Expectation–maximization algorithm with total variation regularization for vector-valued image segmentation

We integrate the total variation (TV) minimization into the expectation–maximization (EM) algorithm to perform the task of image segmentation for general vector-valued images. We first propose a unified variational method to bring together the EM and the TV regularization and to take advantages from both approaches. The idea is based on operator interchange and constraint optimization. In the second part of the paper we propose a simple two-phase approach by splitting the above functional into two steps. In the first phase, a typical EM method can classify pixels into different classes based on the similarity in their measurements. However, since no local geometric information of the image has yet been incorporated into the process, such classification in practice gives unsatisfactory segmentation results. In the second phase, the TV-step obtains the segmentation of the image by applying a TV regularization directly to the clustering result from EM.

► Two statistical–variational algorithms for vector-valued image segmentation.
► The first one unifies the GMM-EM with TVL1 regularization.
► The second part proposes a two-phase algorithm by splitting the EM and the TVL1.
► These algorithms naturally extend to general d-dimensional images.