Stochastic Methods in Global Illumination --- State of the Art Report

Szirmay-Kalos László
Department of Control Engineering and Information Technology, Technical University of Budapest,
Budapest, Muegyetem rkp. 11, H-1111, HUNGARY


This paper presents a state of the art report of those global illumination algorithms which involve Monte-Carlo or quasi-Monte Carlo techniques. First it surveys the basic tasks of global illumination, which can be formulated as the solution of either the rendering or the potential equation, then reviews the basic solution techniques, including inversion, expansion and iteration. The paper explains why stochastic approaches are good to solve these integral equations. It compares, for example, finite-element and continuous methods, pure Monte-Carlo and quasi-Monte Carlo techniques, different versions of importance sampling, Russian roulette, local and global visibility algorithms, etc. Then, a lot of methods are reviewed in a unified framework, that also allows to make comparisons.


Rendering equation, potential equation, Monte-Carlo and quasi-Monte Carlo quadratures, finite-element techniques, radiosity, importance sampling, Russian roulette, shooting and gathering random walks, stochastic iteration, Metropolis sampling, distributed ray-tracing, path tracing, photon tracing, light tracing, bi-directional path tracing, photon-map, instant radiosity, global ray-bundle tracing, stochastic ray-radiosity, transillumination method, first-shot, error and complexity