Performance evaluation of finite normal mixture model-based image segmentation techniques

Finite normal mixture (FNM) model-based image segmentation techniques adopt the following detection-estimation-classification paradigm: (1) detect the number of image regions by using theoretical information criteria; (2) estimate model parameters by using expectation-maximization (EM)/classification-maximization (CM) algorithms; and (3) classify pixels into regions by using various classifiers. This paper presents a theoretical framework to evaluate the performance of this class of image segmentation techniques. For the detection performance, probabilities of over-detection and under-detection of the number of image regions are defined, and the associated formulae in terms of model parameters and image quality are derived. For the estimation performance, both EM and CM algorithms are showed to produce asymptotically unbiased ML estimates of model parameters in the case of no-overlap. Cramer-Rao bounds of variances of these estimates are derived. For the classification performance, misclassification probability for the Bayesian classifier is defined, and a simple formula based on parameter estimates and classified data is derived to evaluate segmentation errors. This evaluation method provides both theoretically approachable accuracy limits of the techniques and practically achievable performance of the given images. Theoretical and experimental results are in good agreement and indicate that, for images of moderate quality, the detection operation is robust, the parameter estimates are accurate, and the segmentation errors are small.