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Markov connected component fields

Part of: Geometric probability and stochastic geometry Stochastic processes Markov processes

Published online by Cambridge University Press:  01 July 2016

Jesper Møller  and
Rasmus Plenge Waagepetersen
Jesper Møller*
Affiliation:
Aalborg University
Rasmus Plenge Waagepetersen*
Affiliation:
Danish Institute of Agricultural Sciences
*
∗ Postal address: Department of Mathematics, Institute of Electronic Systems, Aalborg University, Fredrik Bajers Vej 7E, DK-9220 Aalborg, Denmark.
∗∗ Postal address: Department of Agricultural Systems, P.O. Box 50, Research Centre Foulum, DK-8830 Tjele, Denmark.
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Abstract

A new class of Gibbsian models with potentials associated with the connected components or homogeneous parts of images is introduced. For these models the neighbourhood of a pixel is not fixed as for Markov random fields, but is given by the components which are adjacent to the pixel. The relationship to Markov random fields and marked point processes is explored and spatial Markov properties are established. Extensions to infinite lattices are also studied, and statistical inference problems including geostatistical applications and statistical image analysis are discussed. Finally, simulation studies are presented which show that the models may be appropriate for a variety of interesting patterns, including images exhibiting intermediate degrees of spatial continuity and images of objects against background.

Keywords

Bayesian image analysisexponential family modelsgeostatisticsinfinite lattice processesMarkov chain Monte CarloMarkov partitionsMarkov random fieldsmaximum likelihoodnearest-neighbour Markov point processes

MSC classification

Primary: 60G60: Random fields
Secondary: 60D05: Geometric probability and stochastic geometry 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Stochatic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 30 , Issue 1 , March 1998 , pp. 1 - 35
Copyright
Copyright © Applied Probability Trust 1998 

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