3D point clouds parameterization alogrithm

In this paper, we propose a 3D data clouds parameterization algorithm. Genus-zero clouds data are topologically equivalent to a sphere, hence this is the natural parameter domain for them. Firstly, we parameterize a 3D point onto a spherical domain means assigning a 3D position on the unit sphere for each point of the 3D data clouds, this is called a clouds spherical parameterization. Secondly, we map the sphere to the octahedron and unfold the octahedron to a geometry image. After the operation, we translate the 3D data to the simple 2D image, so we give an optimization procedure to produce geometry image parameterization, which reflect the geometric properties of the given 3D data clouds in various ways.