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A Random Features-Based Method for Interpolating Digital Terrain Models with High Efficiency
- Source :
- Mathematical Geosciences. 52:191-212
- Publication Year :
- 2019
- Publisher :
- Springer Science and Business Media LLC, 2019.
-
Abstract
- Airborne light detection and ranging (lidar) is becoming a widely adopted technique for capturing elevation data, which are mainly used for creating digital terrain models (DTMs). However, the large size of lidar datasets poses a serious computational challenge to the promising radial basis function (RBF) interpolation method. In this work, to reduce the huge computational cost and improve the interpolation accuracy, random Fourier features are first introduced to approximate the Gaussian kernel of RBFs in feature space, then a random features-based weighted RBF interpolation method is developed. Based on randomized Fourier features, the nonlinear kernel-based training and evaluation of the RBF method is transformed into simple linear operations in feature space, and with the help of weighted ridge regression, the negative effect of the non-Gaussian distribution of lidar datasets on DTM production is reduced. In other words, the combination of randomized Fourier features and weighted ridge regression improves the efficiency and accuracy of the RBF interpolation method. Experiments on simulated datasets indicate that the proposed method performs better than the classical or random features-based RBF method for dealing with non-Gaussian distributed samples, with the former being slightly less accurate than the iterative RBF method due to the low-dimensional random features. However, the computational cost of the new method is much lower compared with the classical or iterative RBFs. Interpolation of airborne lidar-derived points demonstrates that the new method has a computational cost similar to the inverse distance weighting and triangulated irregular network (TIN) approaches, and is significantly faster than the ordinary kriging (OK) or thin plate spline (TPS) methods. Quantitatively, for interpolation of 644,433 points, the proposed method is approximately 833 and 21 times faster than OK and TPS, respectively. Moreover, the new method avoids the surface discontinuity artifacts presented by the OK, TPS, and TIN methods.
- Subjects :
- Computer science
Feature vector
0208 environmental biotechnology
MathematicsofComputing_NUMERICALANALYSIS
ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION
02 engineering and technology
010502 geochemistry & geophysics
01 natural sciences
020801 environmental engineering
Triangulated irregular network
symbols.namesake
Mathematics (miscellaneous)
Kriging
Inverse distance weighting
Gaussian function
symbols
General Earth and Planetary Sciences
Radial basis function
Thin plate spline
Algorithm
0105 earth and related environmental sciences
Interpolation
Subjects
Details
- ISSN :
- 18748953 and 18748961
- Volume :
- 52
- Database :
- OpenAIRE
- Journal :
- Mathematical Geosciences
- Accession number :
- edsair.doi...........649a887fe47996be19c7d04b42018bcc