{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T08:44:59Z","timestamp":1780994699111,"version":"3.54.1"},"reference-count":56,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2018,12,4]],"date-time":"2018-12-04T00:00:00Z","timestamp":1543881600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100015599","name":"Toyota Research Institute","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100015599","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2018,12,31]]},"abstract":"<jats:p>Gradient-based methods are becoming increasingly important for computer graphics, machine learning, and computer vision. The ability to compute gradients is crucial to optimization, inverse problems, and deep learning. In rendering, the gradient is required with respect to variables such as camera parameters, light sources, scene geometry, or material appearance. However, computing the gradient of rendering is challenging because the rendering integral includes visibility terms that are not differentiable. Previous work on differentiable rendering has focused on approximate solutions. They often do not handle secondary effects such as shadows or global illumination, or they do not provide the gradient with respect to variables other than pixel coordinates.<\/jats:p>\n          <jats:p>We introduce a general-purpose differentiable ray tracer, which, to our knowledge, is the first comprehensive solution that is able to compute derivatives of scalar functions over a rendered image with respect to arbitrary scene parameters such as camera pose, scene geometry, materials, and lighting parameters. The key to our method is a novel edge sampling algorithm that directly samples the Dirac delta functions introduced by the derivatives of the discontinuous integrand. We also develop efficient importance sampling methods based on spatial hierarchies. Our method can generate gradients in times running from seconds to minutes depending on scene complexity and desired precision.<\/jats:p>\n          <jats:p>We interface our differentiable ray tracer with the deep learning library PyTorch and show prototype applications in inverse rendering and the generation of adversarial examples for neural networks.<\/jats:p>","DOI":"10.1145\/3272127.3275109","type":"journal-article","created":{"date-parts":[[2018,11,28]],"date-time":"2018-11-28T19:16:10Z","timestamp":1543432570000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":260,"title":["Differentiable Monte Carlo ray tracing through edge sampling"],"prefix":"10.1145","volume":"37","author":[{"given":"Tzu-Mao","family":"Li","sequence":"first","affiliation":[{"name":"MIT CSAIL"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Miika","family":"Aittala","sequence":"additional","affiliation":[{"name":"MIT CSAIL"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fr\u00e9do","family":"Durand","sequence":"additional","affiliation":[{"name":"MIT CSAIL"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jaakko","family":"Lehtinen","sequence":"additional","affiliation":[{"name":"Aalto University &amp; NVIDIA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2018,12,4]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925917"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461978"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766967"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/192161.192250"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2014.2377712"},{"key":"e_1_2_2_7_1","unstructured":"Benedikt Bitterli. 2016. Rendering resources. https:\/\/benedikt-bitterli.me\/resources\/.  Benedikt Bitterli. 2016. Rendering resources. https:\/\/benedikt-bitterli.me\/resources\/."},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/311535.311556"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.01975.x"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/2343483.2343493"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/380666.380670"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/3233305"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-46487-9_42"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/2508363.2508377"},{"key":"e_1_2_2_15_1","volume-title":"Explaining and Harnessing Adversarial Examples. In International Conference on Learning Representations.","author":"Goodfellow Ian","year":"2015","unstructured":"Ian Goodfellow , Jonathon Shlens , and Christian Szegedy . 2015 . Explaining and Harnessing Adversarial Examples. In International Conference on Learning Representations. Ian Goodfellow, Jonathon Shlens, and Christian Szegedy. 