Numerical analyses of the boundary effect of radial basis functions in 3D surface reconstruction
Numerical analyses of the boundary effect of radial basis functions in 3D surface reconstruction
复制标题
3D 表面重建中径向基函数边界效应的数值分析
DOI：
10.1007/s11075-008-9185-8
复制
发表时间：
2008
影响因子：
2.1
通讯作者：
X. Jiang
中科院分区：
文献类型：
--
作者：
Xiangchao Zhang;X. Jiang
曲面重构是曲面特征化和图形处理的重要内容。径向基函数是一种从散乱数据重建三维曲面的常用方法。然而，它在边界区域相对不准确。为了解决这个问题，在感兴趣的域之外添加一圈新的中心。通过数值实验定量分析了影响边界行为的因素。它表明，如果新的中心是适当的位置，边界问题可以有效地克服，而不会降低在内部区域的精度。提出了一种改进的Graham扫描技术，从散乱点集中获取边界点。这些边界点向外延伸适当的距离，然后均匀化以形成新的辅助中心。
Surface reconstruction is very important for surface characterization and graph processing. Radial basis function has now become a popular method to reconstruct 3D surfaces from scattered data. However, it is relatively inaccurate at the boundary region. To solve this problem, a circle of new centres are added outside the domain of interest. The factors that influence the boundary behaviour are analyzed quantitatively via numerical experiments. It is demonstrated that if the new centres are properly located, the boundary problem can be effectively overcome whilst not reducing the accuracy at the interior area. A modified Graham scan technique is introduced to obtain the boundary points from a scattered point set. These boundary points are extended outside with an appropriate distance, and then uniformized to form the new auxiliary centres.