{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T04:08:51Z","timestamp":1791259731959,"version":"4.1.0"},"reference-count":58,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2013,6,1]],"date-time":"2013-06-01T00:00:00Z","timestamp":1370044800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100000288","name":"Royal Society","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000288","id-type":"DOI","asserted-by":"publisher"}]},{"name":"INRIA Associate Team CIPRus"},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2013,6]]},"abstract":"<jats:p>The rendering of effects such as motion blur and depth-of-field requires costly 5D integrals. We accelerate their computation through adaptive sampling and reconstruction based on the prediction of the anisotropy and bandwidth of the integrand. For this, we develop a new frequency analysis of the 5D temporal light-field, and show that first-order motion can be handled through simple changes of coordinates in 5D. We further introduce a compact representation of the spectrum using the covariance matrix and Gaussian approximations. We derive update equations for the 5 \u00d7 5 covariance matrices for each atomic light transport event, such as transport, occlusion, BRDF, texture, lens, and motion. The focus on atomic operations makes our work general, and removes the need for special-case formulas. We present a new rendering algorithm that computes 5D covariance matrices on the image plane by tracing paths through the scene, focusing on the single-bounce case. This allows us to reduce sampling rates when appropriate and perform reconstruction of images with complex depth-of-field and motion blur effects.<\/jats:p>","DOI":"10.1145\/2487228.2487239","type":"journal-article","created":{"date-parts":[[2013,7,2]],"date-time":"2013-07-02T14:32:49Z","timestamp":1372775569000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":55,"title":["5D Covariance tracing for efficient defocus and motion blur"],"prefix":"10.1145","volume":"32","author":[{"given":"Laurent","family":"Belcour","sequence":"first","affiliation":[{"name":"Grenoble University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cyril","family":"Soler","sequence":"additional","affiliation":[{"name":"Inria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kartic","family":"Subr","sequence":"additional","affiliation":[{"name":"University College London"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicolas","family":"Holzschuch","sequence":"additional","affiliation":[{"name":"Inria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fredo","family":"Durand","sequence":"additional","affiliation":[{"name":"MIT CSAIL"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2013,7,4]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073319"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2159616.2159637"},{"key":"e_1_2_2_3_1","volume-title":"Proceedings of the International Conference on Computational Science and its Applications.","author":"Barsky B. A.","unstructured":"Barsky , B. A. , Horn , D. R. , Klein , S. A. , Pang , J. A. , and Yu , M . 2003. Camera models and optical systems used in computer graphics: Part II, image based techniques . In Proceedings of the International Conference on Computational Science and its Applications. Barsky, B. A., Horn, D. R., Klein, S. A., Pang, J. A., and Yu, M. 2003. Camera models and optical systems used in computer graphics: Part II, image based techniques. In Proceedings of the International Conference on Computational Science and its Applications."},{"key":"e_1_2_2_4_1","volume-title":"Proceedings of the 12th WSEAS International Conference on Computers. 999--1010","author":"Barsky B. A.","unstructured":"Barsky , B. A. and Kosloff , T. J . 2008. Algorithms for rendering depth of field effects in computer graphics . In Proceedings of the 12th WSEAS International Conference on Computers. 999--1010 . Barsky, B. A. and Kosloff, T. J. 2008. Algorithms for rendering depth of field effects in computer graphics. In Proceedings of the 12th WSEAS International Conference on Computers. 999--1010."},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218497"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280924"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/344779.344932"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/380666.380670"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/7529.8927"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/37402.37414"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/964965.808590"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/325165.325182"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073320"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024214"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/1944846.1944849"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531399"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/1572769.1572780"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/258734.258818"},{"key":"e_1_2_2_19_1","unstructured":"Gerrard A. and Burch J. 1975. Introduction to Matrix Methods in Optics. Wiley Series in Pure and Applied Optics. John Wiley and Sons.  Gerrard A. and Burch J. 1975. Introduction to Matrix Methods in Optics. Wiley Series in Pure and Applied Optics. John Wiley and Sons."