Small-variance asymptotics of hidden Potts-MRFS: Application to fast Bayesian image segmentation

Abstract

This paper presents a new approximate Bayesian estimator for hidden Potts-Markov random fields, with application to fast K-class image segmentation. The estimator is derived by conducting a small-variance-asymptotic analysis of an augmented Bayesian model in which the spatial regularisation and the integer-constrained terms of the Potts model are decoupled. This leads to a new image segmentation methodology that can be efficiently implemented in large 2D and 3D scenarios by using modern convex optimisation techniques. Experimental results on synthetic and real images as well as comparisons with state-of-the-art algorithms confirm that the proposed methodology converges extremely fast and produces accurate segmentation results in only few iterations.