Human Brain Mapping with Conformal Geometry and Multivariate Tensor-Based Morphometry

  • Jie Shi
  • Paul M. Thompson
  • Yalin Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7012)


In this paper, we introduce theories and algorithms in conformal geometry, including Riemann surface, harmonic map, holomorphic 1-form, and Ricci flow, which play important roles in computational anatomy. In order to study the deformation of brain surfaces, we introduce the multivariate tensor-based morphometry (MTBM) method for statistical computing. For application, we introduce our system for detecting Alzheimer’s Disease (AD) symptoms on hippocampal surfaces with an automated surface fluid registration method, which is based on surface conformal mapping and mutual information regularized image fluid registration. Since conformal mappings are diffeomorphic and the mutual information method is able to drive a diffeomorphic flow that is adjusted to enforce appropriate surface correspondences in the surface parameter domain, combining conformal and fluid mappings will generate 3D shape correspondences that are diffeomorphic. We also incorporate in the system a novel method to compute curvatures using surface conformal parameterization. Experimental results in ADNI baseline data diagnostic group difference and APOE4 effects show that our system has better performance than other similar work in the literature.


Conformal Mapping Ricci Flow Circle Packing Conformal Geometry Human Brain Mapping 
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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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jie Shi
    • 1
  • Paul M. Thompson
    • 2
  • Yalin Wang
    • 1
  1. 1.School of Computing, Informatics and Decision Systems EngineeringASUTempeUSA
  2. 2.Lab. of Neuro ImagingUCLA School of MedicineLos AngelesUSA

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