Likelihood Calculation for a Class of Multiscale Stochastic Models, with Application to Texture Discrimination

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Abstract
A class of multiscale stochastic models based on scale-recursive dynamics on trees has recently been introduced. Theoretical and experimental results have shown that these models provide an extremely rich framework for representing both processes which are intrinsically multiscale, e.g., 1/f processes, as well as 1-D Markov processes and 2-D Markov random fields. Moreover, efficient optimal estimation algorithms have been developed for these models by exploiting their scale-recursive structure. In this paper, we exploit this structure in order to develop a computationally efficient and parallelizable algorithm for likelihood calculation. We illustrate one possible application to texture discrimination and demonstrate that likelihood-based methods using our algorithm have substantially better probability of error characteristics than well-known least-squares methods, and achieve performance comparable to that of Gaussian Markov random field based techniques, which in general are prohibitively complex computationally.

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