Shape analysis with conformal invariants for multiply connected domains and its application to analyzing brain morphology

Yalin Wang, Xianfeng Gu, Tony F. Chan, Paul M. Thompson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Scopus citations

Abstract

All surfaces can be classified by the conformal equivalence relation. Conformal invariants, which are shape indices that can be defined intrinsically on a surface, may be used to identify which surfaces are conformally equivalent, and they can also be used to measure surface deformation. Here we propose to compute a conformal invariant, or shape index, that is associated with the perimeter of the inner concentric circle in the hyperbolic parameter plane. With the surface Ricci flow method, we can conformally map a multiply connected domain to a multi-hole disk and this conformal map can preserve the values of the conformal invariant. Our algorithm provides a stable method to map the values of this shape index in the 2D (hyperbolic space) parameter domain. We also applied this new shape index for analyzing abnormalities in brain morphology in Alzheimer's disease (AD) and Williams syndrome (WS). After cutting along various landmark curves on surface models of the cerebral cortex or hippocampus, we obtained multiple connected domains. We conformally projected the surfaces to hyperbolic plane with surface Ricci flow method, accurately computed the proposed conformal invariant for each selected landmark curve, and assembled these into a feature vector.We also detected group differences in brain structure based on multivariate analysis of the surface deformation tensors induced by these Ricci flow mappings. Experimental results with 3D MRI data from 80 subjects demonstrate that our method powerfully detects brain surface abnormalities when combined with a constrained harmonic map based surface registration method.

Original languageEnglish (US)
Title of host publication2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009
PublisherIEEE Computer Society
Pages202-209
Number of pages8
ISBN (Print)9781424439935
DOIs
StatePublished - Jan 1 2009
Externally publishedYes
Event2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Miami, FL, United States
Duration: Jun 20 2009Jun 25 2009

Publication series

Name2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009
Volume2009 IEEE Computer Society Conference on Computer Vision and ...

Conference

Conference2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition
CountryUnited States
CityMiami, FL
Period6/20/096/25/09

ASJC Scopus subject areas

  • Biomedical Engineering
  • Computer Vision and Pattern Recognition

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    Wang, Y., Gu, X., Chan, T. F., & Thompson, P. M. (2009). Shape analysis with conformal invariants for multiply connected domains and its application to analyzing brain morphology. In 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009 (pp. 202-209). [5206578] (2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009; Vol. 2009 IEEE Computer Society Conference on Computer Vision and ...). IEEE Computer Society. https://doi.org/10.1109/CVPRW.2009.5206578