2015. Explaining and Harnessing Adversarial Examples. In International Conference on Learning Representations."},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.5555\/1455489"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925895"},{"key":"e_1_2_2_18_1","doi-asserted-by":"crossref","unstructured":"Eric Heitz and Stephen Hill. 2017. Linear-Light Shading with Linearly Transformed Cosines. In GPU Zen.  Eric Heitz and Stephen Hill. 2017. Linear-Light Shading with Linearly Transformed Cosines. In GPU Zen.","DOI":"10.1145\/2897824.2925895"},{"key":"e_1_2_2_19_1","volume-title":"SIGGRAPH Course Notes. Course on Non-Photorelistic Rendering","author":"Hertzmann Aaron","unstructured":"Aaron Hertzmann . 1999. Introduction to 3D Non-Photorealistic Rendering: Silhouettes and Outlines . In SIGGRAPH Course Notes. Course on Non-Photorelistic Rendering , Stuart Green (Ed.). ACM Press\/ACM SIGGRAPH , New York . Aaron Hertzmann. 1999. Introduction to 3D Non-Photorealistic Rendering: Silhouettes and Outlines. In SIGGRAPH Course Notes. Course on Non-Photorelistic Rendering, Stuart Green (Ed.). ACM Press\/ACM SIGGRAPH, New York."},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/344779.345074"},{"key":"e_1_2_2_21_1","unstructured":"Lars H\u00f6rmander. 1983. The analysis of linear partial differential operators I: Distribution theory and Fourier analysis.  Lars H\u00f6rmander. 1983. The analysis of linear partial differential operators I: Distribution theory and Fourier analysis."},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/311535.311555"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601186"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185554"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/2231816.2231823"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/15886.15902"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601108"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2018.00411"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1145\/2818648"},{"key":"e_1_2_2_32_1","volume-title":"International Conference on Learning Representations.","author":"Kingma Diederick P","year":"2015","unstructured":"Diederick P Kingma and Jimmy Ba . 2015 . Adam: A method for stochastic optimization . In International Conference on Learning Representations. Diederick P Kingma and Jimmy Ba. 2015. Adam: A method for stochastic optimization. In International Conference on Learning Representations."},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2005.83"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/2816795.2818084"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2017.248"},{"key":"e_1_2_2_36_1","volume-title":"OpenDR: An Approximate Differentiable Renderer. In European Conference on Computer Vision","volume":"8695","author":"Matthew","unstructured":"Matthew M. Loper and Michael J. Black. 2014 . OpenDR: An Approximate Differentiable Renderer. In European Conference on Computer Vision , Vol. 8695 . 154--169. Matthew M. Loper and Michael J. Black. 2014. OpenDR: An Approximate Differentiable Renderer. In European Conference on Computer Vision, Vol. 8695. 154--169."},{"key":"e_1_2_2_37_1","unstructured":"Morgan McGuire. 2017. Computer Graphics Archive. https:\/\/casual-effects.com\/data  Morgan McGuire. 2017. Computer Graphics Archive. https:\/\/casual-effects.com\/data"},{"key":"e_1_2_2_38_1","volume-title":"A Light Hierarchy for Fast Rendering of Scenes with Many Lights. Computer Graphics Forum (Proc. Eurographics)","author":"Paquette Eric","year":"1998","unstructured":"Eric Paquette , Pierre Poulin , and George Drettakis . 1998. A Light Hierarchy for Fast Rendering of Scenes with Many Lights. Computer Graphics Forum (Proc. Eurographics) ( 1998 ), 63--74. Eric Paquette, Pierre Poulin, and George Drettakis. 1998. A Light Hierarchy for Fast Rendering of Scenes with Many Lights. Computer Graphics Forum (Proc. Eurographics) (1998), 63--74."},{"key":"e_1_2_2_39_1","unstructured":"Adam Paszke Sam Gross Soumith Chintala Gregory Chanan Edward Yang Zachary DeVito Zeming Lin Alban Desmaison Luca Antiga and Adam Lerer. 2017. Automatic differentiation in PyTorch. (2017).  Adam Paszke Sam Gross Soumith Chintala Gregory Chanan Edward Yang Zachary DeVito Zeming Lin Alban Desmaison Luca Antiga and Adam Lerer. 2017. Automatic differentiation in PyTorch. (2017)."