Representativity for robust and adaptive multiple importance sampling

We present a general method enhancing the robustness of estimators based on multiple importance sampling (MIS) in a numerical integration context. MIS minimizes variance of estimators for a given sampling configuration, but when this configuration is less adapted to the integrand, the resulting estimator suffers from extra variance. We address this issue by introducing the notion of "representativity" of a sampling strategy, and demonstrate how it can be used to increase robustness of estimators, by adapting them to the integrand. We first show how to compute representativities using common rendering informations such as BSDF, photon maps, or caches in order to choose the best sampling strategy for MIS. We then give hints to generalize our method to any integration problem and demonstrate that it can be used successfully to enhance robustness in different common rendering algorithms.