We discuss the use of polygonal Markov fields for model-based image segmentation. The formal construction of consistent multi-coloured polygonal Markov fields by Arak-Clifford-Surgailis and its dynamic representation are recalled and adapted. We then formulate image segmentation as a statistical estimation problem for a Gibbsian modification of an underlying polygonal Markov field, and discuss the choice of Hamiltonian. Monte Carlo techniques for estimating the model parameters and for finding the optimal partition of the image are developed. We shall also discuss a class of Markov random fields that can be understood as discrete versions of polygonal fields. The analogy with continuum polygonal Markov fields is exploited to define Hamiltonians that are such that desirable properties of these processes can be carried over to the discrete context. Moreover, the analogy gives rise to new attractive sampling schemes complementing the usual local Gibbs and Metropolis methods employed for Gibbs fields on finite graphs.
(includes joint work with R. Kluzczynski and T. Schreiber)