Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing

Pui-Tung Choi The Chinese University of Hong Kong Kin Tat Ho The Chinese University of Hong Kong Ronald Lok Ming Lui The Chinese University of Hong Kong

Computational Geometry mathscidoc:1609.09001

SIAM Journal on Imaging Sciences
Point cloud is the most fundamental representation of 3D geometric objects as it provides the most exact information of them. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis require connectivity information. Therefore, it is desirable to develop a mesh structure on point clouds. This task can be simpli fied with the aid of a parameterization. In particular, conformal parameterizations are advantageous in preserving the geometric information of the point cloud data. In this paper, we extend a state-of-the-art spherical conformal parameterization algorithm for genus-0 closed meshes to the case of point clouds, using an improved approximation of the Laplace-Beltrami operator on data points. Then, we propose an iterative scheme called the North-South reiteration for achieving a spherical conformal parameterization. A balancing scheme is introduced to enhance the distribution of the spherical parameterization. High quality triangulations and quadrangulations can then be built on the point clouds with the aid of the parameterizations. Also, the meshes generated are guaranteed to be genus-0 closed meshes. Moreover, using our proposed spherical conformal parameterization, multilevel representations of point clouds can be easily constructed. Experimental results demonstrate the e ffectiveness of our proposed framework.
Mesh generation, Triangulation, Quadrangulation, Spherical conformal parameterization, Surface reconstruction, Point cloud, Multilevel representation
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  title={Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing},
  author={Pui-Tung Choi, Kin Tat Ho, and Ronald Lok Ming Lui},
  booktitle={SIAM Journal on Imaging Sciences},
Pui-Tung Choi, Kin Tat Ho, and Ronald Lok Ming Lui. Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing. In SIAM Journal on Imaging Sciences. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160905145454027242613.
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