Monte Carlo Methods in Global Illumination: Photo-realistic Rendering with Randomization

This book discusses Monte Carlo algorithms and their application to solve the global illumination rendering problem of computer graphics. Mathematically, photo-realistic rendering is equivalent to the solution of an integral equation that can be successfully attacked by Monte Carlo integration techniques. The book first discusses the theory of light-surface interaction and the equations that describe materials and the transfer of the illumination. We examine Monte Carlo and quasi-Monte Carlo approaches, which can be used to solve these equations. A considerable space is devoted to variance reduction techniques, including importance sampling, correlated sampling, the Metropolis method, weighted importance sampling, etc. Then the book presents random walk algorithms, like path tracing, light tracing, bi-directional path tracing, photon mapping, instant radiosity, Metropolis light transport, etc. Stochastic iterative techniques are also surveyed. Finally, implementation details are shortly addressed taking the example of path tracing.