New Approximation of a Scale Space Kernel on SE(3) and Applications in Neuroimaging

摘要

We provide a new, analytic kernel for scale space filtering of dMRI data. Thekernel is an approximation for the Green's function of a hypo-ellipticdiffusion on the 3D rigid body motion group SE(3), for fiber enhancement indMRI. The enhancements are described by linear scale space PDEs in the coupledspace of positions and orientations embedded in SE(3). As initial condition forthe evolution we use either a Fiber Orientation Distribution (FOD) or anOrientation Density Function (ODF). Explicit formulas for the exact kernel donot exist. Although approximations well-suited for fast implementation havebeen proposed in literature, they lack important symmetries of the exactkernel. We introduce techniques to include these symmetries in approximationsbased on the logarithm on SE(3), resulting in an improved kernel. Regardingneuroimaging applications, we apply our enhancement kernel (a) to improve dMRItractography results and (b) to quantify coherence of obtained streamlinebundles.