Selecting an appropriate metric for the processing of Diffusion Tensor Images

For a few years, Diffusion Tensor Imaging (DTI) has received much attention. This new method of imaging allows non-invasive quantification of the diffusion of water in the brain. The formalism introduced by Basser [1] enables to assess the diffusion in each voxel (small cubes) of the brain. Conceptually, a diffusion tensor D is assigned to each voxel. The anisotropy of the tensors is then used to numerically reconstruct nervous fibers of the brain. This new development of brain imaging raises new challenges for its processing. Classical image processing algorithms are indeed developed for scalar images. The processing of Diffusion Tensor Images, which can be viewed as symmetric positive definite matrices fields, thus requires the definition of novel algorithms. One common feature of these algorithms is their use of a distance function between images. At a finer level, a distance function between tensors has to be defined. In this work, we propose a novel metric which is particularly appropriate for the processing of DTI.