Which manifold should be used for group comparison in diffusion tensor imaging?

Abstract

Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) is a modality which allows to investigate the white matter structure by probing water molecule diffusion. A common way to model the diffusion process is to consider a second-order tensor, represented by a symmetric positive-definite matrix. Currently, there is still no consensus on the most appropriate manifold for handling diffusion tensors. We propose to evaluate the influence of considering an Euclidean, a Log-Euclidean or a Riemannian manifold for conducting group comparison in DT-MRI. To this end, we consider a multi-linear regression problem that is solved on each of these manifolds. Statistical analysis is then achieved by computing an F-statistic between two nested (restricted and full) models. Our evaluation on simulated data suggests that the performance of these manifolds varies with the kind of modifications that has to be detected, while the experiments on real data do not exhibit significant difference between the methods.