{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,23]],"date-time":"2025-02-23T05:03:58Z","timestamp":1740287038404,"version":"3.37.3"},"reference-count":96,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2019,11,8]],"date-time":"2019-11-08T00:00:00Z","timestamp":1573171200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2019,12,31]]},"abstract":"\n Designing point patterns with desired properties can require substantial effort, both in hand-crafting coding and mathematical derivation. Retaining these properties in multiple dimensions or for a substantial number of points can be challenging and computationally expensive. Tackling those two issues, we suggest to automatically generate scalable point patterns from design goals using deep learning. We phrase pattern generation as a deep composition of weighted distance-based unstructured filters. Deep point pattern design means to optimize over the space of all such compositions according to a user-provided\n point correlation loss<\/jats:italic>\n , a small program which measures a pattern's fidelity in respect to its spatial or spectral statistics, linear or non-linear (e. g., radial) projections, or any arbitrary combination thereof. Our analysis shows that we can emulate a 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. Our point patterns scale favorably to multiple dimensions and numbers of points: we demonstrate nearly 10k points in 10-D produced in one second on one GPU. All the resources (source code and the pre-trained networks) can be found at https:\/\/sampling.mpi-inf.mpg.de\/deepsampling.html.\n <\/jats:p>","DOI":"10.1145\/3355089.3356562","type":"journal-article","created":{"date-parts":[[2019,11,8]],"date-time":"2019-11-08T20:27:58Z","timestamp":1573244878000},"page":"1-17","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":10,"title":["Deep point correlation design"],"prefix":"10.1145","volume":"38","author":[{"given":"Thomas","family":"Leimk\u00fchler","sequence":"first","affiliation":[{"name":"MPI Informatik"}]},{"given":"Gurprit","family":"Singh","sequence":"additional","affiliation":[{"name":"MPI Informatik"}]},{"given":"Karol","family":"Myszkowski","sequence":"additional","affiliation":[{"name":"MPI Informatik"}]},{"given":"Hans-Peter","family":"Seidel","sequence":"additional","affiliation":[{"name":"MPI Informatik"}]},{"given":"Tobias","family":"Ritschel","sequence":"additional","affiliation":[{"name":"University College London"}]}],"member":"320","published-online":{"date-parts":[[2019,11,8]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"Proc. USENIX.","author":"Abadi","year":"2016","unstructured":"Abadi et al. 2016. TensorFlow: A System for Large-scale Machine Learning. In Proc. USENIX."},{"doi-asserted-by":"crossref","unstructured":"Pankaj K Agarwal Jeff Erickson et al. 1999. Geometric range searching and its relatives. Contemp. Math. 223 (1999).","key":"e_1_2_2_2_1","DOI":"10.1090\/conm\/223\/03131"},{"doi-asserted-by":"publisher","key":"e_1_2_2_3_1","DOI":"10.1145\/2980179.2980218"},{"doi-asserted-by":"publisher","key":"e_1_2_2_4_1","DOI":"10.1145\/3072959.3073704"},{"doi-asserted-by":"publisher","key":"e_1_2_2_5_1","DOI":"10.1145\/3197517.3201301"},{"doi-asserted-by":"publisher","key":"e_1_2_2_6_1","DOI":"10.1145\/3072959.3073708"},{"doi-asserted-by":"publisher","key":"e_1_2_2_7_1","DOI":"10.1145\/1531326.1531392"},{"doi-asserted-by":"publisher","key":"e_1_2_2_8_1","DOI":"10.1145\/2892632"},{"doi-asserted-by":"publisher","key":"e_1_2_2_9_1","DOI":"10.1145\/1882261.1866188"},{"key":"e_1_2_2_10_1","volume-title":"Mean square decay of Fourier transforms in Euclidean and non Euclidean spaces. Tohoku Math J 53, 3","author":"Brandolini Luca","year":"2001","unstructured":"Luca Brandolini, Leonardo Colzani, and Andrea Torlaschi. 