Teichmüller Shape Space Theory and Its Application to Brain Morphometry

Authors:
Yalin Wang;Wei Dai;Xianfeng Gu;Tony F. Chan;Shing-Tung Yau;Arthur W. Toga;Paul M. Thompson
Affiliations:
Lab. of Neuro Imaging, UCLA School of Medicine, Los Angeles, USA 90095 and Mathematics Department, UCLA, Los Angeles, USA 90095;Mathematics Department, Zhejiang Univ, Hangzhou, China;Comp. Sci. Department, SUNY at Stony Brook, Stony Brook, USA 11794;Mathematics Department, UCLA, Los Angeles, USA 90095;Department of Mathematics, Harvard University, Cambridge, USA 02138;Lab. of Neuro Imaging, UCLA School of Medicine, Los Angeles, USA 90095;Lab. of Neuro Imaging, UCLA School of Medicine, Los Angeles, USA 90095
Venue:
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part II
Year:
2009

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Abstract

Here we propose a novel method to compute Teichmüller 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 Poincaré 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 Teichmüller coordinates for lateral ventricular surfaces extracted from their 3D MRI scans.