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Markov connected component fields

Published online by Cambridge University Press:  01 July 2016

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.

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.

Type
Stochatic Geometry and Statistical Applications
Copyright
Copyright © Applied Probability Trust 1998 

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