Bayesian image segmentation using hidden fields: Supervised, unsupervised, and semi-supervised formulations

Segmentation is one of the central problems in image analysis, where the goal is to partition the image domain into regions exhibiting some sort of homogeneity. Most often, the partition is obtained by solving a combinatorial optimization problem, which is, in general, NP-hard. In this paper, we follow an alternative approach, using a Bayesian formulation based on a set of hidden real-valued random fields, which condition the partition. This formulation yields a continuous optimization problem, rather than a combinatorial one. In the supervised case, this problem is convex, and we tackle it with an instance of the alternating direction method of multipliers (ADMM). In the unsupervised and semi-supervised cases, the optimization problem is nonconvex, and we address it using an expectation-maximization (EM) algorithm, where the M-step is implemented via ADMM. The effectiveness and flexibility of the proposed approach is illustrated with experiments on simulated and real data.

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