Statistical Representations of Visual Patterns

Abstract

The goal of vision (especially in the early stage) is to solve the following equation: Graphics(Lighting, Shape, Surface) = Image, where the three visual factors are, respectively, light sources, 3-D geometry of objects and their forms, poses, and relative positions, and the 2-D maps of local geometric and photometric details of object surfaces. Graphics( ) is a function describing how the retina images are produced by the visual factors. To make this inverse graphics problem well defined and to understand the meaning encoded in the images, it is necessary to find low-dimensional representations, or semantics, for visual factors. Such representations can be called patterns. For some patterns, deterministic representations are available, but for most realistic visual patterns, statistical representations are needed. My talk will deal with statistical representations of texture patterns. Part of the talk is based on joint papers with S. C. Zhu, D. Mumford, and X. Liu.