4.1.m1.1b"><ci id="S5.T3.4.4.4.1.m1.1.1.cmml" xref="S5.T3.4.4.4.1.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.T3.4.4.4.1.m1.1c">\uparrow</annotation><annotation encoding="application/x-llamapun" id="S5.T3.4.4.4.1.m1.1d">↑</annotation></semantics></math></span></th> </tr> <tr class="ltx_tr" id="S5.T3.4.6.2"> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_th_row ltx_border_r" id="S5.T3.4.6.2.1" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.6.2.1.1">Method</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T3.4.6.2.2" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.6.2.2.1">Easy</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T3.4.6.2.3" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.6.2.3.1">Mode</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" id="S5.T3.4.6.2.4" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.6.2.4.1">Hard</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T3.4.6.2.5" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.6.2.5.1">Easy</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T3.4.6.2.6" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.6.2.6.1">Mode</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" id="S5.T3.4.6.2.7" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.6.2.7.1">Hard</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T3.4.6.2.8" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.6.2.8.1">Easy</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T3.4.6.2.9" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.6.2.9.1">Mode</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" id="S5.T3.4.6.2.10" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.6.2.10.1">Hard</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T3.4.6.2.11" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.6.2.11.1">Easy</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T3.4.6.2.12" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.6.2.12.1">Mode</span></th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T3.4.6.2.13" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.6.2.13.1">Hard</span></th> </tr> </thead> <tbody class="ltx_tbody"> <tr class="ltx_tr" id="S5.T3.4.7.1"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" id="S5.T3.4.7.1.1" style="padding:2pt 7.0pt;">Network A+B</th> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T3.4.7.1.2" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.7.1.2.1">99.67</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T3.4.7.1.3" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.7.1.3.1">81.88</span></td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T3.4.7.1.4" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.7.1.4.1">72.66</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T3.4.7.1.5" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.7.1.5.1">99.13</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T3.4.7.1.6" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.7.1.6.1">80.85</span></td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T3.4.7.1.7" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.7.1.7.1">71.71</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T3.4.7.1.8" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.7.1.8.1">65.25</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T3.4.7.1.9" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.7.1.9.1">42.79</span></td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T3.4.7.1.10" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.7.1.10.1">35.87</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T3.4.7.1.11" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.7.1.11.1">60.95</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T3.4.7.1.12" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.7.1.12.1">40.24</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T3.4.7.1.13" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T3.4.7.1.13.1">33.33</span></td> </tr> <tr class="ltx_tr" id="S5.T3.4.8.2"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T3.4.8.2.1" style="padding:2pt 7.0pt;">Network A<sup class="ltx_sup" id="S5.T3.4.8.2.1.1">1</sup> </th> <td class="ltx_td ltx_align_center" id="S5.T3.4.8.2.2" style="padding:2pt 7.0pt;">83.61</td> <td class="ltx_td ltx_align_center" id="S5.T3.4.8.2.3" style="padding:2pt 7.0pt;">67.45</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T3.4.8.2.4" style="padding:2pt 7.0pt;">51.96</td> <td class="ltx_td ltx_align_center" id="S5.T3.4.8.2.5" style="padding:2pt 7.0pt;">81.36</td> <td class="ltx_td ltx_align_center" id="S5.T3.4.8.2.6" style="padding:2pt 7.0pt;">65.06</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T3.4.8.2.7" style="padding:2pt 7.0pt;">50.17</td> <td class="ltx_td ltx_align_center" id="S5.T3.4.8.2.8" style="padding:2pt 7.0pt;">38.57</td> <td class="ltx_td ltx_align_center" id="S5.T3.4.8.2.9" style="padding:2pt 7.0pt;">25.27</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T3.4.8.2.10" style="padding:2pt 7.0pt;">24.35</td> <td class="ltx_td ltx_align_center" id="S5.T3.4.8.2.11" style="padding:2pt 7.0pt;">27.63</td> <td class="ltx_td ltx_align_center" id="S5.T3.4.8.2.12" style="padding:2pt 7.0pt;">20.72</td> <td class="ltx_td ltx_align_center" id="S5.T3.4.8.2.13" style="padding:2pt 7.0pt;">16.46</td> </tr> <tr class="ltx_tr" id="S5.T3.4.9.3"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_b ltx_border_r" id="S5.T3.4.9.3.1" style="padding:2pt 7.0pt;">Network B<sup class="ltx_sup" id="S5.T3.4.9.3.1.1">2</sup> </th> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T3.4.9.3.2" style="padding:2pt 7.0pt;">90.68</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T3.4.9.3.3" style="padding:2pt 7.0pt;">81.06</td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="S5.T3.4.9.3.4" style="padding:2pt 7.0pt;">63.27</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T3.4.9.3.5" style="padding:2pt 7.0pt;">89.25</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T3.4.9.3.6" style="padding:2pt 7.0pt;">78.40</td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="S5.T3.4.9.3.7" style="padding:2pt 7.0pt;">61.21</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T3.4.9.3.8" style="padding:2pt 7.0pt;">63.77</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T3.4.9.3.9" style="padding:2pt 7.0pt;">40.92</td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="S5.T3.4.9.3.10" style="padding:2pt 7.0pt;">33.73</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T3.4.9.3.11" style="padding:2pt 7.0pt;">55.07</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T3.4.9.3.12" style="padding:2pt 7.0pt;">34.29</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T3.4.9.3.13" style="padding:2pt 7.0pt;">27.84</td> </tr> </tbody> </table> </div> <div class="ltx_flex_break"></div> <div class="ltx_flex_cell ltx_flex_size_1"> <ul class="ltx_itemize ltx_centering ltx_figure_panel" id="S5.I3"> <li class="ltx_item" id="S5.I3.i1" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item">•</span> <div class="ltx_para" id="S5.I3.i1.p1"> <p class="ltx_p" id="S5.I3.i1.p1.1"><span class="ltx_text" id="S5.I3.i1.p1.1.1" style="font-size:80%;">1 Network A denotes the key area information network.</span></p> </div> </li> <li class="ltx_item" id="S5.I3.i2" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item">•</span> <div class="ltx_para" id="S5.I3.i2.p1"> <p class="ltx_p" id="S5.I3.i2.p1.1"><span class="ltx_text" id="S5.I3.i2.p1.1.1" style="font-size:80%;">2 Network B denotes the global information network.</span></p> </div> </li> </ul> </div> </div> </figure> <div class="ltx_para" id="S5.SS3.p2"> <p class="ltx_p" id="S5.SS3.p2.1"><span class="ltx_text" id="S5.SS3.p2.1.1">The table indicates that both key area and global information networks play a significant role in improving detection performance. Removing any processing network will result in a substantial loss in overall network performance. The results of the ablation experiment verify the rationality of our network design. The global information network provides left-right photometric alignment to support depth inference, while the key area information network captures object feature details essential for 2D detection, all required for the 3D object detection task.<span class="ltx_text" id="S5.SS3.p2.1.1.1"></span></span></p> </div> <div class="ltx_para" id="S5.SS3.p3"> <p class="ltx_p" id="S5.SS3.p3.1"><span class="ltx_text" id="S5.SS3.p3.1.1">Additionally, we perform two ablation studies to assess the effectiveness of the proposed training strategy<span class="ltx_note ltx_role_footnote" id="footnote4"><sup class="ltx_note_mark">4</sup><span class="ltx_note_outer"><span class="ltx_note_content"><sup class="ltx_note_mark">4</sup><span class="ltx_tag ltx_tag_note">4</span><span class="ltx_text" id="footnote4.1">Since training step 5 follows a standard method for training channel codecs, our ablation studies focus on the training strategy for semantic codecs, i.e., training steps 1 to 4.</span></span></span></span>. The first study introduces four comparative strategies to evaluate the advantages of the step-by-step training approach. The first comparison strategy combines training steps 2 and 3 of the proposed method. After training the global information network (with its parameters frozen), the key area information network and the fusion network are jointly trained using the hybrid masked Charbonnier loss. In the second strategy, training step 3 is omitted, and joint training is performed after independently training both the global information and key area information networks, utilizing both the hybrid masked Charbonnier loss and the Charbonnier loss. The third strategy jointly trains of all networks following the training of the global information network with two loss functions. Finally, in the fourth strategy, the entire network is trained from the beginning. The 3D detection performance for each strategy is presented in Table <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.T4" title="TABLE IV ‣ V-C Ablation Study ‣ V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">IV</span></a>.<span class="ltx_text" id="S5.SS3.p3.1.1.1"></span></span></p> </div> <figure class="ltx_table" id="S5.T4"> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_table">TABLE IV: </span>The 3D Detection Results for The Ablation Study 1 of The Training Strategy</figcaption> <table class="ltx_tabular ltx_centering ltx_guessed_headers ltx_align_middle" id="S5.T4.2"> <tbody class="ltx_tbody"> <tr class="ltx_tr" id="S5.T4.2.3.1"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" id="S5.T4.2.3.1.1" rowspan="3" style="padding:2pt 3.5pt;"><span class="ltx_text" id="S5.T4.2.3.1.1.1">Network</span></th> <td class="ltx_td ltx_align_center ltx_border_t" colspan="6" id="S5.T4.2.3.1.2" style="padding:2pt 3.5pt;">3D object detection</td> </tr> <tr class="ltx_tr" id="S5.T4.2.2"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" colspan="3" id="S5.T4.1.1.1" style="padding:2pt 3.5pt;">AP for bird’s-eye view <math alttext="\uparrow" class="ltx_Math" display="inline" id="S5.T4.1.1.1.m1.1"><semantics id="S5.T4.1.1.1.m1.1a"><mo id="S5.T4.1.1.1.m1.1.1" stretchy="false" xref="S5.T4.1.1.1.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S5.T4.1.1.1.m1.1b"><ci id="S5.T4.1.1.1.m1.1.1.cmml" xref="S5.T4.1.1.1.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.T4.1.1.1.m1.1c">\uparrow</annotation><annotation encoding="application/x-llamapun" id="S5.T4.1.1.1.m1.1d">↑</annotation></semantics></math> </td> <td class="ltx_td ltx_align_center ltx_border_t" colspan="3" id="S5.T4.2.2.2" style="padding:2pt 3.5pt;">AP for 3D detection <math alttext="\uparrow" class="ltx_Math" display="inline" id="S5.T4.2.2.2.m1.1"><semantics id="S5.T4.2.2.2.m1.1a"><mo id="S5.T4.2.2.2.m1.1.1" stretchy="false" xref="S5.T4.2.2.2.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S5.T4.2.2.2.m1.1b"><ci id="S5.T4.2.2.2.m1.1.1.cmml" xref="S5.T4.2.2.2.