TY - JOUR
T1 - Markov connected component fields
AU - Møller, Jesper
AU - Plenge Waagepetersen, Rasmus
PY - 1998/1/1
Y1 - 1998/1/1
N2 - A new class ofGibbsian models with potentials associated with the connected components or homogeneous parts of images is introduced. For these models the neighbourhood ofa 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 ofspatial continuity and images of objects against background.
AB - A new class ofGibbsian models with potentials associated with the connected components or homogeneous parts of images is introduced. For these models the neighbourhood ofa 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 ofspatial continuity and images of objects against background.
KW - Bayesian image analysis
KW - Exponential family models
KW - Geostatistics
KW - Infinite lattice processes
KW - Markov chain Monte Carlo
KW - Markov partitions
KW - Markov random fields
KW - Maximum likelihood
KW - Nearest-neighbour Markov point processes
UR - http://www.scopus.com/inward/record.url?scp=85037219262&partnerID=8YFLogxK
U2 - 10.1239/aap/1035227989
DO - 10.1239/aap/1035227989
M3 - Journal article
AN - SCOPUS:85037219262
SN - 0001-8678
VL - 30
SP - 1
EP - 35
JO - Advances in Applied Probability
JF - Advances in Applied Probability
IS - 1
ER -