Unbiased and consistent rendering using biased estimators

SIGGRAPH 2022 (journal)

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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  author = {Zackary Misso and Benedikt Bitterli and Iliyan Georgiev and Wojciech Jarosz},
  title = {Unbiased and consistent rendering using biased estimators},
  journal = {ACM Transactions on Graphics (Proceedings of SIGGRAPH)},
  year = {2022},
  volume = {41},
  number = {4},
  doi = {10.1145/3528223.3530160}