2001. Mean square decay of Fourier transforms in Euclidean and non Euclidean spaces. Tohoku Math J 53, 3 (2001)."},{"key":"e_1_2_2_11_1","article-title":"Interactive Reconstruction of Monte Carlo Image Sequences Using a Recurrent Denoising Autoencoder","volume":"36","author":"Alla Chaitanya Chakravarty R.","year":"2017","unstructured":"Chakravarty R. Alla Chaitanya, Anton S. Kaplanyan, Christoph Schied, Marco Salvi, Aaron Lefohn, Derek Nowrouzezahrai, and Timo Aila. 2017. Interactive Reconstruction of Monte Carlo Image Sequences Using a Recurrent Denoising Autoencoder. ACM Trans. Graph. (Proc. SIGGRAPH) 36, 4 (2017).","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH)"},{"key":"e_1_2_2_12_1","volume-title":"ShapeNet: An Information-Rich 3D Model Repository. arxiv:1512.03012","author":"Chang Angel X.","year":"2015","unstructured":"Angel X. Chang, Thomas A. Funkhouser, Leonidas J. Guibas, Pat Hanrahan, Qi-Xing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu. 2015. ShapeNet: An Information-Rich 3D Model Repository. arxiv:1512.03012 (2015)."},{"doi-asserted-by":"publisher","key":"e_1_2_2_13_1","DOI":"10.1109\/TVCG.2012.94"},{"doi-asserted-by":"crossref","unstructured":"Kenneth Chiu Peter Shirley and Changyaw Wang. 1994. Graphics Gems IV. Chapter Multi-jittered Sampling.","key":"e_1_2_2_14_1","DOI":"10.1016\/B978-0-12-336156-1.50045-8"},{"key":"e_1_2_2_15_1","volume-title":"Progressive multi-jittered sample sequences. Comp. Graph. Forum (Proc. EGSR) 37, 4","author":"Christensen Per","year":"2018","unstructured":"Per Christensen, Andrew Kensler, and Charlie Kilpatrick. 2018. Progressive multi-jittered sample sequences. Comp. Graph. Forum (Proc. EGSR) 37, 4 (2018)."},{"key":"e_1_2_2_16_1","volume-title":"Stochastic Wasserstein Barycenters. arxiv:1802-05757","author":"Claici Sebastian","year":"2018","unstructured":"Sebastian Claici, Edward Chien, and Justin Solomon. 2018. Stochastic Wasserstein Barycenters. arxiv:1802-05757 (2018)."},{"key":"e_1_2_2_17_1","volume-title":"Elizabeth Losos, N. Manokaran, R. Sukumar, and Takuo Yamakura.","author":"Condit Richard","year":"2000","unstructured":"Richard Condit, Peter S. Ashton, Patrick Baker, Sarayudh Bunyavejchewin, Savithri Gunatilleke, Nimal Gunatilleke, Stephen P. Hubbell, Robin B. Foster, Akira Itoh, James V. LaFrankie, Hua Seng Lee, Elizabeth Losos, N. Manokaran, R. Sukumar, and Takuo Yamakura. 2000. Spatial Patterns in the Distribution of Tropical Tree Species. Science 288, 5470 (2000)."},{"doi-asserted-by":"publisher","key":"e_1_2_2_18_1","DOI":"10.1145\/7529.8927"},{"key":"e_1_2_2_19_1","volume-title":"Learning Light Transport the Reinforced Way. arXiv:1701.07403","author":"Dahm Ken","year":"2017","unstructured":"Ken Dahm and Alexander Keller. 2017. Learning Light Transport the Reinforced Way. arXiv:1701.07403 (2017)."},{"key":"e_1_2_2_20_1","volume-title":"Monte Carlo and Quasi-Monte Carlo Methods","author":"Dammertz Sabrina","year":"2006","unstructured":"Sabrina Dammertz and Alexander Keller. 2008. Image Synthesis by Rank-1 Lattices. In Monte Carlo and Quasi-Monte Carlo Methods 2006."},{"key":"e_1_2_2_21_1","article-title":"Blue noise through optimal transport","volume":"31","author":"Goes Fernando De","year":"2012","unstructured":"Fernando De Goes, Katherine Breeden, Victor Ostromoukhov, and Mathieu Desbrun. 