Importance Driven Quasi-Random Walk Solution of the Rendering Equation

Szirmay-Kalos László, Csébfalvi Balázs, Werner Purgathofer
Department of Process Control, Technical University of Budapest,
Budapest, Muegyetem rkp. 11, H-1111, HUNGARY


This paper presents a new method that combines quasi-Monte Carlo quadrature with importance sampling to solve the general rendering equation efficiently. Since classical importance sampling has 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 2-dimensional mappings. Since the integrands of the Neumann expansion of the rendering equation is not available explicitely, 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 and the patches are interconnected by links.