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Point cloud is the most fundamental representation of 3D geometric objects.Analyzing and processing point cloud surfaces is important in computer graphicsand computer vision. However, most of the existing algorithms for surfaceanalysis require connectivity information. Therefore, it is desirable todevelop a mesh structure on point clouds. This task can be simplified with theaid of a parameterization. In particular, conformal parameterizations areadvantageous in preserving the geometric information of the point cloud data.In this paper, we extend a state-of-the-art spherical conformalparameterization algorithm for genus-0 closed meshes to the case of pointclouds, using an improved approximation of the Laplace-Beltrami operator ondata points. Then, we propose an iterative scheme called the North-Southreiteration for achieving a spherical conformal parameterization. A balancingscheme is introduced to enhance the distribution of the sphericalparameterization. High quality triangulations and quadrangulations can then bebuilt on the point clouds with the aid of the parameterizations. Also, themeshes generated are guaranteed to be genus-0 closed meshes. Moreover, usingour proposed spherical conformal parameterization, multilevel representationsof point clouds can be easily constructed. Experimental results demonstrate theeffectiveness of our proposed framework.

Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing