An analysis of Monte Carlo methods for likelihood estimation of Gibbsian images

Authors:
Gerasimos Potamianos;John Goutsias
Affiliations:
Department of Electrical and Computer Engineering, Image Analysis and Communications Laboratory, The Johns Hopkins University, Baltimore, MD;Department of Electrical and Computer Engineering, Image Analysis and Communications Laboratory, The Johns Hopkins University, Baltimore, MD
Venue:
ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: image and multidimensional signal processing - Volume V
Year:
1993

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Monte Carlo methods. Vol. 1: basics

Monte Carlo methods. Vol. 1: basics
Unilateral approximation of gibbs random field images

CVGIP: Graphical Models and Image Processing

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Abstract

We present a unified analysis of two Monte Carlo algorithms for estimating the likelihood function of Gibbs random field images. We show that such an estimation reduces to estimating the partition functions of suitably chosen Gibbs random fields. The first algorithm requires drawing samples from a mutually compatible Gibbs random field, and provides unbiased and consistent estimators of these partition functions. The second algorithm uses samples which are approximately drawn from the Gibbs distribution, and results in asymptotically unbiased and consistent estimators of the partition functions. We introduce a measure of the computational complexity of these algorithms, which enables us to compare them. We conclude that the first algorithm is superior, especially for models with strong interactions.