Texture Mixing via Universal Simulation

A framework for studying texture in general, and for texture mixing in particular, is presented in this paper. The work follows concepts from universal type classes and universal simulation. Based on the well-known Lempel and Ziv (LZ) universal compression scheme, the universal type class of a one dimensional sequence is defined as the set of possible sequences of the same length which span the same tree or dictionary with the classical LZ incremental parsing algorithm. Using universal simulation, beginning with a source texture image, we can synthesize new textures that have the same universal type and statistics as the source texture, yet they are sampled from the broadest pool of possible sequences that comply with the universal type constraint, thereby obtaining new textures with the same statistics and as much uncertainty as possible. When considering two or more textures, a universal type class is obtained for each one, and following the universal sampling approach while combining the corresponding trees, a mixed texture is obtained. As with single texture synthesis, the k-th order statistics of this mixture, for all k, is the weighted mixture of the k-th order statistics of each individual texture used in the mixing. We present the underlaying principles of universal types, universal simulation, and their extensions and application to mixing two or more textures with pre-defined proportions.