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

Content Provider	IEEE Xplore Digital Library
Author	Yalin Wang Xianfeng Gu Chan, T.F. Thompson, P.M.
Copyright Year	2009
Description	Author affiliation: Dept. of Neurology, UCLA, Los Angeles, CA, USA (Thompson, P.M.) \|\| Dept. of Comp. Sci., Stony Brook Univ., Stony Brook, NY, USA (Xianfeng Gu) \|\| Dept. of Neurology/Math, UCLA, Los Angeles, CA, USA (Yalin Wang) \|\| Dept. of Math, UCLA, Los Angeles, CA, USA (Chan, T.F.)
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.
Starting Page	202
Ending Page	209
File Size	2007570
Page Count	8
File Format	PDF
ISBN	9781424439928
ISSN	10636919
DOI	10.1109/CVPR.2009.5206578
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-06-20
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Surface morphology Shape measurement Alzheimer's disease Brain modeling Cerebral cortex Hippocampus Assembly Computer vision Tensile stress Magnetic resonance imaging
Content Type	Text
Resource Type	Article
Subject	Computer Vision and Pattern Recognition Software

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