Gurprit Singh

<!DOCTYPE html> <html lang="en-US"> <head> <meta charset="UTF-8" />  <link rel="shortcut icon" href="" /> <link rel="stylesheet" href="style.css" /> <title> Gurprit Singh</title> </head>  <body>  <header> <h1>Gurprit Singh</h1> </header>  <section> <div class="paper-researchtext"> <p> <h3> Welcome! </h3> I am leading the sampling and rendering group in the <a href = "https://www.mpi-inf.mpg.de/departments/computer-graphics/" target="_blank" > computer graphics</a> department at the <a href = "https://www.mpi-inf.mpg.de/home/" target="_blank"> Max Planck Institute for informatics</a> in Saarbrücken, Germany. Before that, I spent two wonderful years at <a href = "http://dartmouth.edu/" target="_blank"> Dartmouth College</a> working with <a href = "http://www.cs.dartmouth.edu/~wjarosz/" target="_blank" > Wojciech Jarosz</a> followed by another two-year postdoc working with <a href = "https://people.mpi-inf.mpg.de/~karol/" target="_blank" > Karol Myszkowski</a>. I obtained my PhD from <a href = "http://www.univ-lyon1.fr/" target="_blank"> Université Lyon 1</a> in France, under the supervision of <a href= "http://liris.cnrs.fr/victor.ostromoukhov/" target="_blank"> Victor Ostromoukhov</a>. <p> <a href = "http://people.csail.mit.edu/billf/publications/How_To_Do_Research.pdf" target="_blank" > How To Do Research (Bill Freeman's notes)</a> <br> <a href = "https://cs.dartmouth.edu/~wjarosz/writing.html" target="_blank" > Writing tips (Wojciech Jarosz)</a> </p>  </p> </div> <div class="paper-researchimage">  <img src = "gurprit_sinbag.png" alt = "Pipeline teaser image" style="width:15em"/>     </div> </section> <section>  Best way to <a href="mailto:gsingh@mpi-inf.mpg.de"> reach me</a>.<br> <br> X-Twitter: @sinbagga </section> <section> <h3> Research </h3> <p> My research revolves around sampling which is the basic building block in many domains including computer graphics, computer vision, machine learning and generative AI. I strive to understand how different sample correlations affect specific applications and I enjoy developing models to characterize these correlations using various mathematical tools. For example, sample distributions directly affect the error during Monte Carlo and Quasi-Monte Carlo (MCQMC) based numerical estimations of global illumination integrals. Similar numerical approximations are extremely important in quantitative analysis in financial math. On the vision side, the data obtained from scanners in the form of noisy point clouds needs constant improvement for fast and better detection, segmentation and reconstruction of underlying objects/material properties. Similar problems are also encountered in computational geometry for remeshing. In all, I am interested in various aspects of sample correlations/distributions. If you have a specific question or if you wonder why some distributions in nature are the way they are, feel free to send me an email. </p> </section> <section> <a href="management.html">Open positions, PhD students, teaching </a> </section> <section> <h3> Academic service </h3> <p> <a href="https://s2024.siggraph.org/"> SIGGRAPH 2024</a>: Technical program committee member for SIGGRAPH North America <br> <a href="https://eg2024.cyens.org.cy/"> EG 2024</a>: International program committee member for Eurographics <br> <a href="http://iccvm.org/2024/"> CVM 2024</a>: International program committee member for Computational visual media <br> <a href="https://www.egsr2024.uk/"> EGSR 2022-Present</a>: Technical program committee member for Eurographics symposium on rendering <br> EG 2023: Co-chairing Posters and the Diversity & Inclusion Program<br> SIGGRAPH Asia 2022: International program committee member for SIGGRAPH Asia. <br> EGSR 2021: Conference co-chair with Pascal Grittmann and Philipp Slusallek (Saarland University). <br> EG 2020-21: International program committee member for Eurographics Short papers. <br> PG 2019-21: International program committee member for Pacific Graphics. <br> Reviewer: SIGGRAPH, TOG, Eurographics (EG), EGSR, Pacific Graphics, JCST, HELIYON (Elsevier).  </p> </section>  <a name="Publications"></a> <section> <h1> Publications </h1> <h2> 2024 </h2> <h3>Blue noise for diffusion models</h3> SIGGRAPH North America 2024 <br> Xingchang Huang, Corentin Salaun, Cristina Vasconcelos, Christian Theobalt, Cengiz Oztireli, <b>Gurprit Singh</b> <br>  Q:How can we enhance the generated samples simply from noise manipulation?  <br> <a class="iconground" href ="https://xchhuang.github.io/bndm/index.html" target="_blank">webpage</a> <a class="iconground" href ="https://arxiv.org/abs/2402.04930" target="_blank">arXiv </a> <h2> 2023 </h2> <h3>Efficient gradient estimation via adaptive sampling and importance sampling</h3> Corentin Salaun, Xingchang Huang, Iliyan Georgiev, Niloy Mitra, <b>Gurprit Singh</b> <br>  Q: Is there an efficient way to assign importance weight to mini-batch samples in gradient estimation? <br> <a class="iconground" href ="2023-salaun-efficient.html" target="_blank">webpage </a> <a class="iconground" href ="https://arxiv.org/pdf/2311.14468.pdf" target="_blank">arXiv </a> <h3>Joint sampling and optimisation for inverse rendering</h3> SIGGRAPH Asia 2023 <br> Martin Balint, Karol Myszkowski, Hans-Peter Seidel, <b>Gurprit Singh</b> <br>  Q: How to reduce variance in gradient estimation during inverse rendering? <br> <a class="iconground" href ="2023-balint-meta.html" target="_blank">webpage </a> <a class="iconground" href ="https://arxiv.org/abs/2309.15676" target="_blank">arXiv </a> </div> </div> <h3>Perceptual error optimization for Monte Carlo animation rendering </h3> SIGGRAPH Asia 2023 (conference track) <br> Misa Korac*, Corentin Salaun*, Iliyan Georgiev, Pascal Grittmann, Philipp Slusallek, Karol Myszkowski, <b>Gurprit Singh</b> <br> Q: How to design perceptually motivated spatio-temporal masks for Monte carlo animation rendering? <br> <a class="iconground" href ="2023-korac-perceptual.html" target="_blank">webpage </a> <a class="iconground" href ="https://arxiv.org/abs/2310.02955" target="_blank">arXiv </a> (*joint first authors) <h3>Patternshop: Editing point patterns with image manipulations </h3> SIGGRAPH North America 2023 <br> Xingchang Huang, Tobias Ritschel, Hans-Peter Seidel, Pooran Memari, <b>Gurprit Singh</b> <br> Q: How can we design a 2D color-space that allows editing point patterns with Photoshop? <br> <a class="iconground" href ="https://xchhuang.github.io/patternshop/" target="_blank">webpage </a> <a class="iconground" href ="https://arxiv.org/abs/2308.10517" target="_blank">arXiv </a> <h2> 2022 </h2> <h3> Informatik spectrum: Scalable multi-class sampling via filtered sliced optimal transport</h3> Cover Image for Informatik Spectrum, October 2022 <br> Corentin Salaun, Iliyan Georgiev, Hans-Peter Seidel, <b>Gurprit Singh</b> <br>    <a class="iconground" href ="https://link.springer.com/journal/287/volumes-and-issues/45-5" target="_blank">Journal</a> <h3> Scalable multi-class sampling via filtered sliced optimal transport</h3> SIGGRAPH Asia 2022 / ACM Transactions on Graphics, Volume 41 issue 6, December 2022 <br> Corentin Salaun, Iliyan Georgiev, Hans-Peter Seidel, <b>Gurprit Singh</b> <br> Q: How can we build a unified framework for stippling, object placement and perceptually pleasing rendering? <br> <a class="iconground" href ="2022-salaun-multiclass.html" target="_blank">webpage</a> <a class="iconground" href ="https://arxiv.org/abs/2211.04314" target="_blank">arXiv </a> <h3> Point-pattern synthesis using Gabor and random filters </h3> EGSR 2022 / Computer Graphics Forum, Volume 41 issue 6, July 2022 <br> Xingchang Huang, Pooran Memari, Hans-Peter Seidel, <b>Gurprit Singh</b> <br> Q: How can we perform point pattern (texture) synthesis without training a network? <br>    <a class="iconground" href ="2022-huang-gabor.html" target="_blank">webpage</a> <h3> Regression-based Monte Carlo integration </h3> SIGGRAPH North America 2022 / ACM Transactions on Graphics, Volume 41 issue 4, July 2022 <br> Corentin Salaun, Adrien Gruson, Binh-Son Hua, Toshiya Hachisuka, <b>Gurprit Singh</b> <br> Q: What happens if we use a polynomial function to average Monte Carlo estimates? <br>    <a class="iconground" href ="2022-salaun-regressionmc.html" target="_blank">webpage</a> <a class="iconground" href ="https://arxiv.org/abs/2211.07422" target="_blank">arXiv </a> <h3> Perceptual error optimization for Monte Carlo rendering </h3> ACM Transactions on Graphics, Volume 41 issue 3, June 2022 (presented at SIGGRAPH North America 2022) <br> Vassillen Chizhov, Iliyan Georgiev, Karol Myszkowski, <b>Gurprit Singh</b> <br> Q: How can we use a perception-based (human visual system) model to control the error distribution in rendering? <br>    <a class="iconground" href ="2022-chizhov-perception.html" target="_blank">webpage</a> <a class="iconground" href ="https://arxiv.org/abs/2012.02344" target="_blank">arXiv </a> <h2> 2021 </h2> <h3> Informatik Spectrum: Neural Light Field 3D Printing </h3> Cover Image for Informatik Spectrum, October 2021 <br> Quan Zheng, Vahid Babaei, Gordon Wetzstein, Hans-Peter Seidel, Matthias Zwicker, <b>Gurprit Singh</b> <br> <div title="Cover Image for Informatik Spectrum 2021." