Un algorithme basé sur la mesure de distance pour la reconnaissance d'images SAR

<!DOCTYPE html><html lang="fr" dir="ltr"><head>  <script>(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer','GTM-TF44WCG2');</script>  <meta name="google-site-verification" content="qtQTnMSrK6sA-4pRLrqiSiCZUW4v-JjdBfmipk6pNRI"> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1"> <title>Un algorithme basé sur la mesure de distance pour la reconnaissance d'images SAR</title> <meta name="description" content=""> <meta property="og:title" content="Transactions en ligne"> <meta property="og:type" content="website"> <meta property="og:url" content="#"> <meta property="og:image" content="#//assets/img/ogp.jpg"> <meta property="og:site_name" content="Transactions Online"> <meta property="og:description" content=""> <link rel="icon" href="https://global.ieice.org/assets/img/favicon.ico"> <link rel="apple-touch-icon" sizes="180x180" href="https://global.ieice.org/assets/img/apple-touch-icon.png"> <link rel="stylesheet" href="https://global.ieice.org/assets/css/header.css"> <link rel="stylesheet" href="https://global.ieice.org/assets/css/footer.css"> <link rel="stylesheet" href="https://global.ieice.org/assets/css/style.css"> <link rel="stylesheet" href="https://global.ieice.org/assets/css/2nd.css"> <link rel="stylesheet" href="https://global.ieice.org/assets/css/summary.css"> <link href="https://use.fontawesome.com/releases/v5.15.4/css/all.css" rel="stylesheet"> <link rel="stylesheet" type="text/css" href="https://unpkg.com/tippy.js@5.0.3/animations/shift-toward-subtle.css"> <link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/slick-carousel@1.8.1/slick/slick.css"> <link rel="stylesheet" href="https://use.typekit.net/mgs1ayn.css">  <script src="https://global.ieice.org/web/ui/js/custom.js"></script> <link href="https://global.ieice.org/web/ui/site.css" rel="stylesheet">   <meta name="DC.title" content="Un algorithme basé sur la mesure de distance pour la reconnaissance d'images SAR"> <meta name="DC.creator" content="Yuxiu LIU"> <meta name="DC.creator" content="Na WEI"> <meta name="DC.creator" content="Yongjie LI"> <meta name="DC.date.issued" scheme="DCTERMS.W3CDTF" content="2024/12"> <meta name="DC.Date" content="2024/12/01"> <meta name="DC.citation.volume" content="E107-B"> <meta name="DC.citation.issue" content="12"> <meta name="DC.citation.spage" content="989"> <meta name="DC.citation.epage" content="997"> <meta name="DC.identifier" content="https://global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_pdf"> <meta name="DCTERMS.abstract" content="Ces dernières années, les réseaux neuronaux convolutionnels profonds (CNN) ont été largement utilisés dans la reconnaissance d'images radar à synthèse d'ouverture (SAR). Cependant, en raison de la difficulté d'obtenir des échantillons d'images SAR, les données d'apprentissage sont relativement peu nombreuses et le surajustement est facile à se produire lors de l'utilisation de CNNS traditionnels utilisés dans la reconnaissance d'images optiques. Dans cet article, un algorithme de reconnaissance d'images SAR basé sur CNN est proposé, qui peut réduire efficacement les paramètres du réseau, éviter le surajustement du modèle et améliorer la précision de la reconnaissance. L'algorithme construit d'abord un extracteur de caractéristiques de réseau convolutionnel avec un noyau de convolution de petite taille, puis construit un classificateur basé sur la couche de convolution et conçoit une fonction de perte basée sur la mesure de distance. Les réseaux sont entraînés en deux étapes : dans la première étape, la fonction de perte de mesure de distance est utilisée pour entraîner le réseau d'extraction de caractéristiques ; dans la deuxième étape, l'entropie croisée est utilisée pour entraîner l'ensemble du modèle. L'ensemble de données de référence public MSTAR est utilisé pour les expériences. Les expériences de comparaison prouvent que la méthode proposée a une précision supérieure aux algorithmes de pointe et aux algorithmes de reconnaissance d'images classiques. Les résultats de l’expérience d’ablation prouvent l’efficacité de chaque partie de l’algorithme proposé."> <meta name="DC.type" content=""> <meta name="DC.relation.ispartof" content="IEICE Transactions sur la communication"> <meta name="DC.publisher" content="L'Institut des ingénieurs en électronique, information et communication">    <script async="" src="https://www.googletagmanager.com/gtag/js?id=G-FKRLDTXBR3"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-FKRLDTXBR3'); </script> <link rel="canonical" href="https://globals.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <link rel="alternate" hreflang="x-default" href="https://global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <link rel="alternate" hreflang="ja" href="https://ja.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <link rel="alternate" hreflang="zh-cn" href="https://zh-cn.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <link rel="alternate" hreflang="zh-tw" href="https://zh-tw.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <link rel="alternate" hreflang="ko" href="https://ko.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <link rel="alternate" hreflang="fr" href="https://fr.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <link rel="alternate" hreflang="es" href="https://es.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <link rel="alternate" hreflang="pt" href="https://pt.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <link rel="alternate" hreflang="de" href="https://de.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <link rel="alternate" hreflang="it" href="https://it.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <link rel="alternate" hreflang="ru" href="https://ru.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <link rel="alternate" hreflang="th" href="https://th.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <link rel="alternate" hreflang="id" href="https://id.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <link rel="alternate" hreflang="ms" href="https://ms.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <link rel="alternate" hreflang="vi" href="https://vi.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <link rel="alternate" hreflang="uk" href="https://uk.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f"> <meta name="robots" content="noindex"> <meta http-equiv="Pragma" content="no-cache"> <meta http-equiv="Cache-Control" content="no-cache"> <meta http-equiv="Expires" content="0"> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Accueil","item":"https:\/\/global.ieice.org"},{"@type":"ListItem","position":2,"name":"IEICE TRANSACTIONS sur la communication","item":"https:\/\/fr.global.ieice.org\/en_transactions\/communications"},{"@type":"ListItem","position":3,"name":"Tome E107-B n°12","item":"https:\/\/fr.global.ieice.org\/en_transactions\/communications\/E107-B_12"},{"@type":"ListItem","position":4,"name":"Un algorithme basé sur la mesure de distance pour la reconnaissance d'images SAR"}]}</script> </head> <body class="full-html">  <noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-TF44WCG2" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>   <section id="wrapper" class="second b"> <div id="header"></div> <section class="form_box">  <style> .formsel_box { background-color: #fff; 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Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".<br> <span class="copyright js-modal-open" data-target="modal_copyright">Copyrights notice</span> </p> </div> <div class="note_bottom move"><span class="icon"><i class="fas fa-exclamation-triangle"></i></span> <p id="skip_info" class="notranslate">The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. <span class="copyright js-modal-open" data-target="modal_copyright">Copyrights notice</span></p> <p class="close"><i class="fas fa-times-circle"></i></p> </div> <section class="summary_box">  <h3><span id="skip_info" class="notranslate"><span class="open_access2">Open Access</span><br><span class="TEXT-SUMMARY-TITLE" data-gt-block="">An Algorithm Based on Distance Measurement for SAR Image Recognition</span></span> <span class="sub"><span class="open_access2">Open Access</span><br><span class="TEXT-SUMMARY-TITLE" data-gt-block="">Un algorithme basé sur la mesure de distance pour la reconnaissance d'images SAR</span></span> </h3> <p class="notranslate author" id="skip_info"><span class="TEXT-AUTHOR">Yuxiu LIU</span>, <span class="TEXT-AUTHOR">Na WEI</span>, <span class="TEXT-AUTHOR">Yongjie LI</span></p>  <div class="score_action_box"> <div class="score_box"> <ul> <li> <p class="score_name">Vues en texte intégral</p> <p class="score">6</p> </li> </ul> </div> <div class="action_box"> <ul> <li> <span class="cap js-modal-open" data-tippy-content="Add to My Favorites" data-target="modal_sign_personal"> <a href="add_favorites/e107-b_12_989/"><i class="fas fa fa-star" style="color: #C0C0C0"></i></a> </span> </li> <li class="share"><span class="cap" data-tippy-content="share"><a href="#"><i class="fas fa-share-alt-square"></i></a></span></li> <li class="cite js-modal-open" data-target="modal_cite">Citer</li>  <style> .box_ppv:hover { background: #b03527; } .box_ppv { padding: 0.5em 0.5em; background: #FFF; border: solid 1px #b03527; border-radius: 50px; height: 25px; } .box_ppv p { margin: 0; padding: 0; } .hover-text:hover { opacity: 1; color: #FFF; } .hover-text { color: #b03527; } </style><li class="pdf" style="width: 200px;"><a href="https://fr.global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_pdf" onclick="ga('send', 'event', 'PDF', 'Down Load', 'EB');" target="_blank" style="width: 200px;"><i class="fas fa-file-pdf"></i><span id="skip_info" class="notranslate">Free </span><span id="skip_info" class="notranslate">PDF (9.2MB) </span></a></li> </ul> </div> </div> <style> .pdf1 { border: none; width: auto; } .pdf1 a { display: block; text-decoration: none; background-color: #fff; border: solid 1px #b03527; text-align: center; width: 200px; height: 40px; line-height: 40px; border-radius: 25px; font-size: 16px; color: #b03527; } .pdf1 i { margin-right: 10px; } .pdf1 a:hover { opacity: 1; background-color: #b03527; color: #fff; } .pdf_errata { display: block; text-decoration: none; background-color: #fff; border: solid 1px #b03527; text-align: center; width: 260px; height: 35px; line-height: 40px; border-radius: 25px; font-size: 14px; color: #b03527; margin-right: 3%; float: right; margin-top: -5%; margin-right: 80px; } .mmfile { display: block; text-decoration: none; background-color: #fff; border: solid 1px #b03527; text-align: center; width: 100px; height: 35px; line-height: 40px; border-radius: 25px; font-size: 14px; color: #b03527; margin-right: 10%; float: right; margin-top: -5%; margin-right: 235px; } .open_access2 { font-family: "noto-sans", sans-serif; font-weight: 400; font-style: normal; font-size: 14px; color: #fff; background-color: #b03527; padding: 2px 15px; border-radius: 5px; margin-left: 0px; position: relative; top: -1.5px; } </style>   <div class="summary" id="Summary"> <h4>Résumé:</h4> <div class="txt"> <p class="gt-block"> <span class="TEXT-COL">Ces dernières années, les réseaux neuronaux convolutionnels profonds (CNN) ont été largement utilisés dans la reconnaissance d'images radar à synthèse d'ouverture (SAR). Cependant, en raison de la difficulté d'obtenir des échantillons d'images SAR, les données d'apprentissage sont relativement peu nombreuses et le surajustement est facile à se produire lors de l'utilisation de CNNS traditionnels utilisés dans la reconnaissance d'images optiques. Dans cet article, un algorithme de reconnaissance d'images SAR basé sur CNN est proposé, qui peut réduire efficacement les paramètres du réseau, éviter le surajustement du modèle et améliorer la précision de la reconnaissance. L'algorithme construit d'abord un extracteur de caractéristiques de réseau convolutionnel avec un noyau de convolution de petite taille, puis construit un classificateur basé sur la couche de convolution et conçoit une fonction de perte basée sur la mesure de distance. Les réseaux sont entraînés en deux étapes : dans la première étape, la fonction de perte de mesure de distance est utilisée pour entraîner le réseau d'extraction de caractéristiques ; dans la deuxième étape, l'entropie croisée est utilisée pour entraîner l'ensemble du modèle. L'ensemble de données de référence public MSTAR est utilisé pour les expériences. Les expériences de comparaison prouvent que la méthode proposée a une précision supérieure aux algorithmes de pointe et aux algorithmes de reconnaissance d'images classiques. Les résultats de l’expérience d’ablation prouvent l’efficacité de chaque partie de l’algorithme proposé.