The EM Algorithm

The Expectation-Maximization (EM) algorithm is a broadly applicable approach to the iterative computation of maximum likelihood (ML) estimates, useful in a variety of incomplete-data problems. Maximum likelihood estimation and likelihood-based inference are of central importance in statistical theory and data analysis. Maximum likelihood estimation is a general-purpose method with attractive properties. It is the most-often used estimation technique in the frequentist framework; it is also relevant in the Bayesian framework (Chapter III.11). Often Bayesian solutions are justified with the help of likelihoods and maximum likelihood estimates (MLE), and Bayesian solutions are similar to penalized likelihood estimates. Maximum likelihood estimation is an ubiquitous technique and is used extensively in every area where statistical techniques are used. --

Color image segmentation using a self-initializing EM algorithm

This paper presents a new method based on the Expectation-Maximization (EM) algorithm that we apply for color image segmentation. Since this algorithm partitions the data based on an initial set of mixtures, the color segmentation provided by the EM algorithm is highly dependent on the starting condition (initialization stage). Usually the initialization procedure selects the color seeds randomly and often this procedure forces the EM algorithm to converge to numerous local minima and produce inappropriate results. In this paper we propose a simple and yet effective solution to initialize the EM algorithm with relevant color seeds. The resulting self initialised EM algorithm has been included in the development of an adaptive image segmentation scheme that has been applied to a large number of color images. The experimental data indicates that the refined initialization procedure leads to improved color segmentation

Foreword

This report reviews the Expectation Maximization EM algorithm and applies it to the data segmentation problem yielding the Expectation Maximization Segmentation EMS algorithm The EMS algorithm requires batch processing of the data and can be applied to mode switching or jumping linear dynamical state space models The EMS algorithm consists of an optimal fusion of fixed interval Kalman smoothing and discrete optimization. The next section gives a short introduction to the EM algorithm with some background and convergence results In Section the data segmentation problem is dened and in Section the EM algorithm is applied to this problem Section contains simulation results and Section some conclusive remarks