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

TL;DR

This paper introduces a new symmetric approximation of a scale space kernel on SE(3) for dMRI data enhancement, improving tractography and coherence quantification in neuroimaging.

Contribution

It presents an improved symmetric kernel approximation on SE(3) using the logarithm, enhancing fiber imaging in neuroimaging applications.

Findings

Enhanced dMRI tractography results

Better quantification of streamline coherence

Improved kernel symmetry and approximation accuracy

Abstract

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.