</span> </p> </div> <div class="data"> <dl> <dt>Publication</dt> <dd> <span id="skip_info" class="notranslate"> <span class="TEXT-COL">IEICE TRANSACTIONS on Communications <a href="https://fr.global.ieice.org/en_transactions/communications/E107-B_12">Vol.<span class="TEXT-COL">E107-B</span></a> No.<span class="TEXT-COL">12 pp.989-997</span> </span> </span></dd> </dl> <dl> <dt>Date de publication</dt> <dd><span class="TEXT-COL">2024/12/01</span></dd> </dl> <dl> <dt>Publicisé</dt> <dd><span class="TEXT-COL"></span></dd> </dl> <dl> <dt>ISSN en ligne</dt> <dd><span class="TEXT-COL">1745-1345</span></dd> </dl> <dl> <dt><span id="skip_info" class="notranslate">DOI</span></dt> <dd><span id="skip_info" class="notranslate"><span class="TEXT-COL">10.23919/transcom.2023EBP3179</span></span></dd> </dl> <dl> <dt>Type de manuscrit</dt> <dd><span id="skip_info" class="notranslate"><span class="TEXT-COL">PAPER</span><br></span></dd> </dl> <dl> <dt>Catégories</dt> <dd><span class="TEXT-COL">Détection</span></dd> </dl>  </div> </div> <div class="content">  <div class="txt"> <p> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ tex2jax: { inlineMath: [ ['$','$'], ["\$","\$"] ], displayMath: [ ['$$','$$'], ["\\[","\\]"] ], processEnvironments: true, processEscapes: true, ignoreClass: "mathjax-off" }, CommonHTML: { linebreaks: { automatic: true } }, "HTML-CSS": { linebreaks: { automatic: true } }, SVG: { linebreaks: { automatic: true } }, }); </script> <script async="" src="https://cdn.jsdelivr.net/npm/mathjax@2.7.5/MathJax.js?config=TeX-AMS-MML_HTMLorMML-full"></script> <link rel="stylesheet" type="text/css" href="https://global.ieice.org/full_text/full.css"> </p><div class="gt-block fj-sec" data-gt-block="">  <div> <h4 id="sec_1" class="gt-block headline" data-gt-block=""><span></span>1. Introduction</h4> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>Synthetic aperture radar (SAR) can realize high-resolution microwave remote sensing imaging by using the principle of synthetic aperture, which has advantages of all-sky, all-weather and strong penetration etc., and has important application value in Marine monitoring, environmental analysis, military reconnaissance and geological survey [1], [2]. However, the principle of SAR imaging determines that SAR images have strong speckle noise and geometric distortion [3], [4], which poses challenges to SAR image interpretation. Automatic Target Recognition (ATR) which integrates image detection, sign extraction, and image recognition processes, is one of the key technologies for achieving automatic interpretation of SAR images [5]-[7].</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>Image recognition, as the last crucial aspect of ATR, has been the focus of SAR imaging research. Traditional SAR image recognition methods mainly include two steps: feature extraction and classification recognition. The commonly used extracted features include geometric features, projection features and scattering features [8], [9], and the general classification and recognition algorithms include K-Nearest Neighbor classifier (KNN) [10], support vector machine (SVM) [11], sparse representation classifier [11], [12], etc. Traditional SAR image recognition methods have achieved good results and brought certain research progress to SAR ATR. However, the effectiveness of these methods requires experts to manually extract features, which is complicated, inefficient and poor robustness. For different SAR datasets and usage scenarios, feature extraction algorithms need to be redesigned.</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>In recent years, with the development of deep learning technology, especially the development of convolutional neural networks, the research of image recognition technology has made remarkable progress. The proposal and successful application of AlexNet [13] marked the beginning of the development of deep learning, followed by VGGNet [14] and Restnet [15], which made breakthroughs in natural image recognition. Inspired by the achievements of deep learning in optical images, researchers try to apply deep learning to SAR image recognition. Deep learning is an end-to-end learning method that unifies feature extraction and classification recognition. It can automatically learn the required features based on the learning objectives without the need for additional feature extraction algorithms, reducing manual work and greatly improving the robustness of the algorithm. However, deep learning algorithms require a large amount of training data, while obtaining SAR image training data is difficult compared to optical images. As a result, the available samples for SAR image training are relatively few. Directly applying ordinary optical image recognition algorithms to SAR image recognition can easily cause the overfitting phenomenon [16]-[18]. Therefore, multiple researchers have conducted in-depth research on the application of deep learning in SAR image recognition. Y. Li [19] used CNN networks to extract SAR image features, and used meta-learning training methods and distance metric loss functions to classify images. High recognition accuracy was achieved on both OPENSARSHIP and MSTAR datasets. Jian Guan [20] proposed a CNN network that combines multiple-size convolutional kernels and dense residual networks. The method combines the cosine loss function and cross-entropy loss function to train the network in two stages and performs well in small sample data scenarios. Ying Zhang [21] proposed a training method for convolutional networks, which combines deep metric learning (DML) and an imbalanced sampling strategy to improve classification performance in the imbalanced training sample scenario. Zhang Ting [12] used CNN networks to extract multi-layer depth features of SAR images to improve recognition accuracy. S. Chen [17] used a fully convolutional network to reduce parameters while achieving high recognition accuracy.</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>Through the in-depth study of convolutional neural networks, the above algorithms have achieved good results in SAR image recognition scenes. Inspired by the above research, this article proposes a SAR image recognition algorithm based on distance measurement and small-size convolutional networks, which aims to simplify the network structure, prevent overfitting and improve the recognition accuracy. The paper carries out work from optimizing several aspects including loss function, network structure and training method. The main innovations of this paper are as follows:</p> <div> <ol class="list-style-decimal"> <li> <p>A small-size convolutional kernel convolutional network was constructed to form the backbone of the whole model, which can reduce the number of parameters of the model and improve the final image recognition rate.</p> </li> <li> <p>A loss function based on distance measurement is proposed, which considers the distance from samples to the class centre, the distance between class centres, and the class variance, to guide the model to train in the direction of intra-class aggregation and inter-class dispersion.</p> </li> <li> <p>A convolutional network classifier has been constructed, which reduces model parameters and improves model performance when compared with traditional linear layer classifiers.</p> </li> <li> <p>A two-stage training method is proposed. In the first stage, the distance metric loss function is used to train the feature extraction network, and the cross-entropy is used to train the classification in the second stage. Comparative experiments show the effectiveness of this method.</p> </li> </ol> </div> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>The rest of this paper is organized as follows: Section 2 introduces the algorithm proposed in this paper, Sect. 3 introduces the experimental results, and Sect. 4 summarises the work.</p> </div>  <div class="fj-pagetop"><a href="#top">Haut de page</a></div> </div> <div class="gt-block fj-sec" data-gt-block=""> <div> <h4 id="sec_2" class="gt-block headline" data-gt-block=""><span></span>2.  SAR Image Recognition Algorithm Based on Distance Measurement and Small-Size Convolutional Network</h4> <div> <h5 id="sec_2_1" class="gt-block headline" data-gt-block=""><span></span>2.1  Overall Framework</h5> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>The overall framework of the image recognition method is shown in Fig. 1. The entire process is divided into three stages. The first stage is the feature extractor training stage, in which the distance measurement loss function is used. After the first stage is completed, it goes into the second stage, in which a convolutional layer is added to the feature extraction network as a classifier and the cross-entropy loss function is used to fine-tune the whole network. After completion, a trained image recognition model is obtained. In the third stage, the performance of the model is tested using a test dataset.</p> <div id="fig_1" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f01.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f01.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Fig. 1</b>  Overall framework of algorithm.</p></td> </tr> </tbody> </table> </div> </div> <div> <h5 id="sec_2_2" class="gt-block headline" data-gt-block=""><span></span>2.2 Fonction de perte</h5> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>In this paper, the algorithm is trained in two stages. In the first stage, the distance measurement method is used to calculate the loss, and in the second stage, the cross-entropy is used to calculate the loss. The loss function is written as follows: </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} loss=\left\{ \begin{matrix} loss_{distance}\ \ \ \ 0<E<{{E}_{1}} \\ loss_{cross\_entropy}\ \ {{E}_{1}}<E<{{E}_{2}} \\ \end{matrix} \right.\ \ \tag{1} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> dans lequel <span id="skip_info" class="notranslate">$E$</span> is the epoch variant, <span id="skip_info" class="notranslate">${E}_{1}$</span> is the epoch num in the first stage, <span id="skip_info" class="notranslate">${E}_{2}$</span> is the total epoch num.</p> <div> <h6 id="sec_2_2_1" class="gt-block headline" data-gt-block=""><span></span>2.2.1  Loss Function in the First Stage</h6> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>The formula designed in this paper synthesizes three considerations: the distance from samples to their class centre, the distance between class centres, and the class variance, so as to guide the model to train towards the direction of intra-class aggregation and inter-class dispersion. The formula for the distance measurement loss is: </p> <div id="math_2" class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} loss_{distance}\!=\!\alpha \cdot loss_{s-c}+\beta \cdot loss_{var}+(1-\alpha -\beta )\cdot loss_{c-c} \tag{2} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> dans lequel, <span id="skip_info" class="notranslate">$los{s_{s - c}}$</span> is the loss of distance from the sample to its class centre, <span id="skip_info" class="notranslate">$los{s_{{\mathop{\rm var}} }}$</span> is the loss of the class variance, <span id="skip_info" class="notranslate">$los{s_{c - c}}$</span> is the loss of distance between class centres, <span id="skip_info" class="notranslate">$\alpha$</span> et <span id="skip_info" class="notranslate">$\beta$</span> are the hyper-parameters. The following describes the detailed calculation methods of the three parts.