Models for Stochastic Texture Generation

This work explores current models of textures for image synthesis and analysis, with an emphasis on generation of stochastic textures. Digital signal processing techniques are applied to create a general and robust model for the generation of stochastic textures. Martingale sequences are analyzed, and it is determined that the best way to develop martingale sequences is through the use of convolution. Methods of convolution with white noise are discussed. A number of ways to obtain the point spread function or texture filter for a target texture are developed. Important ways include the use of preexisting texture samples and the construction of ensemble averages. The theoretical framework behind the robustness of these methods is developed. Stochastic textures which have been generated with these methods are then used in the rendering process to give greater realism to objects in computer-generated images.