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.T4.2.2.2.m1.1c">\uparrow</annotation><annotation encoding="application/x-llamapun" id="S5.T4.2.2.2.m1.1d">↑</annotation></semantics></math> </td> </tr> <tr class="ltx_tr" id="S5.T4.2.4.2"> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T4.2.4.2.1" style="padding:2pt 3.5pt;">Easy</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T4.2.4.2.2" style="padding:2pt 3.5pt;">Mode</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T4.2.4.2.3" style="padding:2pt 3.5pt;">Hard</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T4.2.4.2.4" style="padding:2pt 3.5pt;">Easy</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T4.2.4.2.5" style="padding:2pt 3.5pt;">Mode</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T4.2.4.2.6" style="padding:2pt 3.5pt;">Hard</td> </tr> <tr class="ltx_tr" id="S5.T4.2.5.3"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" id="S5.T4.2.5.3.1" style="padding:2pt 3.5pt;">Proposed strategy</th> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T4.2.5.3.2" style="padding:2pt 3.5pt;"><span class="ltx_text ltx_font_bold" id="S5.T4.2.5.3.2.1">71.06</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T4.2.5.3.3" style="padding:2pt 3.5pt;"><span class="ltx_text ltx_font_bold" id="S5.T4.2.5.3.3.1">46.72</span></td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T4.2.5.3.4" style="padding:2pt 3.5pt;"><span class="ltx_text ltx_font_bold" id="S5.T4.2.5.3.4.1">39.28</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T4.2.5.3.5" style="padding:2pt 3.5pt;"><span class="ltx_text ltx_font_bold" id="S5.T4.2.5.3.5.1">64.60</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T4.2.5.3.6" style="padding:2pt 3.5pt;"><span class="ltx_text ltx_font_bold" id="S5.T4.2.5.3.6.1">44.38</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T4.2.5.3.7" style="padding:2pt 3.5pt;"><span class="ltx_text ltx_font_bold" id="S5.T4.2.5.3.7.1">37.12</span></td> </tr> <tr class="ltx_tr" id="S5.T4.2.6.4"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T4.2.6.4.1" style="padding:2pt 3.5pt;">Comparison strategy1</th> <td class="ltx_td ltx_align_center" id="S5.T4.2.6.4.2" style="padding:2pt 3.5pt;">70.66</td> <td class="ltx_td ltx_align_center" id="S5.T4.2.6.4.3" style="padding:2pt 3.5pt;">46.61</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T4.2.6.4.4" style="padding:2pt 3.5pt;">39.10</td> <td class="ltx_td ltx_align_center" id="S5.T4.2.6.4.5" style="padding:2pt 3.5pt;">63.80</td> <td class="ltx_td ltx_align_center" id="S5.T4.2.6.4.6" style="padding:2pt 3.5pt;">43.96</td> <td class="ltx_td ltx_align_center" id="S5.T4.2.6.4.7" style="padding:2pt 3.5pt;">36.23</td> </tr> <tr class="ltx_tr" id="S5.T4.2.7.5"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T4.2.7.5.1" style="padding:2pt 3.5pt;">Comparison strategy2</th> <td class="ltx_td ltx_align_center" id="S5.T4.2.7.5.2" style="padding:2pt 3.5pt;">70.98</td> <td class="ltx_td ltx_align_center" id="S5.T4.2.7.5.3" style="padding:2pt 3.5pt;">46.66</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T4.2.7.5.4" style="padding:2pt 3.5pt;">39.17</td> <td class="ltx_td ltx_align_center" id="S5.T4.2.7.5.5" style="padding:2pt 3.5pt;">64.47</td> <td class="ltx_td ltx_align_center" id="S5.T4.2.7.5.6" style="padding:2pt 3.5pt;">44.16</td> <td class="ltx_td ltx_align_center" id="S5.T4.2.7.5.7" style="padding:2pt 3.5pt;">37.01</td> </tr> <tr class="ltx_tr" id="S5.T4.2.8.6"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T4.2.8.6.1" style="padding:2pt 3.5pt;">Comparison strategy3</th> <td class="ltx_td ltx_align_center" id="S5.T4.2.8.6.2" style="padding:2pt 3.5pt;">70.59</td> <td class="ltx_td ltx_align_center" id="S5.T4.2.8.6.3" style="padding:2pt 3.5pt;">46.60</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T4.2.8.6.4" style="padding:2pt 3.5pt;">39.04</td> <td class="ltx_td ltx_align_center" id="S5.T4.2.8.6.5" style="padding:2pt 3.5pt;">63.78</td> <td class="ltx_td ltx_align_center" id="S5.T4.2.8.6.6" style="padding:2pt 3.5pt;">43.99</td> <td class="ltx_td ltx_align_center" id="S5.T4.2.8.6.7" style="padding:2pt 3.5pt;">36.15</td> </tr> <tr class="ltx_tr" id="S5.T4.2.9.7"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_b ltx_border_r" id="S5.T4.2.9.7.1" style="padding:2pt 3.5pt;">Comparison strategy4</th> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T4.2.9.7.2" style="padding:2pt 3.5pt;">67.88</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T4.2.9.7.3" style="padding:2pt 3.5pt;">44.02</td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="S5.T4.2.9.7.4" style="padding:2pt 3.5pt;">36.89</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T4.2.9.7.5" style="padding:2pt 3.5pt;">61.92</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T4.2.9.7.6" style="padding:2pt 3.5pt;">42.97</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T4.2.9.7.7" style="padding:2pt 3.5pt;">35.05</td> </tr> </tbody> </table> </figure> <div class="ltx_para" id="S5.SS3.p4"> <p class="ltx_p" id="S5.SS3.p4.1"><span class="ltx_text" id="S5.SS3.p4.1.1">The table shows that the performance of the proposed strategy is slightly better than the first to third comparison strategies and significantly better than the fourth comparison strategy, which adopts whole-network training. Additionally, since the proposed method employs a module-by-module training strategy, it can reduce the training time for each epoch. Table <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.T5" title="TABLE V ‣ V-C Ablation Study ‣ V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">V</span></a> presents the number of training epochs and the average training time for each step using an Intel Core i5-12400F CPU @ 2.50 GHz and an NVIDIA GeForce GTX 3060. The results demonstrate that the proposed strategy provides the best overall performance with the shortest training time.<span class="ltx_text" id="S5.SS3.p4.1.1.1"></span></span></p> </div> <figure class="ltx_table" id="S5.T5"> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_table">TABLE V: </span>The Training Time for The Ablation Study 1 of The Training Strategy</figcaption><div class="ltx_flex_figure"> <div class="ltx_flex_cell ltx_flex_size_1"> <table class="ltx_tabular ltx_centering ltx_figure_panel ltx_guessed_headers ltx_align_middle" id="S5.T5.1"> <thead class="ltx_thead"> <tr class="ltx_tr" id="S5.T5.1.1.1"> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_th_row ltx_border_r ltx_border_t" id="S5.T5.1.1.1.1" style="padding:2pt 3.5pt;">Strategy</th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T5.1.1.1.2" style="padding:2pt 3.5pt;">Step 1</th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T5.1.1.1.3" style="padding:2pt 3.5pt;">Step 2</th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T5.1.1.1.4" style="padding:2pt 3.5pt;">Step 3</th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="S5.T5.1.1.1.5" style="padding:2pt 3.5pt;">Step 4</th> </tr> </thead> <tbody class="ltx_tbody"> <tr class="ltx_tr" id="S5.T5.1.2.1"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" id="S5.T5.1.2.1.1" rowspan="2" style="padding:2pt 3.5pt;"><span class="ltx_text" id="S5.T5.1.2.1.1.1">Proposed strategy</span></th> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.2.1.2" style="padding:2pt 3.5pt;">12 ep</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.2.1.3" style="padding:2pt 3.5pt;">10 ep</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.2.1.4" style="padding:2pt 3.5pt;">6 ep</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.2.1.5" style="padding:2pt 3.5pt;">10 ep</td> </tr> <tr class="ltx_tr" id="S5.T5.1.3.2"> <td class="ltx_td ltx_align_center" id="S5.T5.1.3.2.1" style="padding:2pt 3.5pt;">61 min/ep</td> <td class="ltx_td ltx_align_center" id="S5.T5.1.3.2.2" style="padding:2pt 3.5pt;">12 min/ep</td> <td class="ltx_td ltx_align_center" id="S5.T5.1.3.2.3" style="padding:2pt 3.5pt;">32 min/ep</td> <td class="ltx_td ltx_align_center" id="S5.T5.1.3.2.4" style="padding:2pt 3.5pt;">78 min/ep</td> </tr> <tr class="ltx_tr" id="S5.T5.1.4.3"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" id="S5.T5.1.4.3.1" rowspan="2" style="padding:2pt 3.5pt;"><span class="ltx_text" id="S5.T5.1.4.3.1.1">Compression strategy1</span></th> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.4.3.2" style="padding:2pt 3.5pt;">12 ep</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.4.3.3" style="padding:2pt 3.5pt;">16ep</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.4.3.4" style="padding:2pt 3.5pt;">10 ep</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.4.3.5" style="padding:2pt 3.5pt;">-</td> </tr> <tr class="ltx_tr" id="S5.T5.1.5.4"> <td class="ltx_td ltx_align_center" id="S5.T5.1.5.4.1" style="padding:2pt 3.5pt;">61 min/ep</td> <td class="ltx_td ltx_align_center" id="S5.T5.1.5.4.2" style="padding:2pt 3.5pt;">39 min/ep</td> <td class="ltx_td ltx_align_center" id="S5.T5.1.5.4.3" style="padding:2pt 3.5pt;">78 min/ep</td> <td class="ltx_td ltx_align_center" id="S5.T5.1.5.4.4" style="padding:2pt 3.5pt;">-</td> </tr> <tr class="ltx_tr" id="S5.T5.1.6.5"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" id="S5.T5.1.6.5.1" rowspan="2" style="padding:2pt 3.5pt;"><span class="ltx_text" id="S5.T5.1.6.5.1.1">Compression strategy2</span></th> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.6.5.2" style="padding:2pt 3.5pt;">12 ep</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.6.5.3" style="padding:2pt 3.5pt;">10 ep</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.6.5.4" style="padding:2pt 3.5pt;">16ep</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.6.5.5" style="padding:2pt 3.5pt;">-</td> </tr> <tr class="ltx_tr" id="S5.T5.1.7.6"> <td class="ltx_td ltx_align_center" id="S5.T5.1.7.6.1" style="padding:2pt 3.5pt;">61 min/ep</td> <td class="ltx_td ltx_align_center" id="S5.T5.1.7.6.2" style="padding:2pt 3.5pt;">12 min/ep</td> <td class="ltx_td ltx_align_center" id="S5.T5.1.7.6.3" style="padding:2pt 3.5pt;">78 min/ep</td> <td class="ltx_td ltx_align_center" id="S5.T5.1.7.6.4" style="padding:2pt 3.5pt;">-</td> </tr> <tr class="ltx_tr" id="S5.T5.1.8.7"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" id="S5.T5.1.8.7.1" rowspan="2" style="padding:2pt 3.5pt;"><span class="ltx_text" id="S5.T5.1.8.7.1.1">Compression strategy3</span></th> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.8.7.2" style="padding:2pt 3.5pt;">12 ep</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.8.7.3" style="padding:2pt 3.5pt;">26 ep</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.8.7.4" style="padding:2pt 3.5pt;">-</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.8.7.5" style="padding:2pt 3.5pt;">-</td> </tr> <tr class="ltx_tr" id="S5.T5.1.9.8"> <td class="ltx_td ltx_align_center" id="S5.T5.1.9.8.1" style="padding:2pt 3.5pt;">61 min/ep</td> <td class="ltx_td ltx_align_center" id="S5.T5.1.9.8.2" style="padding:2pt 3.5pt;">78 min/ep</td> <td class="ltx_td ltx_align_center" id="S5.T5.1.9.8.3" style="padding:2pt 3.5pt;">-</td> <td class="ltx_td ltx_align_center" id="S5.T5.1.9.8.4" style="padding:2pt 3.5pt;">-</td> </tr> <tr class="ltx_tr" id="S5.T5.1.10.9"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_b ltx_border_r ltx_border_t" id="S5.T5.1.10.9.1" rowspan="2" style="padding:2pt 3.5pt;"><span class="ltx_text" id="S5.T5.1.10.9.1.1">Compression strategy4</span></th> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.10.9.2" style="padding:2pt 3.5pt;">38 ep</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.10.9.3" style="padding:2pt 3.5pt;">-</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.10.9.4" style="padding:2pt 3.5pt;">-</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T5.1.10.9.5" style="padding:2pt 3.5pt;">-</td> </tr> <tr class="ltx_tr" id="S5.T5.1.11.10"> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T5.1.11.10.1" style="padding:2pt 3.5pt;">78 min/ep</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T5.1.11.10.2" style="padding:2pt 3.5pt;">-</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T5.1.11.10.3" style="padding:2pt 3.5pt;">-</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T5.1.11.10.4" style="padding:2pt 3.5pt;">-</td> </tr> </tbody> </table> </div> <div class="ltx_flex_break"></div> <div class="ltx_flex_cell ltx_flex_size_1"> <ul class="ltx_itemize ltx_centering ltx_figure_panel" id="S5.I4"> <li class="ltx_item" id="S5.I4.i1" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item">•</span> <div class="ltx_para" id="S5.I4.i1.p1"> <p class="ltx_p" id="S5.I4.i1.p1.1"><span class="ltx_text" id="S5.I4.i1.p1.1.1" style="font-size:80%;">1 “ep” denotes the epoch.</span></p> </div> </li> </ul> </div> </div> </figure> <div class="ltx_para" id="S5.SS3.p5"> <p class="ltx_p" id="S5.SS3.p5.1"><span class="ltx_text" id="S5.SS3.p5.1.1">We also conduct a second study to assess the necessity of the two loss functions. Two comparison strategies are designed following the same five-step training structure as the proposed approach. The Charbonnier loss is applied to all steps in the first comparison strategy, while the second strategy utilizes the hybrid masked Charbonnier loss throughout. The simulation results in Table <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.T6" title="TABLE VI ‣ V-C Ablation Study ‣ V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">VI</span></a> show that the performance of the proposed method is better than the performance of two comparison strategies, which use either loss function individually.<span class="ltx_text" id="S5.SS3.p5.1.1.1"></span></span></p> </div> <figure class="ltx_table" id="S5.T6"> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_table">TABLE VI: </span>The 3D Detection Results for The Ablation Study 2 of The Training Strategy</figcaption> <table class="ltx_tabular ltx_centering ltx_guessed_headers ltx_align_middle" id="S5.T6.2"> <tbody class="ltx_tbody"> <tr class="ltx_tr" id="S5.T6.2.3.1"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" id="S5.T6.2.3.1.1" rowspan="3" style="padding:2pt 3.5pt;"><span class="ltx_text" id="S5.T6.2.3.1.1.1">Network</span></th> <td class="ltx_td ltx_align_center ltx_border_t" colspan="6" id="S5.T6.2.3.1.2" style="padding:2pt 3.5pt;">3D object detection</td> </tr> <tr class="ltx_tr" id="S5.T6.2.2"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" colspan="3" id="S5.T6.1.1.1" style="padding:2pt 3.5pt;">AP for bird’s-eye view <math alttext="\uparrow" class="ltx_Math" display="inline" id="S5.T6.1.1.1.m1.1"><semantics id="S5.T6.1.1.1.m1.1a"><mo id="S5.T6.1.1.1.m1.1.1" stretchy="false" xref="S5.T6.1.1.1.