1 research outputs found
Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing
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