A dual EM algorithm for tv regularized gaussian mixture model in image segmentation

A dual expectation-maximization (EM) algorithm for total variation (TV) regularized Gaussian mixture model (GMM) is proposed in this paper. The algorithm is built upon the EM algorithm with TV regularization (EM-TV) model which combines the statistical and variational methods together for image segmentation. Inspired by the projection algorithm proposed by Chambolle, we give a dual algorithm for the EM-TV model. The related dual problem is smooth and can be easily solved by a projection gradient method, which is stable and fast. Given the parameters of GMM, the proposed algorithm can be seen as a forward-backward splitting method which converges. This method can be easily extended to many other applications. Numerical results show that our algorithm can provide high quality segmentation results with fast computation speed. Compared with the well-known statistics based methods such as hidden Markov random field with EM method (HMRF-EM), the proposed algorithm has a better performance. The proposed method could also be applied to MRI segmentation such as SPM8 software and improve the segmentation results.