{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T02:40:11Z","timestamp":1774924811111,"version":"3.50.1"},"reference-count":38,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2022,7,1]],"date-time":"2022-07-01T00:00:00Z","timestamp":1656633600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1844538,1812796"],"award-info":[{"award-number":["1844538,1812796"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2022,7]]},"abstract":"<jats:p>We introduce a general framework for transforming biased estimators into unbiased and consistent estimators for the same quantity. We show how several existing unbiased and consistent estimation strategies in rendering are special cases of this framework, and are part of a broader debiasing principle. We provide a recipe for constructing estimators using our generalized framework and demonstrate its applicability by developing novel unbiased forms of transmittance estimation, photon mapping, and finite differences.<\/jats:p>","DOI":"10.1145\/3528223.3530160","type":"journal-article","created":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T21:06:27Z","timestamp":1658523987000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":15,"title":["Unbiased and consistent rendering using biased estimators"],"prefix":"10.1145","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2362-2358","authenticated-orcid":false,"given":"Zackary","family":"Misso","sequence":"first","affiliation":[{"name":"Dartmouth College"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8799-7119","authenticated-orcid":false,"given":"Benedikt","family":"Bitterli","sequence":"additional","affiliation":[{"name":"Dartmouth College and NVIDIA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9655-2138","authenticated-orcid":false,"given":"Iliyan","family":"Georgiev","sequence":"additional","affiliation":[{"name":"Autodesk, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1652-0954","authenticated-orcid":false,"given":"Wojciech","family":"Jarosz","sequence":"additional","affiliation":[{"name":"Dartmouth College"}]}],"member":"320","published-online":{"date-parts":[[2022,7,22]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/3414685.3417833"},{"key":"e_1_2_2_2_1","unstructured":"Benedikt Bitterli. 2016. Rendering resources. https:\/\/benedikt-bitterli.me\/resources\/."},{"key":"e_1_2_2_3_1","first-page":"6","article-title":"A Radiative Transfer Framework for Non-Exponential Media","volume":"37","author":"Bitterli Benedikt","year":"2018","unstructured":"Benedikt Bitterli, Srinath Ravichandran, Thomas M\u00fcller, Magnus Wrenninge, Jan Nov\u00e1k, Steve Marschner, and Wojciech Jarosz. 2018. A Radiative Transfer Framework for Non-Exponential Media. ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia) 37, 6 (Nov. 2018), 225:1--225:17. gfz2cm","journal-title":"ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia)"},{"key":"e_1_2_2_4_1","volume-title":"2015 Winter Simulation Conference (WSC). 360--367","author":"Blanchet Jose H.","unstructured":"Jose H. Blanchet, Nan Chen, and Peter W. Glynn. 2015. Unbiased Monte Carlo Computation of Smooth Functions of Expectations via Taylor Expansions. In 2015 Winter Simulation Conference (WSC). 360--367. ggr94p"},{"key":"e_1_2_2_5_1","volume-title":"2015 Winter Simulation Conference (WSC). 3656--3667","author":"Jose","unstructured":"Jose H. Blanchet and Peter W. Glynn. 2015. Unbiased Monte Carlo for Optimization and Functions of Expectations via Multi-Level Randomization. In 2015 Winter Simulation Conference (WSC). 3656--3667. ggr94h"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.13182\/NSE07-A2707"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-018-31574-4"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jqsrt.2010.10.001"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366211"},{"key":"e_1_2_2_10_1","first-page":"6","article-title":"Integral Formulations of Volumetric Transmittance","volume":"38","author":"Georgiev Iliyan","year":"2019","unstructured":"Iliyan Georgiev, Zackary Misso, Toshiya Hachisuka, Derek Nowrouzezahrai, Jaroslav K\u0159iv\u00e1nek, and Wojciech Jarosz. 2019. Integral Formulations of Volumetric Transmittance. ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia) 38, 6 (Nov. 2019), 154:1--154:17. dffn","journal-title":"ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia)"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1070.0496"},{"key":"e_1_2_2_12_1","first-page":"6","article-title":"A Progressive Error Estimation Framework for Photon Density Estimation","volume":"29","author":"Hachisuka Toshiya","year":"2010","unstructured":"Toshiya Hachisuka, Wojciech Jarosz, and Henrik Wann Jensen. 2010. A Progressive Error Estimation Framework for Photon Density Estimation. ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia) 29, 6 (Dec. 2010), 144:1--144:12. dmttfg","journal-title":"ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia)"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1618452.1618487"},{"key":"e_1_2_2_14_1","volume-title":"Proc. of the 3rd St. Petersburg Workshop on Simulation. St","author":"Heinrich S.","year":"1998","unstructured":"S. Heinrich. 1998. A Multilevel Version of the Method of Dependent Tests. In Proc. of the 3rd St. Petersburg Workshop on Simulation. St. Petersburg University Press, 31--35."},{"key":"e_1_2_2_15_1","first-page":"4","article-title":"A Radiative Transfer Framework for Spatially-Correlated Materials","volume":"37","author":"Jarabo Adrian","year":"2018","unstructured":"Adrian Jarabo, Carlos Aliaga, and Diego Gutierrez. 