Computation of thin-plate splines
SIAM Journal on Scientific and Statistical Computing
Knot selection for least squares thin plate splines
SIAM Journal on Scientific and Statistical Computing
Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods
SIAM Journal on Scientific Computing
Smoothing large data sets using discrete thin plate splines
Computing and Visualization in Science
Effect of differing DEM creation methods on the results from a hydrological model
Computers & Geosciences
A method of DEM construction and related error analysis
Computers & Geosciences
Cross-validation as a means of investigating DEM interpolation error
Computers & Geosciences
Orthogonal least square RBF based implicit surface reconstruction methods
VSMM'06 Proceedings of the 12th international conference on Interactive Technologies and Sociotechnical Systems
Computers & Geosciences
Preconditioning for radial basis functions with domain decomposition methods
Mathematical and Computer Modelling: An International Journal
Orthogonal least squares learning algorithm for radial basis function networks
IEEE Transactions on Neural Networks
An orthogonal least-square-based method for DEM generalization
International Journal of Geographical Information Science
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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 20m, and the two versions of kriging at the spatial resolution of 15m. In conclusion, TPS-M, which avoids the ill-conditioning problem, is considered as a robust method for DEM construction.