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S5.T6.1.1.1.m1.1b"><ci id="S5.T6.1.1.1.m1.1.1.cmml" xref="S5.T6.1.1.1.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.T6.1.1.1.m1.1c">\uparrow</annotation><annotation encoding="application/x-llamapun" id="S5.T6.1.1.1.m1.1d">↑</annotation></semantics></math> </td> <td class="ltx_td ltx_align_center ltx_border_t" colspan="3" id="S5.T6.2.2.2" style="padding:2pt 3.5pt;">AP for 3D detection <math alttext="\uparrow" class="ltx_Math" display="inline" id="S5.T6.2.2.2.m1.1"><semantics id="S5.T6.2.2.2.m1.1a"><mo id="S5.T6.2.2.2.m1.1.1" stretchy="false" xref="S5.T6.2.2.2.m1.1.1.cmml">↑</mo><annotation-xml encoding="MathML-Content" id="S5.T6.2.2.2.m1.1b"><ci id="S5.T6.2.2.2.m1.1.1.cmml" xref="S5.T6.2.2.2.m1.1.1">↑</ci></annotation-xml><annotation encoding="application/x-tex" id="S5.T6.2.2.2.m1.1c">\uparrow</annotation><annotation encoding="application/x-llamapun" id="S5.T6.2.2.2.m1.1d">↑</annotation></semantics></math> </td> </tr> <tr class="ltx_tr" id="S5.T6.2.4.2"> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T6.2.4.2.1" style="padding:2pt 3.5pt;">Easy</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T6.2.4.2.2" style="padding:2pt 3.5pt;">Mode</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T6.2.4.2.3" style="padding:2pt 3.5pt;">Hard</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T6.2.4.2.4" style="padding:2pt 3.5pt;">Easy</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T6.2.4.2.5" style="padding:2pt 3.5pt;">Mode</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T6.2.4.2.6" style="padding:2pt 3.5pt;">Hard</td> </tr> <tr class="ltx_tr" id="S5.T6.2.5.3"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r ltx_border_t" id="S5.T6.2.5.3.1" style="padding:2pt 3.5pt;">Proposed strategy</th> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T6.2.5.3.2" style="padding:2pt 3.5pt;"><span class="ltx_text ltx_font_bold" id="S5.T6.2.5.3.2.1">71.06</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T6.2.5.3.3" style="padding:2pt 3.5pt;"><span class="ltx_text ltx_font_bold" id="S5.T6.2.5.3.3.1">46.72</span></td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T6.2.5.3.4" style="padding:2pt 3.5pt;"><span class="ltx_text ltx_font_bold" id="S5.T6.2.5.3.4.1">39.28</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T6.2.5.3.5" style="padding:2pt 3.5pt;"><span class="ltx_text ltx_font_bold" id="S5.T6.2.5.3.5.1">64.60</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T6.2.5.3.6" style="padding:2pt 3.5pt;"><span class="ltx_text ltx_font_bold" id="S5.T6.2.5.3.6.1">44.38</span></td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T6.2.5.3.7" style="padding:2pt 3.5pt;"><span class="ltx_text ltx_font_bold" id="S5.T6.2.5.3.7.1">37.12</span></td> </tr> <tr class="ltx_tr" id="S5.T6.2.6.4"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_r" id="S5.T6.2.6.4.1" style="padding:2pt 3.5pt;">Comparison strategy1</th> <td class="ltx_td ltx_align_center" id="S5.T6.2.6.4.2" style="padding:2pt 3.5pt;">68.91</td> <td class="ltx_td ltx_align_center" id="S5.T6.2.6.4.3" style="padding:2pt 3.5pt;">44.65</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T6.2.6.4.4" style="padding:2pt 3.5pt;">37.81</td> <td class="ltx_td ltx_align_center" id="S5.T6.2.6.4.5" style="padding:2pt 3.5pt;">62.91</td> <td class="ltx_td ltx_align_center" id="S5.T6.2.6.4.6" style="padding:2pt 3.5pt;">43.67</td> <td class="ltx_td ltx_align_center" id="S5.T6.2.6.4.7" style="padding:2pt 3.5pt;">36.05</td> </tr> <tr class="ltx_tr" id="S5.T6.2.7.5"> <th class="ltx_td ltx_align_center ltx_th ltx_th_row ltx_border_b ltx_border_r" id="S5.T6.2.7.5.1" style="padding:2pt 3.5pt;">Comparison strategy2</th> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T6.2.7.5.2" style="padding:2pt 3.5pt;">67.96</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T6.2.7.5.3" style="padding:2pt 3.5pt;">44.11</td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="S5.T6.2.7.5.4" style="padding:2pt 3.5pt;">37.05</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T6.2.7.5.5" style="padding:2pt 3.5pt;">62.03</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T6.2.7.5.6" style="padding:2pt 3.5pt;">43.11</td> <td class="ltx_td ltx_align_center ltx_border_b" id="S5.T6.2.7.5.7" style="padding:2pt 3.5pt;">35.37</td> </tr> </tbody> </table> </figure> </section> <section class="ltx_subsection" id="S5.SS4"> <h3 class="ltx_title ltx_title_subsection"> <span class="ltx_tag ltx_tag_subsection"><span class="ltx_text" id="S5.SS4.5.1.1">V-D</span> </span><span class="ltx_text ltx_font_italic" id="S5.SS4.6.2">Complexity Analysis</span> </h3> <div class="ltx_para" id="S5.SS4.p1"> <p class="ltx_p" id="S5.SS4.p1.1">Table <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#S5.T7" title="TABLE VII ‣ V-D Complexity Analysis ‣ V Simulation Results and Discussions ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">VII</span></a> shows the floating-point operations (FLOPs) and parameter counts of neural networks at both the transmitter and receiver. Compared with performing 3D detection at the transmitter, i.e., directly deploying stereo RCNN at the transmitter, or deploying complex feature extraction and optical flow alignment operations at the transmitter, i.e., adding a network close to the scale of “Net B” at the transmitter, the proposed transmitter has lower time and space complexity and is more lightweight, and hardware-friendly. Meanwhile, the previous results show that the proposed semantic communication system can ensure detection accuracy with low communication overhead.</p> </div> <figure class="ltx_table" id="S5.T7"> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_table">TABLE VII: </span>The Complexity Analysis of The Proposed Network</figcaption><div class="ltx_flex_figure"> <div class="ltx_flex_cell ltx_flex_size_1"> <table class="ltx_tabular ltx_centering ltx_figure_panel ltx_align_middle" id="S5.T7.1"> <tbody class="ltx_tbody"> <tr class="ltx_tr" id="S5.T7.1.1.1"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T7.1.1.1.1" style="padding:2pt 7.0pt;">Network</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T7.1.1.1.2" style="padding:2pt 7.0pt;">Total FLOPs (G)</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T7.1.1.1.3" style="padding:2pt 7.0pt;">Total Parameters (K)</td> </tr> <tr class="ltx_tr" id="S5.T7.1.2.2"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T7.1.2.2.1" style="padding:2pt 7.0pt;">Transmitter (Net A)<sup class="ltx_sup" id="S5.T7.1.2.2.1.1">1</sup> </td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T7.1.2.2.2" style="padding:2pt 7.0pt;">0.9</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T7.1.2.2.3" style="padding:2pt 7.0pt;">2.2</td> </tr> <tr class="ltx_tr" id="S5.T7.1.3.3"> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T7.1.3.3.1" style="padding:2pt 7.0pt;">Transmitter (Net B)<sup class="ltx_sup" id="S5.T7.1.3.3.1.1">2</sup> </td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T7.1.3.3.2" style="padding:2pt 7.0pt;">176.1</td> <td class="ltx_td ltx_align_center" id="S5.T7.1.3.3.3" style="padding:2pt 7.0pt;">686.5</td> </tr> <tr class="ltx_tr" id="S5.T7.1.4.4"> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T7.1.4.4.1" style="padding:2pt 7.0pt;">Transmitter (Total)</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T7.1.4.4.2" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T7.1.4.4.2.1">177</span></td> <td class="ltx_td ltx_align_center" id="S5.T7.1.4.4.3" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T7.1.4.4.3.1">688.7</span></td> </tr> <tr class="ltx_tr" id="S5.T7.1.5.5"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T7.1.5.5.1" style="padding:2pt 7.0pt;">Receiver (Net A)<sup class="ltx_sup" id="S5.T7.1.5.5.1.1">1</sup> </td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="S5.T7.1.5.5.2" style="padding:2pt 7.0pt;">0.5</td> <td class="ltx_td ltx_align_center ltx_border_t" id="S5.T7.1.5.5.3" style="padding:2pt 7.0pt;">1.6</td> </tr> <tr class="ltx_tr" id="S5.T7.1.6.6"> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T7.1.6.6.1" style="padding:2pt 7.0pt;">Receiver (Net B)<sup class="ltx_sup" id="S5.T7.1.6.6.1.1">2</sup> </td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T7.1.6.6.2" style="padding:2pt 7.0pt;">241</td> <td class="ltx_td ltx_align_center" id="S5.T7.1.6.6.3" style="padding:2pt 7.0pt;">6895.6</td> </tr> <tr class="ltx_tr" id="S5.T7.1.7.7"> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T7.1.7.7.1" style="padding:2pt 7.0pt;">Receiver (Net F)<sup class="ltx_sup" id="S5.T7.1.7.7.1.1">3</sup> </td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T7.1.7.7.2" style="padding:2pt 7.0pt;">178.9</td> <td class="ltx_td ltx_align_center" id="S5.T7.1.7.7.3" style="padding:2pt 7.0pt;">113.1</td> </tr> <tr class="ltx_tr" id="S5.T7.1.8.8"> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T7.1.8.8.1" style="padding:2pt 7.0pt;">Receiver (Total)</td> <td class="ltx_td ltx_align_center ltx_border_r" id="S5.T7.1.8.8.2" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T7.1.8.8.2.1">420.4</span></td> <td class="ltx_td ltx_align_center" id="S5.T7.1.8.8.3" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T7.1.8.8.3.1">7010.3</span></td> </tr> <tr class="ltx_tr" id="S5.T7.1.9.9"> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r ltx_border_t" id="S5.T7.1.9.9.1" style="padding:2pt 7.0pt;">stereo RCNN <sup class="ltx_sup" id="S5.T7.1.9.9.1.1">4</sup> </td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r ltx_border_t" id="S5.T7.1.9.9.2" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T7.1.9.9.2.1">448</span></td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_t" id="S5.T7.1.9.9.3" style="padding:2pt 7.0pt;"><span class="ltx_text ltx_font_bold" id="S5.T7.1.9.9.3.1">108432.4</span></td> </tr> </tbody> </table> </div> <div class="ltx_flex_break"></div> <div class="ltx_flex_cell ltx_flex_size_1"> <ul class="ltx_itemize ltx_centering ltx_figure_panel" id="S5.I5"> <li class="ltx_item" id="S5.I5.i1" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item">•</span> <div class="ltx_para" id="S5.I5.i1.p1"> <p class="ltx_p" id="S5.I5.i1.p1.1"><span class="ltx_text" id="S5.I5.i1.p1.1.1" style="font-size:80%;">1 Net A is the key area information network.</span></p> </div> </li> <li class="ltx_item" id="S5.I5.i2" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item">•</span> <div class="ltx_para" id="S5.I5.i2.p1"> <p class="ltx_p" id="S5.I5.i2.p1.1"><span class="ltx_text" id="S5.I5.i2.p1.1.1" style="font-size:80%;">2 Net B is the global information network.</span></p> </div> </li> <li class="ltx_item" id="S5.I5.i3" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item">•</span> <div class="ltx_para" id="S5.I5.i3.p1"> <p class="ltx_p" id="S5.I5.i3.p1.1"><span class="ltx_text" id="S5.I5.i3.p1.1.1" style="font-size:80%;">3 Net F is the fusion network.</span></p> </div> </li> <li class="ltx_item" id="S5.I5.i4" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item">•</span> <div class="ltx_para" id="S5.I5.i4.p1"> <p class="ltx_p" id="S5.I5.i4.p1.1"><span class="ltx_text" id="S5.I5.i4.p1.1.1" style="font-size:80%;">4 Stereo RCNN is the 3D object detection network.</span></p> </div> </li> </ul> </div> </div> </figure> <div class="ltx_para" id="S5.SS4.p2"> <p class="ltx_p" id="S5.SS4.p2.1"><span class="ltx_text" id="S5.SS4.p2.1.1">The proposed method achieves a trade-off between communication and computation for specific scenarios. Compared with the traditional methods, the semantic-level signal processing in the proposed framework increases the transceiver’s computational complexity and computational latency. However, the system also effectively compresses transmitted data and reduces communication latency. This trade-off strategy is particularly suitable for scenarios with limited bandwidth but abundant computing resources at the receiver, such as cloud-car cooperative autonomous driving and cloud-road cooperative monitoring systems.