},{"key":"e_1_2_2_40_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2003.00716.x"},{"key":"e_1_2_2_41_1","doi-asserted-by":"publisher","DOI":"10.1145\/1189762.1189764"},{"key":"e_1_2_2_42_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2017.589"},{"key":"e_1_2_2_43_1","doi-asserted-by":"publisher","DOI":"10.1145\/344779.344935"},{"key":"e_1_2_2_44_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00514"},{"key":"e_1_2_2_45_1","doi-asserted-by":"publisher","DOI":"10.1145\/37402.37408"},{"key":"e_1_2_2_46_1","unstructured":"K. Simonyan and A. Zisserman. 2014. Very Deep Convolutional Networks for Large-Scale Image Recognition. arXiv preprint arXiv:1409.1556 (2014).  K. Simonyan and A. Zisserman. 2014. Very Deep Convolutional Networks for Large-Scale Image Recognition. arXiv preprint arXiv:1409.1556 (2014)."},{"key":"e_1_2_2_47_1","volume-title":"Path Differentials and Applications. In Eurographics Workshop on Rendering Techniques. 257--268","author":"Suykens Frank","unstructured":"Frank Suykens and Yves D. Willems . 2001 . Path Differentials and Applications. In Eurographics Workshop on Rendering Techniques. 257--268 . Frank Suykens and Yves D. Willems. 2001. Path Differentials and Applications. In Eurographics Workshop on Rendering Techniques. 257--268."},{"key":"e_1_2_2_48_1","volume-title":"International Conference on Learning Representations.","author":"Szegedy Christian","year":"2014","unstructured":"Christian Szegedy , Wojciech Zaremba , Ilya Sutskever , Joan Bruna , Dumitru Erhan , Ian Goodfellow , and Rob Fergus . 2014 . Intriguing properties of neural networks . In International Conference on Learning Representations. Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus. 2014. Intriguing properties of neural networks. In International Conference on Learning Representations."},{"key":"e_1_2_2_49_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218498"},{"key":"e_1_2_2_50_1","doi-asserted-by":"publisher","DOI":"10.1145\/258734.258775"},{"key":"e_1_2_2_51_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601199"},{"key":"e_1_2_2_52_1","volume-title":"Notes on the Ward BRDF. Program of Computer Graphics","author":"Walter Bruce","year":"2005","unstructured":"Bruce Walter . 2005. Notes on the Ward BRDF. Program of Computer Graphics , Cornell University , Technical report PCG-05 6 ( 2005 ). Bruce Walter. 2005. Notes on the Ward BRDF. Program of Computer Graphics, Cornell University, Technical report PCG-05 6 (2005)."},{"key":"e_1_2_2_53_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1141997"},{"key":"e_1_2_2_54_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073318"},{"key":"e_1_2_2_55_1","volume-title":"Microfacet models for refraction through rough surfaces. Rendering Techniques (Proc. EGSR)","author":"Walter Bruce","year":"2007","unstructured":"Bruce Walter , Stephen R Marschner , Hongsong Li , and Kenneth E Torrance . 2007. Microfacet models for refraction through rough surfaces. Rendering Techniques (Proc. EGSR) ( 2007 ), 195--206. Bruce Walter, Stephen R Marschner, Hongsong Li, and Kenneth E Torrance. 2007. Microfacet models for refraction through rough surfaces. Rendering Techniques (Proc. EGSR) (2007), 195--206."},{"key":"e_1_2_2_56_1","doi-asserted-by":"publisher","DOI":"10.1145\/1401132.1401225"},{"key":"e_1_2_2_57_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13374"},{"key":"e_1_2_2_58_1","doi-asserted-by":"publisher","DOI":"10.1145\/311535.311559"},{"key":"e_1_2_2_59_1","volume-title":"Chi Keung Tang, and Alan L Yuille","author":"Zeng Xiaohui","year":"2017","unstructured":"Xiaohui Zeng , Chenxi Liu , Weichao Qiu , Lingxi Xie , Yu-Wing Tai , Chi Keung Tang, and Alan L Yuille . 2017 . Adversarial Attacks Beyond the Image Space . arXiv preprint arXiv:1711.07183 (2017). Xiaohui Zeng, Chenxi Liu, Weichao Qiu, Lingxi Xie, Yu-Wing Tai, Chi Keung Tang, and Alan L Yuille. 2017. Adversarial Attacks Beyond the Image Space. arXiv preprint arXiv:1711.07183 (2017)."}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3272127.3275109","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3272127.3275109","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T00:44:26Z","timestamp":1750207466000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3272127.3275109"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,4]]},"references-count":56,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2018,12,31]]}},"alternative-id":["10.1145\/3272127.3275109"],"URL":"https:\/\/doi.org\/10.1145\/3272127.3275109","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,4]]},"assertion":[{"value":"2018-12-04","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}