Fiber enhancement in diffusion-weighted MRI

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 TeX 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 TeX. 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.

@InProceedings { DDGCVH12,
  author       = "Duits, R. and Dela Haije, T.C.J. and Ghosh, A. and Creusen, E.J. and Vilanova, Anna and Haar Romeny, B.M. ter",
  title        = "Fiber enhancement in diffusion-weighted MRI",
  booktitle    = "Scale Space and Variational Methods in Computer Vision (Third International Conference, SSVM 2011, Ein-Gedi,
                  Israel, May 29-June 2, 2011. Revised Selected Papers)",
  volume       = "6667",
  pages        = "1--13",
  year         = "2012",
  editor       = "Bruckstein,A.M. and ter Haar Romeny,B.M. and Bronstein,A.M. and Bronstein,M.M.",
  publisher    = "Springer",
  address      = "Berlin",
  note         = "http://dx.doi.org/10.1007/978-3-642-24785-9_1, journal: Lecture Notes in Computer Science",
  url          = "http://graphics.tudelft.nl/Publications-new/2012/DDGCVH12"
}