Smooth Image Segmentation by Nonparametric Bayesian Inference

A nonparametric Bayesian model for histogram clustering is proposed to automatically determine the number of segments when Markov Random Field constraints enforce smooth class assignments. The nonparametric nature of this model is implemented by a Dirichlet process prior to control the number of clusters. The resulting posterior can be sampled by a modification of a conjugate-case sampling algorithm for Dirichlet process mixture models. This sampling procedure estimates segmentations as efficiently as clustering procedures in the strictly conjugate case. The sampling algorithm can process both single-channel and multi-channel image data. Experimental results are presented for real-world synthetic aperture radar and magnetic resonance imaging data.

[1]  C. Antoniak.  Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems , 1974 .

[2]  L. Devroye.  Non-Uniform Random Variate Generation , 1986 .

[3]  J. Breckenridge.  Replicating Cluster Analysis: Method, Consistency, and Validity. , 1989, Multivariate behavioral research.

[4]  Donald Geman,et al.  Boundary Detection by Constrained Optimization , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  S. MacEachern.  Estimating normal means with a conjugate style dirichlet process prior , 1994 .

[6]  J. Besag,et al.  Bayesian Computation and Stochastic Systems , 1995 .

[7]  Joachim M. Buhmann,et al.  Histogram clustering for unsupervised image segmentation , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[8]  Emanuele Trucco,et al.  Robust motion and correspondence of noisy 3-D point sets with missing data , 1999, Pattern Recognit. Lett..

[9]  Joachim M. Buhmann,et al.  Histogram clustering for unsupervised segmentation and image retrieval , 1999, Pattern Recognit. Lett..

[10]  Steven N. MacEachern,et al.  Efficient MCMC Schemes for Robust Model Extensions Using Encompassing Dirichlet Process Mixture Models , 2000 .

[11]  Thomas L. Griffiths,et al.  Hierarchical Topic Models and the Nested Chinese Restaurant Process , 2003, NIPS.

[12]  Djoerd Hiemstra,et al.  Bayesian extension to the language model for ad hoc information retrieval , 2003, SIGIR.

[13]  Michael I. Jordan,et al.  Variational methods for the Dirichlet process , 2004, ICML.

[14]  Joachim M. Buhmann,et al.  Stability-Based Validation of Clustering Solutions , 2004, Neural Computation.

[15]  Antonio Torralba,et al.  Describing Visual Scenes using Transformed Dirichlet Processes , 2005, NIPS.

[16]  Adrian E. Raftery,et al.  Bayesian inference for multiband image segmentation via model-based cluster trees , 2005, Image Vis. Comput..