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Graph."],"published-print":{"date-parts":[[2026,7,3]]},"abstract":"<jats:p>To enable differentiation with respect to object geometries, boundary path integrals\u2014central to physics-based differentiable rendering\u2014must be estimated numerically. Although their mathematical formulation is well established, designing efficient and robust numerical estimators remains challenging. Most state-of-the-art boundary sampling methods rely on primary-sample-space guiding, which tends to break down on finely tessellated geometries; reparameterization-based alternatives, meanwhile, often incur high variance and\/or significant computational overhead.<\/jats:p>\n                  <jats:p>In this paper, we introduce a simple, robust, and consistent solution to this problem. At the core of our approach is a novel formulation of the boundary integral based on kernel-density estimation. Much like photon mapping, we slightly expand the measure-zero domain of integration with a kernel, sidestepping the need to sample directly on a delta-function region in path space. To our knowledge, this is the first such application of kernel-density methods for boundary integral evaluation. We validate our method by comparing its derivative estimates against finite differences (FD), and further demonstrate its practical utility by benchmarking against several state-of-the-art baselines in synthetic inverse-rendering scenarios.<\/jats:p>","DOI":"10.1145\/3811325","type":"journal-article","created":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:05:51Z","timestamp":1783062351000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Robust Computation of Boundary Path Integrals Using Kernel-Density Estimation"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-0271-2545","authenticated-orcid":false,"given":"Peiyu","family":"Xu","sequence":"first","affiliation":[{"name":"University of Illinois Urbana-Champaign, Champaign, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5735-0998","authenticated-orcid":false,"given":"Lifan","family":"Wu","sequence":"additional","affiliation":[{"name":"NVIDIA, Redmond, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8799-7119","authenticated-orcid":false,"given":"Benedikt","family":"Bitterli","sequence":"additional","affiliation":[{"name":"NVIDIA, Redmond, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3993-5789","authenticated-orcid":false,"given":"Ravi","family":"Ramamoorthi","sequence":"additional","affiliation":[{"name":"NVIDIA, Redmond, USA"},{"name":"University of California San Diego, San Diego, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4759-0514","authenticated-orcid":false,"given":"Shuang","family":"Zhao","sequence":"additional","affiliation":[{"name":"University of Illinois Urbana-Champaign, Champaign, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,7,3]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/3414685.3417833"},{"key":"e_1_2_1_2_1","first-page":"4","article-title":"Beyond Points and Beams: Higher-Dimensional Photon Samples for Volumetric Light Transport","volume":"36","author":"Bitterli Benedikt","year":"2017","unstructured":"Benedikt Bitterli and Wojciech Jarosz. 2017. 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