{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T16:08:35Z","timestamp":1769184515886,"version":"3.49.0"},"reference-count":28,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2023,12,5]],"date-time":"2023-12-05T00:00:00Z","timestamp":1701734400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NSF","award":["1900927, 2105806"],"award-info":[{"award-number":["1900927, 2105806"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2023,12,5]]},"abstract":"<jats:p>Physics-based differentiable rendering is becoming increasingly crucial for tasks in inverse rendering and machine learning pipelines. To address discontinuities caused by geometric boundaries and occlusion, two classes of methods have been proposed: 1) the edge-sampling methods that directly sample light paths at the scene discontinuity boundaries, which require nontrivial data structures and precomputation to select the edges, and 2) the reparameterization methods that avoid discontinuity sampling but are currently limited to hemispherical integrals and unidirectional path tracing.<\/jats:p>\n          <jats:p>We introduce a new mathematical formulation that enjoys the benefits of both classes of methods. Unlike previous reparameterization work that focused on hemispherical integral, we derive the reparameterization in the path space. As a result, to estimate derivatives using our formulation, we can apply advanced Monte Carlo rendering methods, such as bidirectional path tracing, while avoiding explicit sampling of discontinuity boundaries. We show differentiable rendering and inverse rendering results to demonstrate the effectiveness of our method.<\/jats:p>","DOI":"10.1145\/3618330","type":"journal-article","created":{"date-parts":[[2023,12,5]],"date-time":"2023-12-05T10:20:48Z","timestamp":1701771648000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":34,"title":["Warped-Area Reparameterization of Differential Path Integrals"],"prefix":"10.1145","volume":"42","author":[{"given":"Peiyu","family":"Xu","sequence":"first","affiliation":[{"name":"University of California, Irvine, USA"}]},{"given":"Sai","family":"Bangaru","sequence":"additional","affiliation":[{"name":"MIT CSAIL, USA"}]},{"given":"Tzu-Mao","family":"Li","sequence":"additional","affiliation":[{"name":"University of California, San Diego, USA"}]},{"given":"Shuang","family":"Zhao","sequence":"additional","affiliation":[{"name":"University of California, Irvine, USA"}]}],"member":"320","published-online":{"date-parts":[[2023,12,5]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"crossref","unstructured":"Dejan Azinovi\u0107 Tzu-Mao Li Anton Kaplanyan and Matthias Nie\u00dfner. 2019. Inverse Path Tracing for Joint Material and Lighting Estimation. In Computer Vision and Pattern Recognition.","DOI":"10.1109\/CVPR.2019.00255"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/3550469.3555397"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/3414685.3417833"},{"key":"e_1_2_2_4_1","volume-title":"Radiative transfer","author":"Chandrasekhar Subrahmanyan","unstructured":"Subrahmanyan Chandrasekhar. 1960. Radiative transfer. Courier Corporation."},{"key":"e_1_2_2_5_1","volume-title":"Towards Learning-based Inverse Subsurface Scattering. In 2020 IEEE International Conference on Computational Photography (ICCP). IEEE, 1--12","author":"Che Chengqian","year":"2020","unstructured":"Chengqian Che, Fujun Luan, Shuang Zhao, Kavita Bala, and Ioannis Gkioulekas. 2020. Towards Learning-based Inverse Subsurface Scattering. In 2020 IEEE International Conference on Computational Photography (ICCP). IEEE, 1--12."},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1973.11993339"},{"key":"e_1_2_2_7_1","volume-title":"The Rendering Equation. In SIGGRAPH '86","author":"Kajiya James T.","year":"1986","unstructured":"James T. Kajiya. 1986. The Rendering Equation. In SIGGRAPH '86. 143--150."},{"key":"e_1_2_2_8_1","volume-title":"Rendering techniques' 96","author":"Lafortune Eric P","unstructured":"Eric P Lafortune and Yves D Willems. 1996. Rendering participating media with bidirectional path tracing. In Rendering techniques' 96. Springer, 91--100."},{"key":"e_1_2_2_9_1","unstructured":"Tzu-Mao Li. 2023. redner: Differentiable rendering without approximation. https:\/\/github.com\/BachiLi\/redner."},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/3272127.3275109"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/3355089.3356510"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14344"},{"key":"e_1_2_2_13_1","volume-title":"Automatically Synthesize Fast Gradients. In Advances in Neural Information Processing Systems","author":"Moses William","unstructured":"William Moses and Valentin Churavy. 2020. Instead of Rewriting Foreign Code for Machine Learning, Automatically Synthesize Fast Gradients. In Advances in Neural Information Processing Systems, H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin (Eds.), Vol. 33. Curran Associates, Inc., 12472--12485."},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530073"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392406"},{"key":"e_1_2_2_16_1","volume-title":"Papers on mechanical and physical subjects: the sub-mechanics of the universe","author":"Reynolds Osborne","unstructured":"Osborne Reynolds. 1903. Papers on mechanical and physical subjects: the sub-mechanics of the universe. Vol. 3. The University Press."},{"key":"e_1_2_2_17_1","volume-title":"Robust Monte Carlo methods for light transport simulation","author":"Veach Eric","unstructured":"Eric Veach. 1997. Robust Monte Carlo methods for light transport simulation. Vol. 1610. Stanford University PhD thesis."},{"key":"e_1_2_2_18_1","volume-title":"Photorealistic Rendering Techniques","author":"Veach Eric","unstructured":"Eric Veach and Leonidas Guibas. 1995. Bidirectional estimators for light transport. 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