A Huber-derived Robust Multi-quadric Interpolation Method for DEM Construction

CHEN Chuanfa; LIU Fengying; YAN Changqing; DAI Honglei; GUO Jinyun; LIU Guolin

doi:10.13203/j.whugis20140456

Volume 41 Issue 6

Jun. 2016

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Geomatics and Information Science of Wuhan University > 2016 > 41(6): 803-809. > DOI: 10.13203/j.whugis20140456

CHEN Chuanfa, LIU Fengying, YAN Changqing, DAI Honglei, GUO Jinyun, LIU Guolin. A Huber-derived Robust Multi-quadric Interpolation Method for DEM Construction[J]. Geomatics and Information Science of Wuhan University, 2016, 41(6): 803-809. DOI: 10.13203/j.whugis20140456

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A Huber-derived Robust Multi-quadric Interpolation Method for DEM Construction

1.
State Key Laboratory of Mining Disaster Prevention and Control, Shandong University of Science and Technology, Qingdao 266590, China
2.
Shandong Provincial Key Laboratory of Geomatics and Digital Technology, Shandong University of Science and Technology, Qingdao 266590, China
3.
Department of Information Engineering, Shandong University of Science and Technology, Taian 271019, China

Funds:

National Natural Science Foundation of China Nos. 41101433, 41371367

Distinguished Young Scholar Program of Shandong University of Science and Technology

Research Program of Joint Innovative Center for Safe and Effective Mining Technology and Equipment of Coal Resources

Taishan Scholar Program (Special Fund for Construction Engineering) of Shandong Province

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Author Bio:
CHEN Chuanfa, PhD, associate professor. E-mail:chencf@lreis.ac.cn
Received Date: September 06, 2015
Published Date: June 04, 2016

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Abstract

Abstract

In this paper, we propose a robust multi-quadric method (MQ-H) based on Huber loss function to conduct interpolations of contaminated spatial points, especially those derived from remote-sensing techniques. The objective function of the MQ-H has two main parts ; an improved Huber loss function and a regularized penalty term used to improve robustness and avoid overfitting, respectively. A mathematical surface, subject to model error with different distributions, was employed to comparatively analyze the robustness of the MQ-H, the classical MQ, and a least absolute deviation based MQ (MQ-L). The results indicated that when sample errors follow a normal distribution or a Laplacian distribution, the performance of MQ-H is comparatively better than those of MQ, and more accurate than MQ-L. For sample errors with a contaminated normal distribution and Cauchy distribution, MQ-H is more robust than MQ-L and MQ. Moreover, MQ with the improved Huber loss function is superior to MQ with the classical Huber loss function. A real-world example of DEM construction with stereo-image-derived elevation points indicates that compared to the classical interpolation methods including IDW (inverse distance weighting), OK (ordinary Kriging) and ANUDEM (Australian National University DEM), MQ-H has a better ability to reduce the impact of outliers while maintaining subtle terrain features suitable for qualitative analysis.
- robust,
- multi-quadric,
- accuracy,
- DEM,
- Huber loss function

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