Curve Spaces on Genus Zero Surfaces
Xin Li, Xianfeng Gu and Hong Qin
Proceedings of IEEE International Conference on Shape Modeling and Applications 2006
We develop a new surface matching framework to handle surface comparisons based on the mathematical analysis of
curves on surfaces, and propose a unique signature for any closed curve on a surface. The signature describes not only
the shape of the curve, but also the intrinsic relationship between
the curve and its embedding surface; and furthermore, the signature metric is stable across surfaces sharing similar
Riemannian geometry metrics. Based on this theoretical advance, we analyze and align features defined as closed curves
on surfaces using their signatures. These curves segment a surface into different regions which are mapped onto canonical
domains for the matching purpose. The experimental results are very promising, demonstrating that the curve signatures
and the comparison framework are robust and discriminative for the effective shape comparison. Besides its utility
in our current framework, we believe the curve signature will also serve as a powerful shape segmentation/mapping tool
and can be used to aid in many existing techniques towards effective shape analysis.