Cluster expansions for the deterministic computation of Bayesian estimators based on Markov random fields

Author

Wu, Chi-hsin ; Doerschuk, Peter C.

Author_Institution

Dept. of Image Process., Ind. Technol. Res. Inst., Hsinchu, Taiwan

Volume

17

Issue

3

fYear

1995

fDate

3/1/1995 12:00:00 AM

Firstpage

275

Lastpage

293

Abstract

We describe a family of approximations, denoted by “cluster approximations”, for the computation of the mean of a Markov random field (MRF). This is a key computation in image processing when applied to the a posteriori MRF. The approximation is to account exactly for only spatially local interactions. Application of the approximation requires the solution of a nonlinear multivariable fixed-point equation for which we prove several existence, uniqueness, and convergence-of-algorithm results. Four numerical examples are presented, including comparison with Monte Carlo calculations

Keywords

Bayes methods; Markov processes; image recognition; image restoration; nonlinear equations; Bayesian estimators; Markov random fields; Monte Carlo calculations; cluster approximations; cluster expansions; convergence-of-algorithm results; deterministic computation; existence; image processing; nonlinear multivariable fixed-point equation; spatially local interactions; uniqueness; Bayesian methods; Computational modeling; Equations; Gaussian processes; Hidden Markov models; Image converters; Image processing; Image restoration; Image segmentation; Markov random fields;

fLanguage

English

Journal_Title

Pattern Analysis and Machine Intelligence, IEEE Transactions on

Publisher

ieee

ISSN

0162-8828

Type

jour

DOI

10.1109/34.368192

Filename

368192