Diffusion of fiber orientation distribution functions with a rotation-induced riemannian metric

Advanced diffusion weighted MR imaging allows non-invasive study on the structural connectivity of human brains. Fiber orientation distributions (FODs) reconstructed from diffusion data are a popular model to represent crossing fibers. For this sophisticated image representation of connectivity, classical image operations such as smoothing must be redefined. In this paper, we propose a novel rotation-induced Riemannian metric for FODs, and introduce a weighted diffusion process for FODs regarding this Riemannian manifold. We show how this Riemannian manifold can be used for smoothing, interpolation and building image-pyramids, yielding more accurate or intuitively more reasonable results than the linear or the unit hyper-sphere manifold.