Diffusion tensor MRI probes and quantifies the anisotropic diffusion of water molecules in biological tissues, making it possible to non-invasively infer the architecture of the underlying structures. In this article, we present a set of new techniques for the estimation and regularization of diffusion tensors MRI datasets as well as a novel approach to the cerebral white matter connectivity mapping. Numerical experimentations conducted on real diffusion weighted MRI will exhibit promising results.