A fast and rigorous anisotropic smoothing method for DT-MRI

Tensors are nowadays an increasing research domain in different areas, especially in image processing, motivated for example by DT-MRI (Diffusion Tensor Magnetic Resonance Imaging). In this paper, we exploit the theoretically well-founded differential geometrical properties of the space of multivariate normal distributions, where it is possible to define a Riemannian metric and express statistics on the manifold of symmetric positive definite matrices. We focus on the contributions of these tools to the anisotropic filtering and regularization of tensor fields. We present promising results on synthetic and real DT-MRI data.