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Fiber Enhancement in Diffusion-Weighted MRI

  • Remco Duits
  • Tom C. J. Dela Haije
  • Arpan Ghosh
  • Eric Creusen
  • Anna Vilanova
  • Bart ter Haar Romeny
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6667)

Abstract

Diffusion-Weighted MRI (DW-MRI) measures local water diffusion in biological tissue, which reflects the underlying fiber structure. In order to enhance the fiber structure in the DW-MRI data we consider both (convection-)diffusions and Hamilton-Jacobi equations (erosions) on the space \(\mathbb{R}^3 \rtimes S^2\) of 3D-positions and orientations, embedded as a quotient in the group SE(3) of 3D-rigid body movements. These left-invariant evolutions are expressed in the frame of left-invariant vector fields on SE(3), which serves as a moving frame of reference attached to fiber fragments. The linear (convection-)diffusions are solved by a convolution with the corresponding Green’s function, whereas the Hamilton-Jacobi equations are solved by a morphological convolution with the corresponding Green’s function. Furthermore, we combine dilation and diffusion in pseudo-linear scale spaces on \(\mathbb{R}^{3}\rtimes S^2\). All methods are tested on DTI-images of the brain. These experiments indicate that our techniques are useful to deal with both the problem of limited angular resolution of DTI and the problem of spurious, non-aligned crossings in HARDI.

Keywords

DTI HARDI DW-MRI sub-Riemannian geometry scale spaces Lie groups Hamilton-Jacobi equations erosion 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Remco Duits
    • 1
    • 2
  • Tom C. J. Dela Haije
    • 2
  • Arpan Ghosh
    • 1
  • Eric Creusen
    • 1
    • 2
  • Anna Vilanova
    • 2
  • Bart ter Haar Romeny
    • 2
  1. 1.Department of Mathematics and Computer ScienceEindhoven University of TechnologyThe Netherlands
  2. 2.Department of Biomedical EngineeringEindhoven University of TechnologyThe Netherlands

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