Efficient learning of standard finite normal mixtures for image quantification

This paper presents an efficient on-line distribution learning procedure of standard finite normal mixtures for image quantification. Based on the standard finite normal mixture (SFNM) model, we formulate image quantification as a distribution learning problem, and derive the probabilistic self-organizing map (PSOM) algorithm by minimizing the relative entropy between the SFNM distribution and the image histogram. We justify our formulation and hence provide a basis for the use of SFNM, in pixel image modeling in terms of large sample properties of the maximum likelihood estimator. We then establish convergence properties of the PSOM which simulates a Bayesian rule network structure with Gaussian activation functions forming soft splits of the data, and thus providing unbiased estimates. It is shown that by incorporating learning rate adaptation in a sequential mode, PSOM achieves fast convergence and has efficient learning capabilities which make it very attractive for many practical image quantification applications; such as unsupervised image segmentation and diagnosis by medical images.