</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span><span id="skip_info" class="notranslate">$los{s_{s - c}}$</span> is calculated by taking the average of the distance loss from each sample to its class centre. The formula is: </p> <div id="math_3" class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} los{s_{s - c}} = \frac{{\sum\limits_{i = 1}^N {los{s_{}}({x_i})} }}{N} \tag{3} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> où <span id="skip_info" class="notranslate">${los{s_{}}({x_i})}$</span> is the distance loss from the i-th sample to its class centre, N is the total number of samples in the current batch, <span id="skip_info" class="notranslate">${los{s_{}}({x_i})}$</span> is calculated by the formula: </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} loss({x_i}) = - \log (\frac{{{e^{ - Dis({x_i},{c_{y_{i}}})}}}}{{\sum\limits_{l = 0}^{L\text{$-$1}} {{e^{ - Dis({x_i},{c_l})}}} }}) \tag{4} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> dans lequel, <span id="skip_info" class="notranslate">${{y}_{i}}\in \{0...L-1\}$</span> is the label of <span id="skip_info" class="notranslate">$x_i$</span> et <span id="skip_info" class="notranslate">$Dis({x_i},{c_l})$</span>is the distance from the i-th sample to the l-th class centre. The paper uses Euclidean distance which is calculated by: </p> <div id="math_5" class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{eqnarray*} Dis({{x}_{i}},{{c}_{l}})=\sqrt{\sum\limits_{m=0}^{M-1}{{{({{f}_{\theta }}{{({{x}_{i}})}_{[m]}}-{{c}_{l[m]}})}^{2}}}} \tag{5} \end{eqnarray*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> Où <span id="skip_info" class="notranslate">${f_\theta }({x_i})$</span> is the feature vector output of the sample <span id="skip_info" class="notranslate">$x_i$</span> through the feature extraction network, M is the feature vector dimension and <span id="skip_info" class="notranslate">${{f}_{\theta }}{{(x_{i}^{{}})}_{[m]}}$</span> is the m-th dimension of <span id="skip_info" class="notranslate">${f_\theta }({x_i})$</span>. <span id="skip_info" class="notranslate">$c_l$</span> is the l-th class centre, which is the mean value of feature vectors belonging to the l-th class in this batch, <span id="skip_info" class="notranslate">$c_{l[m]}$</span> is the m-th dimension of <span id="skip_info" class="notranslate">$c_l$</span>. <span id="skip_info" class="notranslate">$c_l$</span> est calculé par : </p> <div id="math_6" class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} c_l=\frac{1}{\left| I(l) \right|}\sum\limits_{i\in I(l)}{{{f}_{\theta }}{({x_i})}} \tag{6} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> dans lequel, <span id="skip_info" class="notranslate">$I\equiv \{1...N\}$</span> is the set of indices of all input samples in current batch, <span id="skip_info" class="notranslate">$I(l)\equiv \{p \in I:{{y}_{p}}=l\}$</span> is the set of indices of samples whose label is <span id="skip_info" class="notranslate">$l$</span>. <span id="skip_info" class="notranslate">$\left| I(l) \right|$</span> is its cardinality. It should be noted that <span id="skip_info" class="notranslate">$c_l$</span> will be updated in each batch.</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span><span id="skip_info" class="notranslate">$los{s_{{\mathop{\rm var}} }}$</span> is the loss of sample variance in the same class, and is calculated by: </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} loss_{var} = \frac{1}{L}\sum\limits_{l = 0}^{L\text{$-$1}} {{{{\mathop{\rm var}} }_l}} \tag{7} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> où <span id="skip_info" class="notranslate">$var_l$</span> is the variance of the l-th class, and is calculated by: </p> <div id="math_8" class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} {{\operatorname{var}}_{l}}=\sum\limits_{m=0}^{M-1}{\operatorname{var}({{f}_{\theta }}{{({{X(l)}})}_{[m]}})} \tag{8} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> où <span id="skip_info" class="notranslate">$X(l)\equiv \{{{x}_{i}}:i\in I(l)\}$</span> is the sample set whose label is <span id="skip_info" class="notranslate">$l$</span>, <span id="skip_info" class="notranslate">$var(\centerdot )$</span> is the variance function.</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span><span id="skip_info" class="notranslate">$los{s_{c - c}}$</span> is the loss of distance between class centres. After training, the larger the distance of inter-class, the better the classification effect of the model. However, the absolute distance cannot reflect the distinguishing ability between classes. In this paper, the distance between class centres is compared with the variance of samples belonging to this class. The larger the value, the bigger the difference exists between classes. Figure 2 shows the meaning. Figure 2(a) and Fig. 2(b) have the same distance between class centres, but Fig. 2(a) has a better distinguishing effect. <span id="skip_info" class="notranslate">$los{s_{c - c}}$</span> is calculated by the formula: </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{eqnarray*} &&\!\!\!\!\! los{{s}_{c-c}}=\sum\limits_{i=0}^{L\text{$-$1}}{\frac{1}{DisFunc({{c}_{i}})}} \tag{9} \\ &&\!\!\!\!\! DisFunc({{c}_{i}})=\sum\limits_{l=0}^{L\text{$-$1}}{\frac{D\text{is}({{c}_{i}}, {{c}_{l}})}{{{\operatorname{var}}_{i}}+{{\operatorname{var}}_{l}}}} \tag{10} \end{eqnarray*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> in which the l-th class centre <span id="skip_info" class="notranslate">$c_l$</span> is calculated by formula (6), the l-th class sample variance <span id="skip_info" class="notranslate">$var_l$</span> is calculated by formula (8), <span id="skip_info" class="notranslate">$Dis({c_i},{c_l})$</span> is the Euclidean distance between the centre of the i-th class and the l-th class.</p> <div id="fig_2" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f02.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f02.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Fig. 2</b>  Influence of the ratio of the distance between category centres and variance on discrimination ability. The distance between the two class centres is the same in (a) and (b), but in (a), the variance is smaller and the discrimination ability is stronger, and in (b), the variance is larger and the discrimination ability is weaker.</p></td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>Distance measurement has been applied to both prototype networks [22], supervised contrast learning [23] and Improved Triplet Loss [24], but there are differences in its connotation. In the prototype network, the distance metric loss function is defined as: </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{eqnarray*} &&\!\!\!\!\! loss({{x}_{i}})=-\log (\frac{{{e}^{-Dis({{x}_{i}},{{c}_{y_{i}}})}}}{\sum\limits_{l=0}^{L\text{$-$1}} {{{e}^{-Dis({{x}_{i}},{{c}_{l}})}}}}) \tag{11} \\ &&\!\!\!\!\! loss=\frac{1}{N}\sum\limits_{i=1}^{N}{loss({{x}_{i}})} \tag{12} \end{eqnarray*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block fj-p-no-indent" data-gt-block=""><span></span> </p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>The loss function of the supervised contrast learning is defined as: </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} \begin{aligned} loss&=\sum\limits_{i\in I}{loss({{x}_{i}})} \\ &=\sum\limits_{i\in I}{\frac{-1}{\left| P(i) \right|}\sum\limits_{p\in P(i)}{\log (\frac{{{e}^{{{f}_{\theta }}({{x}_{i}})\centerdot {{f}_{\theta }}({{x}_{p}})/\tau }}}{\sum\limits_{a\in A(i)}{{{e}^{{{f}_{\theta }}({{x}_{i}})\centerdot {{f}_{\theta }}({{x}_{a}})/\tau }}}})}} \end{aligned} \tag{13} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> dans lequel, <span id="skip_info" class="notranslate">$I\equiv \{1...N\}$</span> is the set of indices of all input samples in the current batch, <span id="skip_info" class="notranslate">$A(i)\equiv I\backslash \{i\}$</span> is the set of I excluded i, <span id="skip_info" class="notranslate">$P(i)\equiv \{p\in A(i):{{y}_{p}}={{y}_{i}}\}$</span> is the set of indices of all positives in the batch distinct from i, and <span id="skip_info" class="notranslate">$\left| P(i) \right|$</span> is its cardinality, <span id="skip_info" class="notranslate">$\tau$</span> is the temperature hyper-parameter.</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>In the Improved Triplet Loss, denote <span id="skip_info" class="notranslate">${{X}_{\text{i}}}\text{=}<X_{i}^{o},X_{i}^{+},X_{i}^{-}>$</span> as a group of input, in which <span id="skip_info" class="notranslate">$X_{i}^{o}$</span> et <span id="skip_info" class="notranslate">$X_{i}^{+}$</span> belong to the same class, <span id="skip_info" class="notranslate">$X_{i}^{o}$</span> et <span id="skip_info" class="notranslate">$X_{i}^{-}$</span> are in different classes. The loss function is defined as: </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{aligned} & \mbox{$\displaystyle loss=\frac{1}{N}\sum\limits_{i=1}^{N}{(\max \{{{d}^{n}}\text{(X}_{i}^{o},X_{i}^{+},X_{i}^{-}),{{\tau }_{1}}\} +\beta \max \{{{d}^{p}}\text{(X}_{i}^{o},X_{i}^{+}),{{\tau }_{2}}\})} $} & \end{aligned}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> où <span id="skip_info" class="notranslate">${{\tau }_{1}}$</span>, <span id="skip_info" class="notranslate">${{\tau }_{2}}$</span> et <span id="skip_info" class="notranslate">$\beta$</span> are the hyper-parameters, and: </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{eqnarray*} &&\!\!\!\!\! {{d}^{n}}\text{(X}_{i}^{o},X_{i}^{+},X_{i}^{-})=d({{f}_{\theta }}(X_{i}^{o}),{{f}_{\theta }}(X_{i}^{+}))-d({{f}_{\theta }}(X_{i}^{o}),{{f}_{\theta }}(X_{i}^{-}))\\ &&\!\!\!\!\! {{d}^{p}}\text{(X}_{i}^{o},X_{i}^{+})=d({{f}_{\theta }}(X_{i}^{o}),{{f}_{\theta }}(X_{i}^{+}))\\ &&\!\!\!\!\! d({{f}_{\theta }}(X_{i}^{o}),{{f}_{\theta }}(X_{i}^{+}))=||{{f}_{\theta }}(X_{i}^{o})-{{f}_{\theta }}(X_{i}^{+})|{{|}^{2}} \end{eqnarray*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block fj-p-no-indent" data-gt-block=""><span></span> </p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>From the above formulas, it can be seen that in the prototype network, only the distance between the sample and the centre of samples in the same class (prototype) is used. In supervised comparative learning, only the distance between the sample and other samples in the same class is considered. In Improved Triplet Loss, only the distance between samples belongs to the same class and different classes are used. So all of them only consider the relationship between the sample and other samples. In addition to the above, this article further considers the internal variance of samples of the same class and the distance between different class centres. This paper simultaneously considers both individual and overall loss of the sample, to guide the model to be trained towards the direction of intra-class aggregation and inter-class dispersion comprehensively.</p> </div> <div> <h6 id="sec_2_2_2" class="gt-block headline" data-gt-block=""><span></span>2.2.2  Loss Function in the Second Stage</h6> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>The cross-entropy function is used to calculate the loss in the second stage, the formula is: </p> <div class="fj-math-table-wrap"> <table class="fj-math-table"> <tbody> <tr> <td id="skip_info" class="notranslate">\[\begin{equation*} los{{s}_{cross\_entropy}}=\text{$-$}\frac{1}{N}\sum\limits_{i=1}^{N}{\log (\frac{{{e}^{g{{({{x}_{i}})}_{[{{y}_{i}}]}}}}} {\sum\limits_{l=0}^{L-1}{{{e}^{g{{({{x}_{i}})}_{[l]}}}}}})}\ \ \ \ \tag{14} \end{equation*}\]</td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span> where N is the number of samples in this batch, and, <span id="skip_info" class="notranslate">$g({{x}_{i}})$</span> is the output of classifier for the sample <span id="skip_info" class="notranslate">${x}_{i}$</span>, whose dimension is L, <span id="skip_info" class="notranslate">$g{{({{x}_{i}})}_{[l]}}$</span> is the l-th dimension of <span id="skip_info" class="notranslate">$g({{x}_{i}})$</span>. <span id="skip_info" class="notranslate">${{y}_{i}}\in \{0...L-1\}$</span> is the label of <span id="skip_info" class="notranslate">$x_i$</span>, <span id="skip_info" class="notranslate">$g{{({{x}_{i}})}_{[{{y}_{i}}]}}$</span> est le <span id="skip_info" class="notranslate">$y_i$</span>-th dimension of <span id="skip_info" class="notranslate">$g({{x}_{i}})$</span>.