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Mathematical Geosciences

, Volume 45, Issue 3, pp 297–319 | Cite as

A Robust Multiquadric Method for Digital Elevation Model Construction

  • Chuanfa ChenEmail author
  • Yanyan Li
Article

Abstract

The multiquadric method (MQ) with high interpolation accuracy has been widely used for interpolating spatial data. However, MQ is an exact interpolation method, which is improper to interpolate noisy sampling data. Although the least squares MQ (LSMQ) has the ability to smooth out sampling errors, it is inherently not robust to outliers due to the least squares criterion in estimating the weights of sampling knots. In order to reduce the impact of outliers on the accuracy of digital elevation models (DEMs), a robust method of MQ (MQ-R) has been developed. MQ-R includes two independent procedures: knot selection and the solution of the system of linear equations. The two independent procedures were respectively achieved by the space-filling design and the least absolute deviation, both of which are very robust to outliers. Gaussian synthetic surface, which is subject to a series of errors with different distributions, was employed to compare the performance of MQ-R with that of LSMQ. Results indicate that LSMQ is seriously affected by outliers, whereas MQ-R performs well in resisting outliers, and can construct satisfactory surfaces even though the data are contaminated by severe outliers. A real-world example of DEM construction was employed to evaluate the robustness of MQ-R, LSMQ, and the classical interpolation methods including inverse distance weighting method, thin plate spline, and ANUDEM. Results showed that compared with the classical methods, MQ-R has the highest accuracy in terms of root mean square error. In conclusion, when sampling data is subject to outliers, MQ-R can be considered as an alternative method for DEM construction.

Keywords

Robust Interpolation Radial basis function Digital elevation model 

Notes

Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant No. 41101433), by Young and Middle-Aged Scientists Research Awards Fund of Shangdong Province (Grant No. BS2012HZ010), by the Key Laboratory of Surveying and Mapping Technology on Island and Reef, National Administration of Surveying, Mapping and Geoinfomation (Grant No. 2011B10), by the Key Laboratory of Coastal Zone Environmental Processes, YICCAS (Grant No. 201209), and by the Special Project Fund of Taishan Scholars of Shandong Province.

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Copyright information

© International Association for Mathematical Geosciences 2013

Authors and Affiliations

  1. 1.Geomatics CollegeShandong University of Science and TechnologyQingdaoChina

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