  We provide a new, analytic kernel for scale space filtering of dMRI data. The
kernel is an approximation for the Green's function of a hypo-elliptic
diffusion on the 3D rigid body motion group SE(3), for fiber enhancement in
dMRI. The enhancements are described by linear scale space PDEs in the coupled
space of positions and orientations embedded in SE(3). As initial condition for
the evolution we use either a Fiber Orientation Distribution (FOD) or an
Orientation Density Function (ODF). Explicit formulas for the exact kernel do
not exist. Although approximations well-suited for fast implementation have
been proposed in literature, they lack important symmetries of the exact
kernel. We introduce techniques to include these symmetries in approximations
based on the logarithm on SE(3), resulting in an improved kernel. Regarding
neuroimaging applications, we apply our enhancement kernel (a) to improve dMRI
tractography results and (b) to quantify coherence of obtained streamline
bundles.
