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

  • Jorg Portegies
  • Gonzalo Sanguinetti
  • Stephan Meesters
  • Remco Duits
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9087)

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.

Keywords

Scale space on SE(3) Contextual enhancement Left-invariant diffusion Group convolution Tractography 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jorg Portegies
    • 1
  • Gonzalo Sanguinetti
    • 1
  • Stephan Meesters
    • 1
    • 2
  • Remco Duits
    • 1
    • 3
  1. 1.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenNetherlands
  2. 2.Academic Center for Epileptology Kempenhaeghe and Maastricht UMC+HeezeNetherlands
  3. 3.Department of Biomedical EngineeringEindhoven University of TechnologyEindhovenNetherlands

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