Curve Space: Classifying Curves on Surfaces
Communications on Informationa and System
Xin Li, Xianfeng Gu and Hong Qin
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 Teichmˇ§uller 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.