Single-pass stratified importance resampling

Resampling is the process of selecting from a set of candidate samples to achieve a distribution (approximately) proportional to a desired target. Recent work has revisited its application to Monte Carlo integration, yielding powerful and practical importance sampling methods. One drawback of existing resampling methods is that they cannot generate stratified samples. We propose two complementary techniques to achieve efficient stratified resampling. We first introduce bidirectional CDF sampling which yields the same result as conventional inverse CDF sampling but in a single pass over the candidates, without needing to store them, similarly to reservoir sampling. We then order the candidates along a space-filling curve to ensure that stratified CDF sampling of candidate indices yields stratified samples in the integration domain. We showcase our method on various resampling-based rendering problems.

Automated summary

Resampling is the process of selecting samples from a set of candidates to achieve a distribution that is approximately proportional to a desired target. Recent research has explored its application to Monte Carlo integration, resulting in powerful and practical importance sampling methods. Existing resampling methods have the limitation of not being able to generate stratified samples. We propose two complementary techniques to efficiently achieve stratified resampling.