Disagreement loop and path creation/annihilation algoritms for planar
Markov fields with applications to image segmentation
We introduce a class of Gibbs--Markov random fields that can be understood as discrete versions of coloured polygonal fields built on regular tessellations. Under an appropriate choice of Hamiltonian polygonal we show these fields enjoy striking properties including consistency and solvability by means of dynamic representations. For general Hamiltonians we develop disagreement loop as well as path creation and annihilation dynamics yielding efficient simulation algorithms with non-local updates. Applications to foreground-background segmentation problems are discussed.