Computing Fenchel-Nielsen Coordinates in Teichmuller Shape Space
Teichmüller shape space is a finite dimensional Riemannian manifold, where each point represents a class of surfaces, which are conformally equivalent, and a path represents a deformation process from one shape to the other. Two surfaces in the real world correspond to the same point in the Teichmüller space, only if they can be conformally mapped to each other. Teichmüller shape space can be used for surface classification purpose in shape modeling. This work focuses on the computation of the coordinates of high genus surfaces in the Teichmüller space. The coordinates are called as Fenchel-Nielsen coordinates. The main idea is to decompose the surface to pairs of hyperbolic pants. Each pair of pants is a genus zero surface with three boundaries, equipped with hyperbolic metric. Furthermore, all the boundaries are geodesics. Each pair of hyperbolic pants can be uniquely described by the lengths of its boundaries. The way of gluing different pairs of pants can be represented by the twisting angles between two adjacent pairs of pants which share a common boundary. The algorithms are based on Teichmüller space theory in conformal geometry, and they utilize the discrete surface Ricci flow. Most computations are carried out using hyperbolic geometry. The method is automatic, rigorous and efficient. The Teichm¨ uller shape space coordinates can be used for surface classification and indexing. Experimental results on surfaces acquired from real world showed the potential value of the method for geometric database indexing, shape comparison and classification.
conformal geometry Teichmuller space shape space shape analysis shape classification
Miao Jin Wei Zeng Ning Ding Xianfeng Gu
The Center for Advanced Computer Studies , University of Louisiana at Lafayette, Lafayette 70506, US Department of Computer Science, Stony Brook University, Stony Brook 11794, USA
国际会议
IEEE International Conference on Shape Modeling and Applications (SMI)(2009年形状建模国际会议)
北京
英文
193-200
2009-06-26（万方平台首次上网日期，不代表论文的发表时间）