Go with the winners strategy in path tracing

Abstract

This paper proposes a new random walk strategy that minimizes the variance of the estimate using statistical estimations of local and global features of the scene. Based on the local and global properties, the algorithm decides at each point whether a Russian-roulette like random termination is worth performing, or on the contrary, we should split the path into several child paths. In this sense the algorithm is similar to the go-with-the-winners strategy invented in general Monte Carlo context. However, instead of establishing thresholds to make decisions, we compute the number of child paths on a continuous level and show that Russian roulette can be interpreted as a kind of splitting using fractional number of children. The new method is built into a path tracing algorithm, and a minimum cost heuristic is proposed for choosing the number of rejected rays. Comparing it with the classical path tracing approach we concluded that the new method reduced the variance significantly.