A statistical framework for DTI segmentation

We address the problem of the segmentation of cerebral white matter structures from diffusion tensor images (DTI). DTI can be estimated from a set of diffusion weighted images and provides tensor-valued images where each voxel is assigned with a 3 times 3 symmetric, positive-definite matrix. As we will show in this paper, the definition of a dissimilarity measure and statistics between tensors is a non trivial task which must be carefully tackled. We claim that, by using the differential geometrical properties of the manifold of multivariate normal distributions, it is possible to improve the quality of the segmentation obtained with other dissimilarity measures such as the Euclidean distance or the Kullback-Leibler divergence. Our goal is to prove that the choice of this probability metric has a deep impact on the tensor statistics and, hence, on the achieved results. We introduce a variational formulation to estimate the optimal segmentation of a diffusion tensor image. We show how to estimate diffusion tensors statistics for three different probability metrics and evaluate their respective performances. We validate and compare the results obtained on synthetic and real datasets