EM algorithms for Gaussian mixtures with split-and-merge operation

In order to alleviate the problem of local convergence of the usual EM algorithm, a split-and-merge operation is introduced into the EM algorithm for Gaussian mixtures. The split-and-merge equations are first presented theoretically. These equations show that the merge operation is a well-posed problem, whereas the split operation is an ill-posed problem because it is the inverse procedure of the merge. Two methods for solving this ill-posed problem are developed through the singular value decomposition and the Cholesky decomposition. Accordingly, a new modified EM algorithm is constructed. Our experiments demonstrate that this algorithm is efficient for unsupervised color image segmentation. (C) 2003 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.