| Markov Random Fields, Stochastic Quantization and Image Analysis (2007) | |||||||||||
Abstract | |||||||||||
| Markov random fields based on the lattice Z2 have been extensively used in image analysis in a Bayesian framework as a-priori models for the intensity field and on the dual lattice (Z2)* as models for boundaries. The choice of these models has usually been based on algorithmic considerations in order to exploit the local structure inherent in Markov fields. No fundamental justification has been offered for the use of Markov random fields. It is well known that there is a one-one correspondence between Markov fields and Gibbs fields on a lattice and the Markov Field is simulated by creating a Markov chain whose invariant measure is precisely the Gibbs measure. There are many ways to perform this simulation and one such way is the celebrated Metropolis Algorithm. This is also the basic idea behind Stochastic Quantization. We thus see that if the use of Markov Random fields in the context of Image Analysis can be given some fundamental justification then there is a remarkable connection between Probabilistic Image Analysis, Statistical Mechanics and Lattice-based Euclidean Quantum Field Theory.. Sponsored in part by the Army Research Office (ARO), contract no. DAAL03-86-K-0171. | |||||||||||
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