Point patterns and stochastic structures lie at the heart of Monte Carlo based numerical integration schemes. Physically based rendering algorithms have largely benefited from these Monte Carlo based schemes that inherently solve very high dimensional light transport integrals. However, due to the underlying stochastic nature of the samples, the resultant images are corrupted with noise (unstructured aliasing or variance). This also results in bad convergence rates that prohibit using these techniques in more interactive environments (e.g. games, virtual reality). With the advent of smart rendering techniques and powerful computing units (CPUs/GPUs), it is now possible to perform physically based rendering at interactive rates. However, much is left to understand regarding the underlying sampling structures and patterns which are the primary cause of error in rendering.
This course surveys the most recent state-of-the-art frameworks that are developed to better understand the impact of samples’ structure on the error and its convergence during Monte Carlo integration. It provides best practices and a set of tools for easy integration of such frameworks for sampling decisions in rendering. We revisit stochastic point processes that offers a unified theory explaining stochastic structures and sampling patterns in a common principled framework. We show how this theory generalizes spectral tools developed over the years to analyze error and convergence rates, and allows for analysis of more complex point patterns with adaptive density and correlations. At the end of the course, the audience will have a comprehensive understanding of both theoretical and practical aspects of point processes that would guide them in choosing and designing sampling strategies for applications specific to Monte Carlo rendering.
Slides (Cengiz Oztireli)
Slides (Gurprit Singh)
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