Open Access
December 2008 Shape Analysis by Conformal Modules
Wei Zeng, Lok Ming Lui, Xianfeng Gu, Shing-Tung Yau
Methods Appl. Anal. 15(4): 539-556 (December 2008).


All the surfaces in real life are Riemann surfaces, therefore with conformal structures. Two surfaces share the same conformal structure, if there exists a conformal (angle-preserving) mapping between them. Conformal modules are the complete invariants of conformal structures, which can be treated as shape descriptors for shape analysis applications.

This work focuses on the computational methods of conformal modules for genus zero surfaces with boundaries, including topological quadrilaterals, annuli, multiply connected annuli. The algo- rithms are based on both holomorphic 1-forms and discrete curvature flows, which are rigorous and practical. The conformal module shape descriptors are applied for shape classification and compari- son. Experiments on surfaces acquired from real world demonstrate the efficiency and efficacy of the conformal module method.


Download Citation

Wei Zeng. Lok Ming Lui. Xianfeng Gu. Shing-Tung Yau. "Shape Analysis by Conformal Modules." Methods Appl. Anal. 15 (4) 539 - 556, December 2008.


Published: December 2008
First available in Project Euclid: 2 October 2009

zbMATH: 1184.30035
MathSciNet: MR2550077

Primary: 30F20 , 68R99

Keywords: Conformal module , curvature flow , holomorphic 1-form , shape analysis , shape classification

Rights: Copyright © 2008 International Press of Boston

Vol.15 • No. 4 • December 2008
Back to Top