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 as introduced by Arak and Surgailis (1989) and a few variants thereof, such as those arising in Bayesian analysis of random fields. Extensions to generalized polygonal random fields are presented where the segmentation boundaries are not necessarily straight line segments.