2012. Blue noise through optimal transport. ACM Trans. Graph. 31, 6 (2012).","journal-title":"ACM Trans. Graph."},{"doi-asserted-by":"publisher","key":"e_1_2_2_22_1","DOI":"10.1145\/3132188"},{"unstructured":"Laurent Dinh Jascha Sohl-Dickstein and Samy Bengio. 2017. Density estimation using Real NVP. In ICLR.","key":"e_1_2_2_23_1"},{"doi-asserted-by":"publisher","key":"e_1_2_2_24_1","DOI":"10.1145\/234535.234536"},{"doi-asserted-by":"publisher","key":"e_1_2_2_25_1","DOI":"10.1145\/2463372.2463469"},{"unstructured":"Ron O Dror Thomas K Leung Edward H Adelson and Alan S Willsky. 2001. Statistics of real-world illumination. In CVPR.","key":"e_1_2_2_26_1"},{"doi-asserted-by":"publisher","key":"e_1_2_2_27_1","DOI":"10.1145\/2010324.1964943"},{"key":"e_1_2_2_28_1","volume-title":"Blue-noise Dithered Sampling. In ACM SIGGRAPH 2016 Talks.","author":"Georgiev Iliyan","year":"2016","unstructured":"Iliyan Georgiev and Marcos Fajardo. 2016. Blue-noise Dithered Sampling. In ACM SIGGRAPH 2016 Talks."},{"unstructured":"Ian Goodfellow Jean Pouget-Abadie Mehdi Mirza Bing Xu David Warde-Farley Sherjil Ozair Aaron Courville and Yoshua Bengio. 2014. Generative adversarial nets. In NIPS.","key":"e_1_2_2_29_1"},{"key":"e_1_2_2_30_1","volume-title":"On the Efficiency of Certain Quasi-random Sequences of Points in Evaluating Multi-dimensional Integrals. Numer. Math. 2, 1","author":"Halton John H.","year":"1960","unstructured":"John H. Halton. 1960. On the Efficiency of Certain Quasi-random Sequences of Points in Evaluating Multi-dimensional Integrals. Numer. Math. 2, 1 (1960)."},{"unstructured":"Kaiming He Xiangyu Zhang Shaoqing Ren and Jian Sun. 2016. Deep residual learning for image recognition. In CVPR.","key":"e_1_2_2_31_1"},{"doi-asserted-by":"publisher","key":"e_1_2_2_32_1","DOI":"10.1145\/2487228.2487233"},{"doi-asserted-by":"publisher","key":"e_1_2_2_33_1","DOI":"10.1007\/978-1-4612-1478-6"},{"doi-asserted-by":"publisher","key":"e_1_2_2_34_1","DOI":"10.1145\/2897824.2925875"},{"key":"e_1_2_2_35_1","article-title":"Monte Carlo Convolution for Learning on Non-uniformly Sampled Point Clouds","volume":"37","author":"Hermosilla Pedro","year":"2018","unstructured":"Pedro Hermosilla, Tobias Ritschel, Pere-Pau V\u00e1zquez, \u00c0lvar Vinacua, and Timo Ropinski. 2018. Monte Carlo Convolution for Learning on Non-uniformly Sampled Point Clouds. ACM Trans. Graph (Proc. SIGGRAPH Asia) 37, 5 (2018).","journal-title":"ACM Trans. Graph (Proc. SIGGRAPH Asia)"},{"key":"e_1_2_2_36_1","volume-title":"An efficient method for generating uniformly distributed points on the surface of an n-dimensional sphere. Comm. ACM 2, 4","author":"Hicks JS","year":"1959","unstructured":"JS Hicks and RF Wheeling. 1959. An efficient method for generating uniformly distributed points on the surface of an n-dimensional sphere. Comm. ACM 2, 4 (1959)."},{"key":"e_1_2_2_37_1","volume-title":"Orthogonal array sampling for Monte Carlo rendering. Computer Graphics Forum (Proceedings of EGSR) 38, 4","author":"Jarosz Wojciech","year":"2019","unstructured":"Wojciech Jarosz, Afnan Enayet, Andrew Kensler, Charlie Kilpatrick, and Per Christensen. 2019. Orthogonal array sampling for Monte Carlo rendering. Computer Graphics Forum (Proceedings of EGSR) 38, 4 (2019)."},{"doi-asserted-by":"publisher","key":"e_1_2_2_38_1","DOI":"10.1145\/2816795.2818102"},{"key":"e_1_2_2_39_1","article-title":"Constructing Sobol Sequences with Better Two-Dimensional Projections","volume":"30","author":"Joe S.","year":"2008","unstructured":"S. Joe and F. Kuo. 2008. Constructing Sobol Sequences with Better Two-Dimensional Projections. SIAM J Scientific Comp. 30, 5 (2008).","journal-title":"SIAM J Scientific Comp."