22 September 1998 Multisite updating Markov chain Monte Carlo algorithm for morphologically constrained Gibbs random fields
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Abstract
We study the problem of simulating a class of Gibbs random field models, called morphologically constrained Gibbs random fields, using Markov chain Monte Carlo sampling techniques. Traditional single site updating Markov chain Monte Carlo sampling algorithm, like the Metropolis algorithm, tend to converge extremely slowly when used to simulate these models, particularly at low temperatures and for constraints involving large geometrical shapes. Moreover, the morphologically constrained Gibbs random fields are not, in general, Markov. Hence, a Markov chain Monte Carlo sampling algorithm based on the Gibbs sampler is not possible. We prose a variant of the Metropolis algorithm that, at each iteration, allows multi-site updating and converges substantially faster than the traditional single- site updating algorithm. The set of sites that are updated at a particular iteration is specified in terms of a shape parameter and a size parameter. Computation of the acceptance probability involves a 'test ratio,' which requires computation of the ratio of the probabilities of the current and new realizations. Because of the special structure of our energy function, this computation can be done by means of a simple; local iterative procedure. Therefore lack of Markovianity does not impose any additional computational burden for model simulation. The proposed algorithm has been used to simulate a number of image texture models, both synthetic and natural.
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Krishnamoorthy Sivakumar, Krishnamoorthy Sivakumar, John Ioannis Goutsias, John Ioannis Goutsias, "Multisite updating Markov chain Monte Carlo algorithm for morphologically constrained Gibbs random fields", Proc. SPIE 3459, Bayesian Inference for Inverse Problems, (22 September 1998); doi: 10.1117/12.323807; https://doi.org/10.1117/12.323807
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