The Infinite Hidden Markov Random Field Model

• Published in: IEEE transactions on neural networks Vol. 21; no. 6; pp. 1004 - 1014
• Main Authors: Chatzis, Sotirios P, Tsechpenakis, Gabriel
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2010; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Artificial Intelligence; Bayes Theorem; Bayesian analysis; Bayesian inference; Bayesian methods; Clustering; Clusters; Computer science; control theory; systems; Computer Simulation; Constraints; Dirichlet problem; Dirichlet process (DP); Exact sciences and technology; Hidden Markov models; hidden Markov random field (HMRF); Humans; Image analysis; Image Interpretation, Computer-Assisted; Image segmentation; Inference algorithms; Inference from stochastic processes; time series analysis; Information Storage and Retrieval; Markov Chains; Markov processes; Markov random fields; Mathematical models; Mathematics; Models, Statistical; Multidimensional systems; nonparametric models; Pattern Recognition, Automated - methods; Pattern recognition. Digital image processing. Computational geometry; Probability and statistics; Sciences and techniques of general use; Spatial resolution; Statistics; Yield estimation; Bayes estimation; Markov process; Monte Carlo method; Probabilistic approach; Image processing; Model selection; hidden Markov random field (HMRF); Automatic selection; Mixture theory; Markov model; Approximation algorithm; Modeling; Nonparametric statistics; Unsupervised learning; Markov chain; Image segmentation; nonparametric models; Boundary value problem; Model matching; Hidden Markov model; Dirichlet problem; Bayesian inference; Dirichlet process (DP)
• ISSN: 1045-9227; 1941-0093; 1941-0093
• DOI: 10.1109/TNN.2010.2046910

Hidden Markov random field (HMRF) models are widely used for image segmentation, as they appear naturally in problems where a spatially constrained clustering scheme is asked for. A major limitation of HMRF models concerns the automatic selection of the proper number of their states, i.e., the number of region clusters derived by the image segmentation procedure. Existing methods, including likelihood- or entropy-based criteria, and reversible Markov chain Monte Carlo methods, usually tend to yield noisy model size estimates while imposing heavy computational requirements. Recently, Dirichlet process (DP, infinite) mixture models have emerged in the cornerstone of nonparametric Bayesian statistics as promising candidates for clustering applications where the number of clusters is unknown a priori ; infinite mixture models based on the original DP or spatially constrained variants of it have been applied in unsupervised image segmentation applications showing promising results. Under this motivation, to resolve the aforementioned issues of HMRF models, in this paper, we introduce a nonparametric Bayesian formulation for the HMRF model, the infinite HMRF model, formulated on the basis of a joint Dirichlet process mixture (DPM) and Markov random field (MRF) construction. We derive an efficient variational Bayesian inference algorithm for the proposed model, and we experimentally demonstrate its advantages over competing methodologies.