},{"doi-asserted-by":"publisher","key":"e_1_2_2_40_1","DOI":"10.1145\/2980179.2982435"},{"doi-asserted-by":"publisher","key":"e_1_2_2_41_1","DOI":"10.1145\/2766977"},{"key":"e_1_2_2_42_1","article-title":"Deep Scattering: Rendering Atmospheric Clouds with Radiance-predicting Neural Networks","volume":"36","author":"Kallweit Simon","year":"2017","unstructured":"Simon Kallweit, Thomas M\u00fcller, Brian Mcwilliams, Markus Gross, and Jan Nov\u00e1k. 2017. Deep Scattering: Rendering Atmospheric Clouds with Radiance-predicting Neural Networks. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 36, 6 (2017).","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_2_2_43_1","volume-title":"Advanced (Quasi) Monte Carlo Methods for Image Synthesis. In ACM SIGGRAPH 2012 Courses. Article 21","author":"Keller Alexander","year":"2012","unstructured":"Alexander Keller, Simon Premoze, and Matthias Raab. 2012. Advanced (Quasi) Monte Carlo Methods for Image Synthesis. In ACM SIGGRAPH 2012 Courses. Article 21."},{"key":"e_1_2_2_44_1","volume-title":"Kingma and Jimmy Ba","author":"Diederik","year":"2014","unstructured":"Diederik P. Kingma and Jimmy Ba. 2014. Adam: A Method for Stochastic Optimization. arxiv:1412.6980 (2014)."},{"key":"e_1_2_2_45_1","volume-title":"Auto-encoding variational Bayes. arXiv:1312.6114","author":"Kingma Diederik P","year":"2013","unstructured":"Diederik P Kingma and Max Welling. 2013. Auto-encoding variational Bayes. arXiv:1312.6114 (2013)."},{"doi-asserted-by":"publisher","key":"e_1_2_2_46_1","DOI":"10.1145\/1141911.1141916"},{"key":"e_1_2_2_47_1","volume-title":"Hinton","author":"Krizhevsky Alex","year":"2012","unstructured":"Alex Krizhevsky, Ilya Sutskever, and Geoffrey E. Hinton. 2012. ImageNet Classification with Deep Convolutional Neural Networks. In NIPS."},{"doi-asserted-by":"publisher","key":"e_1_2_2_48_1","DOI":"10.1145\/3180495"},{"unstructured":"Frances Kuo. 2007. Lattice rule generating vectors. web.maths.unsw.edu.au\/~fkuo. Accessed: 2019-07-12.","key":"e_1_2_2_49_1"},{"key":"e_1_2_2_50_1","volume-title":"A Comparison of Methods for Generating Poisson Disk Distributions. Comp. Graph. Forum 27, 1","author":"Lagae Ares","year":"2008","unstructured":"Ares Lagae and Philip Dutre. 2008. A Comparison of Methods for Generating Poisson Disk Distributions. Comp. Graph. Forum 27, 1 (2008)."},{"doi-asserted-by":"publisher","key":"e_1_2_2_51_1","DOI":"10.1145\/3197517.3201383"},{"doi-asserted-by":"publisher","key":"e_1_2_2_52_1","DOI":"10.1109\/TIT.1982.1056489"},{"volume-title":"The fractal geometry of nature","author":"Mandelbrot Benoit B","unstructured":"Benoit B Mandelbrot. 1983. The fractal geometry of nature. WH Freeman New York.","key":"e_1_2_2_53_1"},{"key":"e_1_2_2_54_1","volume-title":"Proc. Graphics interface.","author":"McCool Michael","year":"1992","unstructured":"Michael McCool and Eugene Fiume. 1992. Hierarchical Poisson disk sampling distributions. In Proc. Graphics interface."},{"key":"e_1_2_2_55_1","volume-title":"Ray Tracing and Irregularities of Distribution. In In Third Eurographics Workshop on Rendering.","author":"Mitchell Don P.","year":"1992","unstructured":"Don P. Mitchell. 1992. Ray Tracing and Irregularities of Distribution. In In Third Eurographics Workshop on Rendering."