Efficient reconstruction of large scattered geometric datasets using the partition of unity and radial basis functions

Abstract

We present a new scheme for the reconstruction of large geometric data. It is based on the well-known radial basis function model combined with an adaptive spatial and functional subdivision associated with a family of functions forming a partition of unity. This combination offers robust and efficient solution to a great variety of 2D and 3D reconstruction problems, such as the reconstruction of implicit curves or surfaces with attributes starting from unorganized point sets, image or mesh repairing, shape morphing or shape deformation, etc. After having presented the theoretical background, the paper mainly focuses on implementation details and issues, as well as on applications and experimental results.