A Novel Gauss-Markov Random Field Approach for Regularization of Diffusion Tensor Maps

In this paper we propose a novel Gaussian MRF approach for regularization of tensor fields for fiber tract enhancement. The model follows the Bayesian paradigm: prior and transition. Both models are given by Gaussian distributions. The prior and the posterior distributions are Gauss-MRFs. The prior MRF promotes local spatial interactions. The posterior MRF promotes that local spatial interactions which are compatible with the observed data. All the parameters of the model are estimated directly from the data. The regularized solution is given by means of the Simulated Annealing algorithm. Two measures of regularization are proposed for quantifying the results. A complete volume DR-MRI data have been processed with the current approach. Some results are presented by using some visually meaningful tensor representations and quantitatively assessed by the proposed measures of regularization.