Quasi-interpolation for surface reconstruction from scattered data with radial basis function
Quasi-interpolation for surface reconstruction from scattered data with radial basis function
复制标题
径向基函数散射数据表面重建的准插值
DOI：
10.1016/j.cagd.2012.03.011
复制
发表时间：
2012-10-01
影响因子：
1.5
通讯作者：
Wang, Charlie C. L.
中科院分区：
文献类型：
--
作者：
Liu, Shengjun;Wang, Charlie C. L.
径向基函数（Radial Basis Function，RBF）已用于表面重建方法中来插值或逼近分散的数据点，这涉及求解大型线性系统。在处理大型点集时，用于确定径向基函数系数的线性系统可能会出现病态，从而导致数值结果不稳定。我们引入了一个基于紧支撑RBF的拟插值框架来解决这个问题。在此框架下，隐式曲面可以重建，而无需解决一个大型的线性系统。在自适应空间分割技术的帮助下，我们的方法是鲁棒的，可以成功地重建非均匀和噪声点集上的表面。此外，由于准插值的计算是本地化的，它可以很容易地在多核CPU上并行化。(C)2012爱思唯尔有限公司版权所有。
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. (C) 2012 Elsevier B.V. All rights reserved.