Likelihood-based texture discrimination with multiscale stochastic models

A class of multiscale models describing stochastic processes indexed by the nodes of a tree has recently been introduced by Chou et al. (1994). Experimental and theoretical results indicate that this class of models is quite rich, and moreover these models lead to extremely efficient algorithms for optimal estimation based on noisy observations. This motivates further algorithmic development, and in particular, in this paper we present a likelihood calculation algorithm for this class of multiscale models. That is, we consider the problem of computing the log of the conditional probability of a set of data assuming that they correspond to a particular multiscale model. We exploit the structure of the multiscale models to develop an efficient, scale recursive algorithm that allows for multiresolution data and parameters which vary in both space and scale. We illustrate one possible application of the algorithm to a texture classification problem in which one must choose from a given set of models that model which best represents or most likely corresponds to a given set of random field measurements. Texture modeling with Gaussian Markov random field (GMRF) models is well documented. One difficulty in using GMRF models, however, is that the calculation of likelihoods may be prohibitively complex computationally if there is an irregular sampling pattern. It is shown here that GMRF models can be represented within our multiscale model class which allows us to approximately compute likelihoods for GMRF models based on measurements over arbitrarily sampled regions. As we demonstrate in the context of texture discrimination problems, the multiscale approach not only leads to computationally efficient implementations, but also to virtually the same performance as the optimal GMRF-based likelihood ratio test. We discuss further applications in the area of synthetic aperture radar imagery processing.<<ETX>>