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Robustly and efficiently constructing such fields remains challenging.<\/jats:p>\n                  <jats:p>\n                    We present a novel velocity field construction for differential visibility. Inspired by recent Monte Carlo solvers for partial differential equations (PDEs), we formulate the velocity field via Laplace's equation and solve it with a walk-on-spheres (WoS) algorithm. To improve efficiency, we introduce a\n                    <jats:italic toggle=\"yes\">fixed-step<\/jats:italic>\n                    WoS that terminates random walks after a fixed step count, resulting in a continuous but non-harmonic velocity field still valid for warped-area reparameterization. Furthermore, to practically apply our method to complex 3D scenes, we propose an efficient cone query to find the closest silhouettes on a boundary. Our cone query finds the closest point under the geodesic distance on a unit sphere, and is analogous to the closest point query by WoS to compute Euclidean distance. As a result, our method generalizes WoS to perform random walks on spherical caps over the unit sphere. We demonstrate that this enables a more robust and efficient unbiased estimator for differential visibility.\n                  <\/jats:p>","DOI":"10.1145\/3731174","type":"journal-article","created":{"date-parts":[[2025,7,27]],"date-time":"2025-07-27T04:02:22Z","timestamp":1753588942000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Unbiased Differential Visibility Using Fixed-Step Walk-on-Spherical-Caps And Closest Silhouettes"],"prefix":"10.1145","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5735-0998","authenticated-orcid":false,"given":"Lifan","family":"Wu","sequence":"first","affiliation":[{"name":"NVIDIA, Redmond, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2262-6974","authenticated-orcid":false,"given":"Nathan","family":"Morrical","sequence":"additional","affiliation":[{"name":"NVIDIA, Redmond, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6302-9327","authenticated-orcid":false,"given":"Sai Praveen","family":"Bangaru","sequence":"additional","affiliation":[{"name":"NVIDIA, Cambridge, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3661-1554","authenticated-orcid":false,"given":"Rohan","family":"Sawhney","sequence":"additional","affiliation":[{"name":"NVIDIA, Santa Clara, 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":"NVIDIA, Irvine, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5133-4292","authenticated-orcid":false,"given":"Chris","family":"Wyman","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, La Jolla, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-6526-0922","authenticated-orcid":false,"given":"Aaron","family":"Lefohn","sequence":"additional","affiliation":[{"name":"NVIDIA, Redmond, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2025,7,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/3550469.3555397"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/3618353"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/3414685.3417833"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/3648611"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-012-0161-z"},{"key":"e_1_2_2_6_1","volume-title":"Parameter-space ReSTIR for Differentiable and Inverse Rendering. 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