Markov connected component fields

A new class of Gibbsian models with potentials associated to 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 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. Also extensions to infinite lattices are 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 appropiate for a variety of interesting patterns including images exhibiting intermediate degrees of spatial continuity and images of objects against background.