The use of Markov Random Fields as models of texture

Abstract

We propose Markov Random Fields (MRFs) as probabilistic models of digital image texture where a textured region is viewed as a finite sample of a two-dimensional random process describable by its statistical parameters. MRFs are multidimensional generalizations of Markov chains defined in terms of conditional probabilities associated with spatial neighborhoods. We present an algorithm that generates an MRF on a finite toroidal square lattice from an independent identically distributed (i.i.d.) array of random variables and a given set of independent real-valued statistical parameters. The parametric specification of a consistent collection of MRF conditional probabilities is a general result known as the MRF-Gibbs Random Field (GRF) equivalence. The MRF statistical parameters control the size and directionality of the clusters of adjacent similar pixels which are basic to texture discrimination and thus seem to constitute an efficient model of texture. In the last part of this paper we outline an MRF parameter estimation method and goodness of fit statistical tests applicable to MRF models for a given unknown digital image texture on a finite toroidal square lattice. The estimated parameters may be used as basic features in texture classification. Alternatively these parameters may be used in conjunction with the MRF generation algorithm as a powerful data compression scheme.