Second-Order Approximation for Variance Reduction in Multiple Importance Sampling

Heqi Lu 1, 2, 3 Romain Pacanowski 3, 1 Xavier Granier 1, 2, 3
1 MANAO - Melting the frontiers between Light, Shape and Matter
LaBRI - Laboratoire Bordelais de Recherche en Informatique, Inria Bordeaux - Sud-Ouest, LP2N - Laboratoire Photonique, Numérique et Nanosciences
Abstract : Monte Carlo Techniques are widely used in Computer Graphics to generate realistic images. Multiple Importance Sampling reduces the impact of choosing a dedicated strategy by balancing the number of samples between different strategies. However, an automatic choice of the optimal balancing remains a difficult problem. Without any scene characteristics knowledge, the default choice is to select the same number of samples from different strategies and to use them with heuristic techniques (e.g., balance, power or maximum). In this paper, we introduce a second-order approximation of variance for balance heuristic. Based on this approximation, we introduce an automatic distribution of samples for direct lighting without any prior knowledge of the scene characteristics. We demonstrate that for all our test scenes (with different types of materials, light sources and visibility complexity), our method actually reduces variance in average.We also propose an implementation with low overhead for online and GPU applications. We hope that this approach will help developing new balancing strategies.
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Submitted on : Wednesday, October 30, 2013 - 2:25:38 PM
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Heqi Lu, Romain Pacanowski, Xavier Granier. Second-Order Approximation for Variance Reduction in Multiple Importance Sampling. Computer Graphics Forum, Wiley, 2013, 32 (7), pp.131-136. ⟨10.1111/cgf.12220⟩. ⟨hal-00878654⟩

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