Exploring texture ensembles by efficient Markov chain Monte Carlo-Toward a "trichromacy" theory of texture

Abstract

Presents a mathematical definition of texture, the Julesz ensemble /spl Omega/(h), which is the set of all images (defined on Z/sup 2/) that share identical statistics h. Then texture modeling is posed as an inverse problem: Given a set of images sampled from an unknown /spl Omega/(h/sub */), we search for the statistics h/sub */ which define the ensemble. A /spl Omega/(h) has an associated probability distribution q(I; h), which is uniform over the images in /spl Omega/(h) and has zero probability outside. The authors previously (1999) showed q(I; h) to be the limit distribution of the FRAME (filter, random field, and minimax entropy) model, as the image lattice /spl Lambda//spl rarr/Z/sup 2/. This conclusion establishes the intrinsic link between the scientific definition of texture on Z/sup 2/ and the mathematical models of texture on finite lattices. It brings two advantages: the practice of texture image synthesis by matching statistics is put on a mathematical foundation; and we need not learn the expensive FRAME model in feature pursuit, model selection and texture synthesis. An efficient Markov chain Monte Carte algorithm is proposed for sampling Julesz ensembles. It generates random texture images by moving along the directions of filter coefficients and, thus, extends the traditional single site Gibbs sampler. We compare four popular statistical measures in the literature, in terms of their descriptive abilities. Our experiments suggest that a small number of bins in marginal histograms are sufficient for capturing a variety of texture patterns.