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Graph."],"published-print":{"date-parts":[[2024,12,19]]},"abstract":"<jats:p>\n            Quasi-Monte Carlo integration is at the core of rendering. This technique estimates the value of an integral by evaluating the integrand at well-chosen sample locations. These sample points are designed to cover the domain as uniformly as possible to achieve better convergence rates than purely random points. Deterministic low-discrepancy sequences have been shown to outperform many competitors by guaranteeing good uniformity as measured by the so-called discrepancy metric, and, indirectly, by an integer\n            <jats:italic>t<\/jats:italic>\n            value relating the number of points falling into each domain stratum with the stratum area (lower\n            <jats:italic>t<\/jats:italic>\n            is better). To achieve randomness, scrambling techniques produce multiple realizations preserving the\n            <jats:italic>t<\/jats:italic>\n            value, making the construction stochastic. Among them, Owen scrambling is a popular approach that recursively permutes intervals for each dimension. However, relying on permutation trees makes it incompatible with smooth optimization frameworks. We present a differentiable Owen scrambling that regularizes permutations. We show that it can effectively be used with automatic differentiation tools for optimizing low-discrepancy sequences to improve metrics such as optimal transport uniformity, integration error, designed power spectra or projective properties, while maintaining their initial\n            <jats:italic>t<\/jats:italic>\n            -value as guaranteed by Owen scrambling. In some rendering settings, we show that our optimized sequences improve the rendering error.\n          <\/jats:p>","DOI":"10.1145\/3687764","type":"journal-article","created":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T15:46:04Z","timestamp":1732031164000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["Differentiable Owen Scrambling"],"prefix":"10.1145","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-9225-5407","authenticated-orcid":false,"given":"Bastien","family":"Doignies","sequence":"first","affiliation":[{"name":"Universit\u00e9 Claude Bernard Lyon 1, Villeurbanne, France"},{"name":"CNRS, INSA Lyon, LIRIS, Villeurbanne, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3164-8697","authenticated-orcid":false,"given":"David","family":"Coeurjolly","sequence":"additional","affiliation":[{"name":"CNRS, Villeurbanne, France"},{"name":"Universit\u00e9 Claude Bernard Lyon 1, INSA Lyon, LIRIS, Villeurbanne, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5243-4810","authenticated-orcid":false,"given":"Nicolas","family":"Bonneel","sequence":"additional","affiliation":[{"name":"CNRS, Villeurbanne, France"},{"name":"Universit\u00e9 Claude Bernard Lyon 1, INSA Lyon, LIRIS, Villeurbanne, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0905-0840","authenticated-orcid":false,"given":"Julie","family":"Digne","sequence":"additional","affiliation":[{"name":"CNRS, Villeurbanne, France"},{"name":"Universit\u00e9 Claude Bernard Lyon 1, INSA Lyon, LIRIS, Villeurbanne, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6877-2398","authenticated-orcid":false,"given":"Jean-Claude","family":"Iehl","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Claude Bernard Lyon 1, Villeurbanne, France"},{"name":"CNRS, INSA Lyon, LIRIS, Villeurbanne, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-3123-9388","authenticated-orcid":false,"given":"Victor","family":"Ostromoukhov","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Claude Bernard Lyon 1, Villeurbanne, France"},{"name":"CNRS, INSA Lyon, LIRIS, Villeurbanne, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2024,11,19]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2980179.2980218"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/3618307"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/3550454.3555519"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/3618308"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459880"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531392"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/42288.214372"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.sorms.2012.08.001"},{"key":"e_1_2_2_9_1","first-page":"4","article-title":"Practical Hash-based Owen Scrambling","volume":"10","author":"Burley Brent","year":"2020","unstructured":"Brent Burley. 2020. 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