A Markovian Random field of piecewise straight lines

This paper presents the construction of a vector-valued markovian Random field on a finite lattice, whose equilibrium configurations consist of piecewise straight lines of arbitrary orientations that uses only nearest neighbor interactions. For certain parameter values, this field presents a form of self organization, in which the lattice is partitioned into regions where particular line directions dominate. We also develop a stochastic cellular automaton (based on the Gibbs Sampler algorithm) that simulates this field. To illustrate the usefulness of this construction for the solution of computational vision problems, we present a simple application: the restoration of images that consist on incomplete contours.