The application of the Gibbs-Bogoliubov-Feynman inequality in mean field calculations for Markov random fields
IEEE Transactions on Image ProcessingPublished 1 July 1996
Jun Zhang
Citations30
SJR quartileQ1
SJR score2.50
SNIP3.41
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
The Gibbs-Bogoliubov-Feynman inequality of statistical mechanics is adopted, with an information-theoretic interpretation, as a general optimization framework for deriving and examining various mean field approximations for Markov random fields (MRF's).
Abstract
The Gibbs-Bogoliubov-Feynman (GBF) inequality of statistical mechanics is adopted, with an information-theoretic interpretation, as a general optimization framework for deriving and examining various mean field approximations for Markov random fields (MRF's). The efficacy of this approach is demonstrated through the compound Gauss-Markov (CGM) model, comparisons between different mean field approximations, and experimental results in image restoration.
Keywords
Computer ScienceEngineering
Journal of the Royal Statistical Society Series B (Statistical Methodology)Maximum Likelihood from Incomplete Data Via the <i>EM</i> Algorithm
49,657 Citations1977A. P. Dempster, N. M. Laird +1 more
Elements of Information Theory
37,533 Citations2001Thomas M. Cover, Joy A. Thomas
IEEE Transactions on Pattern Analysis and Machine IntelligenceStochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
17,980 Citations1984Stuart Geman, Donald Geman
The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
Journal of the Royal Statistical Society Series B (Statistical Methodology)Spatial Interaction and the Statistical Analysis of Lattice Systems
6,179 Citations1974Julian Besag
Journal of the Royal Statistical Society Series B (Statistical Methodology)On the Statistical Analysis of Dirty Pictures
4,228 Citations1986Julian Besag
A simple, iterative method of reconstruction is proposed, which does not depend on these large-scale characteristics of the random field, and is illustrated by computer simulations in which the original scene is not directly related to the assumed random field.
Physics Today<i>Introduction to Modern Statistical Mechanics</i>
1,973 Citations1988David Chandler, J. K. Percus
IEEE Transactions on Pattern Analysis and Machine IntelligenceMarkov Random Field Texture Models
1,388 Citations1983George R. Cross, Anil K. Jain
The power of the binomial model to produce blurry, sharp, line-like, and blob-like textures is demonstrated and the synthetic microtextures closely resembled their real counterparts, while the regular and inhomogeneous textures did not.
IEEE Transactions on Pattern Analysis and Machine IntelligenceModeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields
974 Citations1987Haluk Derin, Howard Elliott
This paper presents random field models for noisy and textured image data based upon a hierarchy of Gibbs distributions, and presents dynamic programming based segmentation algorithms for chaotic images, considering a statistical maximum a posteriori (MAP) criterion.
IEEE Transactions on Medical ImagingA generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors
616 Citations1989T.J. Hebert, Richard M. Leahy
A generalized expectation-maximization (GEM) algorithm is developed for Bayesian reconstruction, based on locally correlated Markov random-field priors in the form of Gibbs functions and on the Poisson data model, which reduces to the EM maximum-likelihood algorithm.
Data Fusion for Sensory Information Processing Systems
527 Citations1990James J. Clark, Alan Yuille
The role of data Fusion in Sensory Systems, Bayesian Sensory Information Processing, and Temporal Aspects of Data Fusion are introduced.
IEEE Transactions on Image ProcessingMethods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation
486 Citations1992N.P. Galatsanos, Aggelos K. Katsaggelos
An error analysis based on an objective mean-square-error (MSE) criterion is used to motivate regularization and two approaches for choosing the regularization parameter and estimating the noise variance are proposed.
IEEE Transactions on Pattern Analysis and Machine IntelligenceParallel and deterministic algorithms from MRFs: surface reconstruction
449 Citations1991Davi Geiger, Federico Girosi
Deterministic approximations to Markov random field (MRF) models are derived and one of the models is shown to give in a natural way the graduated nonconvexity (GNC) algorithm proposed by A. Blake and A. Zisserman (1987).
IEEE Transactions on Signal ProcessingThe mean field theory in EM procedures for Markov random fields
340 Citations1992J. Zhang
The efficacy of the mean field theory approach is demonstrated on parameter estimation for one-dimensional mixture data and two-dimensional unsupervised stochastic model-based image segmentation and on parameter estimates for both synthetic and real-world images.
IEEE Transactions on Pattern Analysis and Machine IntelligenceA study of methods of choosing the smoothing parameter in image restoration by regularization
304 Citations1991Adam Thompson, J. C. Brown +2 more
The method of regularization is portrayed as providing a compromise between fidelity to the data and smoothness, with the tradeoff being determined by a scalar smoothing parameter.