</p> </div> </div> <div> <h5 id="sec_2_3" class="gt-block headline" data-gt-block=""><span></span>2.3  Feature Extraction Network and Classifier</h5> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>In 2014, Karen Simonyan from Oxford University proposed VGGNet [14] and explored the depth of the network. Due to its simplicity and practicality, it quickly became the most popular convolutional neural network at that time. The inspirations brought by the VGGNet include: (1) Replacing a large convolutional layer with multiple small convolutional layers can obtain the same receptive field size, but significantly reduces parameter size and computational complexity; (2) Using a unified 2x2 max-pool with a stride of 2 to increase local information diversity and reduce feature size, can better capture local information changes and describe edge and texture structures.</p> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>Inspired by VGGNet, a feature extraction network composed of small-size convolutional layers and a classifier composed of a convolutional layer is designed, as shown in Fig. 3. The feature extraction network consists of 5 convolutional blocks. Each block is composed of two 3x3 convolutional layers, one Batch-Normalize layer, one RELU activation layer, and one max-pool pooling layer. The pooling layer’s size is 2x2 and the stride is 2, it can reduce the feature map size by half. Except for the first convolution block, the number of channels in the first convolution layer of each other convolution block is doubled. In order to reduce network parameters, increase network robustness and avoid overfitting, the 1x1 convolution layer rather than the conventional linear layer is used as the network classifier.</p> <div id="fig_3" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f03.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f03.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Fig. 3</b>  Network structure of proposed algorithm.</p></td> </tr> </tbody> </table> </div> </div> </div> <div class="fj-pagetop"><a href="#top">Haut de page</a></div> </div> <div class="gt-block fj-sec" data-gt-block=""> <div> <h4 id="sec_3" class="gt-block headline" data-gt-block=""><span></span>3. Expériences</h4> <div> <h5 id="sec_3_1" class="gt-block headline" data-gt-block=""><span></span>3.1  Dataset and Parameter Configuration</h5> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>This article uses the MSTAR dataset to verify the performance of the proposed algorithm. The MSTAR dataset is a public dataset for SAR automatic target recognition provided by the US Advanced Research Projects Agency and the Air Force Laboratory (DARPA/AFRL). The images are obtained by an X-band HH polarized constrained radar with resolution of 0.3 m <span id="skip_info" class="notranslate">$\times$</span> 0.3 m. In this paper, 10 types of military ground target data in the Standard Operating Conditions (SOC) of the MSTAR dataset are selected for experiments. The distribution of the dataset is shown in Table 1.</p> <div id="table_1" class="fj-table-g"> <table> <tbody> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Tableau 1</b>  MSTAR SOC training dataset and test dataset.</p></td> </tr> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t01.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t01.jpg" class="fj-table-graphic"></a></td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>In the experiment, Pytorch was used under Ubuntu 20.04 LTS and GPU RTX 3090 was used to accelerate calculation. The experiment parameters were configured as follows: Batch size (N in Eq. (3)) was 100; The dimension of the feature extractor output (M in Eq. (5)) was 512; Adamw optimizer was selected with the learning rate setting to 0.001 and the weight decay setting to 0.004.</p> </div> <div> <h5 id="sec_3_2" class="gt-block headline" data-gt-block=""><span></span>3.2  Training and Test Experiments </h5> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>Figure 4 shows the loss and accuracy changing as the iteration progresses. Figure 4(a) and Fig. 4(b) represent the results in the first stage, and Fig. 4(c) and Fig. 4(d) represent the results in the second stage. As shown in the figure, in the initial stage of training, the loss value drops rapidly and the model converges quickly. In the second stage, the accuracy of training data rises faster than that in the first stage, and the model converges faster. By the 10th round of training, the accuracy has already reached its maximum value, indicating that the model has been adjusted to near the optimal value after the first stage of training.</p> <div id="fig_4" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f04.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f04.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Fig. 4</b>  Model training data (for training data). (a) Loss at stage 1. (b) Accuracy at stage 1. (c) Loss at stage 2. (d) Accuracy at stage 2.</p></td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>Figure 5 shows the confusion matrix evaluated by the trained model on the test dataset. It can be seen that the recognition accuracy is high, even reaching 100% for some classes, and the average recognition accuracy is 99.67%, which proves the effectiveness of this model.</p> <div id="fig_5" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f05.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f05.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Fig. 5</b>  Confusion matrix.</p></td> </tr> </tbody> </table> </div> </div> <div> <h5 id="sec_3_3" class="gt-block headline" data-gt-block=""><span></span>3.3 Expériences comparatives</h5> <div> <h6 id="sec_3_3_1" class="gt-block headline" data-gt-block=""><span></span>3.3.1  Comparison with Algorithms in Other Literature</h6> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>In order to further prove the effectiveness of the proposed algorithm, this paper compares the proposed algorithms with literatures [17], [20], [24], classical image recognition convolutional networks VGG16, ResNet-50, and ResNet-18. This article selects data from the MSTAR dataset both in standard operating conditions (SOC) and extended operating conditions (EOC) for comparative experiments. Compared to SOC, EOC data has a greater difference between the training and testing datasets. This article selects two types of EOC datasets (denoted by EOC-1 and EOC-2) that are consistent with reference [17]. In EOC-1, there is a significant difference in the depression angle between the training and test dataset. The training dataset is composed of four targets (2S1, BRDM-2, T-72, and ZSU-234) in the 17<span id="skip_info" class="notranslate">$^\circ$</span> depression angle chosen from Table 1, and the test dataset (shown in Table 2) is composed of data in the 30<span id="skip_info" class="notranslate">$^\circ$</span> depression angle. In EOC-2, there are significant differences in the serial numbers and configurations of targets between the training and test datasets. The training set is composed of four targets (BMP-2, BRDM-2, BTR-70, and T-72) in the 17<span id="skip_info" class="notranslate">$^\circ$</span> depression angle chosen from Table 1, while the test set contains two groups listed in Table 3 (EOC-2-1) and Table 4 (EOC-2-2), corresponding to configuration variants and version variants.</p> <div id="table_2" class="fj-table-g"> <table> <tbody> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Tableau 2</b>  EOC-1 test dataset (large depression variant).</p></td> </tr> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t02.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t02.jpg" class="fj-table-graphic"></a></td> </tr> </tbody> </table> </div> <div id="table_3" class="fj-table-g"> <table> <tbody> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Tableau 3</b>  EOC-2-1 test dataset (configuration variants).</p></td> </tr> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t03.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t03.jpg" class="fj-table-graphic"></a></td> </tr> </tbody> </table> </div> <div id="table_4" class="fj-table-g"> <table> <tbody> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Tableau 4</b>  EOC-2-2 test dataset (version variants).</p></td> </tr> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t04.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t04.jpg" class="fj-table-graphic"></a></td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>The comparative experimental results are shown in Table 5, in which the results of the literature [17], [20] are obtained from the original data of the literature. Results of VGG16, ResNet-50 and ResNet-18 are obtained through the experiment using the same parameter as the proposed algorithm in this paper. The results of Improved Triplet Loss algorithmn are obtained by replacing the distance measurement method proposed in this paper with that in reference [24], and keeping other parameters and training methods in accordance with this paper. It can be seen from the table that VGG16 performs the worst, followed by ResNet-50. This is mainly due to that the VGG16 and ResNet-50 have a large number of parameters by adopting multiple fully connected layers and multiple layers respectively, and the algorithm complexity comparison can be found in Sect. 3.3.4. Because of the difficulty of obtaining SAR images, the available samples for SAR image training are relatively few, and a model with a big parameter number can easily cause overfitting and performance degradation phenomenon [17]. The models of ResNet-18, literature [17], literature [20], Improved Triplet Loss [24], and this paper have fewer parameters compared to the first two, so their performance is better, reaching over 99% in the SOC dataset. The algorithm proposed in this paper not only achieves optimal performance under the SOC dataset, but also outperforms other algorithms under various EOC datasets, further proving the superiority of the proposed method.</p> <div id="table_5" class="fj-table-g"> <table> <tbody> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Tableau 5</b>  Comparison of accuracy with algorithms in other literature.</p></td> </tr> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t05.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t05.jpg" class="fj-table-graphic"></a></td> </tr> </tbody> </table> </div> </div> <div> <h6 id="sec_3_3_2" class="gt-block headline" data-gt-block=""><span></span>3.3.2  Comparison of Different Feature Extraction Networks (Backbones)</h6> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>To prove the superiority of the feature extraction network of the proposed algorithm, the feature extraction network was replaced as EfficientNetV2 [25] and MobileNetV3 [26], and comparative experiments were conducted on three types of networks under the same condition. The comparison results are shown in Table 6. It can be seen that the feature extraction network used in this paper has a significant advantage in accuracy compared to the other two.</p> <div id="table_6" class="fj-table-g"> <table> <tbody> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Tableau 6</b>  Comparison of experimental results of different feature extraction networks.</p></td> </tr> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t06.