Sequential Monte Carlo Methods for Physically Based Rendering
The goal of global illumination is to generate photo-realistic images by taking into account all of 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 inter-reflections is very expensive. In this dissertation, a novel statistical framework for physically based rendering in computer graphics is presented based on sequential Monte Carlos (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. This approach samples light transport paths that connect a light to the eye, which accounts for the viewer in the sampling process and provides information to improve photon storage. Paths are sampled with a Metropolis-Hastings algorithm that exploits coherence among important light paths. To handle difficult paths in the path space, a technique is presented for including user-selected paths in the sampling process. This allows a user to provide hints about important paths to reduce variance in specific parts of the image.
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 interation can be used to guide subsequent iterations without introducing bias in the final result. This is the first application of the population Monte Carlo method to comptuer graphics.
After getting samples from multiple distributions, how the estimator is constructed for Monte Carlo integration has a big impact on the variance in the rendered images. Combining the idea of importance sampling and control variate, an optimal control variate algorithm is developed that allows samples from multiple distribution functions to be combined optimally. In optimizing nature correlated function that is optimized for each estimate rather than a single highly-tuned one that must work well everywehre.
The population Montge Carlo rendering framework and optimized unbiased estimator result in more efficient and robust algorithms for global illumination. Significant improvements in results are demonstated for various commonly existing environments suvch as scenes with non-uniform variance on the image planes and scenes with difficult but important paths.
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