Smooth Surface Modeling of DEMs Based on a Regularized Least Squares Method of Thin Plate Spline
Smooth Surface Modeling of DEMs Based on a Regularized Least Squares Method of Thin Plate Spline
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基于薄板样条正则最小二乘法的 DEM 光滑曲面建模
DOI：
10.1007/s11004-013-9519-5
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发表时间：
2014-01
影响因子：
2.6
通讯作者：
Dai Honglei
中科院分区：
文献类型：
--
作者：
Chen Chuanfa;Li Yanyan;Cao Xuewei;Dai Honglei
薄板样条 (TPS) 作为一种平滑拟合噪声数据的方法已被广泛接受。然而，当两个样本点非常接近时，经典TPS总是存在病态问题。尽管改进的基于正交最小二乘的TPS（TPS-M）避免了这种病态问题，但当样本点有噪声时，它并不能完全避免过度拟合。本文提出了一种薄板样条正则化最小二乘法（TPS-RLS），该方法在正交最小二乘法（OLS）的误差准则上添加了权重惩罚项。 TPS-RLS结合了正则化和OLS的优点，同时避免了过拟合和病态问题。数值测试表明，无论采样误差的标准差和节数如何，对于噪声数据的平滑拟合，TPS-RLS总是比TPS-M更准确，而如果不预先确定最佳节数，TPS-M会出现严重的过拟合问题。拟合全站仪数据的现实例子表明，在IDW、自然邻域和普通克里金法等经典插值方法中，TPS-RLS对于一系列不同分辨率的DEM，尤其是粗略的DEM，具有最高的精度。使用等高线的 DEM 表面建模表明，TPS-RLS 在均方根误差和浮雕阴影图外观方面比经典方法具有更好的性能。
Thin plate spline (TPS) has been widely accepted as a method for smooth fitting of noisy data. However, the classical TPS always has an ill-conditioning problem when two sample points are very close. Although the modified orthogonal least squares-based TPS (TPS-M) avoids this ill-conditioning problem, it is not completely immune to over-fitting when sample points are noisy. In this paper, a regularized least squares method of thin plate spline (TPS-RLS) was developed, which adds a weight penalty term to the error criterion of orthogonal least squares (OLS). TPS-RLS combines the advantages of both regularization and OLS, which avoid the over-fitting and the ill-conditioning problems simultaneously. Numerical tests indicate that irrespective of the standard deviation of sampling errors and the number of knots, TPS-RLS is always more accurate than TPS-M for smooth fitting of noisy data, whereas TPS-M would have a serious over-fitting problem if the optimal number of knots were not determined in advance. The real-world example of fitting total station instrument data shows that among the classical interpolation methods including IDW, natural neighbor and ordinary kriging, TPS-RLS has the highest accuracy for a series of DEMs with different resolutions, especially for the coarse one. Surface modeling of DEMs with contour lines demonstrate that TPS-RLS has a better performance than the classical methods in terms of both root mean squared error and relief shaded map appearance.
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影响因子：
2
作者：
P. Fisher
通讯作者：
P. Fisher
影响因子：
1.3
作者：
Michael B. Gousie;W. R. Franklin
通讯作者：
Michael B. Gousie;W. R. Franklin
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影响因子：
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作者：
Chen, Chuanfa;Li, Yanyan
通讯作者：
Li, Yanyan
影响因子：
3.6
作者：
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通讯作者：
G. Hunter;M. Goodchild
影响因子：
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作者：
J. Hofierka;T. Cebecauer
通讯作者：
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