Importance driven quasi-random walk solution of the rendering equation

摘要

This paper presents a new method that combines quasi-Monte-Carlo quadrature with importance sampling and Russian roulette to solve the general rendering equation efficiently. Since classical importance sampling a Russian roulette have been proposed for Monte-Carlo integration, first an appropriate formulation is elaborated for deterministic sample sets used in quasi-Monte-Carlo methods. This formulation is based on integration by variable transformation. It is also shown that instead of multi-dimensional inversion methods, the variable transformation can be executed iteratively where each step works only with two-dimensional mappings. Since the integrands of the Neumannj expansion of the rendering equation are not available explicitly, some approximations are used, that are based on a particle shooting step. Although the complete method works for the original geometry, in order to store the results of the initial particle shooting, surfaces are decomposed into patches.