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We propose an approach for unsupervised image segmentation based on the Markov random field by using the Bethe approximation. We first derive the Bayesian information criterion under the Bethe approximation and then propose an iterative algorithm to search a model which fits the image data best. For this aim, we derive a criterion for merging two components among several components in terms of a perturbation expansion. Namely, annihilation of components is implemented by merging two components into one component after each convergence of the supervised segmentation with a fixed number of components. We find by numerical experiments that the optimal number of components is selected from the series of local optima with different numbers of components and the best result for segmentation is obtained with good performance.

Unsupervised Image Segmentation Based on Bethe Approximation