A robust method of thin plate spline and its application to DEM construction
A robust method of thin plate spline and its application to DEM construction
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薄板样条的鲁棒方法及其在DEM构建中的应用
DOI：
10.1016/j.cageo.2012.05.018
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发表时间：
2012-11-01
影响因子：
4.4
通讯作者：
Li, Yanyan
中科院分区：
文献类型：
--
作者：
Chen, Chuanfa;Li, Yanyan
为了避免薄板样条曲线的病态问题，引入了正交最小二乘法，并提出了一种改进的正交最小二乘法。TPS的MOLS （TPS- m）不仅可以从大而密集的采样数据集中选择重要的点（称为节点），而且可以很容易地通过反替换计算节点的权重。为了插值较大的采样点，我们开发了一种局部TPS-M算法，在估计点周围选择一些邻近的采样点进行计算。数值试验表明，无论采样噪声水平如何，平滑TPS都能提高TPS- m的平均性能。在相同的仿真精度下，TPS-M的计算时间随着采样点个数的增加而减小。对激光雷达噪声数据的平滑拟合结果表明，TPS- m具有明显的平滑效果，与平滑TPS相当。以山东省一系列大尺度dem的构建为例，对比分析了两种版本的TPS和经典插值方法（逆距离加权法（IDW）、普通克里格法（OK）和二阶漂移函数通用克里格法（UK））的估计精度。结果表明：无论采样间隔和空间分辨率如何，除了平滑TPS在最优采样间隔为20 m，两种克里格插值方法在空间分辨率为15 m外，TPS- m插值方法的精度都高于经典插值方法。综上所述，TPS-M避免了病态问题，是一种鲁棒的DEM构建方法。(C) 2012 Elsevier Ltd.版权所有。
In order to avoid the ill-conditioning problem of thin plate spline (TPS), the orthogonal least squares (OLS) method was introduced, and a modified OLS (MOLS) was developed. The MOLS of TPS (TPS-M) can not only select significant points, termed knots, from large and dense sampling data sets, but also easily compute the weights of the knots in terms of back-substitution. For interpolating large sampling points, we developed a local TPS-M, where some neighbor sampling points around the point being estimated are selected for computation. Numerical tests indicate that irrespective of sampling noise level, the average performance of TPS-M can advantage with smoothing TPS. Under the same simulation accuracy, the computational time of TPS-M decreases with the increase of the number of sampling points. The smooth fitting results on lidar-derived noise data indicate that TPS-M has an obvious smoothing effect, which is on par with smoothing TPS. The example of constructing a series of large scale DEMs, located in Shandong province, China, was employed to comparatively analyze the estimation accuracies of the two versions of TPS and the classical interpolation methods including inverse distance weighting (IDW), ordinary kriging (OK) and universal kriging with the second-order drift function (UK). Results show that regardless of sampling interval and spatial resolution, TPS-M is more accurate than the classical interpolation methods, except for the smoothing TPS at the finest sampling interval of 20 m, and the two versions of kriging at the spatial resolution of 15 m. In conclusion, TPS-M, which avoids the ill-conditioning problem, is considered as a robust method for DEM construction. (C) 2012 Elsevier Ltd. All rights reserved.