Continuous voxel classification by stochastic relaxation: theory and application to MR imaging and MR angiography

Abstract

In this paper we present a stochastic relaxation method for voxel classification in magnetic resonance (MR) images. This method is based on Bayesian decision theory. In this framework, the optimal classification corresponds to the minimum of an objective function, which is here defined as the expected number of misclassified voxels. The objective function encodes constraints according to two a priori models: the scene model and the camera model. The scene model reflects a priori knowledge of anatomy and morphology; the camera model relates observed MR-image intensities to anatomical objects. Both models are described using the concept of Markov random fields (MRF). This allows continuity and local contextual constraints to be easily modelled via the associated Gibbs Potential Functions. The minimum of the objective function is approximated asymptotically by stochastically sampling the associated Gibbs posterior joint probability distribution. The method is applied to brain tissue classification in MRI and blood vessel classification in MR angiograms. Each application contains a novel aspect: in the former, we introduce topological constraints on neighbouring tissues; in the latter, we incorporate shape constraints on cylindrical structures.