Breast cancer originates when cells grow uncontrollably in the breast resulting into a tumour that can be felt as a lump or observed on x-ray. The tumour is malignant that is cancerous if the cells invade surrounding tissues or spread to distant areas of the body. Breast Cancer can be observed both in women as well as men. Image processing aims at divide one picture into different types of classes or regions, recognition of objects and detecting of edges, etc that is done after the image is segmented. The main aim of this paper is to detect and separate background and foreground by using Gaussians Mixture Model, the parameters of the model and training data are learned by EM-algorithm. Pixel labelling corresponding to each pixel of true image is done by Bayesian rule. This hi labelled image is constructed during of running EM-algorithm.Numerical method of finding maximum a posterior estimation is done by using EM-algorithm and Gaussians mixture model which we called EM-MAP algorithm.