<span class="ltx_text" id="S5.SS4.p2.1.1.1"></span></span></p> </div> </section> </section> <section class="ltx_section" id="S6"> <h2 class="ltx_title ltx_title_section"> <span class="ltx_tag ltx_tag_section">VI </span><span class="ltx_text ltx_font_smallcaps" id="S6.1.1">Conclusion</span> </h2> <div class="ltx_para" id="S6.p1"> <p class="ltx_p" id="S6.p1.1">This paper proposes a framework for semantic communication for the stereo-vision 3D object detection task that improves 3D detection accuracy under limited communication bandwidth by mainly transmitting the semantic information related to 3D detection. Through the DNN-driven semantic extraction and compression modules, the proposed transmitter can extract two types of semantic information related to 3D detection and compress the semantics at different compression rates to reduce the transmission data. Correspondingly, the receiver also focuses on recovering these two types of semantic information based on the semantic characteristic to reduce the loss of semantic information and maintain the performance of 3D detection tasks. Besides, a CNN-based channel codec is designed to overcome the channel impact of the wireless channel. The simulation results show that the proposed method is more effective in achieving accurate 3D detection but with less data transmission than traditional transmission schemes at various SNRs, especially for the low SNR regime.</p> </div> </section> <section class="ltx_appendix" id="A1"> <h2 class="ltx_title ltx_title_appendix"> <span class="ltx_tag ltx_tag_appendix">Appendix A </span>The Parameters of The Proposed Network</h2> <div class="ltx_para" id="A1.p1"> <p class="ltx_p" id="A1.p1.1">This section provides an example of network parameters (Table <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#A1.T8" title="TABLE VIII ‣ Appendix A The Parameters of The Proposed Network ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">VIII</span></a>-<a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#A1.T10" title="TABLE X ‣ Appendix A The Parameters of The Proposed Network ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">X</span></a>) with a 30<math alttext="\times" class="ltx_Math" display="inline" id="A1.p1.1.m1.1"><semantics id="A1.p1.1.m1.1a"><mo id="A1.p1.1.m1.1.1" xref="A1.p1.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="A1.p1.1.m1.1b"><times id="A1.p1.1.m1.1.1.cmml" xref="A1.p1.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="A1.p1.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="A1.p1.1.m1.1d">×</annotation></semantics></math> compression rate. The compression rate can be adjusted by modifying the parameters of the sub-pixel CNN in the model.</p> </div> <figure class="ltx_table" id="A1.T8"> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_table">TABLE VIII: </span>Model Parameters of The Transmitter Network</figcaption><div class="ltx_flex_figure"> <div class="ltx_flex_cell ltx_flex_size_1"> <table class="ltx_tabular ltx_centering ltx_figure_panel ltx_align_middle" id="A1.T8.1"> <tbody class="ltx_tbody"> <tr class="ltx_tr" id="A1.T8.1.1.1"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T8.1.1.1.1" style="padding:0.5pt 10.0pt;">Module Type</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T8.1.1.1.2" style="padding:0.5pt 10.0pt;">Parameters</td> <td class="ltx_td ltx_align_center ltx_border_t" id="A1.T8.1.1.1.3" style="padding:0.5pt 10.0pt;">Activation</td> </tr> <tr class="ltx_tr" id="A1.T8.1.2.2"> <td class="ltx_td ltx_align_center ltx_border_t" colspan="3" id="A1.T8.1.2.2.1" style="padding:0.5pt 10.0pt;">The Key Area Information Network</td> </tr> <tr class="ltx_tr" id="A1.T8.1.3.3"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T8.1.3.3.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T8.1.3.3.2" style="padding:0.5pt 10.0pt;">in=3, out=6, kernel=5</td> <td class="ltx_td ltx_align_center ltx_border_t" id="A1.T8.1.3.3.3" style="padding:0.5pt 10.0pt;">LeakyReLU</td> </tr> <tr class="ltx_tr" id="A1.T8.1.4.4"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T8.1.4.4.1" style="padding:0.5pt 10.0pt;">Inv PS</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T8.1.4.4.2" style="padding:0.5pt 10.0pt;">in=6, out=24</td> <td class="ltx_td ltx_align_center" id="A1.T8.1.4.4.3" style="padding:0.5pt 10.0pt;">-</td> </tr> <tr class="ltx_tr" id="A1.T8.1.5.5"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T8.1.5.5.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T8.1.5.5.2" style="padding:0.5pt 10.0pt;">in=24, out=3, kernel=3</td> <td class="ltx_td ltx_align_center" id="A1.T8.1.5.5.3" style="padding:0.5pt 10.0pt;">-</td> </tr> <tr class="ltx_tr" id="A1.T8.1.6.6"> <td class="ltx_td ltx_align_center ltx_border_t" colspan="3" id="A1.T8.1.6.6.1" style="padding:0.5pt 10.0pt;">The Global Information Network</td> </tr> <tr class="ltx_tr" id="A1.T8.1.7.7"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T8.1.7.7.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T8.1.7.7.2" style="padding:0.5pt 10.0pt;">in=3, out=64, kernel=3</td> <td class="ltx_td ltx_align_center ltx_border_t" id="A1.T8.1.7.7.3" style="padding:0.5pt 10.0pt;">LeakyReLU</td> </tr> <tr class="ltx_tr" id="A1.T8.1.8.8"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T8.1.8.8.1" rowspan="2" style="padding:0.5pt 10.0pt;"><span class="ltx_text" id="A1.T8.1.8.8.1.1">ResNet*3</span></td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T8.1.8.8.2" style="padding:0.5pt 10.0pt;">in=64, out=64, kernel=3</td> <td class="ltx_td ltx_align_center" id="A1.T8.1.8.8.3" style="padding:0.5pt 10.0pt;">ReLU</td> </tr> <tr class="ltx_tr" id="A1.T8.1.9.9"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T8.1.9.9.1" style="padding:0.5pt 10.0pt;">in=64, out=64, kernel=3</td> <td class="ltx_td ltx_align_center" id="A1.T8.1.9.9.2" style="padding:0.5pt 10.0pt;">-</td> </tr> <tr class="ltx_tr" id="A1.T8.1.10.10"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T8.1.10.10.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T8.1.10.10.2" style="padding:0.5pt 10.0pt;">in=128, out=64, kernel=1</td> <td class="ltx_td ltx_align_center ltx_border_t" id="A1.T8.1.10.10.3" style="padding:0.5pt 10.0pt;">LeakyReLU</td> </tr> <tr class="ltx_tr" id="A1.T8.1.11.11"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T8.1.11.11.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T8.1.11.11.2" style="padding:0.5pt 10.0pt;">in=64, out=64, kernel=5</td> <td class="ltx_td ltx_align_center ltx_border_t" id="A1.T8.1.11.11.3" style="padding:0.5pt 10.0pt;">LeakyReLU</td> </tr> <tr class="ltx_tr" id="A1.T8.1.12.12"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T8.1.12.12.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T8.1.12.12.2" style="padding:0.5pt 10.0pt;">in=64, out=4, kernel=5</td> <td class="ltx_td ltx_align_center" id="A1.T8.1.12.12.3" style="padding:0.5pt 10.0pt;">LeakyReLU</td> </tr> <tr class="ltx_tr" id="A1.T8.1.13.13"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T8.1.13.13.1" style="padding:0.5pt 10.0pt;">Inv PS</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T8.1.13.13.2" style="padding:0.5pt 10.0pt;">in=4, out=144</td> <td class="ltx_td ltx_align_center" id="A1.T8.1.13.13.3" style="padding:0.5pt 10.0pt;">-</td> </tr> <tr class="ltx_tr" id="A1.T8.1.14.14"> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="A1.T8.1.14.14.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="A1.T8.1.14.14.2" style="padding:0.5pt 10.0pt;">in=256, out=3, kernel=3</td> <td class="ltx_td ltx_align_center ltx_border_b" id="A1.T8.1.14.14.3" style="padding:0.5pt 10.0pt;">-</td> </tr> </tbody> </table> </div> <div class="ltx_flex_break"></div> <div class="ltx_flex_cell ltx_flex_size_1"> <ul class="ltx_itemize ltx_centering ltx_figure_panel" id="A1.I1"> <li class="ltx_item" id="A1.I1.i1" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item">•</span> <div class="ltx_para" id="A1.I1.i1.p1"> <p class="ltx_p" id="A1.I1.i1.p1.1"><span class="ltx_text" id="A1.I1.i1.p1.1.1" style="font-size:80%;">* “in” and “out” represent the input and output channels.</span></p> </div> </li> <li class="ltx_item" id="A1.I1.i2" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item">•</span> <div class="ltx_para" id="A1.I1.i2.p1"> <p class="ltx_p" id="A1.I1.i2.p1.1"><span class="ltx_text" id="A1.I1.i2.p1.1.1" style="font-size:80%;"># “PS” stands for the pixel shuffling.</span></p> </div> </li> </ul> </div> </div> </figure> <figure class="ltx_table" id="A1.T9"> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_table">TABLE IX: </span>Model Parameters of The CNN-Based Channel Codec</figcaption><div class="ltx_flex_figure"> <div class="ltx_flex_cell ltx_flex_size_1"> <table class="ltx_tabular ltx_centering ltx_figure_panel ltx_align_middle" id="A1.T9.2"> <tbody class="ltx_tbody"> <tr class="ltx_tr" id="A1.T9.2.3.1"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T9.2.3.1.1" style="padding:0.5pt 3.0pt;">Module Type</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T9.2.3.1.2" style="padding:0.5pt 3.0pt;">Parameters</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T9.2.3.1.3" style="padding:0.5pt 3.0pt;">Normalization</td> <td class="ltx_td ltx_align_center ltx_border_t" id="A1.T9.2.3.1.4" style="padding:0.5pt 3.0pt;">Activation</td> </tr> <tr class="ltx_tr" id="A1.T9.2.4.2"> <td class="ltx_td ltx_align_center ltx_border_t" colspan="4" id="A1.T9.2.4.2.1" style="padding:0.5pt 3.0pt;">Transmitter part</td> </tr> <tr class="ltx_tr" id="A1.T9.2.5.3"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T9.2.5.3.1" style="padding:0.5pt 3.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T9.2.5.3.2" style="padding:0.5pt 3.0pt;">in=3, out=64, kernel=3</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T9.2.5.3.3" style="padding:0.5pt 3.0pt;">-</td> <td class="ltx_td ltx_align_center ltx_border_t" id="A1.T9.2.5.3.4" style="padding:0.5pt 3.0pt;">ReLU</td> </tr> <tr class="ltx_tr" id="A1.T9.1.1"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T9.1.1.1" style="padding:0.5pt 3.0pt;">Conv2d <math alttext="\times 3" class="ltx_Math" display="inline" id="A1.T9.1.1.1.m1.1"><semantics id="A1.T9.1.1.1.m1.1a"><mrow id="A1.T9.1.1.1.m1.1.1" xref="A1.T9.1.1.1.m1.1.1.cmml"><mi id="A1.T9.1.1.1.m1.1.1.2" xref="A1.T9.1.1.1.m1.1.1.2.cmml"></mi><mo id="A1.T9.1.1.1.m1.1.1.1" lspace="0.222em" rspace="0.222em" xref="A1.T9.1.1.1.m1.1.1.1.cmml">×</mo><mn id="A1.T9.1.1.1.m1.1.1.3" xref="A1.T9.1.1.1.m1.1.1.3.cmml">3</mn></mrow><annotation-xml encoding="MathML-Content" id="A1.T9.1.1.1.m1.1b"><apply id="A1.T9.1.1.1.m1.1.1.cmml" xref="A1.T9.1.1.1.m1.1.1"><times id="A1.T9.1.1.1.m1.1.1.1.cmml" xref="A1.T9.1.1.1.m1.1.1.1"></times><csymbol cd="latexml" id="A1.T9.1.1.1.m1.1.1.2.cmml" xref="A1.T9.1.1.1.m1.1.1.2">absent</csymbol><cn id="A1.T9.1.1.1.m1.1.1.3.cmml" type="integer" xref="A1.T9.1.1.1.m1.1.1.3">3</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.T9.1.1.1.m1.1c">\times 3</annotation><annotation encoding="application/x-llamapun" id="A1.T9.1.1.1.m1.1d">× 3</annotation></semantics></math> </td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T9.1.1.2" style="padding:0.5pt 3.0pt;">in=64, out=64, kernel=3</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T9.1.1.3" style="padding:0.5pt 3.0pt;">BatchNorm2d</td> <td class="ltx_td ltx_align_center" id="A1.T9.1.1.4" style="padding:0.5pt 3.0pt;">ReLU</td> </tr> <tr class="ltx_tr" id="A1.T9.2.6.4"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T9.2.6.4.1" style="padding:0.5pt 3.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T9.2.6.4.2" style="padding:0.5pt 3.0pt;">in=64, out=9, kernel=3</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T9.2.6.4.3" style="padding:0.5pt 3.0pt;">-</td> <td class="ltx_td ltx_align_center" id="A1.T9.2.6.4.4" style="padding:0.5pt 3.0pt;">-</td> </tr> <tr class="ltx_tr" id="A1.T9.2.7.5"> <td class="ltx_td ltx_align_center ltx_border_t" colspan="4" id="A1.T9.2.7.5.1" style="padding:0.5pt 3.0pt;">Receiver part</td> </tr> <tr class="ltx_tr" id="A1.T9.2.8.6"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T9.2.8.6.1" style="padding:0.5pt 3.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T9.2.8.6.2" style="padding:0.5pt 3.0pt;">in=9, out=64, kernel=3</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T9.2.8.6.3" style="padding:0.5pt 3.0pt;">-</td> <td class="ltx_td ltx_align_center ltx_border_t" id="A1.T9.2.8.6.4" style="padding:0.5pt 3.0pt;">ReLU</td> </tr> <tr class="ltx_tr" id="A1.T9.2.2"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T9.2.2.1" style="padding:0.5pt 3.0pt;">Conv2d <math alttext="\times 5" class="ltx_Math" display="inline" id="A1.T9.2.2.1.m1.1"><semantics id="A1.T9.2.2.1.m1.1a"><mrow id="A1.T9.2.2.1.m1.1.1" xref="A1.T9.2.2.1.m1.1.1.cmml"><mi id="A1.T9.2.2.1.m1.1.1.2" xref="A1.T9.2.2.1.m1.1.1.2.cmml"></mi><mo id="A1.T9.2.2.1.m1.1.1.1" lspace="0.222em" rspace="0.222em" xref="A1.T9.2.2.1.m1.1.1.1.cmml">×</mo><mn id="A1.T9.2.2.1.m1.1.1.3" xref="A1.T9.2.2.1.m1.1.1.3.cmml">5</mn></mrow><annotation-xml encoding="MathML-Content" id="A1.T9.2.2.1.m1.1b"><apply id="A1.T9.2.2.1.m1.1.1.cmml" xref="A1.T9.2.2.1.m1.1.1"><times id="A1.T9.2.2.1.m1.1.1.1.cmml" xref="A1.T9.2.2.1.m1.1.1.1"></times><csymbol cd="latexml" id="A1.T9.2.2.1.m1.1.1.2.cmml" xref="A1.T9.2.2.1.m1.1.1.2">absent</csymbol><cn id="A1.T9.2.2.1.m1.1.1.3.cmml" type="integer" xref="A1.T9.2.2.1.m1.1.1.3">5</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="A1.T9.2.2.1.m1.1c">\times 5</annotation><annotation encoding="application/x-llamapun" id="A1.T9.2.2.1.m1.1d">× 5</annotation></semantics></math> </td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T9.2.2.2" style="padding:0.5pt 3.0pt;">in=64, out=64, kernel=3</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T9.2.2.3" style="padding:0.5pt 3.0pt;">BatchNorm2d</td> <td class="ltx_td ltx_align_center" id="A1.T9.2.2.4" style="padding:0.5pt 3.0pt;">ReLU</td> </tr> <tr class="ltx_tr" id="A1.T9.2.9.7"> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="A1.T9.2.9.7.1" style="padding:0.5pt 3.