Parallel and Deterministic Algorithms from MRFs: Surface Reconstruction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Improving the mean field approximation via the use of mixture distributions
Learning in graphical models
Stochastic Complexity in Statistical Inquiry Theory
Stochastic Complexity in Statistical Inquiry Theory
Pairwise Data Clustering by Deterministic Annealing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Assessing a Mixture Model for Clustering with the Integrated Completed Likelihood
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast automatic unsupervised image segmentation and curve detection in spatial point patterns
Fast automatic unsupervised image segmentation and curve detection in spatial point patterns
Stochastic approximation algorithms for partition function estimation of Gibbs random fields
IEEE Transactions on Information Theory
Approximate maximum likelihood hyperparameter estimation for Gibbs priors
IEEE Transactions on Image Processing
Unsupervised image segmentation using triplet Markov fields
Computer Vision and Image Understanding
Variational Bayesian image modelling
ICML '05 Proceedings of the 22nd international conference on Machine learning
Parallelized segmentation of a serially sectioned whole human brain
Image and Vision Computing
A finite mixture model for image segmentation
Statistics and Computing
Field Sampling from a Segmented Image
ICCSA '08 Proceeding sof the international conference on Computational Science and Its Applications, Part I
Gene Clustering via Integrated Markov Models Combining Individual and Pairwise Features
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Unsupervised image segmentation using triplet Markov fields
Computer Vision and Image Understanding
The infinite hidden Markov random field model
IEEE Transactions on Neural Networks
An extension of the standard mixture model for image segmentation
IEEE Transactions on Neural Networks
Entropic component analysis and its application in geological data
Computers & Geosciences
Dirichlet Gaussian mixture model: Application to image segmentation
Image and Vision Computing
A finite mixture model for detail-preserving image segmentation
Signal Processing
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Hidden Markov random fields appear naturally in problems such as image segmentation, where an unknown class assignment has to be estimated from the observations at each pixel. Choosing the probabilistic model that best accounts for the observations is an important first step for the quality of the subsequent estimation and analysis. A commonly used selection criterion is the Bayesian Information Criterion (BIC) of Schwarz (1978), but for hidden Markov random fields, its exact computation is not tractable due to the dependence structure induced by the Markov model. We propose approximations of BIC based on the mean field principle of statistical physics. The mean field theory provides approximations of Markov random fields by systems of independent variables leading to tractable computations. Using this principle, we first derive a class of criteria by approximating the Markov distribution in the usual BIC expression as a penalized likelihood. We then rewrite BIC in terms of normalizing constants, also called partition functions, instead of Markov distributions. It enables us to use finer mean field approximations and to derive other criteria using optimal lower bounds for the normalizing constants. To illustrate the performance of our partition function-based approximation of BIC as a model selection criterion, we focus on the preliminary issue of choosing the number of classes before the segmentation task. Experiments on simulated and real data point out our criterion as promising: It takes spatial information into account through the Markov model and improves the results obtained with BIC for independent mixture models.