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Monte Carlo Integration

AMonte Carlo IntegrationTHE techniques developed in this dissertation are all Monte Carlo methods. Monte Carlomethods are numerical techniques which rely on random sampling toapproximatetheirresults. Monte Carlo Integration applies this process to the numerical estimation of integrals. Inthis appendix we review the fundamental concepts of Monte Carlo Integration upon which ourmethods are based. From this discussion we will see why Monte Carlo methods are a particularlyattractive choice for the multidimensional Integration problems common in computer references for Monte Carlo Integration in the context of computer graphics include Pharrand Humphreys [2004], Dutr et al.

dimensional integration problems, such as those encountered when computing global illumina-tion. 155 A.2.2 Multidimensional Integration Monte Carlo integration can be generalized to use random variables drawn from arbitrary PDFs and to compute multidimensional integrals, such as ...

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