The problem of global illumination in computer graphics is described by a Fredholm integral equation of the second kind. Due to the complexity of this equation, Monte Carlo methods provide an efficient tool for the estimation of the solution. A new approach, using quasi-Monte Carlo integration, is introduced and compared to Monte Carlo integration. We discuss some theoretical aspects and give n...

We consider the problem of numerical integration in dimension s, with eventually large s; the usual rules need a very huge number of nodes with increasing dimension to obtain some accuracy, say an error bound less than 10−2; this phenomenon is called ”the curse of dimensionality”; to overcome it, two kind of methods have been developped: the so-called Monte-Carlo and Quasi-Monte-Carlo methods. ...

We present a new adaptive Monte Carlo integration algorithm for ill-behaved integrands with non-factorizable singularities. The algorithm combines Vegas with multi channel sampling and performs significantly better than Vegas for a large class of integrals appearing in physics.

Currently, the most eeective constructions of low-discrepancy point sets and sequences are based on the theory of (t; m; s)-nets and (t; s)-sequences. In this work we discuss parallelization techniques for quasi-Monte Carlo integration using (t; s)-sequences. We show that leapfrog parallelization may be very dangerous whereas block-based paral-lelization turns out to be robust.

Monte Carlo methods refer to any method that uses random numbers to get an approximate answer to a problem. In computer graphics Monte Carlo techniques can be used to perform radiosity calculations and can be used in distribution ray tracing for effects such as soft shadows and motion blur. Although these notes are for a course on radiosity, they have a great deal of material from a previous Si...

This paper investigates a class of algorithms for numerical integration of a function in d dimensions over a compact domain by Monte Carlo methods. We construct a histogram approximation to the function using a partition of the integration domain into a set of bins specified by some parameters. We then consider two adaptations; the first is to subtract the histogram approximation, whose integra...

Spatial Monte Carlo integration (SMCI) is an extension of standard and can approximate expectations on Markov random fields with high accuracy. SMCI was applied to pairwise Boltzmann machine (PBM) learning, superior results those from some existing methods. The approximation level be changed, it proved that a higher-order statistically more accurate than lower-order approximation. However, as p...