},{"doi-asserted-by":"publisher","key":"e_1_2_2_56_1","DOI":"10.1145\/3194657"},{"key":"e_1_2_2_57_1","volume-title":"Neural Importance Sampling. arXiv:1808.03856","author":"M\u00fcller Thomas","year":"2018","unstructured":"Thomas M\u00fcller, Brian McWilliams, Fabrice Rousselle, Markus Gross, and Jan Nov'ak. 2018. Neural Importance Sampling. arXiv:1808.03856 (2018)."},{"volume-title":"Human Vision, Visual Processing, and Digital Display III","author":"Mulligan Jeffrey B","unstructured":"Jeffrey B Mulligan and Albert J Ahumada. 1992. Principled halftoning based on human vision models. In Human Vision, Visual Processing, and Digital Display III, Vol. 1666.","key":"e_1_2_2_58_1"},{"key":"e_1_2_2_59_1","volume-title":"Deep Shading: Convolutional Neural Networks for Screen-Space Shading. Comp. Graph. Forum (Proc. EGSR) 36, 4","author":"Nalbach Oliver","year":"2017","unstructured":"Oliver Nalbach, Elena Arabadzhiyska, Dushyant Mehta, Hans-Peter Seidel, and Tobias Ritschel. 2017. Deep Shading: Convolutional Neural Networks for Screen-Space Shading. Comp. Graph. Forum (Proc. EGSR) 36, 4 (2017)."},{"key":"e_1_2_2_60_1","volume-title":"Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Amer. Math. Soc. 84, 6","author":"Niederreiter Harald","year":"1978","unstructured":"Harald Niederreiter. 1978. Quasi-Monte Carlo methods and pseudo-random numbers. Bull. Amer. Math. Soc. 84, 6 (1978)."},{"doi-asserted-by":"crossref","unstructured":"H. Niederreiter. 1992. Random Number Generation and Quasi-Monte-Carlo Methods. SIAM.","key":"e_1_2_2_61_1","DOI":"10.1137\/1.9781611970081"},{"key":"e_1_2_2_62_1","volume-title":"The construction of good lattice rules and polynomial lattice rules. arXiv:1308.3601","author":"Nuyens Dirk","year":"2013","unstructured":"Dirk Nuyens. 2013. The construction of good lattice rules and polynomial lattice rules. arXiv:1308.3601 (2013)."},{"key":"e_1_2_2_63_1","volume-title":"Van Overveld Cornelius, and Strothotte Thomas","author":"Oliver Deussen","year":"2001","unstructured":"Deussen Oliver, Hiller Stefan, Van Overveld Cornelius, and Strothotte Thomas. 2001. Floating Points: A Method for Computing Stipple Drawings. Computer Graphics Forum 19, 3 (2001)."},{"doi-asserted-by":"publisher","key":"e_1_2_2_64_1","DOI":"10.1145\/1015706.1015750"},{"doi-asserted-by":"publisher","key":"e_1_2_2_65_1","DOI":"10.1137\/S0036142994277468"},{"doi-asserted-by":"publisher","key":"e_1_2_2_66_1","DOI":"10.1145\/2932186"},{"key":"e_1_2_2_67_1","article-title":"Analysis and synthesis of point distributions based on pair correlation","volume":"31","author":"Cengiz \u00d6ztireli A","year":"2012","unstructured":"A Cengiz \u00d6ztireli and Markus Gross. 2012. Analysis and synthesis of point distributions based on pair correlation. ACM Trans. Graph. 31, 6 (2012).","journal-title":"ACM Trans. Graph."},{"key":"e_1_2_2_68_1","volume-title":"Sequences with Low-Discrepancy Blue-Noise 2-D Projections. Comp. Graph. Forum (Proc. Eurographics) 37, 2","author":"Perrier H\u00e9l\u00e8ne","year":"2018","unstructured":"H\u00e9l\u00e8ne Perrier, David Coeurjolly, Feng Xie, Matt Pharr, Pat Hanrahan, and Victor Ostromoukhov. 2018. Sequences with Low-Discrepancy Blue-Noise 2-D Projections. Comp. Graph. Forum (Proc. Eurographics) 37, 2 (2018)."},{"key":"e_1_2_2_69_1","volume-title":"Physically Based Rendering: From Theory To Implementation","author":"Pharr Matt","unstructured":"Matt Pharr, Wenzel Jakob, and Greg Humphreys. 