Zero-variance Transmittance Estimation

Eugene d'Eon, Jan Novák

Proceedings of EGSR 2021

abstract

We apply zero-variance theory to the Volterra integral formulation of volumetric transmittance. We solve for the guided sampling decisions in this framework that produce zero-variance ratio tracking and next-flight ratio tracking estimators. In both cases, a zero-variance estimate arises by colliding only with the null particles along the interval. For ratio tracking, this is equivalent to residual ratio tracking with a perfect control. The next-flight zero-variance estimator is of the collision type and can only produce zero-variance estimates if the random walk never terminates. In drawing these new connections, we enrich the theory of Monte Carlo transmittance estimation and provide a new rigorous path-stretching interpretation of residual ratio tracking.

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bibtex

@inproceedings{dEon2021zerovar,
  title        = { Zero-variance Transmittance Estimation },
  author       = { d'Eon, Eugene and Nov\'{a}k, Jan },
  booktitle    = { Eurographics Symposium on Rendering },
  year         = { 2021 },
  month        = { June },
  doi          = { 10.2312/sr.20211286 },
  publisher    = { The Eurographics Association }
}