Spatial and Spectral Methods for Irregular Sampling in Computer Graphics

Abstract

Most general rasterization algorithms in computer graphics are based on point sampling of the underlying images. In computer graphics, the sampling patterns being used are typically irreuglar, mainly to prevent moiré artifacts in rendered images. The best irregular sampling patterns have a blue noise characteristic in the spectral domain:such patterns achieve a particularly good trade-off between moiré prevention and noise-free rendition of low image frequencies. This thesis presents new experimental and theoretical results on irregular sampling patterns. The focus is on the interaction between geometric and spectral properties of sampling patterns and their impact on the sampling process. First, we extend previous results on the spectral analysis of irregular sampling to explain in more detail how the shape of the power spectrum of a sampling pattern affects the visual appearance of aliasing. We then study the limiting case of Poisson disk sampling, which is the prevalent form of irregular sampling used in computer graphics, and demonstrate that it leads to sampling patterns with certain undesirable properties. Finally, we study the mathematical relationship between spatial statistics and spectral measures to make two important contributions to the theory of blue noise sampling. First, we study two realizability conditions, which explain how spatial and spectral characteristics of a point set constrain each other. Second, we show how to derive efficient irregular sampling patterns directly from a specification of their desired spectral properties.