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This paper presents a Gibbs measure approximation method through the adjustment of the associated estimated potential. We use the information criterion to prove the accuracy of this approach and the bootstrap computation method to determine the explicit form. The Gibbs sampler is the tool of our simulations while taking advantage of the use of the only one MCMC inside of the multiple necessary MCMC in the classical approximation. We focus on the validity of our approach for the Gibbs measure of a Markov Random Field with an interaction potential function and the associated uniqueness condition. Some theoretical and numerical results are given.

Bootstrap Approximation of Gibbs Measure for Finite-Range Potential in Image Analysis