Approximate Bayes Factors for Image Segmentation: The Pseudolikelihood Information Criterion (PLIC)

We propose a method for choosing the number of colors or true gray levels in an image; this allows fully automatic segmentation of images. Our underlying probability model is a hidden Markov random field. Each number of colors considered is viewed as corresponding to a statistical model for the image, and the resulting models are compared via approximate Bayes factors. The Bayes factors are approximated using BIC (Bayesian Information Criterion), where the required maximized likelihood is approximated by the Qian-Titterington (1991) pseudolikelihood. We call the resulting criterion PLIC (Pseudolikelihood Information Criterion). We also discuss a simpler approximation, MMIC (Marginal Mixture Information Criterion), which is based only on the marginal distribution of pixel values. This turns out to be useful for initialization and it also has moderately good performance by itself when the amount of spatial dependence in an image is low. We apply PLIC and MMIC to a medical image segmentation problem.

[1]  David R. Cox,et al.  Problems and solutions in theoretical statistics , 1979 .

[2]  W. Qian,et al.  Estimation of parameters in hidden Markov models , 1991, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[3]  A. Raftery.  Bayes Factors and BIC , 1999 .

[4]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[5]  L. Wasserman,et al.  Computing Bayes Factors by Combining Simulation and Asymptotic Approximations , 1997 .

[6]  L. Wasserman,et al.  A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion , 1995 .

[7]  A. Raftery,et al.  Model-based Gaussian and non-Gaussian clustering , 1993 .

[8]  Sudhir S. Dixit.  Quantization of color images for display/printing on limited color output devices , 1991, Comput. Graph..

[9]  M.,et al.  Statistical and Structural Approaches to Texture , 2022 .

[10]  William V. Stoecker,et al.  Unsupervised color image segmentation: with application to skin tumor borders , 1996 .

[11]  Adrian E. Raftery,et al.  Hypothesis testing and model selection , 1996 .

[12]  J. Besag.  Statistical analysis of dirty pictures , 1993 .

[13]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[14]  L. Wasserman,et al.  Practical Bayesian Density Estimation Using Mixtures of Normals , 1997 .

[15]  W. Qian,et al.  Stochastic relaxations and em algorithms for markov random fields , 1992 .

[16]  M J Yaffe,et al.  Thickness-equalization processing for mammographic images. , 1997, Radiology.

[17]  Adrian E. Raftery,et al.  Principal Curve Clustering With Noise , 1997 .

[18]  C. Posse.  Hierarchical Model-Based Clustering for Large Datasets , 2001 .

[19]  Scott E. Umbaugh,et al.  UNSUPERVISED COLOR IMAGE SEGMENTATION , 1996 .

[20]  Adrian E. Raftery,et al.  How Many Clusters? Which Clustering Method? Answers Via Model-Based Cluster Analysis , 1998, Comput. J..

[21]  A. Raftery,et al.  Detecting features in spatial point processes with clutter via model-based clustering , 1998 .

[22]  A. Raftery.  Bayesian Model Selection in Social Research , 1995 .

[23]  J. Thijssen,et al.  Characterization of echographic image texture by cooccurrence matrix parameters. , 1997, Ultrasound in medicine & biology.

[24]  J. Besag,et al.  Bayesian image restoration, with two applications in spatial statistics , 1991 .

[25]  Christine Keribiin,et al.  Estimation consistante de l'ordre de modèles de mélange , 1998 .

[26]  C. Ji,et al.  A consistent model selection procedure for Markov random fields based on penalized pseudolikelihood , 1996 .

[27]  S. Chib.  Marginal Likelihood from the Gibbs Output , 1995 .

[28]  Adrian E. Raftery,et al.  Fast automatic unsupervised image segmentation and curve detection in spatial point patterns , 1999 .

[29]  Håkon Tjelmeland,et al.  Markov Random Fields with Higher‐order Interactions , 1998 .

[30]  Walter R. Gilks,et al.  Hypothesis testing and model selection , 1995 .

[31]  M. Newton.  Approximate Bayesian-inference With the Weighted Likelihood Bootstrap , 1994 .

[32]  Robert M. Haralick,et al.  Textural Features for Image Classification , 1973, IEEE Trans. Syst. Man Cybern..

[33]  Josiane Zerubia,et al.  Estimation of Markov random field prior parameters using Markov chain Monte Carlo maximum likelihood , 1999, IEEE Trans. Image Process..