Studying brain morphometry using conformal equivalence class

Yalin Wang*, Wei Dai, Yi Yu Chou, Xianfeng Gu, Tony F. Chan, Arthur W. Toga, Paul M. Thompson

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

12 Scopus citations


Two surfaces are conformally equivalent if there exists a bijective angle-preserving map between them. The Teichmüller space for surfaces with the same topology is a finite-dimensional manifold, where each point represents a conformal equivalence class, and the conformal map is homotopic to the identity map. In this paper, we propose a novel method to apply conformal equivalence based shape index to study brain morphometry. The shape index is de-fined based on Teichmüller space coordinates. It is intrinsic, and invariant under conformal transformations, rigid motions and scaling. It is also simple to compute; no registration of surfaces is needed. Using the Yamabe flow method, we can conformally map a genus-zero open boundary surface to the Poincaré disk. The shape indices that we compute are the lengths of a special set of geodesics under hyperbolic metric. By computing and studying this shape index and its statistical behavior, we can analyze differences in anatomical morphometry due to disease or development. Study on twin lateral ventricular surface data shows it may help detect generic influence on lateral ventricular shapes. 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.Our conformal invariants, the Teichmüller coordinates, successfully classified all lateral ventricular surfaces, showing their promise for analyzing anatomical surface morphometry.

Original languageEnglish (US)
Title of host publication2009 IEEE 12th International Conference on Computer Vision, ICCV 2009
Number of pages8
StatePublished - 2009
Event12th International Conference on Computer Vision, ICCV 2009 - Kyoto, Japan
Duration: Sep 29 2009Oct 2 2009

Publication series

NameProceedings of the IEEE International Conference on Computer Vision


Conference12th International Conference on Computer Vision, ICCV 2009

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition


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