Stochastic sampling is a fundamental component in most computer graphics applications, including rendering, imaging, modeling, and simulation. For example, in rendering, stochastic sampling is crucial to efficiently solving complex integrals; in texture synthesis, it is the key to generate visually pleasing patterns; in geometry processing, it is used to characterize important geometry features. While much previous work has focused on planar samples with blue noise spectrum, little research has studied more general types of stochastic sampling. This research aims to advance the state of the art in general stochastic sampling, providing new theoretical insights, computational methods, and practical applications. The outcome benefits not only computer graphics and vision, but many other disciplines that rely on stochastic sampling techniques.
This project studies new methods for analyzing and synthesizing stochastic samples. On the analysis side, the research introduces new techniques, based on spatial statistics, to quantify the distribution properties of stochastic samples. On the synthesis side, the research presents computationally efficient methods to generate high-quality samples with desired distribution properties. Modern GPUs are employed to achieve parallel computation. These techniques in turn enable new applications. In rendering, the project answers fundamental questions such as the optimal sample patterns for anti-aliasing and half-toning. In computational photography, the project introduces novel scene-dependent coded patterns that allow a camera system to capture more details (spatially, temporally, and spectrally) in a single shot. In geometry processing, the project presents new technique to generate samples on surfaces, for remeshing, defining shape features, and performing shape matching.
