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1 2002

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Generalized multiple importance sampling for Monte-Carlo global illumination

Csonka F., Szirmay-Kalos L., Antal G.

Machine Graphics and Vision

2002

Vol. 11, No. 1

3-20

The global illumination or transport problems can be considered as a sequence of integrals, while their Monte-Carlo solutions - as different sampling techniques. Multiple importance sampling takes advantage of different sampling strategies, and combines the results obtained with them to estaglish a quasi-optimal sampling for Monte--Carlo quadratures. This offers a combination of totally different global illumination algorithms which preserves thier strengths. However, implementation of this general concept poses two problems. The solution of the global illumination problem does not contain a single integral, but a sequence of integrals that are approximated simulataneously. One objective of this paper is to generalize the fundamental theory of multiple importance sampling to sequences of integrals. The cost of the computation and the contribution of a single integral to the final result vary. On the other hand, different methods compute a sample with different computational burdens, which should also be taken into account. This paper attacks this problem and introduces the concept of computational cost in multiple importance sampling. The theoretical results are used to combine bi--directional path tracing and ray-bundle based stochastic iteration. We conclude that the combined method preserves the high initial speed of stochastic interation, but can also accurately compute the specular light paths through bi-directional path tracing.