On the convergence of EM-like algorithms for image segmentation using Markov random fields

Inference of Markov random field images segmentation models is usually performed using itera- tive methods which adapt the well-known expectation–maximization (EM) algorithm for independent mixture models. However, some of these adaptations are ad hoc and may turn out numerically unstable. In this paper, we review three EM-like variants for Markov random field segmentation and compare their convergence properties both at the theoretical and practical levels. We specifically advocate a numerical scheme involving asynchronous voxel updating, for which general convergence results can be established. Our experiments on brain tissue classification in magnetic resonance images provide evidence that this algorithm may achieve significantly faster convergence than its competitors while yielding at least as good segmentation results. [Display omitted] ► Some inference algorithms used in medical image segmentation are numerically unstable. ► The proposed asynchronous variational expectation–maximization scheme is provably convergent. ► In brain image segmentation, it achieves faster convergence than exsiting competitors. Inference of Markov random field images segmentation models is usually performed using iterative methods which adapt the well-known expectation–maximization (EM) algorithm for independent mixture models. However, some of these adaptations are ad hoc and may turn out numerically unstable. In this paper, we review three EM-like variants for Markov random field segmentation and compare their convergence properties both at the theoretical and practical levels. We specifically advocate a numerical scheme involving asynchronous voxel updating, for which general convergence results can be established. Our experiments on brain tissue classification in magnetic resonance images provide evidence that this algorithm may achieve significantly faster convergence than its competitors while yielding at least as good segmentation results.