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Disagreement Loop and Path Creation/Annihilation Algorithms for Binary Planar Markov Fields with Applications to Image Segmentation
Author(s) -
SCHREIBER TOMASZ,
VAN LIESHOUT MARIECOLETTE
Publication year - 2010
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2009.00678.x
Subject(s) - mathematics , random field , markov chain , segmentation , path (computing) , markov random field , annihilation , algorithm , gibbs measure , image segmentation , planar , markov process , statistical physics , consistency (knowledge bases) , discrete mathematics , artificial intelligence , computer science , mathematical analysis , statistics , physics , computer graphics (images) , quantum mechanics , programming language
. We introduce a class of Gibbs–Markov random fields built on regular tessellations that can be understood as discrete counterparts of Arak–Surgailis polygonal fields. We focus first on consistent polygonal fields, for which we show consistency, Markovianity and solvability by means of dynamic representations. Next, we develop disagreement loop as well as path creation and annihilation dynamics for their general Gibbsian modifications, which cover most lattice‐based Gibbs–Markov random fields subject to certain mild conditions. Applications to foreground–background image segmentation problems are discussed.