Applied and computational complex analysis. Vol. 3: discrete Fourier analysis—Cauchy integrals—construction of conformal maps---univalent functions
A Numerical Solution to the Generalized Mapmaker's Problem: Flattening Nonconvex Polyhedral Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Analysis of Brain Ventricles Using SPHARM
MMBIA '01 Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA'01)
2D-Shape Analysis Using Conformal Mapping
International Journal of Computer Vision
Conformal Slit Mapping and Its Applications to Brain Surface Parameterization
MICCAI '08 Proceedings of the 11th international conference on Medical Image Computing and Computer-Assisted Intervention - Part I
IEEE Transactions on Visualization and Computer Graphics
Ricci Flow for 3D Shape Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Computational Model of Multidimensional Shape
International Journal of Computer Vision
Shape analysis of planar objects with arbitrary topologies using conformal geometry
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Brain surface conformal parameterization with algebraic functions
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Deformation similarity measurement in quasi-conformal shape space
Graphical Models
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We propose a novel method to apply Teichmüller space theory to study the signature of a family of nonintersecting closed 3D curves on a general genus zero closed surface. Our algorithm provides an efficient method to encode both global surface and local contour shape information. The signature--Teichmüller shape descriptor--is computed by surface Ricci flow method, which is equivalent to solving an elliptic partial differential equation on surfaces and is numerically stable. We propose to apply the new signature to analyze abnormalities in brain cortical morphometry. Experimental results with 3D MRI data from Alzheimer's disease neuroimaging initiative (ADNI) dataset [152 healthy control subjects versus 169 Alzheimer's disease (AD) patients] demonstrate the effectiveness of our method and illustrate its potential as a novel surface-based cortical morphometry measurement in AD research.