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="publications/2021-zheng-display-image/2021-zheng-display-image.pdf" target="_blank">Magazine</a> <a class="iconground" href ="https://link.springer.com/journal/287/volumes-and-issues/44-5" target="_blank">Journal</a> <h3> Neural Relightable Participating Media Rendering </h3> NeurIPS 2021 <br> Quan Zheng, <b>Gurprit Singh</b>, Hans-Peter Seidel <br> <div title="We propose a method to learn a volumetric representation for scenes with participating media from a set of images." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="https://arxiv.org/abs/2110.12993" target="_blank">arXiv</a> <h3> Blue Noise Plots </h3> Eurographics 2021 / Computer Graphics Forum, Volume 40 issue 2, May 2021 <br> Christian van Onzenoodt, <b> Gurprit Singh</b>, Timo Ropinski, Tobias Ritschel <br> <div title="We improve the visualization of 1D cluttered data using blue noise sample placement." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="https://arxiv.org/pdf/2102.04072.pdf" target="_blank">arXiv</a> <a class="iconground" href ="https://github.com/onc/BlueNoisePlots" target="_blank">source code</a> <h2> 2020 </h2> <h3> Neural Light Field 3D Printing </h3> SIGGRAPH ASIA 2020 / ACM Transactions on Graphics, Volume 39 issue 6, December 2020 <br> Quan Zheng, Vahid Babaei, Gordon Wetzstein, Hans-Peter Seidel, Matthias Zwicker, <b>Gurprit Singh</b> <br> <div title="We propose a novel approach to 3D print light fields as attenuation-based volumetric displays, for which we end-to-end optimize a neural network based implicit representation in a continuous space." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="2020-zheng-display.html" target="_blank">webpage</a> <h3> LadyBird: Quasi-Monte Carlo Sampling for Deep Implicit Field Based 3D Reconstruction with Symmetry </h3> ECCV (Oral), August 2020 <br> Yifan Xu*, Tianqi Fan*, Yi Yuan, <b>Gurprit Singh</b> (*contributed equally) <br> <div title="We study the effect of point set discrepancy on the network training and propose FPS-based sampling approach that theoretically encourages better generalization performance, and results in fast convergence for SGD-based optimization algorithms." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="2020-xu-ladybird.html" target="_blank">webpage</a> <h3> Real-time Monte Carlo Denoising with the Neural Bilateral Grid </h3> Eurographics Symposium on Rendering (EGSR), June 2020 <br> Xiaoxu Meng, Quan Zheng, Amitabh Varshney, <b>Gurprit Singh</b>, Matthias Zwicker <br> <div title="We develop an efficient convolutional neural network architecture to denoise noisy inputs in a data-dependent bilateral space. The efficiency comes from the fact that the effective data-dependent splatting into the bilateral grid can be learned with a simpler network than denoising the image itself." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="2020-xiaoxu-denoising.html" target="_blank">webpage</a> <h2> 2019 </h2> <h3> Deep Point Correlation Design </h3> SIGGRAPH ASIA 2019 / ACM Transactions on Graphics, Volume 38 issue 6, October 2019 <br> Thomas Leimkühler, <b>Gurprit Singh</b>, Karol Myszkowski, Hans-Peter Seidel, Tobias Ritschel <br> <div title="We propose a deep learning based framework to automatically generate scalable point patterns from design goals. We phrase pattern generation as a deep composition of weighted distance-based unstructured filters. As a result, we can emulate large set of existing patterns (blue, green, step, projective, stair, etc.-noise), generalize them to countless new combinations in a systematic way and leverage existing error estimation formulations to generate novel point patterns for a user-provided class of integrand functions." