{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T14:27:38Z","timestamp":1790519258038,"version":"4.1.0"},"reference-count":37,"publisher":"Association for Computing Machinery (ACM)","issue":"5","license":[{"start":{"date-parts":[[2015,11,3]],"date-time":"2015-11-03T00:00:00Z","timestamp":1446508800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"ALTA","award":["ANR-11-B502-006"],"award-info":[{"award-number":["ANR-11-B502-006"]}]},{"name":"MITACS Engage Cluster"},{"name":"NSERC Discovery"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2015,11,3]]},"abstract":"<jats:p>\n                    Spherical filtering is fundamental to many problems in image synthesis, such as computing the reflected light over a surface or anti-aliasing mirror reflections over a pixel. This operation is challenging since the profile of spherical filters (e.g., the view-evaluated BRDF or the geometry-warped pixel footprint, mentioned before) typically exhibits both spatial and rotational variation at each pixel, precluding precomputed solutions. We accelerate complex spherical filtering tasks using\n                    <jats:italic>isotropic spherical decomposition<\/jats:italic>\n                    (ISD), decomposing spherical filters into a linear combination of simpler isotropic kernels. Our general ISD is flexible to the choice of the isotropic kernels, and we demonstrate practical realizations of ISD on several problems in rendering: shading and prefiltering with spatially varying BRDFs, anti-aliasing-environment-mapped mirror reflections, and filtering of noisy reflectance data. Compared to previous basis-space rendering solutions, our shading solution generates ground-truth-quality results at interactive rates, avoiding costly reconstruction and large approximation errors.\n                  <\/jats:p>","DOI":"10.1145\/2797136","type":"journal-article","created":{"date-parts":[[2015,10,30]],"date-time":"2015-10-30T08:58:59Z","timestamp":1446195539000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":15,"title":["Efficient and Accurate Spherical Kernel Integrals Using Isotropic Decomposition"],"prefix":"10.1145","volume":"34","author":[{"given":"Cyril","family":"Soler","sequence":"first","affiliation":[{"name":"INRIA and Grenoble University, Montbonnot-Saint-Martin, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mahdi M.","family":"Bagher","sequence":"additional","affiliation":[{"name":"University of Montreal and Microsoft Corporation, QC, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Derek","family":"Nowrouzezahrai","sequence":"additional","affiliation":[{"name":"University of Montreal, QC, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2015,11,3]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.5555\/949531.949560"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/34.93808"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185529"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2007.01072.x"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1109\/38.656788"},{"key":"e_1_2_2_6_1","first-page":"2","article-title":"HealPix: A framework for high-resolution discretization and fast analysis distributed on the sphere","volume":"622","author":"Grski K. M.","year":"2005","unstructured":"K. M. Grski , E. Hivon , A. J. Banday , B. D. Wandelt , F. K. Hansen , M. Reinecke , and M. Bartelmann . 2005 . HealPix: A framework for high-resolution discretization and fast analysis distributed on the sphere . Astrophys. J. 622 , 2 , 759. K. M. Grski, E. Hivon, A. J. Banday, B. D. Wandelt, F. K. Hansen, M. Reinecke, and M. Bartelmann. 2005. HealPix: A framework for high-resolution discretization and fast analysis distributed on the sphere. Astrophys. J. 622, 2, 759.","journal-title":"Astrophys. J."},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276412"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/311535.311554"},{"key":"e_1_2_2_9_1","volume-title":"The Theory of Spherical and Ellipsoidal Harmonics","author":"Hobson E.","unstructured":"E. Hobson . 1931. The Theory of Spherical and Ellipsoidal Harmonics . The University Press , Chicago . E. Hobson. 1931. The Theory of Spherical and Ellipsoidal Harmonics. The University Press, Chicago."},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2003.10.010"},{"key":"e_1_2_2_11_1","volume-title":"Proceedings of the 13th Eurographics Workshop on Rendering (EGRW'02)","author":"Kautz J.","unstructured":"J. Kautz , P.-P. Sloan , and J. Snyder . 2002. Fast, arbitrary BRDF shading for low-frequency lighting using spherical harmonics . In Proceedings of the 13th Eurographics Workshop on Rendering (EGRW'02) . Eurographics Association, 291--296. J. Kautz, P.-P. Sloan, and J. Snyder. 2002. Fast, arbitrary BRDF shading for low-frequency lighting using spherical harmonics. In Proceedings of the 13th Eurographics Workshop on Rendering (EGRW'02). Eurographics Association, 291--296."},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/1866158.1866175"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1731047.1731052"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2008.01252.x"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2011.09.014"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-006-0064-9"},{"key":"e_1_2_2_17_1","volume-title":"A Wavelet Tour of Signed Processing: The Sparse Way","author":"Mallat S.","unstructured":"S. Mallat . 2008. A Wavelet Tour of Signed Processing: The Sparse Way . 3 rd Ed. Academic Press . S. Mallat. 2008. A Wavelet Tour of Signed Processing: The Sparse Way. 3rd Ed. Academic Press.","edition":"3"},{"key":"e_1_2_2_18_1","unstructured":"K. Mardia and P. Jupp. 2009. Directional Statistics. Wiley Series in Probability and Statistics. Wiley.  K. Mardia and P. Jupp. 2009. Directional Statistics. Wiley Series in Probability and Statistics. Wiley."},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882343"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/383259.383276"},{"key":"e_1_2_2_21_1","doi-asserted-by":"crossref","unstructured":"J. McCormack K. I. Farkas R. Perry and N. P. Jouppi. 1999. Simple and table feline: Fast elliptical lines for anisotropic texture mapping. Res. rep. HP Labs. http:\/\/www.hpl.hp.com\/techreports\/Compaq-DEC\/WRL-99-1.pdf.  J. McCormack K. I. Farkas R. Perry and N. P. Jouppi. 1999. Simple and table feline: Fast elliptical lines for anisotropic texture mapping. Res. rep. HP Labs. http:\/\/www.hpl.hp.com\/techreports\/Compaq-DEC\/WRL-99-1.pdf.","DOI":"10.1145\/311535.311562"},{"key":"e_1_2_2_22_1","unstructured":"G. S. Miller and C. R. Hoffman. 1984. 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