Quasi-interpolation for surface reconstruction from scattered data with radial basis function

Abstract

Radial Basis Function (RBF) has been used in surface reconstruction methods to interpolate or approximate scattered data points, which involves solving a large linear system. The linear systems for determining coefficients of RBF may be ill-conditioned when processing a large point set, which leads to unstable numerical results. We introduce a quasi-interpolation framework based on compactly supported RBF to solve this problem. In this framework, implicit surfaces can be reconstructed without solving a large linear system. With the help of an adaptive space partitioning technique, our approach is robust and can successfully reconstruct surfaces on non-uniform and noisy point sets. Moreover, as the computation of quasi-interpolation is localized, it can be easily parallelized on multi-core CPUs.