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\nbasis function model combined with an adaptive spatial and functional subdivision associated with a family of\nfunctions forming a partition of unity. This combination offers robust and efficient solution to a great variety\nof 2D and 3D reconstruction problems, such as the reconstruction of implicit curves or surfaces with attributes\nstarting from unorganized point sets, image or mesh repairing, shape morphing or shape deformation, etc. After\nhaving presented the theoretical background, the paper mainly focuses on implementation details and issues, as\nwell as on applications and experimental results.