Open Access
2007 Curve Space: Classifying Curves On Surfaces
Xin Li, Xianfeng Gu, Hong Qin
Commun. Inf. Syst. 7(3): 207-226 (2007).


We design signatures for curves defined on genus zero surfaces. The signature classifies curves according to the conformal geometry of the given curves and their embedded surface. Based on Teichmüller theory, our signature describes not only the curve shape but also the intrinsic relationship between the curve and its embedded surface. Furthermore, the signature metric is stable, it is close to identity between surfaces sharing similar Riemannian geometry metrics. Based on this, we propose a surface matching framework: first, with curve signatures, we match the partitioning of two surfaces defined by simple closed curves on them; second, the segmented subregions are pairwisely matched and then compared on canonical planar domains.


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Xin Li. Xianfeng Gu. Hong Qin. "Curve Space: Classifying Curves On Surfaces." Commun. Inf. Syst. 7 (3) 207 - 226, 2007.


Published: 2007
First available in Project Euclid: 28 January 2008

zbMATH: 1167.68451
MathSciNet: MR2516241

Rights: Copyright © 2007 International Press of Boston

Vol.7 • No. 3 • 2007
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