Probabilistic Connections for Bidirectional Path Tracing

Abstract

Bidirectional path tracing (BDPT) with Multiple Importance Sampling is one of the most versatile unbiased rendering algorithms today. BDPT repeatedly generates sub-paths from the eye and the lights, which are connected for each pixel and then discarded. Unfortunately, many such bidirectional connections turn out to have low contribution to the solution. Our key observation is that we can importance sample connections to an eye sub-path by considering multiple light sub-paths at once and creating connections probabilistically. We do this by storing light paths, and estimating probability mass functions of the discrete set of possible connections to all light paths. This has two key advantages: we efficiently create connections with low variance by Monte Carlo sampling, and we reuse light paths across different eye paths. We also introduce a caching scheme by deriving an approximation to sub-path contribution which avoids high-dimensional path distance computations. Our approach builds on caching methods developed in the different context of VPLs. Our Probabilistic Connections for Bidirectional Path Tracing approach raises a major challenge, since reuse results in high variance due to correlation between paths. We analyze the problem of path correlation and derive a conservative upper bound of the variance, with computationally tractable sample weights. We present results of our method which shows significant improvement over previous unbiased global illumination methods, and evaluate our algorithmic choices.