Image Segmentation using Gaussian Mixture Models

Abstract. Recently stochastic models such as mixture models, graphical models, Markov random fields and hidden Markov models have key role in probabilistic data analysis. Also image segmentation means to divide one picture into different types of classes or regions, for example a picture of geometric shapes has some classes with different colors such as ’circle’, ’rectangle’, ’triangle’ and so on. Therefore we can suppose that each class has normal distribution with specify mean and variance. Thus in general a picture can be Gaussian mixture model. In this paper, we have learned Gaussian mixture model to the pixel of an image as training data and the parameter of the model are learned by EM-algorithm. Meanwhile pixel labeling corresponded to each pixel of true image is done by Bayes rule. This hidden or labeled image is constructed during of running EM-algorithm. In fact, we introduce a new numerically method of finding maximum a posterior estimation by using of EM-algorithm and Gaussians mixture model which we called EM-MAP algorithm. In this algorithm, we have made a sequence of the priors, posteriors and they then convergent to a posterior probability that is called the reference posterior probability. So Maximum a posterior estimation can be determined by this reference posterior probability which will make labeled image. This labeled image shows our segmented image with reduced noises. This method will show in several experiments.