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 f ashion in that training data is not available and the class-conditione d feature vectors must be estimated directly from the data. A major pr oblem in such applications is the determination of the number of class es actually present in an image. This problem, called the cluster vali dation problem, remains essentially unsolved. In this paper, we invest igate the cluster validation problem associated with the use of a prev iously developed unsupervised segmentation algorithm based upon the ex pectation-maximization (EM) algorithm. More specifically, we consider several well-known information-theoretic criteria (IC's) as candidate solutions to the validation problem when used in conjunction with this EM-based segmentation scheme, We show that these criteria generally p rovide inappropriate solutions due to the domination of the penalty te rm by the associated log-likelihood function, As an alternative we pro pose a model-fitting technique in which the complete data log-likeliho od functional is modeled as an exponential function in the number of c lasses 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 th e IC's in our experiments. Experimental results for both synthetic and real world imagery are detailed.