Neighborhood selection for differential coordinates of 3D point clouds

Many digital geometric processes that handle three-dimensional (3D) polygonal models benefit greatly from the differential coordinate and its associated Laplacian operator. The differential coordinate is an intrinsic surface representation that encodes each vertex as a local coordinate relative to its neighboring vertices. Given a point cloud data sampled from an unknown surface, the critical problem in the point cloud preprocessing is how to determine the vertex topological neighborhood. In this paper, we introduce a novel neighborhood selection approach aimed at obtaining accurate differential coordinates for point clouds. The neighborhood selection is regarded as an optimization problem and solved by a genetic algorithm. The fitness function, or called objective function, in the genetic algorithm is defined according to the properties of the differential coordinates. Therefore, we obtain not only the vertex neighborhood but also the accurate differential coordinates. The experimental results show that the differential coordinates generated by our approach can faithfully represent the geometry of 3D point cloud. Thus, they are helpful in related applications such as meshless smoothing, parameterization, and modeling.