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Multivariate Statistics of the Jacobian Matrices in Tensor Based Morphometry and Their Application to HIV/AIDS

  • Natasha Lepore
  • Caroline A. Brun
  • Ming-Chang Chiang
  • Yi-Yu Chou
  • Rebecca A. Dutton
  • Kiralee M. Hayashi
  • Oscar L. Lopez
  • Howard J. Aizenstein
  • Arthur W. Toga
  • James T. Becker
  • Paul M. Thompson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4190)

Abstract

Tensor-based morphometry (TBM) is widely used in computational anatomy as a means to understand shape variation between structural brain images. A 3D nonlinear registration technique is typically used to align all brain images to a common neuroanatomical template, and the deformation fields are analyzed statistically to identify group differences in anatomy. However, the differences are usually computed solely from the determinants of the Jacobian matrices that are associated with the deformation fields computed by the registration procedure. Thus, much of the information contained within those matrices gets thrown out in the process. Only the magnitude of the expansions or contractions is examined, while the anisotropy and directional components of the changes are ignored.

Here we remedy this problem by computing multivariate shape change statistics using the strain matrices. As the latter do not form a vector space, means and covariances are computed on the manifold of positive-definite matrices to which they belong. We study the brain morphology of 26 HIV/AIDS patients and 14 matched healthy control subjects using our method.

The images are registered using a high-dimensional 3D fluid registration algorithm, which optimizes the Jensen-Rényi divergence, an information-theoretic measure of image correspondence. The anisotropy of the deformation is then computed. We apply a manifold version of Hotelling’s T 2 test to the strain matrices. Our results complement those found from the determinants of the Jacobians alone and provide greater power in detecting group differences in brain structure.

Keywords

Jacobian Matrice Manifold Version Deformable Image Registration Medical Image Computing Strain Matrice 
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 2006

Authors and Affiliations

  • Natasha Lepore
    • 1
  • Caroline A. Brun
    • 1
  • Ming-Chang Chiang
    • 1
  • Yi-Yu Chou
    • 1
  • Rebecca A. Dutton
    • 1
  • Kiralee M. Hayashi
    • 1
  • Oscar L. Lopez
    • 2
  • Howard J. Aizenstein
    • 3
  • Arthur W. Toga
    • 1
  • James T. Becker
    • 2
  • Paul M. Thompson
    • 1
  1. 1.Laboratory of Neuro Imaging, Department of NeurologyDavid Geffen School of Medicine at UCLALos AngelesUSA
  2. 2.Department of PsychiatryUniversity of PittsburghPittsburghUSA
  3. 3.Department of NeurologyUniversity of PittsburghPittsburghUSA

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