Implicit Fitting and Smoothing Using Radial Basis Functions with Partition of Unity

Abstract

A new scheme for 3D reconstruction of implicit surfaces from large scattered point sets based on the radial basis functions (RBFs) is proposed in this paper. The partition of unity (POU) method and a binary tree is used to organize the point sets into some overlapping local subdomains and reconstructing a local surface for each of the subdomains from non-disjunct subsets of the points, we use only a single point at the offset of the surface to avoid the trivial solution of RBF linear system. When the offset point is chosen properly, the technique is not only efficient but also robust, offering a higher level of scalability. The global solution can be obtained by combining the local solutions with POU equations. We also adapt the methodology of level set propagation of a dynamic surface and employ it for smoothing the reconstructed surfaces. We develop versatile computational framework with many benefits in topological flexibility and numerical efficiency.