Magnetic resonance voxel labeling based on Bayesian Decision Theory

摘要

Abstract: In this paper, Bayesian decision theory is applied to the labelling of voxels in Magnetic Resonance (MR) images of the brain. The Bayes optimal decision rule defines a cost function that consists of a loss function weighted by the a posteriori probability of the labelling. Two options for the loss function are presented in this paper. A zero-one loss function gives rise to the maximum a posteriori (MAP) estimate, which requires a simulated annealing optimization process. The probability term of the cost function is the product of the a priori probability of the labelling (or an a priori model of the underlying scene) and the conditional probability of the data, given the labelling (or the model for the imaging modality). By modelling the label image as a Markov random field, the model for the underlying scene can be described by a Gibbs distribution. In the application discussed, here, they reflect the compatibility of anatomical structures. The imaging method represents the expected voxel intensities and possible noise or image distortions.!26