2016. Physically Based Rendering: From Theory To Implementation (3rd ed.). Morgan Kaufmann Publishers Inc., San Francisco, CA, USA.","edition":"3"},{"doi-asserted-by":"publisher","key":"e_1_2_2_70_1","DOI":"10.1145\/2766930"},{"key":"e_1_2_2_71_1","volume-title":"Pointnet: Deep learning on point sets for 3D classification and segmentation. CVPR","author":"Qi Charles R","year":"2017","unstructured":"Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas. 2017. Pointnet: Deep learning on point sets for 3D classification and segmentation. CVPR (2017)."},{"doi-asserted-by":"publisher","key":"e_1_2_2_72_1","DOI":"10.1145\/3072959.3119910"},{"key":"e_1_2_2_73_1","volume-title":"Projective Blue-Noise Sampling. Comp. Graph. Forum 35, 1","author":"Reinert Bernhard","year":"2016","unstructured":"Bernhard Reinert, Tobias Ritschel, Hans-Peter Seidel, and Iliyan Georgiev. 2016. Projective Blue-Noise Sampling. Comp. Graph. Forum 35, 1 (2016)."},{"key":"e_1_2_2_74_1","volume-title":"Image Based Relighting Using Neural Networks. ACM Trans. Graph. 34","author":"Ren Peiran","year":"2015","unstructured":"Peiran Ren, Yue Dong, Stephen Lin, Xin Tong, and Baining Guo. 2015. Image Based Relighting Using Neural Networks. ACM Trans. Graph. 34 (2015)."},{"key":"e_1_2_2_75_1","volume-title":"Variational inference with normalizing flows. arXiv:1505.05770","author":"Rezende Danilo Jimenez","year":"2015","unstructured":"Danilo Jimenez Rezende and Shakir Mohamed. 2015. Variational inference with normalizing flows. arXiv:1505.05770 (2015)."},{"key":"e_1_2_2_76_1","volume-title":"Graph. Forum","author":"Schmaltz Christian","year":"2010","unstructured":"Christian Schmaltz, Pascal Gwosdek, Andres Bruhn, and Joachim Weickert. 2010. Electrostatic Halftoning. Comp. Graph. Forum (2010)."},{"key":"e_1_2_2_77_1","volume-title":"On optimal and data-based histograms. Biometrika 66, 3","author":"Scott David W","year":"1979","unstructured":"David W Scott. 1979. On optimal and data-based histograms. Biometrika 66, 3 (1979)."},{"doi-asserted-by":"publisher","key":"e_1_2_2_78_1","DOI":"10.1145\/508530.508537"},{"key":"e_1_2_2_79_1","volume-title":"Proc. Eurographics.","author":"Shirley Peter","year":"1991","unstructured":"Peter Shirley. 1991. Discrepancy as a quality measure for sample distributions. In Proc. Eurographics."},{"doi-asserted-by":"publisher","key":"e_1_2_2_80_1","DOI":"10.1146\/annurev.neuro.24.1.1193"},{"doi-asserted-by":"publisher","key":"e_1_2_2_81_1","DOI":"10.1145\/3072959.3073656"},{"key":"e_1_2_2_82_1","volume-title":"Analysis of Sample Correlations for Monte Carlo Rendering. Comp. Graph Form. (Proc. EGSR) 38, 2","author":"Singh Gurprit","year":"2019","unstructured":"Gurprit Singh, Cengiz Oztireli, Abdalla G.M. Ahmed, David Coeurjolly, Kartic Subr, Oliver Deussen, Victor Ostromoukhov, Ravi Ramamoorthi, and Wojciech Jarosz. 2019a. Analysis of Sample Correlations for Monte Carlo Rendering. Comp. Graph Form. (Proc. EGSR) 38, 2 (2019)."},{"key":"e_1_2_2_83_1","volume-title":"Fourier Analysis of Correlated Monte Carlo Importance Sampling. Comp. Graph. Forum 38, 1","author":"Singh Gurprit","year":"2019","unstructured":"Gurprit Singh, Kartic Subr, David Coeurjolly, Victor Ostromoukhov, and Wojciech Jarosz. 2019b. Fourier Analysis of Correlated Monte Carlo Importance Sampling. Comp. Graph. Forum 38, 1 (2019)."},{"doi-asserted-by":"crossref","unstructured":"I.H. Sloan and S. Joe. 1994. Lattice methods for multiple integration. Clarendon Press.","key":"e_1_2_2_84_1","DOI":"10.1093\/oso\/9780198534723.001.0001"},{"key":"e_1_2_2_85_1","volume-title":"The distribution of points in a cube and the approximate evaluation of integrals. U. S. S. R. Comput. Math. and Math. Phys. 7","author":"Sobol I. M.","year":"1967","unstructured":"I. M. Sobol. 