Image segmentation is one of the central problems in image analysis, where the goal is to partition the image domain such that each element of the partition exhibits some kind of homogeneity. Most often, the partitions are obtained by solving a discrete optimization problem, which is, in general, NP-hard. We sidestep this discrete optimization hurdle by formulating the problem in the Bayesian framework, with the help of a set of hidden real-valued random fields, informative with respect to the probability of the partitions. Armed with this model, the original discrete optimization is replaced with a continuous optimization problem. In the supervised case, the optimization is convex and solved with an instance of ADMM. In the semi-supervised case, the optimization is nonconvex and solved with expectation maximization. The effectiveness and flexibility of the proposed approach is illustrated with simulated
and real data.