Sequential Monte Carlo Methods for Physically Based Rendering
Shaohua Fan, Ph.D. Dissertation, University of Wisconsin - Madison, August 2006.

Abstract

The goal of global illumination is to generate photo-realistic images by taking into account all the light interactions in the scene. It does so by simulating light transport behaviors based on physical principles. The main challenge of global illumination is that simulating the complex light interreflections is very expensive. In this dissertation, a novel statistical framework for physically based rendering in computer graphics is presented based on sequential Monte Carlo (SMC) methods. This framework can substantially improve the efficiency of physically based rendering by adapting and reusing the light path samples without introducing bias. Applications of the framework to a variety of problems in global illumination are demonstrated.

For the task of photo-realistic rendering, only light paths that reach the image plane are important because only those paths contribute to the final image. A visual importance-driven algorithm is proposed to generate visually important paths. The photons along those paths are also cached in photon maps for further reuse. To handle difficult paths in the path space, a technique is presented for including user-selected paths in the sampling process. Then, a more general statistical method for light path sample adaptation and reuse is studied in the context of sequential Monte Carlo. Based on the population Monte Carlo method, an unbiased adaptive sampling method is presented that works on a population of samples. The samples are sampled and resampled through distributions that are modified over time. Information found at one iteration can be used to guide subsequent iterations without introducing bias in the final result. After obtaining samples from multiple distributions, an optimal control variate algorithm is developed that allows samples from multiple distribution functions to be combined optimally.