A dense class of Markov random fields and associated parameter estimation

In this paper, we address the problem of estimating parameters of Markov random fields (MRFs). We consider polynomial energy functions. We show both theoretically and by using simulations that this model represents a wide class of MRFs. We then develop a general scheme for estimating the MRF parameters associated with the gradient of such an energy function. The degree of the polynomial energy function as well as a super-set of the neighborhood of pixels are assumed to be known. This method, based on Euler's lemma, requires a partition of the space of neighborhood configurations. Simulations allow us to give a texture interpretation of the parameters associated with polynomial MRFs. Some results of the estimation method are presented for short, middle, and long range interactions. (C) 1997 Academic Press.