2 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
TEMPO: Feature-Endowed Teichm\"uller Extremal Mappings of Point Clouds
In recent decades, the use of 3D point clouds has been widespread in computer
industry. The development of techniques in analyzing point clouds is
increasingly important. In particular, mapping of point clouds has been a
challenging problem. In this paper, we develop a discrete analogue of the
Teichm\"{u}ller extremal mappings, which guarantee uniform conformality
distortions, on point cloud surfaces. Based on the discrete analogue, we
propose a novel method called TEMPO for computing Teichm\"{u}ller extremal
mappings between feature-endowed point clouds. Using our proposed method, the
Teichm\"{u}ller metric is introduced for evaluating the dissimilarity of point
clouds. Consequently, our algorithm enables accurate recognition and
classification of point clouds. Experimental results demonstrate the
effectiveness of our proposed method