Variance-aware multiple importance sampling

SIGGRAPH Asia 2019

Equal-time comparison of bidirectional path tracing (BPT) with different MIS heuristics. The balance (b) and power (c) heuristics perform visibly worse than using only the unidirectional path tracing samples that BPT includes (b). The error reduction in parentheses is w.r.t. the balance heuristic combination; lower is better. Our variance-aware balance heuristic significantly improves the result (e), especially the direct illumination component (bottom row).


Many existing Monte Carlo methods rely on multiple importance sampling (MIS) to achieve robustness and versatility. Typically, the balance or power heuristics are used, mostly thanks to the seemingly strong guarantees on their variance. We show that these MIS heuristics are oblivious to the effect of certain variance reduction techniques like stratification. This shortcoming is particularly pronounced when unstratified and stratified techniques are combined (e.g., in a bidirectional path tracer). We propose to enhance the balance heuristic by injecting variance estimates of individual techniques, to reduce the variance of the combined estimator in such cases. Our method is simple to implement and introduces little overhead.

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BibTeX reference

  author = {Iliyan Georgiev and Zackary Misso and Toshiya Hachisuka and Derek Nowrouzezahrai and Jaroslav K\v{r}iv\'{a}nek and Wojciech Jarosz},
  title = {Integral formulations of volumetric transmittance},
  journal = {ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia)},
  volume = {38},
  number = {6},
  year = {2019},
  month = nov,
  keywords = {participating media, transmittance, null collision, null scattering, stochastic sampling, Monte Carlo integration}