Coloured continuum triangulation models in the Bayesian analysis of two dimensional change point problems

We consider Bayesian image segmentation from a continuum parametric model. This is a class of problems in which a great deal of prior information is generally available. This information is often hierarchical in character, concerning the appearance of a range of different types of composite structures, including edges, vertices, regions, and the topology of the boundary graphs. Bayesian inference proceeds most simply, and flexibly, when the states of the chosen prior model are described in terms of the same elements used to specify prior information. We explore a model in which coloured continuum triangulations are used to represent image structure. We show how an initial model may be modified to take account of image structure. Changes to the density are incorporated in a Metropolis Hasting MCMC algorithm by slight modifications of generation and/or acceptance probabilities, which can require just a