Jaroslav Křivánek

MIS Compensation: Optimizing Sampling Techniques in Multiple Importance Sampling

Ondřej Karlík Chaos Czech a. s.

Martin Šik Chaos Czech a. s.

Petr Vévoda Charles University, Prague Chaos Czech a.s.

Tomáš Skřivan IST Austria

Jaroslav Křivánek Charles University, Prague Chaos Czech a. s.

Equal-time (5 s) comparison of basic multiple importance sampling with the balance heuristic (Basic MIS), resampled importance sampling (RIS) and our (normal-independent) method applied to image-based lighting computation. While RIS performs similarly to Basic MIS here, our method achieves 2.75× lower normalized mean square error (NMSE) by redefining the pdf of one of the sampling techniques, while taking into account that MIS is being applied. The pdfs are shown in the bottom row. The pdf optimization presented in this paper is general and can be applied in any MIS estimator.

Abstract

Multiple importance sampling (MIS) has become an indispensable tool in Monte Carlo rendering, widely accepted as a near-optimal solution for combining different sampling techniques. But an MIS combination, using the common balance or power heuristics, often results in an overly defensive estimator, leading to high variance. We show that by generalizing the MIS framework, variance can be substantially reduced. Specifically, we optimize one of the combined sampling techniques so as to decrease the overall variance of the resulting MIS estimator. We apply the approach to the computation of direct illumination due to an HDR environment map and to the computation of global illumination using a path guiding algorithm. The implementation can be as simple as subtracting a constant value from the tabulated sampling density done entirely in a preprocessing step. This produces a consistent noise reduction in all our tests with no negative influence on run time, no artifacts or bias, and no failure cases.

Reference

Ondřej Karlík, Martin Šik, Petr Vévoda, Tomáš Skřivan, and Jaroslav Křivánek. MIS Compensation: Optimizing Sampling Techniques in Multiple Importance Sampling. ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia 2019), 38(6), 2019.
DOI | BibTeX

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Acknowledgments

This work was supported by the Czech Science Foundation Grant 19- 07626S and the Charles University Grant SVV-2017-260452.