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="deepsampling.html" target="_blank">webpage</a>  </p> <p> <h3> Analysis of Sample Correlations for Monte Carlo Rendering </h3> Computer Graphics Forum (Proceedings of Eurographics - State of the art reports) 2019 <br> <b>Gurprit Singh</b>, Cengiz Öztireli, Abdalla G.M. Ahmed, David Coeurjolly, Kartic Subr, Oliver Deussen, Victor Ostromoukhov, Ravi Ramamoorthi, Wojciech Jarosz <br>  <div title="Monte Carlo based integrators are the choice for complex scenes and effects in modern physically based renderers. These integrators work by sampling the integrand at sample point locations. In this work, we aim at providing a comprehensive and accessible overview of the techniques developed over the last decades to analyze such correlations, relate them to error in integrators, and understand when and how to use existing sampling algorithms for effective rendering workflows." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="2019-singh-star.html" target="_blank">webpage</a> </p> <p> <h3> Fourier Analysis of Correlated Monte Carlo Importance Sampling </h3> Computer Graphics Forum, 38(1), 2019 <br> <b>Gurprit Singh</b>, Kartic Subr, David Coeurjolly, Victor Ostromoukhov, Wojciech Jarosz <br> <div title="Existing Fourier-based tools are only able to analyze Monte Carlo error convergence under simplifying assumptions (such as randomized shifts) which are not applied in practice during rendering. We reformulate the expressions for bias and variance of sampling-based integrators to unify non-uniform sample distributions (importance sampling) as well as correlations between samples while respecting finite sampling domains. Our unified formulation hints at fundamental limitations of Fourier-based tools in performing variance analysis for MC integration. At the same time, it reveals that, when combined with correlated sampling, importance sampling (IS) can impact convergence rate by introducing or inhibiting discontinuities in the integrand. We demonstrate that the convergence of multiple importance sampling (MIS) is determined by the strategy which converges slowest and propose several simple approaches to overcome this limitation. We show that smoothing light boundaries (as commonly done in production to reduce variance) can improve (M)IS convergence (at a cost of introducing a small amount of bias) since it removes C0 discontinuities within the integration domain." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="2019-singh-fourier.html" target="_blank">webpage</a> </p> <p> <h3> A Perception-driven Hybrid Decomposition for Multi-layer Accommodative Displays </h3> IEEE VR 2019 <br> Hyeonseung Yu, Mojtaba Bemana, Marek Wernikowski, Michał Chwesiuk, Okan Tarhan Tursun, <b>Gurprit Singh</b>, Karol Myszkowski, Radosław Mantiuk, Hans-Peter Seidel, Piotr Didyk <br> <div title="Multi-focal plane and multi-layered light-field displays are promising solutions for addressing all visual cues observed in the real world. Unfortunately, these devices usually require expensive optimizations to compute a suitable decomposition of the input light field or focal stack to drive individual display layers. Although these methods provide near-correct image reconstruction, a significant computational cost prevents real-time applications. A simple alternative is a linear blending strategy which decomposes a single 2D image using depth information. This method provides real-time performance, but it generates inaccurate results at occlusion boundaries and on glossy surfaces. This paper proposes a perception-based hybrid decomposition technique which combines the advantages of the above strategies and achieves both real-time performance and high-fidelity results. The fundamental idea is to apply expensive optimizations only in regions where it is perceptually superior, e.g., depth discontinuities at the fovea, and fall back to less costly linear blending otherwise. We present a complete, perception-informed analysis and model that locally determine which of the two strategies should be applied. The prediction is later utilized by our new synthesis method which performs the image decomposition. The results are analyzed and validated in user experiments on a custom multi-plane display." