快速Hermite径向基函数曲面重构

Fast Hermite radial basis function surface reconstruction

在这篇论文中,我们提出了一个使用局部支撑径向基函数对三维散乱点进行Hermite插值或逼近的快速曲面重构方法.通过构造给定数据点集的一个层次结构,采用逐层精化的方式实现了全局曲面重构的效果,解决了因使用局部支撑径向基函数导致的问题.另外,设计一个基于逼近误差导向的径向基函数中心点选择策略,减少每层进行插值的数据点,从而使Hermite径向基函数曲面重构方法能处理百万以上规模的点云数据.实验结果显示,我们的方法还适用于极度非均匀分布或带噪声的点云数据的曲面重构.

In this paper, a fast method with compactly supported radial basis functions （CSRBFs） is presented for Hermite surface interpolation or approximation from scattered points. By constructing a hierarchy of the given points, a global surface reconstruction is achieved in a coarse-to-fine way which overcome the problems resulted from using CSRBFs. Moreover, we design a radial basis function center selection approach based on approximat- ing errors, to reduce the interpolating points on each level, which make the Hermite radial basis function implicits to be able to deal with point clouds more than one million of points. The experiments demonstrate our method is also suitable for handling extremely nonuniform or noisy point clouds.