Q-Ball Images Segmentation Using Region-Based Statistical Surface Evolution

apport de recherche N 0249-6399Unité de recherche INRIA Sophia Antipoli

apport de rechercheDTI Segmentation by Statistical Surface Evolution

Abstract: We address the problem of the segmentation of cerebral white matter structures from diffusion tensor images (DTI). DTI produces, from a set of diffusion-weighted MR images, tensorvalued images where each voxel is assigned with a 3 × 3 symmetric, positive-definite matrix. This second order tensor is simply the covariance matrix of a local Gaussian process, with zero mean, modeling the average motion of water molecules. As we will show in this article, the definition of a dissimilarity measure and statistics between such quantities is a non trivial task which must be tackled carefully. We claim and demonstrate that, by using the theoretically wellfounded differential geometrical properties of the manifold of multivariate normal distributions, it is possible to improve the quality of the segmentation results obtained with other dissimilarity measures such as the Euclidean distance or the Kullback-Leibler divergence. The main goal of this work is to prove that the choice of the probability metric, i.e. the dissimilarity measure, has a deep impact on the tensor statistics and, hence, on the achieved results. We introduce a variational formulation, in the level-set framework, to estimate the optimal segmentation of a diffusion tensor image according to the following hypothesis: Diffusion tensors exhibit a Gaussian distribution in the different partitions. We must also respect the geometric constraints imposed by the interface