# 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 } }