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.
email: jm@math.auc.dk
Øivind Skare
Norwegian Computing Center
P.O. Box 114 Blindern
N–0314 Oslo, Norway.
email: skare@nr.no
Abstract:
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.
Keywords:
Markov chain Monte Carlo; Markov connected component fields;
Markov random fields; Nearest-neighbour Markov point processes;
Polygonal partitions.
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