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.


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.


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

Links and Downloads

Corona Renderer
pdf (36 MB)
pdf (0.7 MB)
Corona implements the method as described in the paper


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