Importance driven quasi-random walk solution of the rendering equation

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 particleshooting, surfaces are decomposed into patches and the patches are interconnected by links.