Department of Statistics, UCLA

This paper presents a class of statistical models that integrate two statistical modeling paradigms in the literature: I) Descriptive methods, such as Markov random fields and minimax entropy learning [41] and II) Generative methods, such as principal component analysis, independent component analysis [2] transformed component analysis [11], wavelet coding [27, 5], and sparse coding [30, 24]. In this paper, we demonstrate the integrated framwork by constructing a class of hierarchical models for texton patterns ) the term "texton" was coined by psychologist Julez in the early 80's). At the bottom level of the model, we assume that an observed texture image is generated by multiple hidden "texton maps", and textons on each map are translated, scaled, stretched, and oriented versions of a window function, like mini-templates or wavelet bases. The texton maps generate the observed image by occlusion or linear superposition. this bottom level of the model is generative in nature. At the top level of the model, the spatial arrangements of the textons in the texton maps are characterized by minimax entropy principle, which leads to embellished versions of Gibbs point rocess [34]. The top level of the model is descriptive in nature. We demonstrate the integrated model by a set of experiments.