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t06.jpg" class="fj-table-graphic"></a></td> </tr> </tbody> </table> </div> </div> <div> <h6 id="sec_3_3_3" class="gt-block headline" data-gt-block=""><span></span>3.3.3  Comparison of Different Distance Measurement Methods</h6> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>In order to prove the superiority of the distance measurement method proposed in this paper, the loss function trained in the first stage is replaced by the loss function of the prototype network [22], the supervised contrastive learning network [23] and Improved Triplet Loss [24]. Experiments were conducted under the same conditions, and the comparison results are shown in Table 7. It can be seen that the algorithm proposed in this paper performs best. Using three different loss functions to train the model, the output features are dimensionally reduced by PCA, and the visualization results are shown in Fig. 6. It can be seen that the algorithm in this paper distinguishes each category more clearly and has a stronger classification ability.</p> <div id="table_7" class="fj-table-g"> <table> <tbody> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Tableau 7</b>  Comparison of different distance measurement loss functions.</p></td> </tr> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t07.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t07.jpg" class="fj-table-graphic"></a></td> </tr> </tbody> </table> </div> <div id="fig_6" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f06.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f06.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Fig. 6</b>  Visualization of the output features of models trained with different loss functions after PCA reduction. (a) Prototype network loss function. (b) Supervised contrast learning network loss function. (c) Improved Triplet Loss. (d) This paper.</p></td> </tr> </tbody> </table> </div> </div> <div> <h6 id="sec_3_3_4" class="gt-block headline" data-gt-block=""><span></span>3.3.4  Comparison of Algorithm Complexity</h6> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>Table 8 provides a comparison between our algorithm and other algorithms in terms of parameter size, floating point operations (FLOPs), and accuracy. It can be seen that the algorithm in this paper has the minimum parameter size, and FLOPs are only higher than MobileNetV3_S, but the accuracy is the highest. The overall algorithm complexity is low while ensuring a high recognition rate.</p> <div id="table_8" class="fj-table-g"> <table> <tbody> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Tableau 8</b>  Comparaison de la complexité des algorithmes.</p></td> </tr> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t08.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t08.jpg" class="fj-table-graphic"></a></td> </tr> </tbody> </table> </div> </div> </div> <div> <h5 id="sec_3_4" class="gt-block headline" data-gt-block=""><span></span>3.4 Expérience d'ablation</h5> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>In order to verify the effectiveness of the three design ideas proposed in this paper, namely, convolution classifier, small-size convolution kernel and distance measurement loss function(represented by A, B, and C respectively), this paper uses several variants of the algorithm to conduct ablation experiments, namely Variant 1: use a linear layer as the final classifier; Variant 2: use a 7x7 convolutional kernel instead of three 3x3 convolutional kernels, and use a 5x5 convolutional kernel instead of two 3x3 convolutional kernels; Variant 3: do not use the distance measurement loss function, and directly use cross entropy for training. The experimental results of the three variants are shown in Table 9, which shows that all three variants perform varying degrees of reduction in accuracy. Figure 7 shows their training processes, and it can be seen that after using the two-stage training method, the convergence speed of the second training is significantly accelerated due to the completion of the first training. From the embedded zoomed figure, we can see that Variant 1 has the worst performance, followed by Variant 2 which has large-scale convolution kernels, followed by Variant 3 with the model that does not use the distance metric. The model that does not make any changes has the best performance. This proves the effectiveness of convolution classifier, distance measurement loss function and small-size convolution. In addition, from the experimental results, it can be seen that the accuracy of variant 1 and variant 2 are relatively low, which can be ascribed to that the use of linear classifiers and large convolutional kernels has increased the number of model parameters to a certain extent, and the overfitting occurs. The phenomenon of performance degradation caused by increasing the number of parameters is also reflected in reference [17]. In this paper, the model can reduce the number of parameters by simplifying the network, thus supress overfitting to a certain extent.</p> <div id="table_9" class="fj-table-g"> <table> <tbody> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Tableau 9</b>  Ablation experiment result of variant algorithms.</p></td> </tr> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t09.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/t09.jpg" class="fj-table-graphic"></a></td> </tr> </tbody> </table> </div> <div id="fig_7" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f07.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f07.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Fig. 7</b>  Comparison of the training process of variant algorithms.</p></td> </tr> </tbody> </table> </div> <p class="gt-block gt-block fj-p" data-gt-block=""><span></span>Figure 8 shows the visualization of the feature extraction network’s output after PCA dimensionality reduction. Figure 8(a) and Fig. 8(b) show the results of the trained model with and without distance measurement loss function, respectively. It can be seen that after training with the distance measurement loss function, categories are distinguished more clearly and the classification ability is stronger.</p> <div id="fig_8" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f08.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f08.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Fig. 8</b>  Visualization of feature extraction network’s output after PCA dimensionality reduction. (a) The model trained with distance measurement loss. (b) The model trained without distance measurement loss.</p></td> </tr> </tbody> </table> </div> </div> <div> <h5 id="sec_3_5" class="gt-block headline" data-gt-block=""><span></span>3.5  Hyper-Parameter Settings</h5> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><span id="skip_info" class="notranslate">$\alpha$</span> et <span id="skip_info" class="notranslate">$\beta$</span> in Eq. (2) are the two important parameters of the loss function in this paper. Experiments were conducted by changing <span id="skip_info" class="notranslate">$\alpha$</span> et <span id="skip_info" class="notranslate">$\beta$</span> from 0.1 to 0.8 (we choose the value meet <span id="skip_info" class="notranslate">$\alpha \text{+}\beta <1$</span> since the ratio of <span id="skip_info" class="notranslate">$los{{s}_{c-c}}$</span> is <span id="skip_info" class="notranslate">$1\text{-}\alpha\text{-}\beta$</span>) respectively, other parameters are consistent with that in Sect. 3.1, and the accuracy results are shown in Fig. 9. It can be seen that high accuracy can be obtained at several points such as (<span id="skip_info" class="notranslate">$\alpha$</span>,<span id="skip_info" class="notranslate">$\beta$</span>)={(0.8,0.1),(0.3,0.2),(0.7,0.2)}. The paper chooses the point of (<span id="skip_info" class="notranslate">$\alpha$</span>= 0.8, <span id="skip_info" class="notranslate">$\beta$</span>= 0.1).</p> <div id="fig_9" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f09.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/f09.jpg" class="fj-fig-graphic"></a></td> </tr> <tr> <td><p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span><b>Fig. 9</b>  Results with different <span id="skip_info" class="notranslate">$\alpha$</span> et <span id="skip_info" class="notranslate">$\beta$</span> paramètres.</p></td> </tr> </tbody> </table> </div> </div> </div> <div class="fj-pagetop"><a href="#top">Haut de page</a></div> </div> <div class="gt-block fj-sec" data-gt-block=""> <div> <h4 id="sec_4" class="gt-block headline" data-gt-block=""><span></span>4.Conclusion</h4> <p class="gt-block gt-block fj-p-no-indent" data-gt-block=""><span></span>In order to improve the accuracy of SAR image recognition, this paper proposes a small-size full convolutional network based on distance measurement. The feature extraction part of the network is composed of multiple 3x3 convolution layers, and the classifier of the network is composed of a 1x1 convolution layer. The design of small-size and convolution classifiers improves accuracy while reducing network parameters and computational complexity. A loss function based on distance measurement is designed, which makes comprehensive use of the distance from the sample to the category centre, the distance between category centres and the variance of samples in the same category. Feature map visualization shows, after training with the distance measurement loss function, categories are distinguished more clearly and the features of samples in the same category are more clustered, the classification ability is stronger. Finally, multiple comparative experiments have shown that the method proposed in this paper is superior to the methods proposed in other papers and classic image recognition models.</p> </div> <div class="fj-pagetop"><a href="#top">Haut de page</a></div> </div> <div class="gt-block fj-sec" data-gt-block=""> <div id="skip_info" class="notranslate"> <h4 id="acknowledgments" class="headline" data-gt-block=""><span></span>Acknowledgments</h4> <p class="fj-p-no-indent" data-gt-block=""><span></span>The authors would like to thank Jinling Xing for full text statement and logicall review, and thank their colleagues in the lab for suggestions.</p> </div> <div class="fj-pagetop"><a href="#top">Haut de page</a></div> </div> <div id="sec-references" class="gt-block fj-sec" data-gt-block=""> <h4 id="references" class="gt-block headline" data-gt-block=""><span></span>Références </h4> <div id="skip_info" class="notranslate"> <div id="ref-1" class="fj-list-ref"> <p>[1] R. Yang, Z. Hu, Y. Liu, and Z. Xu, “A novel polarimetric sar classification method integrating pixel-based and patch-based classification,” IEEE Geosci. 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IEEE/CVF International Conference on Computer Vision, pp.1314-1324, 2019. <br><a target="_blank" href="https://doi.org/10.1109/iccv.2019.00140">CrossRef</a></p> </div> </div> <div class="fj-pagetop"><a href="#top">Haut de page</a></div> </div> <div id="sec-authors" class="fj-sec-authors"> <h4 id="authors" class="gt-block headline" data-gt-block=""><span></span>Auteurs</h4> <div id="skip_info" class="notranslate"> <div class="fj-author"> <b><a href="https://fr.global.ieice.org/en_transactions/Author/a_name=Yuxiu%20LIU"><span>Yuxiu LIU</span></a></b><br>  <span style="font-Size:15px;"><b>Naval University of Engineering</b></span><br> <p class="fj-p-no-indent" data-gt-block=""><span></span>received the B.S. in Communication engineering from Central South University in 2006, received the M.S. degrees in Signal and information processing from South China University of Technologyin 2013. During 2013-2019, she stayed in Microsoft (China) Co. LTD, studied news-related data. During 2019-2023, she is a lecturer in Naval University of engineering. Her research interests focus on image recognition.</p> <div id="graphic_1" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/a1.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/a1.jpg" class="fj-bio-graphic"></a></td> </tr> </tbody> </table> </div> </div> <div class="fj-author"> <b><a href="https://fr.global.ieice.org/en_transactions/Author/a_name=Na%20WEI"><span>Na WEI</span></a></b><br>  <span style="font-Size:15px;"><b>Naval University of Engineering</b></span><br> <p class="fj-p-no-indent" data-gt-block=""><span></span>born in 1980, received Ph.D. from Beijing University of Aeronautics and Astronautics in signal and information processing, reveived M.S. from Naval University of engineering in computer application technology, His research interests focus on pattern recognition.</p> <div id="graphic_2" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/a2.