On the optimization of probability vector MRFs in image segmentation

In the context of image segmentation, Markov random fields (MRF) are extensively used. However solution of MRF-based models is heavily dependent on how successfully the MRF energy minimization is performed. In this framework, two methodologies, complementary to each other, are proposed for random field optimization. We address the special class of models comprising a random field imposed on the probabilities of the pixel labels. This class of segmentation models poses a special optimization problem, as, in this case, the variables constituting the MRF are continuous and subject to probability constraints (positivity, sum-to-unity). The proposed methods are evaluated numerically in terms of objective function value and segmentation performance, and compare favorably to existing corresponding optimization schemes.