Rahman Farnoosh - Department of Applied Mathematics, Iran University of Science and Technology
Behnam Zarpak - Department of Applied Mathematics, Iran University of Science and Technology

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 used Gaussian mixture model to the pixels of an image. The parameters of the model were estimated by EM-algorithm.In addition pixel labeling corresponded to each pixel of true image was made by Bayes rule. In fact, a new numerically method was introduced for finding the maximum a posterior estimation by using EM-algorithm and Gaussians mixture distribution. In this algorithm, we were made a sequence of priors, posteriors were made and then converged to a posterior probability that is called the reference posterior probability. Maximum a posterior estimated can determine by the reference posterior probability which can make labeled image. This labeled image shows our segmented image with reduced noises. We presented this method in several experiments.

Bayesian Rule, Gaussian Mixture Model (GMM), Maximum a Posterior (MAP), Expectation- Maximization (EM) Algorithm, Reference Analysis