1967. The distribution of points in a cube and the approximate evaluation of integrals. U. S. S. R. Comput. Math. and Math. Phys. 7 (1967)."},{"key":"e_1_2_2_86_1","volume-title":"Fourier analysis of stochastic sampling strategies for assessing bias and variance in integration. ACM Trans. Graph. 32","author":"Subr Kartic","year":"2013","unstructured":"Kartic Subr and Jan Kautz. 2013. Fourier analysis of stochastic sampling strategies for assessing bias and variance in integration. ACM Trans. Graph. 32 (2013)."},{"doi-asserted-by":"publisher","key":"e_1_2_2_87_1","DOI":"10.1109\/5.3288"},{"doi-asserted-by":"publisher","key":"e_1_2_2_88_1","DOI":"10.1145\/2601097.2601107"},{"doi-asserted-by":"crossref","unstructured":"Shenlong Wang Simon Suo Wei-Chiu Ma Andrei Pokrovsky and Raquel Urtasun. 2018b. Deep parametric continuous convolutional neural networks. In CVPR.","key":"e_1_2_2_89_1","DOI":"10.1109\/CVPR.2018.00274"},{"key":"e_1_2_2_90_1","volume-title":"Solomon","author":"Wang Yue","year":"2018","unstructured":"Yue Wang, Yongbin Sun, Ziwei Liu, Sanjay E. Sarma, Michael M. Bronstein, and Justin M. Solomon. 2018a. Dynamic Graph CNN for Learning on Point Clouds. arxiv:1801.07829 (2018)."},{"doi-asserted-by":"publisher","key":"e_1_2_2_91_1","DOI":"10.1145\/2010324.1964945"},{"key":"e_1_2_2_92_1","article-title":"A survey of blue-noise sampling and its applications","volume":"30","author":"Yan Dong-Ming","year":"2015","unstructured":"Dong-Ming Yan, Jian-Wei Guo, Bin Wang, Xiao-Peng Zhang, and Peter Wonka. 2015. A survey of blue-noise sampling and its applications. J Comp. Sci. and Tech. 30, 3 (2015).","journal-title":"J Comp. Sci. and Tech."},{"key":"e_1_2_2_93_1","volume-title":"Spectral consequences of photoreceptor sampling in the rhesus retina. Science 221, 4608","author":"Yellott John I","year":"1983","unstructured":"John I Yellott. 1983. Spectral consequences of photoreceptor sampling in the rhesus retina. Science 221, 4608 (1983)."},{"key":"e_1_2_2_94_1","volume-title":"Learning to Importance Sample in Primary Sample Space. arxiv:1808.07840","author":"Zheng Quan","year":"2018","unstructured":"Quan Zheng and Matthias Zwicker. 2018. Learning to Importance Sample in Primary Sample Space. arxiv:1808.07840 (2018)."},{"doi-asserted-by":"publisher","key":"e_1_2_2_95_1","DOI":"10.1145\/2185520.2185572"},{"key":"e_1_2_2_96_1","article-title":"A brief introduction to weakly supervised learning","volume":"5","author":"Zhou Zhi-Hua","year":"2017","unstructured":"Zhi-Hua Zhou. 2017. A brief introduction to weakly supervised learning. National Science Review 5, 1 (2017).","journal-title":"National Science Review"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3355089.3356562","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,22]],"date-time":"2025-02-22T04:48:35Z","timestamp":1740199715000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3355089.3356562"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,8]]},"references-count":96,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2019,12,31]]}},"alternative-id":["10.1145\/3355089.3356562"],"URL":"https:\/\/doi.org\/10.1145\/3355089.3356562","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"type":"print","value":"0730-0301"},{"type":"electronic","value":"1557-7368"}],"subject":[],"published":{"date-parts":[[2019,11,8]]},"assertion":[{"value":"2019-11-08","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}