Mixture of random walk solution and quasi-random walk solution to global illumination

Abstract

Conventional Monte Carlo methods are often used to solve some hard second kind Fredholm integral equations such as the difficult global illumination problems due to its dimensional independence. However, the convergence rate of the quasi-Monte Carlo methods for numerical integration is superior to that of the Monte Carlo methods. We present two mixed strategies that make use of both the statistical properties of random numbers and the uniformity properties of quasi-random numbers to build up walk histories for solving the global illumination. In the framework of the proposed strategies, experimental results have been obtained from rendering the test scenes. The computations indicate that the mixed strategies can outperform Monte Carlo or quasi-Monte Carlo used alone.