},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360632"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276410"},{"key":"e_1_2_2_22_1","volume-title":"Master's thesis, UCB\/CSD 89\/516CS, UC Berkeley","author":"Heckbert P. S.","unstructured":"Heckbert , P. S. 1989. Fundamentals of texture mapping and image warping , Master's thesis, UCB\/CSD 89\/516CS, UC Berkeley . University of Californiya . Heckbert, P. S. 1989. Fundamentals of texture mapping and image warping, Master's thesis, UCB\/CSD 89\/516CS, UC Berkeley. University of Californiya."},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/1833349.1778801"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/311535.311555"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/127719.122735"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218463"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2007.01088.x"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/1618452.1618480"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778802"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/2010324.1964950"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2010.01736.x"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531403"},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360670"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.5555\/2383654.2383669"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276454"},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1145\/325334.325188"},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1145\/37401.37410"},{"key":"e_1_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/122718.122736"},{"key":"e_1_2_2_39_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-6453-2_21"},{"key":"e_1_2_2_40_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073256"},{"key":"e_1_2_2_41_1","doi-asserted-by":"publisher","DOI":"10.1145\/1618452.1618486"},{"key":"e_1_2_2_42_1","doi-asserted-by":"publisher","DOI":"10.1145\/965161.806818"},{"key":"e_1_2_2_43_1","doi-asserted-by":"publisher","DOI":"10.1145\/964967.801169"},{"key":"e_1_2_2_44_1","volume-title":"Proceedings of the Eurographics Symposium on Point-Based Graphics. 19--28","author":"Quinn J. A.","unstructured":"Quinn , J. A. , Langbein , F. C. , and Martin , R. R . 2007. Lowdiscrepancy point sampling of meshes for rendering . In Proceedings of the Eurographics Symposium on Point-Based Graphics. 19--28 . Quinn, J. A., Langbein, F. C., and Martin, R. R. 2007. Lowdiscrepancy point sampling of meshes for rendering. In Proceedings of the Eurographics Symposium on Point-Based Graphics. 19--28."},{"key":"e_1_2_2_45_1","doi-asserted-by":"publisher","DOI":"10.1145\/383259.383271"},{"key":"e_1_2_2_46_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2005.22"},{"key":"e_1_2_2_47_1","doi-asserted-by":"publisher","DOI":"10.1145\/1189762.1189764"},{"key":"e_1_2_2_48_1","doi-asserted-by":"publisher","DOI":"10.1145\/2024156.2024193"},{"key":"e_1_2_2_49_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2010.46"},{"key":"e_1_2_2_50_1","doi-asserted-by":"publisher","DOI":"10.1145\/2167076.2167083"},{"key":"e_1_2_2_51_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882281"},{"key":"e_1_2_2_52_1","doi-asserted-by":"publisher","DOI":"10.1145\/1516522.1516529"},{"key":"e_1_2_2_53_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015795"},{"key":"e_1_2_2_54_1","volume-title":"Proceedings of the Rendering Techniques'01 (EG Workshop on Rendering). 257--268","author":"Suykens F.","unstructured":"Suykens , F. and Willems , Y . 2001. Path differentials and applications . In Proceedings of the Rendering Techniques'01 (EG Workshop on Rendering). 257--268 . Suykens, F. and Willems, Y. 2001. Path differentials and applications. In Proceedings of the Rendering Techniques'01 (EG Workshop on Rendering). 257--268."},{"key":"e_1_2_2_55_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1141997"},{"key":"e_1_2_2_56_1","volume-title":"Proceedings of the Workshop on Rendering (EG'92)","author":"Ward G. J.","unstructured":"Ward , G. J. and Heckbert , P . 1992. Irradiance gradients . In Proceedings of the Workshop on Rendering (EG'92) . 85--98. Ward, G. J. and Heckbert, P. 1992. Irradiance gradients. In Proceedings of the Workshop on Rendering (EG'92). 85--98."},{"key":"e_1_2_2_57_1","doi-asserted-by":"publisher","DOI":"10.1145\/358876.358882"},{"key":"e_1_2_2_58_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2007.00935.x"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2487228.2487239","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2487228.2487239","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T08:48:39Z","timestamp":1750236519000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2487228.2487239"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6]]},"references-count":58,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,6]]}},"alternative-id":["10.1145\/2487228.2487239"],"URL":"https:\/\/doi.org\/10.1145\/2487228.2487239","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,6]]},"assertion":[{"value":"2012-01-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2013-02-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2013-07-04","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}