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="A1.T9.2.9.7.2" style="padding:0.5pt 3.0pt;">in=64, out=3, kernel=3</td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="A1.T9.2.9.7.3" style="padding:0.5pt 3.0pt;">-</td> <td class="ltx_td ltx_align_center ltx_border_b" id="A1.T9.2.9.7.4" style="padding:0.5pt 3.0pt;">-</td> </tr> </tbody> </table> </div> <div class="ltx_flex_break"></div> <div class="ltx_flex_cell ltx_flex_size_1"> <ul class="ltx_itemize ltx_centering ltx_figure_panel" id="A1.I2"> <li class="ltx_item" id="A1.I2.i1" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item">•</span> <div class="ltx_para" id="A1.I2.i1.p1"> <p class="ltx_p" id="A1.I2.i1.p1.1"><span class="ltx_text" id="A1.I2.i1.p1.1.1" style="font-size:80%;">* “in” represents the input channels, “out” represents the output channels</span></p> </div> </li> </ul> </div> </div> </figure> <figure class="ltx_table" id="A1.T10"> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_table">TABLE X: </span>Model Parameters of The Receiver Network</figcaption><div class="ltx_flex_figure"> <div class="ltx_flex_cell ltx_flex_size_1"> <table class="ltx_tabular ltx_centering ltx_figure_panel ltx_align_middle" id="A1.T10.1"> <tbody class="ltx_tbody"> <tr class="ltx_tr" id="A1.T10.1.1.1"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T10.1.1.1.1" style="padding:0.5pt 10.0pt;">Module Type</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T10.1.1.1.2" style="padding:0.5pt 10.0pt;">Parameters</td> <td class="ltx_td ltx_align_center ltx_border_t" id="A1.T10.1.1.1.3" style="padding:0.5pt 10.0pt;">Activation</td> </tr> <tr class="ltx_tr" id="A1.T10.1.2.2"> <td class="ltx_td ltx_align_center ltx_border_t" colspan="3" id="A1.T10.1.2.2.1" style="padding:0.5pt 10.0pt;">The Key Area Information Network</td> </tr> <tr class="ltx_tr" id="A1.T10.1.3.3"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T10.1.3.3.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T10.1.3.3.2" style="padding:0.5pt 10.0pt;">in=3, out=24, kernel=3</td> <td class="ltx_td ltx_align_center ltx_border_t" id="A1.T10.1.3.3.3" style="padding:0.5pt 10.0pt;">-</td> </tr> <tr class="ltx_tr" id="A1.T10.1.4.4"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.4.4.1" style="padding:0.5pt 10.0pt;">PS</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.4.4.2" style="padding:0.5pt 10.0pt;">in=24, out=6</td> <td class="ltx_td ltx_align_center" id="A1.T10.1.4.4.3" style="padding:0.5pt 10.0pt;">LeakyReLU</td> </tr> <tr class="ltx_tr" id="A1.T10.1.5.5"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.5.5.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.5.5.2" style="padding:0.5pt 10.0pt;">in=6, out=3, kernel=3</td> <td class="ltx_td ltx_align_center" id="A1.T10.1.5.5.3" style="padding:0.5pt 10.0pt;">LeakyReLU</td> </tr> <tr class="ltx_tr" id="A1.T10.1.6.6"> <td class="ltx_td ltx_align_center ltx_border_t" colspan="3" id="A1.T10.1.6.6.1" style="padding:0.5pt 10.0pt;">The Global Information Network</td> </tr> <tr class="ltx_tr" id="A1.T10.1.7.7"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T10.1.7.7.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T10.1.7.7.2" style="padding:0.5pt 10.0pt;">in=3, out=64, kernel=3</td> <td class="ltx_td ltx_align_center ltx_border_t" id="A1.T10.1.7.7.3" style="padding:0.5pt 10.0pt;">LeakyReLU</td> </tr> <tr class="ltx_tr" id="A1.T10.1.8.8"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.8.8.1" rowspan="2" style="padding:0.5pt 10.0pt;"><span class="ltx_text" id="A1.T10.1.8.8.1.1">ResNet*30</span></td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.8.8.2" style="padding:0.5pt 10.0pt;">in=64, out=64, kernel=3</td> <td class="ltx_td ltx_align_center" id="A1.T10.1.8.8.3" style="padding:0.5pt 10.0pt;">ReLU</td> </tr> <tr class="ltx_tr" id="A1.T10.1.9.9"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.9.9.1" style="padding:0.5pt 10.0pt;">in=64, out=64, kernel=3</td> <td class="ltx_td ltx_align_center" id="A1.T10.1.9.9.2" style="padding:0.5pt 10.0pt;">-</td> </tr> <tr class="ltx_tr" id="A1.T10.1.10.10"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.10.10.1" style="padding:0.5pt 10.0pt;">Flow warp</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.10.10.2" style="padding:0.5pt 10.0pt;">in=66, out=64</td> <td class="ltx_td ltx_align_center" id="A1.T10.1.10.10.3" style="padding:0.5pt 10.0pt;">-</td> </tr> <tr class="ltx_tr" id="A1.T10.1.11.11"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.11.11.1" rowspan="2" style="padding:0.5pt 10.0pt;"><span class="ltx_text" id="A1.T10.1.11.11.1.1">ResNet*30</span></td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.11.11.2" style="padding:0.5pt 10.0pt;">in=64, out=64, kernel=3</td> <td class="ltx_td ltx_align_center" id="A1.T10.1.11.11.3" style="padding:0.5pt 10.0pt;">ReLU</td> </tr> <tr class="ltx_tr" id="A1.T10.1.12.12"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.12.12.1" style="padding:0.5pt 10.0pt;">in=64, out=64, kernel=3</td> <td class="ltx_td ltx_align_center" id="A1.T10.1.12.12.2" style="padding:0.5pt 10.0pt;">-</td> </tr> <tr class="ltx_tr" id="A1.T10.1.13.13"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T10.1.13.13.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T10.1.13.13.2" style="padding:0.5pt 10.0pt;">in=128, out=64, kernel=1</td> <td class="ltx_td ltx_align_center ltx_border_t" id="A1.T10.1.13.13.3" style="padding:0.5pt 10.0pt;">LeakyReLU</td> </tr> <tr class="ltx_tr" id="A1.T10.1.14.14"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.14.14.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.14.14.2" style="padding:0.5pt 10.0pt;">in=64, out=256, kernel=3</td> <td class="ltx_td ltx_align_center" id="A1.T10.1.14.14.3" style="padding:0.5pt 10.0pt;">-</td> </tr> <tr class="ltx_tr" id="A1.T10.1.15.15"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.15.15.1" style="padding:0.5pt 10.0pt;">PS</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.15.15.2" style="padding:0.5pt 10.0pt;">in=256, out=64</td> <td class="ltx_td ltx_align_center" id="A1.T10.1.15.15.3" style="padding:0.5pt 10.0pt;">LeakyReLU</td> </tr> <tr class="ltx_tr" id="A1.T10.1.16.16"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.16.16.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.16.16.2" style="padding:0.5pt 10.0pt;">in=64, out=576, kernel=3</td> <td class="ltx_td ltx_align_center" id="A1.T10.1.16.16.3" style="padding:0.5pt 10.0pt;">-</td> </tr> <tr class="ltx_tr" id="A1.T10.1.17.17"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.17.17.1" style="padding:0.5pt 10.0pt;">PS</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.17.17.2" style="padding:0.5pt 10.0pt;">in=576, out=64</td> <td class="ltx_td ltx_align_center" id="A1.T10.1.17.17.3" style="padding:0.5pt 10.0pt;">LeakyReLU</td> </tr> <tr class="ltx_tr" id="A1.T10.1.18.18"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.18.18.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.18.18.2" style="padding:0.5pt 10.0pt;">in=64, out=64, kernel=3</td> <td class="ltx_td ltx_align_center" id="A1.T10.1.18.18.3" style="padding:0.5pt 10.0pt;">LeakyReLU</td> </tr> <tr class="ltx_tr" id="A1.T10.1.19.19"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.19.19.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.19.19.2" style="padding:0.5pt 10.0pt;">in=64, out=3, kernel=3</td> <td class="ltx_td ltx_align_center" id="A1.T10.1.19.19.3" style="padding:0.5pt 10.0pt;">-</td> </tr> <tr class="ltx_tr" id="A1.T10.1.20.20"> <td class="ltx_td ltx_align_center ltx_border_t" colspan="3" id="A1.T10.1.20.20.1" style="padding:0.5pt 10.0pt;">The Fusion Network</td> </tr> <tr class="ltx_tr" id="A1.T10.1.21.21"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T10.1.21.21.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A1.T10.1.21.21.2" style="padding:0.5pt 10.0pt;">in=6, out=64, kernel=5</td> <td class="ltx_td ltx_align_center ltx_border_t" id="A1.T10.1.21.21.3" style="padding:0.5pt 10.0pt;">LeakyReLU</td> </tr> <tr class="ltx_tr" id="A1.T10.1.22.22"> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.22.22.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_r" id="A1.T10.1.22.22.2" style="padding:0.5pt 10.0pt;">in=64, out=64, kernel=5</td> <td class="ltx_td ltx_align_center" id="A1.T10.1.22.22.3" style="padding:0.5pt 10.0pt;">LeakyReLU</td> </tr> <tr class="ltx_tr" id="A1.T10.1.23.23"> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="A1.T10.1.23.23.1" style="padding:0.5pt 10.0pt;">Conv2d</td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r" id="A1.T10.1.23.23.2" style="padding:0.5pt 10.0pt;">in=64, out=3, kernel=3</td> <td class="ltx_td ltx_align_center ltx_border_b" id="A1.T10.1.23.23.3" style="padding:0.5pt 10.0pt;">-</td> </tr> </tbody> </table> </div> <div class="ltx_flex_break"></div> <div class="ltx_flex_cell ltx_flex_size_1"> <ul class="ltx_itemize ltx_centering ltx_figure_panel" id="A1.I3"> <li class="ltx_item" id="A1.I3.i1" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item">•</span> <div class="ltx_para" id="A1.I3.i1.p1"> <p class="ltx_p" id="A1.I3.i1.p1.1"><span class="ltx_text" id="A1.I3.i1.p1.1.1" style="font-size:80%;">* “in” and “out” represent the input and output channels.</span></p> </div> </li> <li class="ltx_item" id="A1.I3.i2" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item">•</span> <div class="ltx_para" id="A1.I3.i2.p1"> <p class="ltx_p" id="A1.I3.i2.p1.1"><span class="ltx_text" id="A1.I3.i2.p1.1.1" style="font-size:80%;"># “PS” stands for pixel shuffling.</span></p> </div> </li> </ul> </div> </div> </figure> </section> <section class="ltx_appendix" id="A2"> <h2 class="ltx_title ltx_title_appendix"> <span class="ltx_tag ltx_tag_appendix">Appendix B </span>The Settings of The Proposed Training Strategy</h2> <div class="ltx_para" id="A2.p1"> <p class="ltx_p" id="A2.p1.1">The detailed parameter settings of the proposed training strategy are shown in Table <a class="ltx_ref" href="https://arxiv.org/html/2502.12735v1#A2.T11" title="TABLE XI ‣ Appendix B The Settings of The Proposed Training Strategy ‣ Task-Oriented Semantic Communication for Stereo-Vision 3D Object Detection"><span class="ltx_text ltx_ref_tag">XI</span></a>, where ”Network A” represents the key area information network and ”Network B” represents the global information network. The optimization algorithm of all steps adopts the Adam algorithm.</p> </div> <figure class="ltx_table" id="A2.T11"> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_table">TABLE XI: </span>Parameters of The Training Strategy</figcaption><div class="ltx_flex_figure"> <div class="ltx_flex_cell ltx_flex_size_1"> <table class="ltx_tabular ltx_centering ltx_figure_panel ltx_guessed_headers ltx_align_middle" id="A2.T11.20"> <thead class="ltx_thead"> <tr class="ltx_tr" id="A2.T11.20.21.1"> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" id="A2.T11.20.21.1.1" style="padding:0.5pt 3.0pt;">Step No.</th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_r ltx_border_t" colspan="2" id="A2.T11.20.21.1.2" style="padding:0.5pt 3.0pt;">Learning Rate</th> <th class="ltx_td ltx_align_center ltx_th ltx_th_column ltx_border_t" id="A2.T11.20.21.1.3" style="padding:0.5pt 3.0pt;">Epochs</th> </tr> </thead> <tbody class="ltx_tbody"> <tr class="ltx_tr" id="A2.T11.4.4"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A2.T11.4.4.5" style="padding:0.5pt 3.0pt;">Step 1</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A2.T11.4.4.6" style="padding:0.5pt 3.0pt;"> <table class="ltx_tabular ltx_align_middle" id="A2.T11.4.4.6.1"> <tr class="ltx_tr" id="A2.T11.4.4.6.1.1"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.4.4.6.1.1.1" style="padding:0.5pt 3.0pt;">Network B in Transmitter</td> </tr> <tr class="ltx_tr" id="A2.T11.4.4.6.1.2"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.4.4.6.1.2.1" style="padding:0.5pt 3.0pt;">Network B in Receiver</td> </tr> <tr class="ltx_tr" id="A2.T11.4.4.6.1.3"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.4.4.6.1.3.1" style="padding:0.5pt 3.0pt;">SpyNet</td> </tr> <tr class="ltx_tr" id="A2.T11.4.4.6.1.4"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.4.4.6.1.4.1" style="padding:0.5pt 3.0pt;">Fusion Network</td> </tr> </table> </td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A2.T11.4.4.4" style="padding:0.5pt 3.0pt;"> <table class="ltx_tabular ltx_align_middle" id="A2.T11.4.4.4.4"> <tr class="ltx_tr" id="A2.T11.1.1.1.1.1"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.1.1.1.1.1.1" style="padding:0.5pt 3.0pt;"><math alttext="2\times 10^{-4}" class="ltx_Math" display="inline" id="A2.T11.1.1.1.1.1.1.m1.1"><semantics id="A2.T11.1.1.1.1.1.1.m1.1a"><mrow id="A2.T11.1.1.1.1.1.1.m1.1.1" xref="A2.T11.1.1.1.1.1.1.m1.1.1.cmml"><mn id="A2.T11.1.1.1.1.1.1.m1.1.1.2" xref="A2.T11.1.1.1.1.1.1.m1.1.1.2.cmml">2</mn><mo id="A2.T11.1.1.1.1.1.1.m1.1.1.1" lspace="0.222em" rspace="0.222em" xref="A2.T11.1.1.1.1.1.1.m1.1.1.1.cmml">×</mo><msup id="A2.T11.1.1.1.1.1.1.m1.1.1.3" xref="A2.T11.1.1.1.1.1.1.m1.1.1.3.cmml"><mn id="A2.T11.1.1.1.1.1.1.m1.1.1.3.2" xref="A2.T11.1.1.1.1.1.1.m1.1.1.3.2.cmml">10</mn><mrow id="A2.T11.1.1.1.1.1.1.m1.1.1.3.3" xref="A2.T11.1.1.1.1.1.1.m1.1.1.3.3.cmml"><mo id="A2.T11.1.1.1.1.1.1.m1.1.1.3.3a" xref="A2.T11.1.1.1.1.1.1.m1.1.1.3.3.cmml">−</mo><mn id="A2.T11.1.1.1.1.1.1.m1.1.1.3.3.2" xref="A2.T11.1.1.1.1.1.1.m1.1.1.3.3.2.cmml">4</mn></mrow></msup></mrow><annotation-xml encoding="MathML-Content" id="A2.T11.1.1.1.1.1.1.m1.1b"><apply id="A2.T11.1.1.1.1.1.1.m1.1.1.cmml" xref="A2.T11.1.1.1.1.1.1.m1.1.1"><times id="A2.T11.1.1.1.1.1.1.m1.1.1.1.cmml" xref="A2.T11.1.1.1.1.1.1.m1.1.1.1"></times><cn id="A2.T11.1.1.1.1.1.1.m1.1.1.2.cmml" type="integer" xref="A2.T11.1.1.1.1.1.1.m1.1.1.2">2</cn><apply id="A2.T11.1.1.1.1.1.1.m1.1.1.3.cmml" xref="A2.T11.1.1.1.1.1.1.m1.1.1.3"><csymbol cd="ambiguous" id="A2.T11.1.1.1.1.1.1.m1.1.1.3.1.cmml" xref="A2.T11.1.1.1.1.1.1.m1.1.1.3">superscript</csymbol><cn id="A2.T11.1.1.1.1.1.