Прямой расчет оптимального веса для MIS

Abstract

A Monte-Carlo ray tracing is nowadays standard approach for lighting simulation and generation of realistic images. A widely used method for noise reduction in Monte-Carlo ray tracing is combing different means of sampling, known as Multiple Importance Sampling (MIS). For bi-directional Monte-Carlo ray tracing with photon maps (BDPM) the join paths are obtained by merging camera and light sub-paths. Since several light paths are checked against the same camera path and vice versa, the join paths obtained are not statistically independent. Thus the noise in this method does not obey the laws which are correct in simple classic Monte-Carlo with independent samples. And, correspondingly, the MIS weights that minimize that noise must also be calculated differently. In this paper we calculate these weights for a simple model scene directly minimizing the noise of calculation. This is a pure direct numerical minimization that does not involve any doubtful hypothesis or approximations. We show that the weights obtained are qualitatively different from those calculated from classic “balance heuristic” for Monte-Carlo with independent samples. They depend on the scene distance, but not only on scattering properties of the surfaces and the distribution of light source emission.