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Teichmller shape space theory and its application to brain morphometry

Yalin Wang Wei Dai Xianfeng Gu Tony F Chan Shing-Tung Yau Arthur W Toga Paul M Thompson

Computational Geometry mathscidoc:1912.43608

133-140, 2009.9
Here we propose a novel method to compute Teichmller shape space based shape index to study brain morphometry. Such a shape index is intrinsic, and invariant under conformal transformations, rigid motions and scaling. We conformally map a genus-zero open boundary surface to the Poincar disk with the Yamabe flow method. The shape indices that we compute are the lengths of a special set of geodesics under hyperbolic metric. Tests on longitudinal brain imaging data were used to demonstrate the stability of the derived feature vectors. In leave-one-out validation tests, we achieved 100% accurate classification (versus only 68% accuracy for volume measures) in distinguishing 11 HIV/AIDS individuals from 8 healthy control subjects, based on Teichmller coordinates for lateral ventricular surfaces extracted from their 3D MRI scans.
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@inproceedings{yalin2009teichmller,
  title={Teichmller shape space theory and its application to brain morphometry},
  author={Yalin Wang, Wei Dai, Xianfeng Gu, Tony F Chan, Shing-Tung Yau, Arthur W Toga, and Paul M Thompson},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204410699986172},
  pages={133-140},
  year={2009},
}
Yalin Wang, Wei Dai, Xianfeng Gu, Tony F Chan, Shing-Tung Yau, Arthur W Toga, and Paul M Thompson. Teichmller shape space theory and its application to brain morphometry. 2009. pp.133-140. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204410699986172.
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