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.1.1.1.1.1.1.m1.1.1.3.2">10</cn><apply id="A2.T11.1.1.1.1.1.1.m1.1.1.3.3.cmml" xref="A2.T11.1.1.1.1.1.1.m1.1.1.3.3"><minus id="A2.T11.1.1.1.1.1.1.m1.1.1.3.3.1.cmml" xref="A2.T11.1.1.1.1.1.1.m1.1.1.3.3"></minus><cn id="A2.T11.1.1.1.1.1.1.m1.1.1.3.3.2.cmml" type="integer" xref="A2.T11.1.1.1.1.1.1.m1.1.1.3.3.2">4</cn></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.1.1.1.1.1.1.m1.1c">2\times 10^{-4}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.1.1.1.1.1.1.m1.1d">2 × 10 start_POSTSUPERSCRIPT - 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4 end_POSTSUPERSCRIPT</annotation></semantics></math></td> </tr> <tr class="ltx_tr" id="A2.T11.3.3.3.3.3"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.3.3.3.3.3.1" style="padding:0.5pt 3.0pt;"><math alttext="2.5\times 10^{-5}" class="ltx_Math" display="inline" id="A2.T11.3.3.3.3.3.1.m1.1"><semantics id="A2.T11.3.3.3.3.3.1.m1.1a"><mrow id="A2.T11.3.3.3.3.3.1.m1.1.1" xref="A2.T11.3.3.3.3.3.1.m1.1.1.cmml"><mn id="A2.T11.3.3.3.3.3.1.m1.1.1.2" xref="A2.T11.3.3.3.3.3.1.m1.1.1.2.cmml">2.5</mn><mo id="A2.T11.3.3.3.3.3.1.m1.1.1.1" lspace="0.222em" rspace="0.222em" xref="A2.T11.3.3.3.3.3.1.m1.1.1.1.cmml">×</mo><msup id="A2.T11.3.3.3.3.3.1.m1.1.1.3" xref="A2.T11.3.3.3.3.3.1.m1.1.1.3.cmml"><mn id="A2.T11.3.3.3.3.3.1.m1.1.1.3.2" xref="A2.T11.3.3.3.3.3.1.m1.1.1.3.2.cmml">10</mn><mrow id="A2.T11.3.3.3.3.3.1.m1.1.1.3.3" xref="A2.T11.3.3.3.3.3.1.m1.1.1.3.3.cmml"><mo id="A2.T11.3.3.3.3.3.1.m1.1.1.3.3a" xref="A2.T11.3.3.3.3.3.1.m1.1.1.3.3.cmml">−</mo><mn id="A2.T11.3.3.3.3.3.1.m1.1.1.3.3.2" xref="A2.T11.3.3.3.3.3.1.m1.1.1.3.3.2.cmml">5</mn></mrow></msup></mrow><annotation-xml encoding="MathML-Content" id="A2.T11.3.3.3.3.3.1.m1.1b"><apply id="A2.T11.3.3.3.3.3.1.m1.1.1.cmml" xref="A2.T11.3.3.3.3.3.1.m1.1.1"><times id="A2.T11.3.3.3.3.3.1.m1.1.1.1.cmml" xref="A2.T11.3.3.3.3.3.1.m1.1.1.1"></times><cn id="A2.T11.3.3.3.3.3.1.m1.1.1.2.cmml" type="float" xref="A2.T11.3.3.3.3.3.1.m1.1.1.2">2.5</cn><apply id="A2.T11.3.3.3.3.3.1.m1.1.1.3.cmml" xref="A2.T11.3.3.3.3.3.1.m1.1.1.3"><csymbol cd="ambiguous" id="A2.T11.3.3.3.3.3.1.m1.1.1.3.1.cmml" xref="A2.T11.3.3.3.3.3.1.m1.1.1.3">superscript</csymbol><cn id="A2.T11.3.3.3.3.3.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.3.3.3.3.3.1.m1.1.1.3.2">10</cn><apply id="A2.T11.3.3.3.3.3.1.m1.1.1.3.3.cmml" xref="A2.T11.3.3.3.3.3.1.m1.1.1.3.3"><minus id="A2.T11.3.3.3.3.3.1.m1.1.1.3.3.1.cmml" xref="A2.T11.3.3.3.3.3.1.m1.1.1.3.3"></minus><cn id="A2.T11.3.3.3.3.3.1.m1.1.1.3.3.2.cmml" type="integer" xref="A2.T11.3.3.3.3.3.1.m1.1.1.3.3.2">5</cn></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.3.3.3.3.3.1.m1.1c">2.5\times 10^{-5}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.3.3.3.3.3.1.m1.1d">2.5 × 10 start_POSTSUPERSCRIPT - 5 end_POSTSUPERSCRIPT</annotation></semantics></math></td> </tr> <tr class="ltx_tr" id="A2.T11.4.4.4.4.4"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.4.4.4.4.4.1" style="padding:0.5pt 3.0pt;"><math alttext="10^{-4}" class="ltx_Math" display="inline" id="A2.T11.4.4.4.4.4.1.m1.1"><semantics id="A2.T11.4.4.4.4.4.1.m1.1a"><msup id="A2.T11.4.4.4.4.4.1.m1.1.1" xref="A2.T11.4.4.4.4.4.1.m1.1.1.cmml"><mn id="A2.T11.4.4.4.4.4.1.m1.1.1.2" xref="A2.T11.4.4.4.4.4.1.m1.1.1.2.cmml">10</mn><mrow id="A2.T11.4.4.4.4.4.1.m1.1.1.3" xref="A2.T11.4.4.4.4.4.1.m1.1.1.3.cmml"><mo id="A2.T11.4.4.4.4.4.1.m1.1.1.3a" xref="A2.T11.4.4.4.4.4.1.m1.1.1.3.cmml">−</mo><mn id="A2.T11.4.4.4.4.4.1.m1.1.1.3.2" xref="A2.T11.4.4.4.4.4.1.m1.1.1.3.2.cmml">4</mn></mrow></msup><annotation-xml encoding="MathML-Content" id="A2.T11.4.4.4.4.4.1.m1.1b"><apply id="A2.T11.4.4.4.4.4.1.m1.1.1.cmml" xref="A2.T11.4.4.4.4.4.1.m1.1.1"><csymbol cd="ambiguous" id="A2.T11.4.4.4.4.4.1.m1.1.1.1.cmml" xref="A2.T11.4.4.4.4.4.1.m1.1.1">superscript</csymbol><cn id="A2.T11.4.4.4.4.4.1.m1.1.1.2.cmml" type="integer" xref="A2.T11.4.4.4.4.4.1.m1.1.1.2">10</cn><apply id="A2.T11.4.4.4.4.4.1.m1.1.1.3.cmml" xref="A2.T11.4.4.4.4.4.1.m1.1.1.3"><minus id="A2.T11.4.4.4.4.4.1.m1.1.1.3.1.cmml" xref="A2.T11.4.4.4.4.4.1.m1.1.1.3"></minus><cn id="A2.T11.4.4.4.4.4.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.4.4.4.4.4.1.m1.1.1.3.2">4</cn></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.4.4.4.4.4.1.m1.1c">10^{-4}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.4.4.4.4.4.1.m1.1d">10 start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT</annotation></semantics></math></td> </tr> </table> </td> <td class="ltx_td ltx_align_center ltx_border_t" id="A2.T11.4.4.7" style="padding:0.5pt 3.0pt;">2+10<sup class="ltx_sup" id="A2.T11.4.4.7.1">*</sup> </td> </tr> <tr class="ltx_tr" id="A2.T11.6.6"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A2.T11.6.6.3" style="padding:0.5pt 3.0pt;">Step 2</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A2.T11.6.6.4" style="padding:0.5pt 3.0pt;"> <table class="ltx_tabular ltx_align_middle" id="A2.T11.6.6.4.1"> <tr class="ltx_tr" id="A2.T11.6.6.4.1.1"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.6.6.4.1.1.1" style="padding:0.5pt 3.0pt;">Network A in Transmitter</td> </tr> <tr class="ltx_tr" id="A2.T11.6.6.4.1.2"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.6.6.4.1.2.1" style="padding:0.5pt 3.0pt;">Network A in Receiver</td> </tr> </table> </td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A2.T11.6.6.2" style="padding:0.5pt 3.0pt;"> <table class="ltx_tabular ltx_align_middle" id="A2.T11.6.6.2.2"> <tr class="ltx_tr" id="A2.T11.5.5.1.1.1"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.5.5.1.1.1.1" style="padding:0.5pt 3.0pt;"><math alttext="10^{-4}" class="ltx_Math" display="inline" id="A2.T11.5.5.1.1.1.1.m1.1"><semantics id="A2.T11.5.5.1.1.1.1.m1.1a"><msup id="A2.T11.5.5.1.1.1.1.m1.1.1" xref="A2.T11.5.5.1.1.1.1.m1.1.1.cmml"><mn id="A2.T11.5.5.1.1.1.1.m1.1.1.2" xref="A2.T11.5.5.1.1.1.1.m1.1.1.2.cmml">10</mn><mrow id="A2.T11.5.5.1.1.1.1.m1.1.1.3" xref="A2.T11.5.5.1.1.1.1.m1.1.1.3.cmml"><mo id="A2.T11.5.5.1.1.1.1.m1.1.1.3a" xref="A2.T11.5.5.1.1.1.1.m1.1.1.3.cmml">−</mo><mn id="A2.T11.5.5.1.1.1.1.m1.1.1.3.2" xref="A2.T11.5.5.1.1.1.1.m1.1.1.3.2.cmml">4</mn></mrow></msup><annotation-xml encoding="MathML-Content" id="A2.T11.5.5.1.1.1.1.m1.1b"><apply id="A2.T11.5.5.1.1.1.1.m1.1.1.cmml" xref="A2.T11.5.5.1.1.1.1.m1.1.1"><csymbol cd="ambiguous" id="A2.T11.5.5.1.1.1.1.m1.1.1.1.cmml" xref="A2.T11.5.5.1.1.1.1.m1.1.1">superscript</csymbol><cn id="A2.T11.5.5.1.1.1.1.m1.1.1.2.cmml" type="integer" xref="A2.T11.5.5.1.1.1.1.m1.1.1.2">10</cn><apply id="A2.T11.5.5.1.1.1.1.m1.1.1.3.cmml" xref="A2.T11.5.5.1.1.1.1.m1.1.1.3"><minus id="A2.T11.5.5.1.1.1.1.m1.1.1.3.1.cmml" xref="A2.T11.5.5.1.1.1.1.m1.1.1.3"></minus><cn id="A2.T11.5.5.1.1.1.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.5.5.1.1.1.1.m1.1.1.3.2">4</cn></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.5.5.1.1.1.1.m1.1c">10^{-4}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.5.5.1.1.1.1.m1.1d">10 start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT</annotation></semantics></math></td> </tr> <tr class="ltx_tr" id="A2.T11.6.6.2.2.2"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.6.6.2.2.2.1" style="padding:0.5pt 3.0pt;"><math alttext="2\times 10^{-4}" class="ltx_Math" display="inline" id="A2.T11.6.6.2.2.2.1.m1.1"><semantics id="A2.T11.6.6.2.2.2.1.m1.1a"><mrow id="A2.T11.6.6.2.2.2.1.m1.1.1" xref="A2.T11.6.6.2.2.2.1.m1.1.1.cmml"><mn id="A2.T11.6.6.2.2.2.1.m1.1.1.2" xref="A2.T11.6.6.2.2.2.1.m1.1.1.2.cmml">2</mn><mo id="A2.T11.6.6.2.2.2.1.m1.1.1.1" lspace="0.222em" rspace="0.222em" xref="A2.T11.6.6.2.2.2.1.m1.1.1.1.cmml">×</mo><msup id="A2.T11.6.6.2.2.2.1.m1.1.1.3" xref="A2.T11.6.6.2.2.2.1.m1.1.1.3.cmml"><mn id="A2.T11.6.6.2.2.2.1.m1.1.1.3.2" xref="A2.T11.6.6.2.2.2.1.m1.1.1.3.2.cmml">10</mn><mrow id="A2.T11.6.6.2.2.2.1.m1.1.1.3.3" xref="A2.T11.6.6.2.2.2.1.m1.1.1.3.3.cmml"><mo id="A2.T11.6.6.2.2.2.1.m1.1.1.3.3a" xref="A2.T11.6.6.2.2.2.1.m1.1.1.3.3.cmml">−</mo><mn id="A2.T11.6.6.2.2.2.1.m1.1.1.3.3.2" xref="A2.T11.6.6.2.2.2.1.m1.1.1.3.3.2.cmml">4</mn></mrow></msup></mrow><annotation-xml encoding="MathML-Content" id="A2.T11.6.6.2.2.2.1.m1.1b"><apply id="A2.T11.6.6.2.2.2.1.m1.1.1.cmml" xref="A2.T11.6.6.2.2.2.1.m1.1.1"><times id="A2.T11.6.6.2.2.2.1.m1.1.1.1.cmml" xref="A2.T11.6.6.2.2.2.1.m1.1.1.1"></times><cn id="A2.T11.6.6.2.2.2.1.m1.1.1.2.cmml" type="integer" xref="A2.T11.6.6.2.2.2.1.m1.1.1.2">2</cn><apply id="A2.T11.6.6.2.2.2.1.m1.1.1.3.cmml" xref="A2.T11.6.6.2.2.2.1.m1.1.1.3"><csymbol cd="ambiguous" id="A2.T11.6.6.2.2.2.1.m1.1.1.3.1.cmml" xref="A2.T11.6.6.2.2.2.1.m1.1.1.3">superscript</csymbol><cn id="A2.T11.6.6.2.2.2.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.6.6.2.2.2.1.m1.1.1.3.2">10</cn><apply id="A2.T11.6.6.2.2.2.1.m1.1.1.3.3.cmml" xref="A2.T11.6.6.2.2.2.1.m1.1.1.3.3"><minus id="A2.T11.6.6.2.2.2.1.m1.1.1.3.3.1.cmml" xref="A2.T11.6.6.2.2.2.1.m1.1.1.3.3"></minus><cn id="A2.T11.6.6.2.2.2.1.m1.1.1.3.3.2.cmml" type="integer" xref="A2.T11.6.6.2.2.2.1.m1.1.1.3.3.2">4</cn></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.6.6.2.2.2.1.m1.1c">2\times 10^{-4}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.6.6.2.2.2.1.m1.1d">2 × 10 start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT</annotation></semantics></math></td> </tr> </table> </td> <td class="ltx_td ltx_align_center ltx_border_t" id="A2.T11.6.6.5" style="padding:0.5pt 3.0pt;">10</td> </tr> <tr class="ltx_tr" id="A2.T11.7.7"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A2.T11.7.7.2" style="padding:0.5pt 3.0pt;">Step 3</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A2.T11.7.7.3" style="padding:0.5pt 3.0pt;">Fusion Network</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A2.T11.7.7.1" style="padding:0.5pt 3.0pt;"><math alttext="10^{-4}" class="ltx_Math" display="inline" id="A2.T11.7.7.1.m1.1"><semantics id="A2.T11.7.7.1.m1.1a"><msup id="A2.T11.7.7.1.m1.1.1" xref="A2.T11.7.7.1.m1.1.1.cmml"><mn id="A2.T11.7.7.1.m1.1.1.2" xref="A2.T11.7.7.1.m1.1.1.2.cmml">10</mn><mrow id="A2.T11.7.7.1.m1.1.1.3" xref="A2.T11.7.7.1.m1.1.1.3.cmml"><mo id="A2.T11.7.7.1.m1.1.1.3a" xref="A2.T11.7.7.1.m1.1.1.3.cmml">−</mo><mn id="A2.T11.7.7.1.m1.1.1.3.2" xref="A2.T11.7.7.1.m1.1.1.3.2.cmml">4</mn></mrow></msup><annotation-xml encoding="MathML-Content" id="A2.T11.7.7.1.m1.1b"><apply id="A2.T11.7.7.1.m1.1.1.cmml" xref="A2.T11.7.7.1.m1.1.1"><csymbol cd="ambiguous" id="A2.T11.7.7.1.m1.1.1.1.cmml" xref="A2.T11.7.7.1.m1.1.1">superscript</csymbol><cn id="A2.T11.7.7.1.m1.1.1.2.cmml" type="integer" xref="A2.T11.7.7.1.m1.1.1.2">10</cn><apply id="A2.T11.7.7.1.m1.1.1.3.cmml" xref="A2.T11.7.7.1.m1.1.1.3"><minus id="A2.T11.7.7.1.m1.1.1.3.1.cmml" xref="A2.T11.7.7.1.m1.1.1.3"></minus><cn id="A2.T11.7.7.