Direct Glyph-based Visualization of Diffusion MR Data Using Deformed Spheres

  • Martin Domin
  • Sönke Langner
  • Norbert Hosten
  • Lars Linsen
Part of the Mathematics and Visualization book series (MATHVISUAL)


For visualization of medical diffusion data one typically computes a tensor field from a set of diffusion volume images scanned with different gradient directions. The resulting diffusion tensor field is visualized using glyph- or tracking-based approaches. The derivation of the tensor, in general, involves a loss in information, as the n > 6 diffusion values for the n gradient directions are reduced to six diverse entries of the symmetric 3 × 3 tensor matrix. We propose a direct diffusion visualization approach that does not operate on the diffusion tensor. Instead, we assemble the gradient vectors on a unit sphere and deform the sphere by the measured diffusion values in the respective gradient directions. We compute a continuous deformation model from the few discrete directions by applying several processing steps. First, we compute a triangulation of the spherical domain using a convex hull algorithm. The triangulation leads to neighborhood information for the position vectors of the discrete directions. Using a parameterization over the sphere we perform a Powell-Sabin interpolation, where the surface gradients are computed using least-squares fitting. The resulting triangular mesh is subdivided using a few Loop subdivision steps. The rendering of this subdivided triangular mesh directly leads to a glyph-based visualization of the directional diffusion measured in the respective voxel. In a natural and intuitive fashion, our deformed sphere visualization can exhibit additional, possibly valuable information in comparison to the classical tensor glyph visualization.


Fractional Anisotropy Triangular Mesh Gradient Direction Subdivision Scheme High Angular Resolution 
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 2008

Authors and Affiliations

  • Martin Domin
    • 1
  • Sönke Langner
    • 1
  • Norbert Hosten
    • 1
  • Lars Linsen
    • 2
  1. 1.Department of Diagnostic Radiology and NeuroradiologyErnst-Moritz-Arndt-Universität GreifswaldGreifswaldGermany
  2. 2.Computational Science and Computer Science School of Engineering and ScienceJacobs UniversityBremenGermany

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