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="2019-yu-perception.html" target="_blank">webpage</a> </p> <h2> 2018 </h2> <p> <h3> Spectral Measures of Distortion for Change Detection in Dynamic Graphs </h3> Complex Networks 2018 <b>(Oral) </b> <br> Luca Castelli Aleardi, Semih Salihoglu, <b>Gurprit Singh</b>, Maks Ovsjanikov <br> <div title="We propose a novel framework for detecting, quantifying and visualizing changes between two snapshots of a dynamic network. Unlike existing approaches, which can be sensitive to minor and isolated changes, and are often based on heuristics, we show how a theoretically-justified, inherently multi-scale notion of change, or distortion, can be defined and computed using spectral graph-theoretic tools. Our primary observation is that informative, robust and multi-scale measures of change can be obtained by computing a real-valued function (which we call the distortion function) on the nodes of the input graph, via the optimization of a pre-defined distortion energy in a provably optimal way. Based on extensive tests on a wide variety of networks, we demonstrate the ability of our approach to highlight the evolution of the network in an informative and multi-scale manner." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="2018-aleardi-spectral.html" target="_blank">webpage</a> </p> <p> <h3> Sampling Analysis using Correlations for Monte Carlo Rendering </h3> SIGGRAPH Asia Courses 2018 <br> Cengiz Öztireli, <b>Gurprit Singh</b> <br> <div title="This course surveys the most recent state-of-the-art frameworks that are developed to better understand the impact of samples' structure on the error and its convergence during Monte Carlo integration. It provides best practices and a set of tools for easy integration of such frameworks for sampling decisions in rendering. We revisit stochastic point processes that offers a unified theory explaining stochastic structures and sampling patterns in a common principled framework. We show how this theory generalizes spectral tools developed over the years to analyze error and convergence rates, and allows for analysis of more complex point patterns with adaptive density and correlations." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="2018-oztireli-sampling.html" target="_blank">webpage</a> </p> <p> <h3> End-to-end Sampling Patterns </h3> Thomas Leimkühler, <b>Gurprit Singh</b>, Karol Myszkowski, Hans-Peter Seidel, Tobias Ritschel <br> <div title="We suggest a deep learning based toolkit to end-to-end optimize over all sampling methods to find the one producing user-prescribed properties such as discrepancy or a spectrum that best fit the end-task. A user simply implements the forward losses and the sampling method is found automatically -- without coding or mathematical derivation -- by making use of back-propagation abilities of modern deep learning frameworks. The resulting sampling patterns has properties such as multi-dimensional blue noise with projective properties." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="http://arxiv.org/abs/1806.06710" onclick="ga('send', 'event', 'Tech Report' 'Directing External Link', 'End-to-end sampling patterns');" target="_blank">Technical Report</a> </p> <h2> 2017 </h2> <p> <h3>Convergence Analysis for Anisotropic Monte Carlo Sampling Spectra </h3> SIGGRAPH 2017 / ACM Transactions on Graphics, 36 (4), July 2017 <br> <b>Gurprit Singh</b>, Wojciech Jarosz <br> <div title="Most of the well-known samplers used for Monte Carlo integration in graphics—e.g. jittered, Latin-hypercube (N-rooks), multijittered—are anisotropic in nature. In this work, we develop a Fourier-domain mathematical tool to analyze the variance, and subsequently the convergence rate, of Monte Carlo integration using any arbitrary (anisotropic) sampling power spectrum. We also validate and leverage our theoretical analysis, demonstrating that judicious alignment of anisotropic sampling and integrand spectra can improve variance and convergence rates in MC rendering, and that similar improvements can apply to (anisotropic) deterministic samplers." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="2017-singh-convergence.html" target="_blank">webpage</a> </p> <p> <h3>Variance and Convergence Analysis of Monte Carlo Line and Segment Samples </h3> Computer Graphics Forum (Proceedings of EGSR), 36 (4), June 2017 <br> <b>Gurprit Singh</b>, Bailey Miller, Wojciech Jarosz <br> <div title="In this work, we propose a theoretical formulation for lines and finite-length segment samples in the frequency domain that allows analyzing their anisotropic power spectra using previous isotropic variance and convergence tools. Our analysis shows that judiciously oriented line samples not only reduce the dimensionality but also pre-filter C0 discontinuities, resulting in further improvement in variance and convergence rates. Our theoretical insights also explain how finite-length segment samples impact variance and convergence rates only by pre-filtering discontinuities." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="https://www.cs.dartmouth.edu/~wjarosz/publications/singh17variance.html" target="_blank">webpage</a> <a class="iconground" href ="https://github.com/sinbag/ao-line-segment-sampling" target="_blank">source code (AO example)</a> </p> <h2> 2016 </h2> <p> <h3> Monte Carlo Convergence Analysis for Anisotropic Sampling Power Spectra </h3> <b>Gurprit Singh</b>, Wojciech Jarosz <br> <div title="In this work, we propose a mathematical tool in the Fourier domain that allows analyzing the variance, and subsequently the convergence rate, of Monte Carlo integration using any arbitrary (anisotropic) sampling power spectrum. We apply our analysis to common anisotropic point sampling strategies in Monte Carlo integration, and extend our analysis to recent Monte Carlo approaches relying on line samples which have inherently anisotropic power spectra. We validate our theoretical results with several experiments using both point and line samples." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="http://www.cs.dartmouth.edu/reports/TR2016-816.pdf" onclick="ga('send', 'event', 'Tech Report' 'Directing External Link', 'MC Convergence Anisotropic power spectra');" target="_blank">Technical Report</a> </p> <p> <h3> Fourier Analysis of Numerical Integration in Monte Carlo Rendering: Theory and Practice </h3> SIGGRAPH Courses 2016 <br> Kartic Subr, <b> Gurprit Singh</b>, Wojciech Jarosz <br> <div title= "In this course, we survey the recent developments and insights that Fourier analyses have provided about the magnitude and convergence rate of Monte Carlo integration error. We provide a historical perspective of Monte Carlo in graphics, review the necessary mathematical background, summarize the most recent developments, discuss the practical implications of these analyzes on the design of Monte Carlo rendering algorithms, and identify important remaining research problems that can propel the field forward." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="https://www.cs.dartmouth.edu/~wjarosz/publications/subr16fourier.html" target="_blank">webpage</a> <a class="iconground" href ="http://dl.acm.org/citation.cfm?id=2927356" target="_blank">acm.org</a> <a class="iconground" href ="https://github.com/sinbag/EmpiricalErrorAnalysis" target="_blank">source code</a> </p> <h2> 2015 </h2> <p> <h3> Variance and Sampling Analysis for Monte Carlo Integration in the Spherical Domain </h3> Ph.D. Dissertation, Université Lyon 1, France, September 2015. <br> Gurprit Singh <br> <div title= "This dissertation introduces a theoretical framework to study different sampling patterns in the spherical domain and their effects in the evaluation of global illumination integrals. Evaluating illumination (light transport) is one of the most essential aspect in image synthesis to achieve realism which involves solving multi-dimensional space integrals. Monte Carlo based numerical integration schemes are heavily employed to solve these high dimensional integrals. One of the most important aspect of any numerical integration method is sampling. The way samples are distributed on an integration domain can greatly affect the final result. For example, in images, the effects of various sampling patterns appear in the form of either structural artifacts or completely unstructured noise. In many cases, we may get completely false (biased) results due to the sampling pattern used in integration. The distribution of sampling patterns can be characterized using their Fourier power spectra. It is also possible to use the Fourier power spectrum as input, to generate the corresponding sample distribution. This further allows spectral control over the sample distributions. Since this spectral control allows tailoring new sampling patterns directly from the input Fourier power spectrum, it can be used to improve error in integration. However, a direct relation between the error in Monte Carlo integration and the sampling power spectrum is missing. In this work, we propose a variance formulation, that establishes a direct link between the variance in Monte Carlo integration and the power spectra of both the sampling pattern and the integrand involved. To derive our closed-form variance formulation, we use the notion of homogeneous sample distributions that allows expression of error in Monte Carlo integration, only in the form of variance. Based on our variance formulation, we develop an analysis tool that can be used to derive theoretical variance convergence rates of various state-of-the-art sampling patterns. Our analysis gives insights to design principles that can be used to tailor new sampling patterns based on the integrand." