Riemann-Finsler Multi-valued Geodesic Tractography for HARDI

  • Neda Sepasian
  • Jan H. M. ten Thije Boonkkamp
  • Luc M. J. Florack
  • Bart M. Ter Haar Romeny
  • Anna Vilanova
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


We introduce a geodesic based tractography method for High Angular Resolution Diffusion Imaging (HARDI). The concepts used are similar to the ones in geodesic based tractography for Diffusion Tensor Imaging (DTI). In DTI, the inverse of the second-order diffusion tensor is used to define the manifold where the geodesics are traced. HARDI models have been developed to resolve complex fiber populations within a voxel, and higher order tensors (HOT) are possible representations for HARDI data. In our framework, we apply Finsler geometry, which extends Riemannian geometry to a directionally dependent metric. A Finsler metric is defined in terms of HARDI higher order tensors. Furthermore, the Euler-Lagrange geodesic equations are derived based on the Finsler geometry. In contrast to other geodesic based tractography algorithms, the multi-valued numerical solution of the geodesic equations can be obtained. This gives the possibility to capture all geodesics arriving at a single voxel instead of only computing the shortest one. Results are analyzed to show the potential and characteristics of our algorithm.


Diffusion Tensor Imaging Orientation Distribution Function Geodesic Equation Diffusion Profile Diffusion Tensor Imaging Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Neda Sepasian
    • 1
  • Jan H. M. ten Thije Boonkkamp
    • 2
  • Luc M. J. Florack
    • 1
  • Bart M. Ter Haar Romeny
    • 3
  • Anna Vilanova
    • 4
  1. 1.Department of Biomedical Engineering, Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  3. 3.Department of Biomedical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands
  4. 4.Faculty Electrical Engineering, Mathematics and Computer Science, Computer Graphics and VisualizationDelft University of TechnologyDelftThe Netherlands

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