Variance Reduction via Footprint Estimation in the Presence of Path Reuse

Multiple importance sampling is a tool to weight the results of different samplers with the goal of a minimal variance for the sampled function. If applied to light transport paths, this tool enables techniques such as bidirectional path tracing and vertex connection and merging. The latter generalizes the path probability measure to merges—also known as photon mapping. Unfortunately, the resulting heuristic can fail, resulting in a noticeable increase of noise. This chapter provides an insight into why things go wrong and proposes a simple-to-implement heuristic that is closer to an optimal solution and more reliable over different scenes. The trick is to use footprint estimates of sub-paths to predict the true variance reduction that is introduced by reusing all the photons.