Cluster validation for unsupervised stochastic model-based image segmentation

Image segmentation is an important and early processing stage in many image analysis problems. Often, this must be done in an unsupervised fashion in that training data is not available and the class-conditioned feature vectors must be estimated directly from the data. A major problem in such applications is the determination of the number of classes actually present in an image. This problem, called the cluster validation problem, remains essentially unsolved. We investigate the cluster validation problem associated with the use of a previously developed unsupervised segmentation algorithm based upon the expectation-maximization (EM) algorithm. More specifically, we consider several well-known information-theoretic criteria (ICs) as candidate solutions to the validation problem when used in conjunction with this EM-based segmentation scheme. We show that these criteria generally provide inappropriate solutions due to the domination of the penalty term by the associated log-likelihood function. As an alternative we propose a model-fitting technique in which the complete data log-likelihood functional is modeled as an exponential function in the number of classes acting. The estimated number of classes are then determined in a manner similar to finding the rise time of the exponential function. This new validation technique is shown to be robust and outperform the ICs in our experiments. Experimental results for both synthetic and real world imagery are detailed.