Shape Analysis with Conformal Invariants for Multiply Connected Domains and its Application to Analyzing Brain Morphology

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 cereb...

• Type: Conference
• Year: 2009
• Where: CVPR
• Authors: Paul M. Thompson, Tony F. Chan, Xianfeng Gu, Yalin Wang
• Keywords: Computer Vision, Conformal Invariants, CVPR 2009