Parameter Estimation of Finite Mixtures for Image Processing Using the EM Algorithm and Information Criteria

A method for parameter estimation in image classification or segmentation is studied within the statistical frame of finite mixture distributions. The method models an image as a finite mixture. Each mixture component corresponds to an image class. Each image class is characterized by parameters, such as the intensity mean, the standard deviation and the number of image pixels in that class. The method uses a maximum likelihood (ML) approach to estimate the parameters of each class, and employs information criteria of Akaike (AIC) and/or Schwarz (MDL) to determine the number of classes in the image. In computing the ML solution of the mixture, the method adopts the expectation maximization (EM) algorithm. Mathematical formula for the method are presented. The initial estimation and convergence of the ML-EM algorithm are studied. The parameters estimated from a simulated phantom are very close to those of the phantom. The determined number of image classes agrees with that of the phantom. The accuracy in determining the number of image classes using AIC and MDL is compared. The MDL criterion performs better than the AIC criterion. A modified MDL shows further improvement. The results obtained from real images are very encouraging.