Multi-region image segmentation aims at partitioning an image into several "meaningful" regions. The associated optimization problem is non-convex and generally difficult to solve. Finding the global optimum, or good approximations of it, hence is a problem of first interest in computer vision. We propose an alternating split Bregman algorithm for a large class of convex relaxations of the continuous Potts segmentation model. We compare the algorithm to the primal-dual approach and show examples from the Berkeley image database and from live-cell fluorescence microscopy.