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Graph."],"published-print":{"date-parts":[[2026,7,3]]},"abstract":"<jats:p>The theory of light transport on Gaussian process implicit surface (GPIS) provides a unified framework for rendering surfaces, participating media, and the intermediate spectrum. However, previous approaches rely on brute-force ray marching for surface intersections, requiring full noise evaluations at each marching point, whether using multivariate Gaussian sampling or sparse convolution noise approximation. This imposes a severe limitation on the rendering efficiency.<\/jats:p>\n                  <jats:p>In this paper, we derive bounds to significantly reduce the total number of full noise evaluations, leading to efficient ray marching for ray-surface intersections. We introduce stratified Bernoulli impulses, enabling a fast point-level bound for individual realizations to replace unnecessary full noise evaluations. To further reduce the number of point-level bound evaluations, we propose a region-level bound, leveraging a spatial acceleration structure to prune probabilistically empty regions, thereby avoiding unnecessary marching points in advance. By combining these two bounds, our bounded ray marching accelerates ray-surface intersections in GPIS, and consequently significantly improves overall GPIS rendering efficiency. Code for this paper are at https:\/\/github.com\/Cchen-77\/bounded-gpis.<\/jats:p>","DOI":"10.1145\/3811311","type":"journal-article","created":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:05:51Z","timestamp":1783062351000},"page":"1-15","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Bounding Stratified Bernoulli Impulses for Ray Marching Gaussian Process Implicit Surfaces"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-6299-3098","authenticated-orcid":false,"given":"Junjie","family":"Chen","sequence":"first","affiliation":[{"name":"State Key Lab for Novel Software Technology, Nanjing University, Nanjing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-6620-1900","authenticated-orcid":false,"given":"Zhimin","family":"Fan","sequence":"additional","affiliation":[{"name":"State Key Lab for Novel Software Technology, Nanjing University, Nanjing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9379-094X","authenticated-orcid":false,"given":"Ling-Qi","family":"Yan","sequence":"additional","affiliation":[{"name":"Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, United Arab Emirates"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8736-6317","authenticated-orcid":false,"given":"Junqiu","family":"Zhu","sequence":"additional","affiliation":[{"name":"Shandong University, Shandong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7605-5206","authenticated-orcid":false,"given":"Yanwen","family":"Guo","sequence":"additional","affiliation":[{"name":"State Key Lab for Novel Software Technology, Nanjing University, Nanjing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4243-6112","authenticated-orcid":false,"given":"Kun","family":"Zhou","sequence":"additional","affiliation":[{"name":"State Key Lab of CAD&amp;CG, Zhejiang University, Hangzhou, China"},{"name":"Institute of Hangzhou Holographic Intelligent Technology, Hangzhou, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4176-7617","authenticated-orcid":false,"given":"Jie","family":"Guo","sequence":"additional","affiliation":[{"name":"State Key Lab for Novel Software Technology, Nanjing University, Nanjing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,7,3]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729437"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.70057"},{"key":"e_1_2_2_3_1","unstructured":"Benedikt Bitterli. 2018. 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