Estimation of Point Normals from Positional Relationship of Three-Dimensional Scattered Point Data

The surface reconstruction problem for three-dimensional (3D) scattered point data derived from 3D range scanners has been investigated in fields such as computer graphics (CG) and computer-aided design (CAD) [1, 2]. By using an implicit function-based method, the surface reconstruction problem can be solved. However, it must be noted here that, for generation of an implicit function in general domain, point normals on each of given points may be required. For example, the multi-level partition of unity implicits (MPU) method [2], which is a typical method for generating an implicit function, requires the point normals. However, there are some cases that point data do not contain normal data. In this case, surface reconstruction from 3D scattered point data is not easy. Hence, development of an estimation method of point normals from complicated point data is desired. The purpose of the present study is to propose an estimation method of point normals from a positional relationship of given point data.