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.7.7.1.m1.1.1.3.2">4</cn></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.7.7.1.m1.1c">10^{-4}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.7.7.1.m1.1d">10 start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT</annotation></semantics></math></td> <td class="ltx_td ltx_align_center ltx_border_t" id="A2.T11.7.7.4" style="padding:0.5pt 3.0pt;">6</td> </tr> <tr class="ltx_tr" id="A2.T11.13.13"> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A2.T11.13.13.7" style="padding:0.5pt 3.0pt;">Step 4</td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A2.T11.13.13.8" style="padding:0.5pt 3.0pt;"> <table class="ltx_tabular ltx_align_middle" id="A2.T11.13.13.8.1"> <tr class="ltx_tr" id="A2.T11.13.13.8.1.1"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.13.13.8.1.1.1" style="padding:0.5pt 3.0pt;">Network B in Transmitter</td> </tr> <tr class="ltx_tr" id="A2.T11.13.13.8.1.2"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.13.13.8.1.2.1" style="padding:0.5pt 3.0pt;">Network B in Receiver</td> </tr> <tr class="ltx_tr" id="A2.T11.13.13.8.1.3"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.13.13.8.1.3.1" style="padding:0.5pt 3.0pt;">Network A in Transmitter</td> </tr> <tr class="ltx_tr" id="A2.T11.13.13.8.1.4"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.13.13.8.1.4.1" style="padding:0.5pt 3.0pt;">Network A in Receiver</td> </tr> <tr class="ltx_tr" id="A2.T11.13.13.8.1.5"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.13.13.8.1.5.1" style="padding:0.5pt 3.0pt;">SpyNet</td> </tr> <tr class="ltx_tr" id="A2.T11.13.13.8.1.6"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.13.13.8.1.6.1" style="padding:0.5pt 3.0pt;">Fusion Network</td> </tr> </table> </td> <td class="ltx_td ltx_align_center ltx_border_r ltx_border_t" id="A2.T11.13.13.6" style="padding:0.5pt 3.0pt;"> <table class="ltx_tabular ltx_align_middle" id="A2.T11.13.13.6.6"> <tr class="ltx_tr" id="A2.T11.8.8.1.1.1"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.8.8.1.1.1.1" style="padding:0.5pt 3.0pt;"><math alttext="10^{-4}" class="ltx_Math" display="inline" id="A2.T11.8.8.1.1.1.1.m1.1"><semantics id="A2.T11.8.8.1.1.1.1.m1.1a"><msup id="A2.T11.8.8.1.1.1.1.m1.1.1" xref="A2.T11.8.8.1.1.1.1.m1.1.1.cmml"><mn id="A2.T11.8.8.1.1.1.1.m1.1.1.2" xref="A2.T11.8.8.1.1.1.1.m1.1.1.2.cmml">10</mn><mrow id="A2.T11.8.8.1.1.1.1.m1.1.1.3" xref="A2.T11.8.8.1.1.1.1.m1.1.1.3.cmml"><mo id="A2.T11.8.8.1.1.1.1.m1.1.1.3a" xref="A2.T11.8.8.1.1.1.1.m1.1.1.3.cmml">−</mo><mn id="A2.T11.8.8.1.1.1.1.m1.1.1.3.2" xref="A2.T11.8.8.1.1.1.1.m1.1.1.3.2.cmml">4</mn></mrow></msup><annotation-xml encoding="MathML-Content" id="A2.T11.8.8.1.1.1.1.m1.1b"><apply id="A2.T11.8.8.1.1.1.1.m1.1.1.cmml" xref="A2.T11.8.8.1.1.1.1.m1.1.1"><csymbol cd="ambiguous" id="A2.T11.8.8.1.1.1.1.m1.1.1.1.cmml" xref="A2.T11.8.8.1.1.1.1.m1.1.1">superscript</csymbol><cn id="A2.T11.8.8.1.1.1.1.m1.1.1.2.cmml" type="integer" xref="A2.T11.8.8.1.1.1.1.m1.1.1.2">10</cn><apply id="A2.T11.8.8.1.1.1.1.m1.1.1.3.cmml" xref="A2.T11.8.8.1.1.1.1.m1.1.1.3"><minus id="A2.T11.8.8.1.1.1.1.m1.1.1.3.1.cmml" xref="A2.T11.8.8.1.1.1.1.m1.1.1.3"></minus><cn id="A2.T11.8.8.1.1.1.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.8.8.1.1.1.1.m1.1.1.3.2">4</cn></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.8.8.1.1.1.1.m1.1c">10^{-4}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.8.8.1.1.1.1.m1.1d">10 start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT</annotation></semantics></math></td> </tr> <tr class="ltx_tr" id="A2.T11.9.9.2.2.2"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.9.9.2.2.2.1" style="padding:0.5pt 3.0pt;"><math alttext="10^{-4}" class="ltx_Math" display="inline" id="A2.T11.9.9.2.2.2.1.m1.1"><semantics id="A2.T11.9.9.2.2.2.1.m1.1a"><msup id="A2.T11.9.9.2.2.2.1.m1.1.1" xref="A2.T11.9.9.2.2.2.1.m1.1.1.cmml"><mn id="A2.T11.9.9.2.2.2.1.m1.1.1.2" xref="A2.T11.9.9.2.2.2.1.m1.1.1.2.cmml">10</mn><mrow id="A2.T11.9.9.2.2.2.1.m1.1.1.3" xref="A2.T11.9.9.2.2.2.1.m1.1.1.3.cmml"><mo id="A2.T11.9.9.2.2.2.1.m1.1.1.3a" xref="A2.T11.9.9.2.2.2.1.m1.1.1.3.cmml">−</mo><mn id="A2.T11.9.9.2.2.2.1.m1.1.1.3.2" xref="A2.T11.9.9.2.2.2.1.m1.1.1.3.2.cmml">4</mn></mrow></msup><annotation-xml encoding="MathML-Content" id="A2.T11.9.9.2.2.2.1.m1.1b"><apply id="A2.T11.9.9.2.2.2.1.m1.1.1.cmml" xref="A2.T11.9.9.2.2.2.1.m1.1.1"><csymbol cd="ambiguous" id="A2.T11.9.9.2.2.2.1.m1.1.1.1.cmml" xref="A2.T11.9.9.2.2.2.1.m1.1.1">superscript</csymbol><cn id="A2.T11.9.9.2.2.2.1.m1.1.1.2.cmml" type="integer" xref="A2.T11.9.9.2.2.2.1.m1.1.1.2">10</cn><apply id="A2.T11.9.9.2.2.2.1.m1.1.1.3.cmml" xref="A2.T11.9.9.2.2.2.1.m1.1.1.3"><minus id="A2.T11.9.9.2.2.2.1.m1.1.1.3.1.cmml" xref="A2.T11.9.9.2.2.2.1.m1.1.1.3"></minus><cn id="A2.T11.9.9.2.2.2.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.9.9.2.2.2.1.m1.1.1.3.2">4</cn></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.9.9.2.2.2.1.m1.1c">10^{-4}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.9.9.2.2.2.1.m1.1d">10 start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT</annotation></semantics></math></td> </tr> <tr class="ltx_tr" id="A2.T11.10.10.3.3.3"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.10.10.3.3.3.1" style="padding:0.5pt 3.0pt;"><math alttext="2\times 10^{-5}" class="ltx_Math" display="inline" id="A2.T11.10.10.3.3.3.1.m1.1"><semantics id="A2.T11.10.10.3.3.3.1.m1.1a"><mrow id="A2.T11.10.10.3.3.3.1.m1.1.1" xref="A2.T11.10.10.3.3.3.1.m1.1.1.cmml"><mn id="A2.T11.10.10.3.3.3.1.m1.1.1.2" xref="A2.T11.10.10.3.3.3.1.m1.1.1.2.cmml">2</mn><mo id="A2.T11.10.10.3.3.3.1.m1.1.1.1" lspace="0.222em" rspace="0.222em" xref="A2.T11.10.10.3.3.3.1.m1.1.1.1.cmml">×</mo><msup id="A2.T11.10.10.3.3.3.1.m1.1.1.3" xref="A2.T11.10.10.3.3.3.1.m1.1.1.3.cmml"><mn id="A2.T11.10.10.3.3.3.1.m1.1.1.3.2" xref="A2.T11.10.10.3.3.3.1.m1.1.1.3.2.cmml">10</mn><mrow id="A2.T11.10.10.3.3.3.1.m1.1.1.3.3" xref="A2.T11.10.10.3.3.3.1.m1.1.1.3.3.cmml"><mo id="A2.T11.10.10.3.3.3.1.m1.1.1.3.3a" xref="A2.T11.10.10.3.3.3.1.m1.1.1.3.3.cmml">−</mo><mn id="A2.T11.10.10.3.3.3.1.m1.1.1.3.3.2" xref="A2.T11.10.10.3.3.3.1.m1.1.1.3.3.2.cmml">5</mn></mrow></msup></mrow><annotation-xml encoding="MathML-Content" id="A2.T11.10.10.3.3.3.1.m1.1b"><apply id="A2.T11.10.10.3.3.3.1.m1.1.1.cmml" xref="A2.T11.10.10.3.3.3.1.m1.1.1"><times id="A2.T11.10.10.3.3.3.1.m1.1.1.1.cmml" xref="A2.T11.10.10.3.3.3.1.m1.1.1.1"></times><cn id="A2.T11.10.10.3.3.3.1.m1.1.1.2.cmml" type="integer" xref="A2.T11.10.10.3.3.3.1.m1.1.1.2">2</cn><apply id="A2.T11.10.10.3.3.3.1.m1.1.1.3.cmml" xref="A2.T11.10.10.3.3.3.1.m1.1.1.3"><csymbol cd="ambiguous" id="A2.T11.10.10.3.3.3.1.m1.1.1.3.1.cmml" xref="A2.T11.10.10.3.3.3.1.m1.1.1.3">superscript</csymbol><cn id="A2.T11.10.10.3.3.3.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.10.10.3.3.3.1.m1.1.1.3.2">10</cn><apply id="A2.T11.10.10.3.3.3.1.m1.1.1.3.3.cmml" xref="A2.T11.10.10.3.3.3.1.m1.1.1.3.3"><minus id="A2.T11.10.10.3.3.3.1.m1.1.1.3.3.1.cmml" xref="A2.T11.10.10.3.3.3.1.m1.1.1.3.3"></minus><cn id="A2.T11.10.10.3.3.3.1.m1.1.1.3.3.2.cmml" type="integer" xref="A2.T11.10.10.3.3.3.1.m1.1.1.3.3.2">5</cn></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.10.10.3.3.3.1.m1.1c">2\times 10^{-5}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.10.10.3.3.3.1.m1.1d">2 × 10 start_POSTSUPERSCRIPT - 5 end_POSTSUPERSCRIPT</annotation></semantics></math></td> </tr> <tr class="ltx_tr" id="A2.T11.11.11.4.4.4"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.11.11.4.4.4.1" style="padding:0.5pt 3.0pt;"><math alttext="2\times 10^{-5}" class="ltx_Math" display="inline" id="A2.T11.11.11.4.4.4.1.m1.1"><semantics id="A2.T11.11.11.4.4.4.1.m1.1a"><mrow id="A2.T11.11.11.4.4.4.1.m1.1.1" xref="A2.T11.11.11.4.4.4.1.m1.1.1.cmml"><mn id="A2.T11.11.11.4.4.4.1.m1.1.1.2" xref="A2.T11.11.11.4.4.4.1.m1.1.1.2.cmml">2</mn><mo id="A2.T11.11.11.4.4.4.1.m1.1.1.1" lspace="0.222em" rspace="0.222em" xref="A2.T11.11.11.4.4.4.1.m1.1.1.1.cmml">×</mo><msup id="A2.T11.11.11.4.4.4.1.m1.1.1.3" xref="A2.T11.11.11.4.4.4.1.m1.1.1.3.cmml"><mn id="A2.T11.11.11.4.4.4.1.m1.1.1.3.2" xref="A2.T11.11.11.4.4.4.1.m1.1.1.3.2.cmml">10</mn><mrow id="A2.T11.11.11.4.4.4.1.m1.1.1.3.3" xref="A2.T11.11.11.4.4.4.1.m1.1.1.3.3.cmml"><mo id="A2.T11.11.11.4.4.4.1.m1.1.1.3.3a" xref="A2.T11.11.11.4.4.4.1.m1.1.1.3.3.cmml">−</mo><mn id="A2.T11.11.11.4.4.4.1.m1.1.1.3.3.2" xref="A2.T11.11.11.4.4.4.1.m1.1.1.3.3.2.cmml">5</mn></mrow></msup></mrow><annotation-xml encoding="MathML-Content" id="A2.T11.11.11.4.4.4.1.m1.1b"><apply id="A2.T11.11.11.4.4.4.1.m1.1.1.cmml" xref="A2.T11.11.11.4.4.4.1.m1.1.1"><times id="A2.T11.11.11.4.4.4.1.m1.1.1.1.cmml" xref="A2.T11.11.11.4.4.4.1.m1.1.1.1"></times><cn id="A2.T11.11.11.4.4.4.1.m1.1.1.2.cmml" type="integer" xref="A2.T11.11.11.4.4.4.1.m1.1.1.2">2</cn><apply id="A2.T11.11.11.4.4.4.1.m1.1.1.3.cmml" xref="A2.T11.11.11.4.4.4.1.m1.1.1.3"><csymbol cd="ambiguous" id="A2.T11.11.11.4.4.4.1.m1.1.1.3.1.cmml" xref="A2.T11.11.11.4.4.4.1.m1.1.1.3">superscript</csymbol><cn id="A2.T11.11.11.4.4.4.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.11.11.4.4.4.1.m1.1.1.3.2">10</cn><apply id="A2.T11.11.11.4.4.4.1.m1.1.1.3.3.cmml" xref="A2.T11.11.11.4.4.4.1.m1.1.1.3.3"><minus id="A2.T11.11.11.4.4.4.1.m1.1.1.3.3.1.cmml" xref="A2.T11.11.11.4.4.4.1.m1.1.1.3.3"></minus><cn id="A2.T11.11.11.4.4.4.1.m1.1.1.3.3.2.cmml" type="integer" xref="A2.T11.11.11.4.4.4.1.m1.1.1.3.3.2">5</cn></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.11.11.4.4.4.1.m1.1c">2\times 10^{-5}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.11.11.4.4.4.1.m1.1d">2 × 10 start_POSTSUPERSCRIPT - 5 end_POSTSUPERSCRIPT</annotation></semantics></math></td> </tr> <tr class="ltx_tr" id="A2.T11.12.12.5.5.5"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.12.12.5.5.5.1" style="padding:0.5pt 3.0pt;"><math alttext="1.25\times 10^{-5}" class="ltx_Math" display="inline" id="A2.T11.12.12.5.5.5.1.m1.1"><semantics id="A2.T11.12.12.5.5.5.1.m1.1a"><mrow id="A2.T11.12.12.5.5.5.1.m1.1.1" xref="A2.T11.12.12.5.5.5.1.m1.1.1.cmml"><mn id="A2.T11.12.12.5.5.5.1.m1.1.1.2" xref="A2.T11.12.12.5.5.5.1.m1.1.1.2.cmml">1.25</mn><mo id="A2.T11.12.12.5.5.5.1.m1.1.1.1" lspace="0.222em" rspace="0.222em" xref="A2.T11.12.12.5.5.5.1.m1.1.1.1.cmml">×</mo><msup id="A2.T11.12.12.5.5.5.1.m1.1.1.3" xref="A2.T11.12.12.5.5.5.1.m1.1.1.3.cmml"><mn id="A2.T11.12.12.5.5.5.1.m1.1.1.3.2" xref="A2.T11.12.12.5.5.5.1.m1.1.1.3.2.cmml">10</mn><mrow id="A2.T11.12.12.5.5.5.1.m1.1.1.3.3" xref="A2.T11.12.12.5.5.5.1.m1.1.1.3.3.cmml"><mo id="A2.T11.12.12.5.5.5.1.m1.1.1.3.3a" xref="A2.T11.12.12.5.5.5.1.m1.1.1.3.3.cmml">−</mo><mn id="A2.T11.12.12.5.5.5.1.m1.1.1.3.3.2" xref="A2.T11.12.12.5.5.5.1.m1.1.1.3.3.2.cmml">5</mn></mrow></msup></mrow><annotation-xml encoding="MathML-Content" id="A2.T11.12.12.5.5.5.1.m1.1b"><apply id="A2.T11.12.12.5.5.5.1.m1.1.1.cmml" xref="A2.T11.12.12.5.5.5.1.m1.1.1"><times id="A2.T11.12.12.5.5.5.1.m1.1.1.1.cmml" xref="A2.T11.12.12.5.5.5.1.m1.1.1.1"></times><cn id="A2.T11.12.12.5.5.5.1.m1.1.1.2.cmml" type="float" xref="A2.T11.12.12.5.5.5.1.m1.1.1.2">1.25</cn><apply id="A2.T11.12.12.5.5.5.1.m1.1.1.3.cmml" xref="A2.T11.12.12.5.5.5.1.m1.1.1.3"><csymbol cd="ambiguous" id="A2.T11.12.12.5.5.5.1.m1.1.1.3.1.cmml" xref="A2.T11.12.12.5.5.5.1.m1.1.1.3">superscript</csymbol><cn id="A2.T11.12.12.5.5.5.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.12.12.5.5.5.1.m1.1.1.3.2">10</cn><apply id="A2.T11.12.12.5.5.5.1.m1.1.1.3.3.cmml" xref="A2.T11.12.12.5.5.5.1.m1.1.1.3.3"><minus id="A2.T11.12.12.5.5.5.1.m1.1.1.3.3.1.cmml" xref="A2.T11.12.12.5.5.5.1.m1.1.1.3.3"></minus><cn id="A2.T11.12.12.5.5.5.1.m1.1.1.3.3.2.cmml" type="integer" xref="A2.T11.12.12.5.5.5.1.m1.1.1.3.3.2">5</cn></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.12.12.5.5.5.1.m1.1c">1.25\times 10^{-5}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.12.12.5.5.5.1.m1.1d">1.25 × 10 start_POSTSUPERSCRIPT - 5 end_POSTSUPERSCRIPT</annotation></semantics></math></td> </tr> <tr class="ltx_tr" id="A2.T11.13.13.6.6.6"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.13.13.6.6.6.1" style="padding:0.5pt 3.0pt;"><math alttext="2\times 10^{-5}" class="ltx_Math" display="inline" id="A2.T11.13.13.6.6.6.1.m1.1"><semantics id="A2.T11.13.13.6.6.6.1.m1.1a"><mrow id="A2.T11.13.13.6.6.6.1.m1.1.1" xref="A2.T11.13.13.6.6.6.1.m1.1.1.cmml"><mn id="A2.T11.13.13.6.6.6.1.m1.1.1.2" xref="A2.T11.13.13.6.6.6.1.m1.1.1.2.cmml">2</mn><mo id="A2.T11.13.13.6.6.6.1.m1.1.1.1" lspace="0.222em" rspace="0.222em" xref="A2.T11.13.13.6.6.6.1.m1.1.1.1.cmml">×</mo><msup id="A2.T11.13.13.6.6.6.1.m1.1.1.3" xref="A2.T11.13.13.6.6.6.1.m1.1.1.3.cmml"><mn id="A2.T11.13.13.6.6.6.1.m1.1.1.3.2" xref="A2.T11.13.13.6.6.6.1.m1.1.1.3.2.cmml">10</mn><mrow id="A2.T11.13.13.6.6.6.1.m1.1.1.3.3" xref="A2.T11.13.13.6.6.6.1.m1.1.1.3.3.cmml"><mo id="A2.T11.13.13.6.6.6.1.m1.1.1.3.3a" xref="A2.T11.13.13.6.6.6.1.m1.1.1.3.3.cmml">−</mo><mn id="A2.T11.13.13.6.6.6.1.m1.1.1.3.3.2" xref="A2.T11.13.13.6.6.6.1.m1.1.1.3.3.2.cmml">5</mn></mrow></msup></mrow><annotation-xml encoding="MathML-Content" id="A2.T11.13.13.6.6.6.1.m1.1b"><apply id="A2.T11.13.13.6.6.6.1.m1.1.1.cmml" xref="A2.T11.13.13.6.6.6.1.m1.1.1"><times id="A2.T11.13.13.6.6.6.1.m1.1.1.1.cmml" xref="A2.T11.13.13.6.6.6.1.m1.1.1.1"></times><cn id="A2.T11.13.13.6.6.6.1.m1.1.1.2.cmml" type="integer" xref="A2.T11.13.13.6.6.6.1.m1.1.1.2">2</cn><apply id="A2.T11.13.13.6.6.6.1.m1.1.1.3.cmml" xref="A2.T11.13.13.6.6.6.1.m1.1.1.3"><csymbol cd="ambiguous" id="A2.T11.13.13.6.6.6.1.m1.1.1.3.1.cmml" xref="A2.T11.13.13.6.6.6.1.m1.1.1.3">superscript</csymbol><cn id="A2.T11.13.13.6.6.6.