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

Authors:
Shengjun Liu;Charlie C. L. Wang
Affiliations:
School of Mathematical Science and Computing Technology, Central South University, China;Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, China
Venue:
Computer Aided Geometric Design
Year:
2012

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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.