2018. A Radiative Transfer Framework for Spatially-Correlated Materials. ACM Transactions on Graphics (Proceedings of SIGGRAPH) 37, 4 (July 2018), 83:1--83:13. gd52qq","journal-title":"ACM Transactions on Graphics (Proceedings of SIGGRAPH)"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024215"},{"key":"e_1_2_2_17_1","first-page":"6","article-title":"Progressive Photon Beams","volume":"30","author":"Jarosz Wojciech","year":"2011","unstructured":"Wojciech Jarosz, Derek Nowrouzezahrai, Robert Thomas, Peter-Pike Sloan, and Matthias Zwicker. 2011b. Progressive Photon Beams. ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia) 30, 6 (Dec. 2011), 181:1--181:12. fn5xzj","journal-title":"ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia)"},{"key":"e_1_2_2_18_1","volume-title":"Realistic Image Synthesis Using Photon Mapping","author":"Jensen Henrik Wann","unstructured":"Henrik Wann Jensen. 2001. Realistic Image Synthesis Using Photon Mapping. AK Peters, Ltd., Natick, MA, USA."},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2020.2969439"},{"key":"e_1_2_2_20_1","volume-title":"Direct Transmittance Estimation in Heterogeneous Participating Media Using Approximated Taylor Expansions","author":"Jonsson Daniel","year":"2020","unstructured":"Daniel Jonsson, Joel Kronander, Jonas Unger, Thomas B. Schon, and Magnus Wrenninge. 2020. Direct Transmittance Estimation in Heterogeneous Participating Media Using Approximated Taylor Expansions. IEEE Transactions on Visualization and Computer Graphics (2020), 1--1. gj32rc"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(00)00248-2"},{"key":"e_1_2_2_22_1","volume-title":"An Unbiased Ray-Marching Transmittance Estimator. (Feb","author":"Kettunen Markus","year":"2021","unstructured":"Markus Kettunen, Eugene d'Eon, Jacopo Pantaleoni, and Jan Novak. 2021. An Unbiased Ray-Marching Transmittance Estimator. (Feb. 2021). arXiv:2102.10294 [cs.GR]"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/1966394.1966404"},{"key":"e_1_2_2_24_1","first-page":"4","article-title":"Spectral and Decomposition Tracking for Rendering Heterogeneous Volumes","volume":"36","author":"Kutz Peter","year":"2017","unstructured":"Peter Kutz, Ralf Habel, Yining Karl Li, and Jan Nov\u00e1k. 2017. Spectral and Decomposition Tracking for Rendering Heterogeneous Volumes. ACM Transactions on Graphics (Proceedings of SIGGRAPH) 36, 4 (July 2017), 111:1--111:16. gbxjxg","journal-title":"ACM Transactions on Graphics (Proceedings of SIGGRAPH)"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1515\/mcma.2011.013"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","unstructured":"Zackary Misso Benedikt Bitterli Iliyan Georgiev and Wojciech Jarosz. 2022. Unbiased and consistent rendering using biased estimators supplemental code and data. 10.5281\/zenodo.6515009","DOI":"10.5281\/zenodo.6515009"},{"key":"e_1_2_2_27_1","volume-title":"Unbiased Estimation of the Reciprocal Mean for Non-Negative Random Variables. In 2019 Winter Simulation Conference (WSC). 404--415","author":"Moka Sarat Babu","year":"2019","unstructured":"Sarat Babu Moka, Dirk P. Kroese, and Sandeep Juneja. 2019. Unbiased Estimation of the Reciprocal Mean for Non-Negative Random Variables. In 2019 Winter Simulation Conference (WSC). 404--415. ggr944"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/2661229.2661292"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/3414685.3417793"},{"key":"e_1_2_2_30_1","volume-title":"Physically Based Rendering: From Theory to Implementation","author":"Pharr Matt","unstructured":"Matt Pharr, Wenzel Jakob, and Greg Humphreys. 2016. Physically Based Rendering: From Theory to Implementation (3rd ed.). Morgan Kaufmann, Cambridge, MA.","edition":"3"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1145\/2816795.2818119"},{"key":"e_1_2_2_32_1","volume-title":"Unbiased Estimation with Biased Samplers. Ph. D. Dissertation","unstructured":"Chang-han Rhee. 2013. Unbiased Estimation with Biased Samplers. Ph. D. Dissertation. Stanford University."},{"key":"e_1_2_2_33_1","volume-title":"Glynn","author":"Rhee","year":"2012","unstructured":"Chang-han Rhee and Peter W. Glynn. 2012. A New Approach to Unbiased Estimation for SDE's. (July 2012). arXiv:1207.2452 [q-fin.CP]"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.2015.1404"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459804"},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925912"},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610928708829512"},{"key":"e_1_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/3386569.3392408"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3528223.3530160","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3528223.3530160","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3528223.3530160","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T19:02:49Z","timestamp":1750186969000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3528223.3530160"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7]]},"references-count":38,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,7]]}},"alternative-id":["10.1145\/3528223.3530160"],"URL":"https:\/\/doi.org\/10.1145\/3528223.3530160","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7]]},"assertion":[{"value":"2022-07-22","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}