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/a2.jpg" class="fj-bio-graphic"></a></td> </tr> </tbody> </table> </div> </div> <div class="fj-author"> <b><a href="https://fr.global.ieice.org/en_transactions/Author/a_name=Yongjie%20LI"><span>Yongjie LI</span></a></b><br>  <span style="font-Size:15px;"><b>Naval University of Engineering</b></span><br> <p class="fj-p-no-indent" data-gt-block=""><span></span>born in 1977, received Ph.D. from Naval University of engineering in systems engineering and M.S. from Naval University of engineering in computer application technology. He is an associate professor in Naval University of engineering. His research interests focus on database and information techniques.</p> <div id="graphic_3" class="fj-fig-g"> <table> <tbody> <tr> <td><a target="_blank" href="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/a3.jpg"><img alt="" src="https://fr.global.ieice.org/full_text/transcom/E107.B/12/E107.B_989/Graphics/a3.jpg" class="fj-bio-graphic"></a></td> </tr> </tbody> </table> </div> </div> </div> <div class="fj-pagetop"><a href="#top">Haut de page</a></div> </div> <div> <p></p> <p></p> </div> </div>   </div> <div style="border-bottom: solid 1px #ccc;"></div> <h4 id="Keyword">Mots-clés</h4> <div> <p class="gt-block"> <a href="https://fr.global.ieice.org/en_transactions/Keyword/keyword=SAR%20image%20recognition"><span class="TEXT-COL">SAR image recognition</span></a>,  <a href="https://fr.global.ieice.org/en_transactions/Keyword/keyword=convolutional%20neural%20networks"><span class="TEXT-COL">réseaux de neurones convolutifs</span></a>,  <a href="https://fr.global.ieice.org/en_transactions/Keyword/keyword=distance%20measurement"><span class="TEXT-COL">mesure de distance</span></a>,  <a href="https://fr.global.ieice.org/en_transactions/Keyword/keyword=all%20convolutional%20network"><span class="TEXT-COL">all convolutional network</span></a> </p></div>  </section>  </div> <div class="right_box">   <section class="latest_issue"> <h4 id="skip_info" class="notranslate">Latest Issue</h4> <ul id="skip_info" class="notranslate"> <li class="a"><a href="https://fr.global.ieice.org/en_transactions/fundamentals">IEICE Trans. Fundamentals</a></li> <li class="b"><a href="https://fr.global.ieice.org/en_transactions/communications">IEICE Trans. Communications</a></li> <li class="c"><a href="https://fr.global.ieice.org/en_transactions/electronics">IEICE Trans. Electronics</a></li> <li class="d"><a href="https://fr.global.ieice.org/en_transactions/information">IEICE Trans. Inf. & Syst.</a></li> <li class="elex"><a href="https://fr.global.ieice.org/en_publications/elex">IEICE Electronics Express</a></li> </ul> </section> </div> <div class="index_box"> <h4>Table des matières</h4> <ul> <li><a href="#Summary">Résumé</a></li> <li> <ul> <li><a href="#sec_1">1. Introduction</a></li> <li><a href="#sec_2">2.  SAR Image Recognition Algorithm Based on Distance Measurement and Small-Size Convolutional Network</a></li> <li><a href="#sec_3">3. Expériences</a></li> <li><a href="#sec_4">4.Conclusion</a></li> </ul> </li> <li><a href="#acknowledgments">Remerciements</a></li> <li><a href="#references">Références </a></li> <li><a href="#authors">Auteurs</a></li> <li><a href="#Keyword">Mots-clés</a></li> </ul> </div> </div>  <div id="modal_copyright" class="modal js-modal"> <div class="modal-wrap"> <div class="modal__bg"></div> <div class="modal__content"> <div class="notranslate modal__inner" id="skip_info"> <h4>Copyrights notice of machine-translated contents</h4> <p>The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See <a href="https://www.ieice.org/eng/copyright/files/copyright.pdf" target="_blank">IEICE Provisions on Copyright</a> for details.</p> <p class="js-modal-close"><i class="fas fa-times"></i></p> </div> </div> </div> </div>   <div id="modal_cite" class="modal js-modal"> <div class="modal-wrap"> <div class="modal__bg"></div> <div class="modal__content"> <div class="modal__inner"> <h4 id="skip_info" class="notranslate">Cite this</h4> <nav class="nav-tab"> <ul> <li class="notranslate tab is-active" id="skip_info">Plain Text</li> <li class="notranslate tab" id="skip_info">BibTeX</li> <li class="notranslate tab" id="skip_info">RIS</li> <li class="notranslate tab" id="skip_info">Refworks</li> </ul> </nav> <div class="copy_box"> <div class="box is-show"> <p class="gt-block btn" id="js-copy"><i class="fas fa-copy"></i>Copier</p> <p class="notranslate copy-text" id="skip_info">Yuxiu LIU, Na WEI, Yongjie LI, "An Algorithm Based on Distance Measurement for SAR Image Recognition" in IEICE TRANSACTIONS on Communications, vol. E107-B, no. 12, pp. 989-997, December 2024, doi: <span class="TEXT-COL">10.23919/transcom.2023EBP3179</span>.<br> Abstract: <span class="TEXT-COL">In recent years, deep convolutional neural networks (CNN) have been widely used in synthetic aperture radar (SAR) image recognition. However, due to the difficulty in obtaining SAR image samples, training data is relatively few and overfitting is easy to occur when using traditional CNNS used in optical image recognition. In this paper, a CNN-based SAR image recognition algorithm is proposed, which can effectively reduce network parameters, avoid model overfitting and improve recognition accuracy. The algorithm first constructs a convolutional network feature extractor with a small size convolution kernel, then constructs a classifier based on the convolution layer, and designs a loss function based on distance measurement. The networks are trained in two stages: in the first stage, the distance measurement loss function is used to train the feature extraction network; in the second stage, cross-entropy is used to train the whole model. The public benchmark dataset MSTAR is used for experiments. Comparison experiments prove that the proposed method has higher accuracy than the state-of-the-art algorithms and the classical image recognition algorithms. The ablation experiment results prove the effectiveness of each part of the proposed algorithm.</span><br> URL: https://global.ieice.org/en_transactions/communications/10.23919/transcom.2023EBP3179/_f</p> </div> <div class="box"> <p class="gt-block btn" id="js-copy-BibTeX"><i class="fas fa-copy"></i>Copier</p> <p class="notranslate copy-BibTeX" id="skip_info">@ARTICLE{e107-b_12_989,<br> author={Yuxiu LIU, Na WEI, Yongjie LI, },<br> journal={IEICE TRANSACTIONS on Communications}, <br> title={An Algorithm Based on Distance Measurement for SAR Image Recognition}, <br> year={2024},<br> volume={E107-B},<br> number={12},<br> pages={989-997},<br> abstract={<span class="TEXT-COL">In recent years, deep convolutional neural networks (CNN) have been widely used in synthetic aperture radar (SAR) image recognition. However, due to the difficulty in obtaining SAR image samples, training data is relatively few and overfitting is easy to occur when using traditional CNNS used in optical image recognition. In this paper, a CNN-based SAR image recognition algorithm is proposed, which can effectively reduce network parameters, avoid model overfitting and improve recognition accuracy. The algorithm first constructs a convolutional network feature extractor with a small size convolution kernel, then constructs a classifier based on the convolution layer, and designs a loss function based on distance measurement. The networks are trained in two stages: in the first stage, the distance measurement loss function is used to train the feature extraction network; in the second stage, cross-entropy is used to train the whole model. The public benchmark dataset MSTAR is used for experiments. Comparison experiments prove that the proposed method has higher accuracy than the state-of-the-art algorithms and the classical image recognition algorithms. The ablation experiment results prove the effectiveness of each part of the proposed algorithm.</span>},<br> keywords={},<br> doi={<span class="TEXT-COL">10.23919/transcom.2023EBP3179</span>},<br> ISSN={<span class="TEXT-COL">1745-1345</span>},<br> month={December},}</p> </div> <div class="box"> <p class="gt-block btn" id="js-copy-RIS"><i class="fas fa-copy"></i>Copier</p> <p class="notranslate copy-RIS" id="skip_info">TY - JOUR<br> TI - An Algorithm Based on Distance Measurement for SAR Image Recognition<br> T2 - IEICE TRANSACTIONS on Communications<br> SP - 989<br> EP - 997<br> AU - Yuxiu LIU<br> AU - Na WEI<br> AU - Yongjie LI<br> PY - 2024<br> DO - <span class="TEXT-COL">10.23919/transcom.2023EBP3179</span><br> JO - IEICE TRANSACTIONS on Communications<br> SN - <span class="TEXT-COL">1745-1345</span><br> VL - E107-B<br> IS - 12<br> JA - IEICE TRANSACTIONS on Communications<br> Y1 - December 2024<br> AB - <span class="TEXT-COL">In recent years, deep convolutional neural networks (CNN) have been widely used in synthetic aperture radar (SAR) image recognition. However, due to the difficulty in obtaining SAR image samples, training data is relatively few and overfitting is easy to occur when using traditional CNNS used in optical image recognition. In this paper, a CNN-based SAR image recognition algorithm is proposed, which can effectively reduce network parameters, avoid model overfitting and improve recognition accuracy. The algorithm first constructs a convolutional network feature extractor with a small size convolution kernel, then constructs a classifier based on the convolution layer, and designs a loss function based on distance measurement. The networks are trained in two stages: in the first stage, the distance measurement loss function is used to train the feature extraction network; in the second stage, cross-entropy is used to train the whole model. The public benchmark dataset MSTAR is used for experiments. Comparison experiments prove that the proposed method has higher accuracy than the state-of-the-art algorithms and the classical image recognition algorithms. The ablation experiment results prove the effectiveness of each part of the proposed algorithm.</span><br> ER - </p> </div> <div class="box"> <p id="skip_info" class="notranslate"></p> </div> </div> <p class="js-modal-close"><i class="fas fa-times"></i></p> </div> </div> </div>  </div></section>  <div id="link"></div> <div id="footer"></div> </section>  <script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.3/jquery.min.js"></script> <script> $(function() { // $("#header").load("/assets/tpl/header.html"); // $("#footer").load("/assets/tpl/footer.html"); // $("#form").load("/assets/tpl/form.html"); // $("#link").load("/assets/tpl/link.html"); // $("#aside").load("/assets/tpl/aside.html"); }); </script>  <script type="text/javascript" src="https://cdn.jsdelivr.net/npm/slick-carousel@1.8.1/slick/slick.min.js"></script>  <header> <div class="nav_sub">  <h1><a href="https://www.ieice.org/eng_r/index.html"><img src="https://global.ieice.org/assets/img/logo_w.png" alt=""></a></h1> 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The paper chooses the point of (","Comparison of different distance measurement loss functions.","is calculated by the formula:","is the loss of sample variance in the same class, and is calculated by:","The formula designed in this paper synthesizes three considerations: the distance from samples to their class centre, the distance between class centres, and the class variance, so as to guide the model to train towards the direction of intra-class aggregation and inter-class dispersion. The formula for the distance measurement loss is:","This article uses the MSTAR dataset to verify the performance of the proposed algorithm. The MSTAR dataset is a public dataset for SAR automatic target recognition provided by the US Advanced Research Projects Agency and the Air Force Laboratory (DARPA\/AFRL). The images are obtained by an X-band HH polarized constrained radar with resolution of 0.3 m","2.3 Feature Extraction Network and Classifier","where N is the number of samples in this batch, and,","is the epoch variant,","-th dimension of","2. SAR Image Recognition Algorithm Based on Distance Measurement and Small-Size Convolutional Network","depression angle chosen from Table 1, and the test dataset (shown in Table 2) is composed of data in the 30","is the feature vector output of the sample","In 2014, Karen Simonyan from Oxford University proposed VGGNet [14] and explored the depth of the network. Due to its simplicity and practicality, it quickly became the most popular convolutional neural network at that time. The inspirations brought by the VGGNet include: (1) Replacing a large convolutional layer with multiple small convolutional layers can obtain the same receptive field size, but significantly reduces parameter size and computational complexity; (2) Using a unified 2x2 max-pool with a stride of 2 to increase local information diversity and reduce feature size, can better capture local information changes and describe edge and texture structures.","To prove the superiority of the feature extraction network of the proposed algorithm, the feature extraction network was replaced as EfficientNetV2 [25] and MobileNetV3 [26], and comparative experiments were conducted on three types of networks under the same condition. The comparison results are shown in Table 6. It can be seen that the feature extraction network used in this paper has a significant advantage in accuracy compared to the other two.","all convolutional network","SAR image recognition","are in different classes. The loss function is defined as:","From the above formulas, it can be seen that in the prototype network, only the distance between the sample and the centre of samples in the same class (prototype) is used. In supervised comparative learning, only the distance between the sample and other samples in the same class is considered. In Improved Triplet Loss, only the distance between samples belongs to the same class and different classes are used. So all of them only consider the relationship between the sample and other samples. In addition to the above, this article further considers the internal variance of samples of the same class and the distance between different class centres. This paper simultaneously considers both individual and overall loss of the sample, to guide the model to be trained towards the direction of intra-class aggregation and inter-class dispersion comprehensively.","In order to improve the accuracy of SAR image recognition, this paper proposes a small-size full convolutional network based on distance measurement. The feature extraction part of the network is composed of multiple 3x3 convolution layers, and the classifier of the network is composed of a 1x1 convolution layer. The design of small-size and convolution classifiers improves accuracy while reducing network parameters and computational complexity. A loss function based on distance measurement is designed, which makes comprehensive use of the distance from the sample to the category centre, the distance between category centres and the variance of samples in the same category. Feature map visualization shows, after training with the distance measurement loss function, categories are distinguished more clearly and the features of samples in the same category are more clustered, the classification ability is stronger. Finally, multiple comparative experiments have shown that the method proposed in this paper is superior to the methods proposed in other papers and classic image recognition models.","Ablation experiment result of variant algorithms.",") respectively, other parameters are consistent with that in Sect. 3.1, and the accuracy results are shown in Fig. 9. It can be seen that high accuracy can be obtained at several points such as (","is calculated by formula (6), the l-th class sample variance","depression angle. In EOC-2, there are significant differences in the serial numbers and configurations of targets between the training and test datasets. The training set is composed of four targets (BMP-2, BRDM-2, BTR-70, and T-72) in the 17","are the hyper-parameters, and:","In this paper, the algorithm is trained in two stages. In the first stage, the distance measurement method is used to calculate the loss, and in the second stage, the cross-entropy is used to calculate the loss. The loss function is written as follows:","In recent years, with the development of deep learning technology, especially the development of convolutional neural networks, the research of image recognition technology has made remarkable progress. The proposal and successful application of AlexNet [13] marked the beginning of the development of deep learning, followed by VGGNet [14] and Restnet [15], which made breakthroughs in natural image recognition. Inspired by the achievements of deep learning in optical images, researchers try to apply deep learning to SAR image recognition. Deep learning is an end-to-end learning method that unifies feature extraction and classification recognition. It can automatically learn the required features based on the learning objectives without the need for additional feature extraction algorithms, reducing manual work and greatly improving the robustness of the algorithm. However, deep learning algorithms require a large amount of training data, while obtaining SAR image training data is difficult compared to optical images. As a result, the available samples for SAR image training are relatively few. Directly applying ordinary optical image recognition algorithms to SAR image recognition can easily cause the overfitting phenomenon [16]-[18]. Therefore, multiple researchers have conducted in-depth research on the application of deep learning in SAR image recognition. Y. Li [19] used CNN networks to extract SAR image features, and used meta-learning training methods and distance metric loss functions to classify images. High recognition accuracy was achieved on both OPENSARSHIP and MSTAR datasets. Jian Guan [20] proposed a CNN network that combines multiple-size convolutional kernels and dense residual networks. The method combines the cosine loss function and cross-entropy loss function to train the network in two stages and performs well in small sample data scenarios. Ying Zhang [21] proposed a training method for convolutional networks, which combines deep metric learning (DML) and an imbalanced sampling strategy to improve classification performance in the imbalanced training sample scenario. Zhang Ting [12] used CNN networks to extract multi-layer depth features of SAR images to improve recognition accuracy. S. Chen [17] used a fully convolutional network to reduce parameters while achieving high recognition accuracy.","from 0.1 to 0.8 (we choose the value meet","is the sample set whose label is","Comparison of the training process of variant algorithms.","is the loss of distance from the sample to its class centre,","3.3.4 Comparison of Algorithm Complexity","The comparative experimental results are shown in Table 5, in which the results of the literature [17], [20] are obtained from the original data of the literature. Results of VGG16, ResNet-50 and ResNet-18 are obtained through the experiment using the same parameter as the proposed algorithm in this paper. The results of Improved Triplet Loss algorithmn are obtained by replacing the distance measurement method proposed in this paper with that in reference [24], and keeping other parameters and training methods in accordance with this paper. It can be seen from the table that VGG16 performs the worst, followed by ResNet-50. This is mainly due to that the VGG16 and ResNet-50 have a large number of parameters by adopting multiple fully connected layers and multiple layers respectively, and the algorithm complexity comparison can be found in Sect. 3.3.4. Because of the difficulty of obtaining SAR images, the available samples for SAR image training are relatively few, and a model with a big parameter number can easily cause overfitting and performance degradation phenomenon [17]. The models of ResNet-18, literature [17], literature [20], Improved Triplet Loss [24], and this paper have fewer parameters compared to the first two, so their performance is better, reaching over 99% in the SOC dataset. The algorithm proposed in this paper not only achieves optimal performance under the SOC dataset, but also outperforms other algorithms under various EOC datasets, further proving the superiority of the proposed method.","Visualization of feature extraction network’s output after PCA dimensionality reduction. (a) The model trained with distance measurement loss. (b) The model trained without distance measurement loss.","is its cardinality. It should be noted that","Figure 8 shows the visualization of the feature extraction network’s output after PCA dimensionality reduction. Figure 8(a) and Fig. 8(b) show the results of the trained model with and without distance measurement loss function, respectively. It can be seen that after training with the distance measurement loss function, categories are distinguished more clearly and the classification ability is stronger.","in Eq. (2) are the two important parameters of the loss function in this paper. Experiments were conducted by changing","is the distance from the i-th sample to the l-th class centre. The paper uses Euclidean distance which is calculated by:","Results with different","In order to verify the effectiveness of the three design ideas proposed in this paper, namely, convolution classifier, small-size convolution kernel and distance measurement loss function(represented by A, B, and C respectively), this paper uses several variants of the algorithm to conduct ablation experiments, namely Variant 1: use a linear layer as the final classifier; Variant 2: use a 7x7 convolutional kernel instead of three 3x3 convolutional kernels, and use a 5x5 convolutional kernel instead of two 3x3 convolutional kernels; Variant 3: do not use the distance measurement loss function, and directly use cross entropy for training. The experimental results of the three variants are shown in Table 9, which shows that all three variants perform varying degrees of reduction in accuracy. Figure 7 shows their training processes, and it can be seen that after using the two-stage training method, the convergence speed of the second training is significantly accelerated due to the completion of the first training. From the embedded zoomed figure, we can see that Variant 1 has the worst performance, followed by Variant 2 which has large-scale convolution kernels, followed by Variant 3 with the model that does not use the distance metric. The model that does not make any changes has the best performance. This proves the effectiveness of convolution classifier, distance measurement loss function and small-size convolution. In addition, from the experimental results, it can be seen that the accuracy of variant 1 and variant 2 are relatively low, which can be ascribed to that the use of linear classifiers and large convolutional kernels has increased the number of model parameters to a certain extent, and the overfitting occurs. The phenomenon of performance degradation caused by increasing the number of parameters is also reflected in reference [17]. In this paper, the model can reduce the number of parameters by simplifying the network, thus supress overfitting to a certain extent.","MSTAR SOC training dataset and test dataset.","Visualization of the output features of models trained with different loss functions after PCA reduction. (a) Prototype network loss function. (b) Supervised contrast learning network loss function. (c) Improved Triplet Loss. (d) This paper.","In order to prove the superiority of the distance measurement method proposed in this paper, the loss function trained in the first stage is replaced by the loss function of the prototype network [22], the supervised contrastive learning network [23] and Improved Triplet Loss [24]. Experiments were conducted under the same conditions, and the comparison results are shown in Table 7. It can be seen that the algorithm proposed in this paper performs best. Using three different loss functions to train the model, the output features are dimensionally reduced by PCA, and the visualization results are shown in Fig. 6. It can be seen that the algorithm