IEEE Transactions on Pattern Analysis and Machine IntelligenceBayesian estimation of motion vector fields
286 Citations1992Janusz Konrad, Éric Dubois
A stochastic approach to the estimation of 2D motion vector fields from time-varying images is presented and the maximum a posteriori probability (MAP) estimation is incorporated into a hierarchical environment to deal efficiently with large displacements.
Neural ComputationGeneralized Deformable Models, Statistical Physics, and Matching Problems
224 Citations1990Alan Yuille
Techniques from statistical physics are used to exploit the power of statistical techniques to put global constraints on the set of allowable states of the binary matching elements and be preferable to existing methods of imposing such constraints by adding bias terms in the energy functions.
IEEE Transactions on Signal ProcessingCompound Gauss-Markov random fields for image estimation
182 Citations1991Fure-Ching Jeng, John W. Woods
The authors consider both the maximum a posteriori probability (MAP) estimate and the minimum mean-squared error (MMSE) estimate for image estimation and image restoration for images modeled as compound Gauss-Markov random fields.
International Journal of Computer VisionA common framework for image segmentation
180 Citations1991Davi Geiger, Alan Yuille
The Markov random field formalism is considered, a special case of the Bayesian approach, in which the probability distributions are specified by an energy function, and simple modifications to the energy can give a direct relation to robust statistics or can encourage hysteresis and nonmaximum suppression.
IEEE Transactions on Acoustics Speech and Signal ProcessingAdaptive segmentation of speckled images using a hierarchical random field model
118 Citations1988Patrick A. Kelly, Haluk Derin +1 more
A two-level hierarchical random-field model developed for speckled images and, in particular, for synthetic-aperture radar (SAR) imagery, is described and a MAP segmentation using simulated annealing and based on the hierarchical model is presented.
IEEE Transactions on Image ProcessingThe application of mean field theory to image motion estimation
68 Citations1995Jun Zhang, G.G. Hanauer
The present paper shows how the mean field theory can be applied to MRF model-based motion estimation, and it provides results nearly as good as SA but with much faster convergence.
IEEE Transactions on Information TheorySimulated annealing in compound Gaussian random fields (image processing)
62 Citations1990Fure-Ching Jeng, John W. Woods
The proof of convergence of the stochastic relaxation method is extended to a class of compound Gauss-Markov random fields and results are provided to show the power of these methods.
Journal of the Optical Society of America ARestoration of piecewise-constant images by mean-field annealing
62 Citations1989Harish P. Hiriyannaiah, R.C. Mann +2 more
An algorithm is described that removes the noise from images without causing blurring or other distortions of edges, using a new minimization strategy called mean-field annealing (MFA).
International Conference on Acoustics, Speech, and Signal ProcessingMean field approximation using compound Gauss-Markov random field for edge detection and image restoration
41 Citations2002Josiane Zerubia, R. Challappa
A composed Gauss-Markov random field (CGMRF) model is used with mean field approximation for edge detection and image restoration and the same equations as those of Geiger and Girosi (1989) are obtained.
Neural Information Processing SystemsRange Image Restoration Using Mean Field Annealing
41 Citations1988Griff L. Bilbro, Wesley E. Snyder
A new optimization strategy, Mean Field Annealing, is presented and its application to MAP restoration of noisy range images is derived and experimentally verified.
Estimation of image motion fields: Bayesian formulation and stochastic solution
35 Citations2003Janusz Konrad, Éric Dubois
It is shown that motion estimation, an ill-posed problem, can be regularized by means of a Bayesian estimation approach and a probabilistic formulation for motion estimation in images and a stochastic algorithm for minimization of the associated objective function.
Image and Vision ComputingComparison of stochastic and deterministic solution methods in Bayesian estimation of 2D motion
25 Citations1990Janusz Konrad, Éric Dubois
Signal ProcessingEnergy minimization approach to motion estimation
23 Citations1992Ikhlas Abdel‐Qader, Sarah A. Rajala +2 more
Motion estimation is cast as a problem in energy minimization by modeling the displacement field as a Markov random field using the Mean Field Annealing algorithm, a technique which finds the global or near global minima in nonconvex optimization problems.
International Conference on Acoustics, Speech, and Signal ProcessingGraduated nonconvexity algorithm for image estimation using compound Gauss Markov field models
23 Citations2003T. Simchony, Rama Chellappa +1 more
The authors describe the development of a deterministic algorithm for obtaining the global maximum a posteriori probability (MAP) estimate from an image corrupted by additive Gaussian noise that finds the global MAP estimate in a small number of iterations.
Image restoration by parallel simulated annealing using compound Gauss-Markov models
11 Citations1991Shikha Rastogi, John W. Woods
A parallel simulated annealing algorithm is presented for image restoration using a compound Gauss-Markov field model for the image, and the total time required for restoring a monochrome blurred and noisy image with continuous range of intensities is reduced.