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.13.13.6.6.6.1.m1.1.1.3.2">10</cn><apply id="A2.T11.13.13.6.6.6.1.m1.1.1.3.3.cmml" xref="A2.T11.13.13.6.6.6.1.m1.1.1.3.3"><minus id="A2.T11.13.13.6.6.6.1.m1.1.1.3.3.1.cmml" xref="A2.T11.13.13.6.6.6.1.m1.1.1.3.3"></minus><cn id="A2.T11.13.13.6.6.6.1.m1.1.1.3.3.2.cmml" type="integer" xref="A2.T11.13.13.6.6.6.1.m1.1.1.3.3.2">5</cn></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.13.13.6.6.6.1.m1.1c">2\times 10^{-5}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.13.13.6.6.6.1.m1.1d">2 × 10 start_POSTSUPERSCRIPT - 5 end_POSTSUPERSCRIPT</annotation></semantics></math></td> </tr> </table> </td> <td class="ltx_td ltx_align_center ltx_border_t" id="A2.T11.13.13.9" style="padding:0.5pt 3.0pt;">10</td> </tr> <tr class="ltx_tr" id="A2.T11.20.20"> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r ltx_border_t" id="A2.T11.20.20.8" style="padding:0.5pt 3.0pt;">Step 5</td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r ltx_border_t" id="A2.T11.20.20.9" style="padding:0.5pt 3.0pt;"> <table class="ltx_tabular ltx_align_middle" id="A2.T11.20.20.9.1"> <tr class="ltx_tr" id="A2.T11.20.20.9.1.1"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.20.20.9.1.1.1" style="padding:0.5pt 3.0pt;">Channel Codec Network</td> </tr> <tr class="ltx_tr" id="A2.T11.20.20.9.1.2"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.20.20.9.1.2.1" style="padding:0.5pt 3.0pt;">Network B in Transmitter</td> </tr> <tr class="ltx_tr" id="A2.T11.20.20.9.1.3"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.20.20.9.1.3.1" style="padding:0.5pt 3.0pt;">Network B in Receiver</td> </tr> <tr class="ltx_tr" id="A2.T11.20.20.9.1.4"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.20.20.9.1.4.1" style="padding:0.5pt 3.0pt;">Network A in Transmitter</td> </tr> <tr class="ltx_tr" id="A2.T11.20.20.9.1.5"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.20.20.9.1.5.1" style="padding:0.5pt 3.0pt;">Network A in Receiver</td> </tr> <tr class="ltx_tr" id="A2.T11.20.20.9.1.6"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.20.20.9.1.6.1" style="padding:0.5pt 3.0pt;">SpyNet</td> </tr> <tr class="ltx_tr" id="A2.T11.20.20.9.1.7"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.20.20.9.1.7.1" style="padding:0.5pt 3.0pt;">Fusion Network</td> </tr> </table> </td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_r ltx_border_t" id="A2.T11.20.20.7" style="padding:0.5pt 3.0pt;"> <table class="ltx_tabular ltx_align_middle" id="A2.T11.20.20.7.7"> <tr class="ltx_tr" id="A2.T11.14.14.1.1.1"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.14.14.1.1.1.1" style="padding:0.5pt 3.0pt;"><math alttext="10^{-4}" class="ltx_Math" display="inline" id="A2.T11.14.14.1.1.1.1.m1.1"><semantics id="A2.T11.14.14.1.1.1.1.m1.1a"><msup id="A2.T11.14.14.1.1.1.1.m1.1.1" xref="A2.T11.14.14.1.1.1.1.m1.1.1.cmml"><mn id="A2.T11.14.14.1.1.1.1.m1.1.1.2" xref="A2.T11.14.14.1.1.1.1.m1.1.1.2.cmml">10</mn><mrow id="A2.T11.14.14.1.1.1.1.m1.1.1.3" xref="A2.T11.14.14.1.1.1.1.m1.1.1.3.cmml"><mo id="A2.T11.14.14.1.1.1.1.m1.1.1.3a" xref="A2.T11.14.14.1.1.1.1.m1.1.1.3.cmml">−</mo><mn id="A2.T11.14.14.1.1.1.1.m1.1.1.3.2" xref="A2.T11.14.14.1.1.1.1.m1.1.1.3.2.cmml">4</mn></mrow></msup><annotation-xml encoding="MathML-Content" id="A2.T11.14.14.1.1.1.1.m1.1b"><apply id="A2.T11.14.14.1.1.1.1.m1.1.1.cmml" xref="A2.T11.14.14.1.1.1.1.m1.1.1"><csymbol cd="ambiguous" id="A2.T11.14.14.1.1.1.1.m1.1.1.1.cmml" xref="A2.T11.14.14.1.1.1.1.m1.1.1">superscript</csymbol><cn id="A2.T11.14.14.1.1.1.1.m1.1.1.2.cmml" type="integer" xref="A2.T11.14.14.1.1.1.1.m1.1.1.2">10</cn><apply id="A2.T11.14.14.1.1.1.1.m1.1.1.3.cmml" xref="A2.T11.14.14.1.1.1.1.m1.1.1.3"><minus id="A2.T11.14.14.1.1.1.1.m1.1.1.3.1.cmml" xref="A2.T11.14.14.1.1.1.1.m1.1.1.3"></minus><cn id="A2.T11.14.14.1.1.1.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.14.14.1.1.1.1.m1.1.1.3.2">4</cn></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.14.14.1.1.1.1.m1.1c">10^{-4}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.14.14.1.1.1.1.m1.1d">10 start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT</annotation></semantics></math></td> </tr> <tr class="ltx_tr" id="A2.T11.15.15.2.2.2"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.15.15.2.2.2.1" style="padding:0.5pt 3.0pt;"><math alttext="10^{-4}" class="ltx_Math" display="inline" id="A2.T11.15.15.2.2.2.1.m1.1"><semantics id="A2.T11.15.15.2.2.2.1.m1.1a"><msup id="A2.T11.15.15.2.2.2.1.m1.1.1" xref="A2.T11.15.15.2.2.2.1.m1.1.1.cmml"><mn id="A2.T11.15.15.2.2.2.1.m1.1.1.2" xref="A2.T11.15.15.2.2.2.1.m1.1.1.2.cmml">10</mn><mrow id="A2.T11.15.15.2.2.2.1.m1.1.1.3" xref="A2.T11.15.15.2.2.2.1.m1.1.1.3.cmml"><mo id="A2.T11.15.15.2.2.2.1.m1.1.1.3a" xref="A2.T11.15.15.2.2.2.1.m1.1.1.3.cmml">−</mo><mn id="A2.T11.15.15.2.2.2.1.m1.1.1.3.2" xref="A2.T11.15.15.2.2.2.1.m1.1.1.3.2.cmml">4</mn></mrow></msup><annotation-xml encoding="MathML-Content" id="A2.T11.15.15.2.2.2.1.m1.1b"><apply id="A2.T11.15.15.2.2.2.1.m1.1.1.cmml" xref="A2.T11.15.15.2.2.2.1.m1.1.1"><csymbol cd="ambiguous" id="A2.T11.15.15.2.2.2.1.m1.1.1.1.cmml" xref="A2.T11.15.15.2.2.2.1.m1.1.1">superscript</csymbol><cn id="A2.T11.15.15.2.2.2.1.m1.1.1.2.cmml" type="integer" xref="A2.T11.15.15.2.2.2.1.m1.1.1.2">10</cn><apply id="A2.T11.15.15.2.2.2.1.m1.1.1.3.cmml" xref="A2.T11.15.15.2.2.2.1.m1.1.1.3"><minus id="A2.T11.15.15.2.2.2.1.m1.1.1.3.1.cmml" xref="A2.T11.15.15.2.2.2.1.m1.1.1.3"></minus><cn id="A2.T11.15.15.2.2.2.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.15.15.2.2.2.1.m1.1.1.3.2">4</cn></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.15.15.2.2.2.1.m1.1c">10^{-4}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.15.15.2.2.2.1.m1.1d">10 start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT</annotation></semantics></math></td> </tr> <tr class="ltx_tr" id="A2.T11.16.16.3.3.3"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.16.16.3.3.3.1" style="padding:0.5pt 3.0pt;"><math alttext="10^{-4}" class="ltx_Math" display="inline" id="A2.T11.16.16.3.3.3.1.m1.1"><semantics id="A2.T11.16.16.3.3.3.1.m1.1a"><msup id="A2.T11.16.16.3.3.3.1.m1.1.1" xref="A2.T11.16.16.3.3.3.1.m1.1.1.cmml"><mn id="A2.T11.16.16.3.3.3.1.m1.1.1.2" xref="A2.T11.16.16.3.3.3.1.m1.1.1.2.cmml">10</mn><mrow id="A2.T11.16.16.3.3.3.1.m1.1.1.3" xref="A2.T11.16.16.3.3.3.1.m1.1.1.3.cmml"><mo id="A2.T11.16.16.3.3.3.1.m1.1.1.3a" xref="A2.T11.16.16.3.3.3.1.m1.1.1.3.cmml">−</mo><mn id="A2.T11.16.16.3.3.3.1.m1.1.1.3.2" xref="A2.T11.16.16.3.3.3.1.m1.1.1.3.2.cmml">4</mn></mrow></msup><annotation-xml encoding="MathML-Content" id="A2.T11.16.16.3.3.3.1.m1.1b"><apply id="A2.T11.16.16.3.3.3.1.m1.1.1.cmml" xref="A2.T11.16.16.3.3.3.1.m1.1.1"><csymbol cd="ambiguous" id="A2.T11.16.16.3.3.3.1.m1.1.1.1.cmml" xref="A2.T11.16.16.3.3.3.1.m1.1.1">superscript</csymbol><cn id="A2.T11.16.16.3.3.3.1.m1.1.1.2.cmml" type="integer" xref="A2.T11.16.16.3.3.3.1.m1.1.1.2">10</cn><apply id="A2.T11.16.16.3.3.3.1.m1.1.1.3.cmml" xref="A2.T11.16.16.3.3.3.1.m1.1.1.3"><minus id="A2.T11.16.16.3.3.3.1.m1.1.1.3.1.cmml" xref="A2.T11.16.16.3.3.3.1.m1.1.1.3"></minus><cn id="A2.T11.16.16.3.3.3.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.16.16.3.3.3.1.m1.1.1.3.2">4</cn></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.16.16.3.3.3.1.m1.1c">10^{-4}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.16.16.3.3.3.1.m1.1d">10 start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT</annotation></semantics></math></td> </tr> <tr class="ltx_tr" id="A2.T11.17.17.4.4.4"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.17.17.4.4.4.1" style="padding:0.5pt 3.0pt;"><math alttext="2\times 10^{-5}" class="ltx_Math" display="inline" id="A2.T11.17.17.4.4.4.1.m1.1"><semantics id="A2.T11.17.17.4.4.4.1.m1.1a"><mrow id="A2.T11.17.17.4.4.4.1.m1.1.1" xref="A2.T11.17.17.4.4.4.1.m1.1.1.cmml"><mn id="A2.T11.17.17.4.4.4.1.m1.1.1.2" xref="A2.T11.17.17.4.4.4.1.m1.1.1.2.cmml">2</mn><mo id="A2.T11.17.17.4.4.4.1.m1.1.1.1" lspace="0.222em" rspace="0.222em" xref="A2.T11.17.17.4.4.4.1.m1.1.1.1.cmml">×</mo><msup id="A2.T11.17.17.4.4.4.1.m1.1.1.3" xref="A2.T11.17.17.4.4.4.1.m1.1.1.3.cmml"><mn id="A2.T11.17.17.4.4.4.1.m1.1.1.3.2" xref="A2.T11.17.17.4.4.4.1.m1.1.1.3.2.cmml">10</mn><mrow id="A2.T11.17.17.4.4.4.1.m1.1.1.3.3" xref="A2.T11.17.17.4.4.4.1.m1.1.1.3.3.cmml"><mo id="A2.T11.17.17.4.4.4.1.m1.1.1.3.3a" xref="A2.T11.17.17.4.4.4.1.m1.1.1.3.3.cmml">−</mo><mn id="A2.T11.17.17.4.4.4.1.m1.1.1.3.3.2" xref="A2.T11.17.17.4.4.4.1.m1.1.1.3.3.2.cmml">5</mn></mrow></msup></mrow><annotation-xml encoding="MathML-Content" id="A2.T11.17.17.4.4.4.1.m1.1b"><apply id="A2.T11.17.17.4.4.4.1.m1.1.1.cmml" xref="A2.T11.17.17.4.4.4.1.m1.1.1"><times id="A2.T11.17.17.4.4.4.1.m1.1.1.1.cmml" xref="A2.T11.17.17.4.4.4.1.m1.1.1.1"></times><cn id="A2.T11.17.17.4.4.4.1.m1.1.1.2.cmml" type="integer" xref="A2.T11.17.17.4.4.4.1.m1.1.1.2">2</cn><apply id="A2.T11.17.17.4.4.4.1.m1.1.1.3.cmml" xref="A2.T11.17.17.4.4.4.1.m1.1.1.3"><csymbol cd="ambiguous" id="A2.T11.17.17.4.4.4.1.m1.1.1.3.1.cmml" xref="A2.T11.17.17.4.4.4.1.m1.1.1.3">superscript</csymbol><cn id="A2.T11.17.17.4.4.4.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.17.17.4.4.4.1.m1.1.1.3.2">10</cn><apply id="A2.T11.17.17.4.4.4.1.m1.1.1.3.3.cmml" xref="A2.T11.17.17.4.4.4.1.m1.1.1.3.3"><minus id="A2.T11.17.17.4.4.4.1.m1.1.1.3.3.1.cmml" xref="A2.T11.17.17.4.4.4.1.m1.1.1.3.3"></minus><cn id="A2.T11.17.17.4.4.4.1.m1.1.1.3.3.2.cmml" type="integer" xref="A2.T11.17.17.4.4.4.1.m1.1.1.3.3.2">5</cn></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.17.17.4.4.4.1.m1.1c">2\times 10^{-5}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.17.17.4.4.4.1.m1.1d">2 × 10 start_POSTSUPERSCRIPT - 5 end_POSTSUPERSCRIPT</annotation></semantics></math></td> </tr> <tr class="ltx_tr" id="A2.T11.18.18.5.5.5"> <td class="ltx_td ltx_nopad_r ltx_align_center" id="A2.T11.18.18.5.5.5.1" style="padding:0.5pt 3.0pt;"><math alttext="2\times 10^{-5}" class="ltx_Math" display="inline" id="A2.T11.18.18.5.5.5.1.m1.1"><semantics id="A2.T11.18.18.5.5.5.1.m1.1a"><mrow id="A2.T11.18.18.5.5.5.1.m1.1.1" xref="A2.T11.18.18.5.5.5.1.m1.1.1.cmml"><mn id="A2.T11.18.18.5.5.5.1.m1.1.1.2" xref="A2.T11.18.18.5.5.5.1.m1.1.1.2.cmml">2</mn><mo id="A2.T11.18.18.5.5.5.1.m1.1.1.1" lspace="0.222em" rspace="0.222em" xref="A2.T11.18.18.5.5.5.1.m1.1.1.1.cmml">×</mo><msup id="A2.T11.18.18.5.5.5.1.m1.1.1.3" xref="A2.T11.18.18.5.5.5.1.m1.1.1.3.cmml"><mn id="A2.T11.18.18.5.5.5.1.m1.1.1.3.2" xref="A2.T11.18.18.5.5.5.1.m1.1.1.3.2.cmml">10</mn><mrow id="A2.T11.18.18.5.5.5.1.m1.1.1.3.3" xref="A2.T11.18.18.5.5.5.1.m1.1.1.3.3.cmml"><mo id="A2.T11.18.18.5.5.5.1.m1.1.1.3.3a" xref="A2.T11.18.18.5.5.5.1.m1.1.1.3.3.cmml">−</mo><mn id="A2.T11.18.18.5.5.5.1.m1.1.1.3.3.2" xref="A2.T11.18.18.5.5.5.1.m1.1.1.3.3.2.cmml">5</mn></mrow></msup></mrow><annotation-xml encoding="MathML-Content" id="A2.T11.18.18.5.5.5.1.m1.1b"><apply id="A2.T11.18.18.5.5.5.1.m1.1.1.cmml" xref="A2.T11.18.18.5.5.5.1.m1.1.1"><times id="A2.T11.18.18.5.5.5.1.m1.1.1.1.cmml" xref="A2.T11.18.18.5.5.5.1.m1.1.1.1"></times><cn id="A2.T11.18.18.5.5.5.1.m1.1.1.2.cmml" type="integer" xref="A2.T11.18.18.5.5.5.1.m1.1.1.2">2</cn><apply id="A2.T11.18.18.5.5.5.1.m1.1.1.3.cmml" xref="A2.T11.18.18.5.5.5.1.m1.1.1.3"><csymbol cd="ambiguous" id="A2.T11.18.18.5.5.5.1.m1.1.1.3.1.cmml" xref="A2.T11.18.18.5.5.5.1.m1.1.1.3">superscript</csymbol><cn id="A2.T11.18.18.5.5.5.1.m1.1.1.3.2.cmml" type="integer" xref="A2.T11.18.18.5.5.5.1.m1.1.1.3.2">10</cn><apply id="A2.T11.18.18.5.5.5.1.m1.1.1.3.3.cmml" xref="A2.T11.18.18.5.5.5.1.m1.1.1.3.3"><minus id="A2.T11.18.18.5.5.5.1.m1.1.1.3.3.1.cmml" xref="A2.T11.18.18.5.5.5.1.m1.1.1.3.3"></minus><cn id="A2.T11.18.18.5.5.5.1.m1.1.1.3.3.2.cmml" type="integer" xref="A2.T11.18.18.5.5.5.1.m1.1.1.3.3.2">5</cn></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="A2.T11.18.18.5.5.5.1.m1.1c">2\times 10^{-5}</annotation><annotation encoding="application/x-llamapun" id="A2.T11.18.18.5.5.5.1.m1.1d">2 × 10 start_POSTSUPERSCRIPT - 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5 end_POSTSUPERSCRIPT</annotation></semantics></math></td> </tr> </table> </td> <td class="ltx_td ltx_align_center ltx_border_b ltx_border_t" id="A2.T11.20.20.10" style="padding:0.5pt 3.0pt;">25+20<sup class="ltx_sup" id="A2.T11.20.20.10.1">#</sup> </td> </tr> </tbody> </table> </div> <div class="ltx_flex_break"></div> <div class="ltx_flex_cell ltx_flex_size_1"> <ul class="ltx_itemize ltx_centering ltx_figure_panel" id="A2.I1"> <li class="ltx_item" id="A2.I1.i1" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item">•</span> <div class="ltx_para" id="A2.I1.i1.p1"> <p class="ltx_p" id="A2.I1.i1.p1.1"><span class="ltx_text" id="A2.I1.i1.p1.1.1" style="font-size:80%;">* 2 epochs with the frozen SpyNet, 10 epochs with the unfrozen SpyNet.</span></p> </div> </li> <li class="ltx_item" id="A2.I1.i2" style="list-style-type:none;"> <span class="ltx_tag ltx_tag_item">•</span> <div class="ltx_para" id="A2.I1.i2.p1"> <p class="ltx_p" id="A2.I1.i2.p1.1"><span class="ltx_text" id="A2.I1.i2.p1.1.1" style="font-size:80%;"># 25 epochs for only the channel codec, 20 epochs for the whole network.</span></p> </div> </li> </ul> </div> </div> </figure> </section> <section class="ltx_bibliography" id="bib"> <h2 class="ltx_title ltx_title_bibliography">References</h2> <ul class="ltx_biblist"> <li class="ltx_bibitem" id="bib.bib1"> <span class="ltx_tag ltx_tag_bibitem">[1]</span> <span class="ltx_bibblock"> E. 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