Stochastic processes that generate polygonal and related random fields

A reversible, ergodic, Markov process taking values in the space of polygonally segmented images is constructed. The stationary distribution of this process can be made to correspond to a Gibbs-type distribution for polygonal random fields introduced by Arak and Surgailis and a few variants thereof, such as those arising in Bayesian analysis of such random fields. Extensions to generalized polygonal random fields are presented wherein the segmentation boundaries are not necessarily straight line segments.