A Bayesian Monte Carlo Approach to Global Illumination

Abstract

International audienceMost Monte Carlo rendering algorithms rely on importance sampling to reduce the variance of estimates. Importance sampling is efficient when the proposal sample distribution is well-suited to the form of the integrand but fails otherwise. The main reason is that the sample location information is not exploited. All sample values are given the same importance regardless of their proximity to one another. Two samples falling in a similar location will have equal importance whereas they are likely to contain redundant information. The Bayesian approach we propose in this paper uses both the location and value of the data to infer an integral value based on a prior probabilistic model of the integrand. The Bayesian estimate depends only on the sample values and locations, and not how these samples have been chosen. We show how this theory can be applied to the final gathering problem and present results that clearly demonstrate the benefits of Bayesian Monte Carlo

A Spherical Gaussian Framework for Bayesian Monte Carlo Rendering of Glossy Surfaces

“…However, it is not suited to the particularities of spherical functions we are faced with in global illumination problems. Brouillat et al [2] have proposed solutions in the context of final gathering for photon mapping and have clearly shown the benefit of BMC over MCIS. However, this method can only deal with diffuse reflections.…”

“…However, all these advantages are obtained at the expense of the quadrature complexity and additional preprocessing. Brouillat et al [2] have proposed efficient solutions that make the overhead of computing the BMC quadrature negligible compared to CMC. Moreover, their results show that BMC can significantly outperform CMC methods, even when including the preprocessing step.…”

“…A direct application of the method to view dependent BRDFs would require massive precomputations of multidimensional tables so as to allow an acceptable rendering time. The prior model construction strategy presented in Brouillat et al [2] would also be inappropriate to the sharpness features of glossy BRDFs. It would require performing a learning phase for each BRDF present in the scene, which would represent a high computational cost.…”

“…We account for the BRDF sharpness by using a new computation method for the prior mean function and by introducing a new factor in the method of Brouillat et al [2] for constructing optimized samples set. Lastly, we propose a fast hyperparameters evaluation method that avoids the learning step.…”

“…Detailed information can be found in [1], [2], [3]. The notations used throughout the paper are described in Tab.…”