Fast unsupervised Bayesian image segmentation with adaptive spatial regularisation

This paper presents two new Bayesian estimation techniques for hidden Potts-Markov random fields, with application to fast K-class image segmentation. The techniques are derived by first conducting a small-variance-asymptotic (SVA) analysis of an augmented Bayesian model in which the spatial regularisation and the integer-constrained terms of the Potts model are decoupled. The evaluation of this SVA Bayesian estimator is then relaxed into a partially convex problem that can be computed efficiently by iteratively solving a total-variation denoising problem and a least-squares clustering (K-means) problem, both of which can be solved straightforwardly, even in high-dimensions, and with parallel computing techniques. This leads to a fast semi-supervised Bayesian image segmentation methodology that can be easily applied in large 2D and 3D scenarios or in applications requiring low computing times. Following on from this, we extend the proposed Bayesian model and inference technique to the case where the value of the spatial regularisation parameter is unknown and removed from the model by marginalisation. This leads to a new fully unsupervised fast Bayesian segmentation algorithm in which the strength of the spatial regularisation is adapted automatically to the observed image during the inference procedure. Experimental results on synthetic and real images, as well as extensive comparisons with state-of-the-art algorithms, confirm that the proposed semi-supervised and unsupervised methodologies offer extremely fast convergence and produce accurate segmentation results, with the important additional advantage of self-adjusting regularisation parameters.