Statistical Modelling 1 (2001), 213–232

Coloured Voronoi Tessellations for Bayesian Image Analysis and Reservoir Modelling

Jesper Møller
Department of Mathematical Sciences, Aalborg University
Fredrik Bajers Vej 7G, DK-9220 Aalborg, Denmark.

Øivind Skare
Norwegian Computing Center
P.O. Box 114 Blindern
N–0314 Oslo, Norway.


A new flexible prior for Bayesian image analysis and reservoir modelling is defined in terms of interacting coloured Voronoi cells described by a certain nearest-neighbour Markov point process. This prior can be defined in both 2 and 3 (as well as higher) dimensions, and simple MCMC algorithms can be used for drawing inference from the posterior distribution. Various 2D and 3D applications are considered.


Markov chain Monte Carlo; Markov connected component fields; Markov random fields; Nearest-neighbour Markov point processes; Polygonal partitions.


Software and documentation in zipped archive