3D-Polishing for Triangular Mesh Compression of Point Cloud Data

Triangular meshes are commonly used to reconstruct the surfaces of 3-dimensional (3D) objects based on the point cloud data. With an increasing demand for high-quality approximation, the sizes of point cloud data and the generated triangular meshes continue to increase, resulting in high computational cost in data processing, visualization, analysis, transmission and storage. Motivated by the process of sculpture polishing, we develop a novel progressive mesh compression approach, called the greedy 3D-polishing algorithm, to sequentially remove redundant points and triangles in a greedy manner while maintaining the approximation quality of the surface. Based on the polishing algorithm, we propose the approximate curvature radius to evaluate the scale of features polished at each iteration. By reformulating the compression rate selection as a change-point detection problem, a rank-based procedure is developed to select the optimal compression rate so that most of the global features of the 3D object surface can be preserved with statistical guarantee. Experiments on both moderate- and large-scale 3D shape datasets show that the proposed method can substantially reduce the size of the point cloud data and the corresponding triangular mesh, so that most of the surface information can be retained by a much smaller number of points and triangles.