in this paper distinguishes each category more clearly and has a stronger classification ability.","3.3.3 Comparison of Different Distance Measurement Methods","3.3.1 Comparison with Algorithms in Other Literature","in which the l-th class centre","Influence of the ratio of the distance between category centres and variance on discrimination ability. The distance between the two class centres is the same in (a) and (b), but in (a), the variance is smaller and the discrimination ability is stronger, and in (b), the variance is larger and the discrimination ability is weaker.","Comparison of experimental results of different feature extraction networks.","is the loss of distance between class centres. After training, the larger the distance of inter-class, the better the classification effect of the model. However, the absolute distance cannot reflect the distinguishing ability between classes. In this paper, the distance between class centres is compared with the variance of samples belonging to this class. The larger the value, the bigger the difference exists between classes. Figure 2 shows the meaning. Figure 2(a) and Fig. 2(b) have the same distance between class centres, but Fig. 2(a) has a better distinguishing effect.","will be updated in each batch.","are the hyper-parameters. The following describes the detailed calculation methods of the three parts.","is its cardinality,","is the set of indices of samples whose label is","Comparison of accuracy with algorithms in other literature.","3.5 Hyper-Parameter Settings","depression angle chosen from Table 1, while the test set contains two groups listed in Table 3 (EOC-2-1) and Table 4 (EOC-2-2), corresponding to configuration variants and version variants.","as a group of input, in which","is the loss of distance between class centres,",", whose dimension is L,","EOC-1 test dataset (large depression variant).","EOC-2-2 test dataset (version variants).","A loss function based on distance measurement is proposed, which considers the distance from samples to the class centre, the distance between class centres, and the class variance, to guide the model to train in the direction of intra-class aggregation and inter-class dispersion.","3.2 Training and Test Experiments","Confusion matrix.","Figure 5 shows the confusion matrix evaluated by the trained model on the test dataset. It can be seen that the recognition accuracy is high, even reaching 100% for some classes, and the average recognition accuracy is 99.67%, which proves the effectiveness of this model.","is the set of I excluded i,","The loss function of the supervised contrast learning is defined as:","Model training data (for training data). (a) Loss at stage 1. (b) Accuracy at stage 1. (c) Loss at stage 2. (d) Accuracy at stage 2.","is the label of","Figure 4 shows the loss and accuracy changing as the iteration progresses. Figure 4(a) and Fig. 4(b) represent the results in the first stage, and Fig. 4(c) and Fig. 4(d) represent the results in the second stage. As shown in the figure, in the initial stage of training, the loss value drops rapidly and the model converges quickly. In the second stage, the accuracy of training data rises faster than that in the first stage, and the model converges faster. By the 10th round of training, the accuracy has already reached its maximum value, indicating that the model has been adjusted to near the optimal value after the first stage of training.","is the set of indices of all positives in the batch distinct from i, and","3.1 Dataset and Parameter Configuration","Table 8 provides a comparison between our algorithm and other algorithms in terms of parameter size, floating point operations (FLOPs), and accuracy. It can be seen that the algorithm in this paper has the minimum parameter size, and FLOPs are only higher than MobileNetV3_S, but the accuracy is the highest. The overall algorithm complexity is low while ensuring a high recognition rate.","is the output of classifier for the sample","The overall framework of the image recognition method is shown in Fig. 1. The entire process is divided into three stages. The first stage is the feature extractor training stage, in which the distance measurement loss function is used. After the first stage is completed, it goes into the second stage, in which a convolutional layer is added to the feature extraction network as a classifier and the cross-entropy loss function is used to fine-tune the whole network. After completion, a trained image recognition model is obtained. In the third stage, the performance of the model is tested using a test dataset.","2.2.2 Loss Function in the Second Stage","Distance measurement has been applied to both prototype networks [22], supervised contrast learning [23] and Improved Triplet Loss [24], but there are differences in its connotation. In the prototype network, the distance metric loss function is defined as:","through the feature extraction network, M is the feature vector dimension and","is the set of indices of all input samples in the current batch,","The rest of this paper is organized as follows: Section 2 introduces the algorithm proposed in this paper, Sect. 3 introduces the experimental results, and Sect. 4 summarises the work.","belong to the same class,","Network structure of proposed algorithm.","EOC-2-1 test dataset (configuration variants).","is the m-th dimension of","is the loss of the class variance,","is the l-th dimension of","is calculated by formula (8),","is the Euclidean distance between the centre of the i-th class and the l-th class.","Through the in-depth study of convolutional neural networks, the above algorithms have achieved good results in SAR image recognition scenes. Inspired by the above research, this article proposes a SAR image recognition algorithm based on distance measurement and small-size convolutional networks, which aims to simplify the network structure, prevent overfitting and improve the recognition accuracy. The paper carries out work from optimizing several aspects including loss function, network structure and training method. The main innovations of this paper are as follows:","2.1 Overall Framework","Inspired by VGGNet, a feature extraction network composed of small-size convolutional layers and a classifier composed of a convolutional layer is designed, as shown in Fig. 3. The feature extraction network consists of 5 convolutional blocks. Each block is composed of two 3x3 convolutional layers, one Batch-Normalize layer, one RELU activation layer, and one max-pool pooling layer. The pooling layer’s size is 2x2 and the stride is 2, it can reduce the feature map size by half. Except for the first convolution block, the number of channels in the first convolution layer of each other convolution block is doubled. In order to reduce network parameters, increase network robustness and avoid overfitting, the 1x1 convolution layer rather than the conventional linear layer is used as the network classifier.","is the epoch num in the first stage,","The cross-entropy function is used to calculate the loss in the second stage, the formula is:","A small-size convolutional kernel convolutional network was constructed to form the backbone of the whole model, which can reduce the number of parameters of the model and improve the final image recognition rate.","A two-stage training method is proposed. In the first stage, the distance metric loss function is used to train the feature extraction network, and the cross-entropy is used to train the classification in the second stage. Comparative experiments show the effectiveness of this method.","Synthetic aperture radar (SAR) can realize high-resolution microwave remote sensing imaging by using the principle of synthetic aperture, which has advantages of all-sky, all-weather and strong penetration etc., and has important application value in Marine monitoring, environmental analysis, military reconnaissance and geological survey [1], [2]. However, the principle of SAR imaging determines that SAR images have strong speckle noise and geometric distortion [3], [4], which poses challenges to SAR image interpretation. Automatic Target Recognition (ATR) which integrates image detection, sign extraction, and image recognition processes, is one of the key technologies for achieving automatic interpretation of SAR images [5]-[7].","Overall framework of algorithm.","since the ratio of","2.2.1 Loss Function in the First Stage","is calculated by taking the average of the distance loss from each sample to its class centre. The formula is:","is the distance loss from the i-th sample to its class centre, N is the total number of samples in the current batch,","is the set of indices of all input samples in current batch,","3.3.2 Comparison of Different Feature Extraction Networks (Backbones)","is the l-th class centre, which is the mean value of feature vectors belonging to the l-th class in this batch,","is the variance of the l-th class, and is calculated by:","In order to further prove the effectiveness of the proposed algorithm, this paper compares the proposed algorithms with literatures [17], [20], [24], classical image recognition convolutional networks VGG16, ResNet-50, and ResNet-18. This article selects data from the MSTAR dataset both in standard operating conditions (SOC) and extended operating conditions (EOC) for comparative experiments. Compared to SOC, EOC data has a greater difference between the training and testing datasets. This article selects two types of EOC datasets (denoted by EOC-1 and EOC-2) that are consistent with reference [17]. In EOC-1, there is a significant difference in the depression angle between the training and test dataset. The training dataset is composed of four targets (2S1, BRDM-2, T-72, and ZSU-234) in the 17","A convolutional network classifier has been constructed, which reduces model parameters and improves model performance when compared with traditional linear layer classifiers.","is the variance function.","In the Improved Triplet Loss, denote","0.3 m. In this paper, 10 types of military ground target data in the Standard Operating Conditions (SOC) of the MSTAR dataset are selected for experiments. The distribution of the dataset is shown in Table 1.","In the experiment, Pytorch was used under Ubuntu 20.04 LTS and GPU RTX 3090 was used to accelerate calculation. The experiment parameters were configured as follows: Batch size (N in Eq. (3)) was 100; The dimension of the feature extractor output (M in Eq. (5)) was 512; Adamw optimizer was selected with the learning rate setting to 0.001 and the weight decay setting to 0.004.","Image recognition, as the last crucial aspect of ATR, has been the focus of SAR imaging research. Traditional SAR image recognition methods mainly include two steps: feature extraction and classification recognition. The commonly used extracted features include geometric features, projection features and scattering features [8], [9], and the general classification and recognition algorithms include K-Nearest Neighbor classifier (KNN) [10], support vector machine (SVM) [11], sparse representation classifier [11], [12], etc. Traditional SAR image recognition methods have achieved good results and brought certain research progress to SAR ATR. However, the effectiveness of these methods requires experts to manually extract features, which is complicated, inefficient and poor robustness. For different SAR datasets and usage scenarios, feature extraction algorithms need to be redesigned."]; document.cookie="googtrans=/auto/fr; domain=.global.ieice.org"; document.cookie="googtrans=/auto/fr"; function googleTranslateElementInit3(){new google.translate.TranslateElement({pageLanguage:'auto',layout:google.translate.TranslateElement.InlineLayout.SIMPLE,autoDisplay:false,multilanguagePage:true},'google_translate_element3')} </script> <script data-cfasync="false" src="//translate.google.com/translate_a/element.js?cb=googleTranslateElementInit3"></script> </body></html>

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Un algorithme basé sur la mesure de distance pour la reconnaissance d'images SAR