Segmentation of High Angular Resolution Diffusion MRI Modeled as a Field of von Mises-Fisher Mixtures

  • Tim McGraw
  • Baba Vemuri
  • Robert Yezierski
  • Thomas Mareci
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3953)


High angular resolution diffusion imaging (HARDI) permits the computation of water molecule displacement probabilities over a sphere of possible displacement directions. This probability is often referred to as the orientation distribution function (ODF). In this paper we present a novel model for the diffusion ODF namely, a mixture of von Mises-Fisher (vMF) distributions. Our model is compact in that it requires very few variables to model complicated ODF geometries which occur specifically in the presence of heterogeneous nerve fiber orientation. We also present a Riemannian geometric framework for computing intrinsic distances, in closed-form, and performing interpolation between ODFs represented by vMF mixtures. As an example, we apply the intrinsic distance within a hidden Markov measure field segmentation scheme. We present results of this segmentation for HARDI images of rat spinal cords – which show distinct regions within both the white and gray matter. It should be noted that such a fine level of parcellation of the gray and white matter cannot be obtained either from contrast MRI scans or Diffusion Tensor MRI scans. We validate the segmentation algorithm by applying it to synthetic data sets where the ground truth is known.


Symmetric Space Gaussian Mixture Model Orientation Distribution Function Spherical Harmonic Expansion High Angular Resolution 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tim McGraw
    • 1
  • Baba Vemuri
    • 2
  • Robert Yezierski
    • 3
  • Thomas Mareci
    • 4
  1. 1.Dept. of Computer Science and Electrical EngineeringWest Virginia UniversityMorgantown
  2. 2.Dept. of Computer and Information Sciences and EngineeringUniversity of FloridaGainesville
  3. 3.Dept. of Neuroscience, Dept. of OrthodonticsUniversity of FloridaGainesville
  4. 4.Dept. of BiochemistryUniversity of FloridaGainesville

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