Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing

TL;DR

This paper introduces a novel spherical conformal parameterization method for genus-0 point clouds, enabling high-quality meshing and multilevel representations by extending surface analysis techniques to unconnected data points.

Contribution

It extends spherical conformal parameterization algorithms to point clouds using an improved Laplace-Beltrami approximation and introduces an iterative North-South scheme for better parameterization quality.

Findings

Effective in generating genus-0 closed meshes from point clouds

Produces high-quality triangulations and quadrangulations

Facilitates multilevel point cloud representations

Abstract

Point cloud is the most fundamental representation of 3D geometric objects. 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 simplified 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 effectiveness of our proposed framework.