Determining the Number of Colors or Gray Levels in an Image Using Approximate Bayes Factors: The Pseudolikelihood Information Criterion (PLIC)
WASHINGTON UNIV SEATTLE DEPT OF STATISTICS
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We propose a method for choosing the number of colors., or true gray levels, in an image. This is motivated by medical and satellite image segmentation, and may also be useful for color and gray scale image quantization, the display and storage of computer-generated holograms, and the use of cooccurrence matrices for assessing texture in 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, where the required maximized likelihood is approximated by the Qian-Titterington pseudolikelihood. We call the resulting criterion PLIC Pseudolikelihood Information Criterion. We also discuss a simpler approximation, MMIC Margiual Mixture Information Criterion, which is based only on the marginal distribution of pixel values. This turns out to be useful for initialization, and also to have moderately good, albeit suboptimal, performance in its own right. We apply PLIC to three examples a simulated two-band image, a medical segmentation problem, and a satellite image, and in each case it gives good results in practice.
- Statistics and Probability