Stochastic models such as mixture models, graphical models, Markov random fields and hidden Markov models have key role in probabilistic data analysis. In this paper, we have learned Gaussian mixture model to the pixels of an image. The parameters of the model have estimated by EM-algorithm.

  In addition pixel labeling corresponded to each pixel of true image is made by Bayes rule. In fact, we introduce a new numerically method of finding maximum a posterior estimation by using EM-algorithm and Gaussians mixture distribution. In this algorithm, we have made a sequence of priors, posteriors and they converge to a posterior probability that is called the reference posterior probability. Maximum a posterior estimated can determine by the reference posterior probability that will make labeled image. This labeled image shows our segmented image with reduced noises. We show this method in several experiments.