Unbiased and consistent rendering using biased estimators

1Dartmouth College 2NVIDIA 3Autodesk

In ACM Transactions on Graphics (Proceedings of SIGGRAPH), 2022

Decomposition of our unbiased photon mapping into the sum of a biased estimate and a bias term. We separate the bias into positive and negative parts for ease of visualization.


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.



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The cloud model in Fig. 8 is from Walt Disney Animation Studios. The scenes for Fig. 2, Fig. 4 and Fig. 10 were based off of scenes from Bitterli [2016]. This work was generously supported by NSF awards 1812796 and 1844538, a Neukom Institute CompX faculty grant, and a Facebook PhD fellowship.


Zackary Misso, Benedikt Bitterli, Iliyan Georgiev, Wojciech Jarosz. Unbiased and consistent rendering using biased estimators. ACM Transactions on Graphics (Proceedings of SIGGRAPH), 41(4), July 2022.
    author  = {Misso, Zackary and Bitterli, Benedikt and Georgiev, Iliyan and Jarosz, Wojciech},
    title   = {Unbiased and consistent rendering using biased estimators},
    journal = {ACM Transactions on Graphics (Proceedings of SIGGRAPH)},
    year    = {2022},
    month   = jul,
    volume  = {41},
    number  = {4},
    doi     = {10/gqjn66}
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