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="https://hal.archives-ouvertes.fr/tel-01217082" onClick=”_gaq.push(['_trackEvent', 'External Link', 'PhD Thesis', 'HAL Link']);” target="_blank">HAL</a> </p> <p> <h3> Variance Analysis for Monte Carlo Integration </h3> SIGGRAPH 2015 / ACM Transactions on Graphics, 34 (4), 2015 <br> *Adrien Pilleboue, *<b>Gurprit Singh</b>, David Coeurjolly, Michael Kazhdan, Victor Ostromoukhov (<i>*joint first authors</i>) <br> <div title=" We propose a new spectral analysis of the variance in Monte Carlo integration, expressed in terms of the power spectra of the sampling pattern and the integrand involved. We build our framework in the Euclidean space using Fourier tools and on the sphere using spherical harmonics. We further provide a theoretical background that explains how our spherical framework can be extended to the hemispherical domain. We use our framework to estimate the variance convergence rate of different state-of-the-art sampling patterns in both the Euclidean and spherical domains, as the number of samples increases. Furthermore, we formulate design principles for constructing sampling methods that can be tailored according to available resources. We validate our theoretical framework by performing numerical integration over several integrands sampled using different sampling patterns." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="https://liris.cnrs.fr/variance/" target="_blank">webpage</a> <a class="iconground" href ="http://dl.acm.org/citation.cfm?id=2766930" target="_blank">acm.org</a> <a class="iconground" href ="https://github.com/stk-team/stk" target="_blank">source code</a> </p> <p> <h3> Variance Analysis for Monte Carlo Integration: A Representation-Theoretic Perspective </h3> Michael Kazhdan, <b>Gurprit Singh</b>, Adrien Pilleboue, David Coeurjolly, Victor Ostromoukhov <br> <div title=" In this report, we revisit the work of Pilleboue et al. [2015], providing a representation-theoretic derivation of the closed-form expression for the expected value and variance in homogeneous Monte Carlo integration. We show that the results obtained for the variance estimation of Monte Carlo integration on the torus, the sphere, and Euclidean space can be formulated as specific instances of a more general theory. We review the related representation theory and show how it can be used to derive a closed-form solution." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="http://arxiv.org/abs/1506.00021" target="_blank">arXiv Report</a> </p> <h2> 2014 </h2> <p> <h3> Fast Tile-Based Adaptive Sampling with User-Specified Fourier Spectra </h3> SIGGRAPH 2014 / ACM Transactions on Graphics, 33 (4), 2014 <br> Florent Wachtel, Adrien Pilleboue, David Coeurjolly, Katherine Breeden, <b>Gurprit Singh</b>, Gaël Cathelin, Fernando de Goes, Mathieu Desbrun, Victor Ostromoukhov <br> <div title="We introduce a novel tile-based method for adaptive two-dimensional sampling with user-specified spectral properties. Our approach achieves several orders of magnitude speed improvement over current spectrum-controlled sampling methods through a deterministic, hierarchical construction of self-similar, equi-area tiles whose spatial distribution is free of spurious spectral peaks. A lookup table of sample points, computed offline using any existing procedure that optimizes point sets to shape their Fourier spectrum, is then used to populate the tiles. The result is a linear-time, adaptive, and high-quality sampling of arbitrary density functions that conforms to the desired spectral distribution." class="tooltip"><span title="">summary</span> </div> <a class="iconground" href ="http://liris.cnrs.fr/~polyhex/" target="_blank">webpage</a> <a class="iconground" href ="http://dl.acm.org/citation.cfm?id=2601107" target="_blank">acm.org</a> </p> </section> <a href="https://imprint.mpi-klsb.mpg.de/inf/sampling.mpi-inf.mpg.de"><p style="text-align:center">Imprint</a> / <a href="https://data-protection.mpi-klsb.mpg.de/inf/sampling.mpi-inf.mpg.de">Data Protection</a> </body> </html>

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Gurprit Singh