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These combine to produce a single estimator that is universally optimal relative to prior work, with up to several orders of magnitude lower variance at the same cost, and has zero variance for any ray with non-varying extinction. We first reduce the variance of truncated power-series estimators using a novel efficient application of U-statistics. We then greatly reduce the average expansion order of the power series and redistribute density evaluations to filter the optical depth estimates with an equidistant sampling comb. Combined with the use of an online control variate built from a sampled mean density estimate, the resulting estimator effectively performs ray marching most of the time while using rarely-sampled higher-order terms to correct the bias.<\/jats:p>","DOI":"10.1145\/3450626.3459937","type":"journal-article","created":{"date-parts":[[2021,7,20]],"date-time":"2021-07-20T00:04:27Z","timestamp":1626739467000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":22,"title":["An unbiased ray-marching transmittance estimator"],"prefix":"10.1145","volume":"40","author":[{"given":"Markus","family":"Kettunen","sequence":"first","affiliation":[{"name":"NVIDIA"}]},{"given":"Eugene","family":"D'Eon","sequence":"additional","affiliation":[{"name":"NVIDIA"}]},{"given":"Jacopo","family":"Pantaleoni","sequence":"additional","affiliation":[{"name":"NVIDIA"}]},{"given":"Jan","family":"Nov\u00e1k","sequence":"additional","affiliation":[{"name":"NVIDIA"}]}],"member":"320","published-online":{"date-parts":[[2021,7,19]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.2312\/egtp.19871000"},{"key":"e_1_2_2_2_1","unstructured":"Nir Benty Kai-Hwa Yao Petrik Clarberg Lucy Chen Simon Kallweit Tim Foley Matthew Oakes Conor Lavelle and Chris Wyman. 2020. 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