Global parameterization and quadrilateral meshing of point cloud

Abstract

Point data are basic media for shape information acquisition and representation. A new approach is presented for global parameterization of unorganized point data and application to the meshing of point models with noises. While most of recent researches focus on quadrangulation of mesh models, it is extended to point models in this work, so as to loosely reconstruct the shape model by quadrilateral meshing of curvature isolines. The new approach is guided by principal directions, so as to preserve intrinsic geometric properties. A robust method is applied to estimate curvatures in presence of noise and outliers based on fitting surface normals. The parameterization of [Ray et al. 2006] is then adapted to point data by local Delaunay triangulation. Isolines are extracted by discarding and merging the redundant segments in each local triangle. This method is totally automatic, and a high-quality quadrilateral dominated mesh can be generated, as shown in Figure 1.