Bayesian Image Segmentation Using Gaussian Field Priors

Abstract

The goal of segmentation is to partition an image into a finite set of regions, homogeneous in some (e.g., statistical) sense, thus being an intrinsically discrete problem. Bayesian approaches to segmentation use priors to impose spatial coherence; the discrete nature of segmentation demands priors defined on discrete-valued fields, thus leading to difficult combinatorial problems.

This paper presents a formulation which allows using continuous priors, namely Gaussian fields, for image segmentation. Our approach completely avoids the combinatorial nature of standard Bayesian approaches to segmentation. Moreover, it’s completely general, i.e., it can be used in supervised, unsupervised, or semi-supervised modes, with any probabilistic observation model (intensity, multispectral, or texture features).

To use continuous priors for image segmentation, we adopt a formulation which is common in Bayesian machine learning: introduction of hidden fields to which the region labels are probabilistically related. Since these hidden fields are real-valued, we can adopt any type of spatial prior for continuous-valued fields, such as Gaussian priors. We show how, under this model, Bayesian MAP segmentation is carried out by a (generalized) EM algorithm. Experiments on synthetic and real data shows that the proposed approach performs very well at a low computational cost.