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.

We present a method for characterizing clutter in images by using multiscale hidden Markov models in the wavelet domain, and we discuss the application of this in predicting the performance of automatic target recognition (ATR) systems. Wavelet Markov models explicitly include dependence across scale, which allows us to characterize highly structured clutter. Since structured clutter is a common cause of false alarms in modern ATR systems, these models give us the ability to analyze and predict false alarm rates and other ATR performance characteristics. These predictions can lead to adaptive ATR systems which automatically adjust to local clutter conditions.

Clustering about principal curves combines parametric modeling of noise with nonparametric modeling of feature shape. This is useful for detecting curvilinear features in spatial point patterns, with or without background noise. Applications include the detection of curvilinear minefields from reconnaissance images, some of the points in which represent false detections, and the detection of seismic faults from earthquake catalogs. Our algorithm for principal curve clustering is in two steps: The first is hierarchical and agglomerative (HPCC) and the second consists of iterative relocation based on the classification EM algorithm (CEM-PCC). HPCC is used to combine potential feature clusters, while CEM-PCC refines the results and deals with background noise. It is important to have a good starting point for the algorithm: This can be found manually or automatically using, for example, nearest neighbor clutter removal or model-based clustering. We choose the number of features and the amount of smoothing simultaneously, using approximate Bayes factors.