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 Citations (Scopus)

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
Pages202-209
Number of pages8
DOIs
StatePublished - 2009
Externally publishedYes
Event2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009 - Miami, FL, United States
Duration: Jun 20 2009Jun 25 2009

Other

Other2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009
CountryUnited States
CityMiami, FL
Period6/20/096/25/09

Fingerprint

Brain
Magnetic resonance imaging
Tensors

ASJC Scopus subject areas

  • Computer Vision and Pattern Recognition
  • Biomedical Engineering

Cite this

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] https://doi.org/10.1109/CVPRW.2009.5206578

Shape analysis with conformal invariants for multiply connected domains and its application to analyzing brain morphology. / Wang, Yalin; Gu, Xianfeng; Chan, Tony F.; Thompson, Paul M.

2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009. 2009. p. 202-209 5206578.

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

Wang, Y, Gu, X, Chan, TF & Thompson, PM 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., 5206578, pp. 202-209, 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009, Miami, FL, United States, 6/20/09. https://doi.org/10.1109/CVPRW.2009.5206578
Wang Y, Gu X, Chan TF, Thompson PM. 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. 2009. p. 202-209. 5206578 https://doi.org/10.1109/CVPRW.2009.5206578
Wang, Yalin ; Gu, Xianfeng ; Chan, Tony F. ; Thompson, Paul M. / Shape analysis with conformal invariants for multiply connected domains and its application to analyzing brain morphology. 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009. 2009. pp. 202-209
@inproceedings{497f60818ec14c0b9e8894bcd39f4a4e,
title = "Shape analysis with conformal invariants for multiply connected domains and its application to analyzing brain morphology",
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.",
author = "Yalin Wang and Xianfeng Gu and Chan, {Tony F.} and Thompson, {Paul M.}",
year = "2009",
doi = "10.1109/CVPRW.2009.5206578",
language = "English (US)",
isbn = "9781424439935",
pages = "202--209",
booktitle = "2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009",

}

TY - GEN

T1 - Shape analysis with conformal invariants for multiply connected domains and its application to analyzing brain morphology

AU - Wang, Yalin

AU - Gu, Xianfeng

AU - Chan, Tony F.

AU - Thompson, Paul M.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70450172720&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70450172720&partnerID=8YFLogxK

U2 - 10.1109/CVPRW.2009.5206578

DO - 10.1109/CVPRW.2009.5206578

M3 - Conference contribution

SN - 9781424439935

SP - 202

EP - 209

BT - 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009

ER -