New approximation of a scale space kernel on SE(3) and applications in neuroimaging

J.M. Portegies, G.R. Sanguinetti, S.P.L. Meesters, R. Duits

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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
Original languageEnglish
Title of host publicationScale Space and Variational Methods in Computer Vision (5th International Conference, SSVM 2015, Lège-Cap Ferret, France, May 31-June 4, 2015, Proceedings)
EditorsJ.-F. Aujol, M. Nikolova, N. Papadakis
PublisherSpringer
Pages40-52
ISBN (Print)978-3-319-18460-9
DOIs
Publication statusPublished - 2015

Publication series

NameLecture Notes in Computer Science
Volume9087
ISSN (Print)0302-9743

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Portegies, J. M., Sanguinetti, G. R., Meesters, S. P. L., & Duits, R. (2015). New approximation of a scale space kernel on SE(3) and applications in neuroimaging. In J-F. Aujol, M. Nikolova, & N. Papadakis (Eds.), Scale Space and Variational Methods in Computer Vision (5th International Conference, SSVM 2015, Lège-Cap Ferret, France, May 31-June 4, 2015, Proceedings) (pp. 40-52). (Lecture Notes in Computer Science; Vol. 9087). Springer. https://doi.org/10.1007/978-3-319-18461-6_4