Image segmentation by polygonal Markov fields

This paper advocates the use of multi-coloured 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. The approach is illustrated by means of toy examples.