Application of the Gibbs-Bogoliubov-Feynman inequality in mean field calculations for Markov random fields

Jun Zhang

doi:10.1117/12.186042

16 September 1994 Application of the Gibbs-Bogoliubov-Feynman inequality in mean field calculations for Markov random fields

Jun Zhang

Author Affiliations +

Proceedings Volume 2308, Visual Communications and Image Processing '94; (1994) https://doi.org/10.1117/12.186042
Event: Visual Communications and Image Processing '94, 1994, Chicago, IL, United States

Abstract

Recently, there has been growing interest in the use of mean field theory (MFT) in Markov random field (MRF) model-based estimation problems. In many image processing and computer vision applications, the MFT approach can provide comparable performance to that of the simulated annealing, but requires much less computational effort and has easy hardware implementation. The Gibbs-Bogoliubov-Feynman inequality from statistical mechanics provides a general, systematic, and optimal approach for deriving mean field approximations. In this paper, this approach is applied to two important classes of MRF's, the compound Gauss-Markov model and the vector Ising model. The results obtained are compared and related to other methods of deriving mean field equations. Experimental results are also provided to demonstrate the efficacy of this approach.

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Jun Zhang "Application of the Gibbs-Bogoliubov-Feynman inequality in mean field calculations for Markov random fields", Proc. SPIE 2308, Visual Communications and Image Processing '94, (16 September 1994); https://doi.org/10.1117/12.186042

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