Least Squares Compactly Supported Radial Basis Function for Digital Terrain Model Interpolation from Airborne Lidar Point Clouds

Abstract

To overcome the huge volume problem of light detection and ranging (LiDAR) data for the derivation of digital terrain models (DTMs), a least squares compactly supported radial basis function (CSRBF) interpolation method is proposed in this paper. The proposed method has a limited support radius and fewer RBF centers than the sample points, selected by a newly developed surface variation-based algorithm. Those make the linear system of the proposed method not only much sparser but also efficiently solvable. Tests on a synthetic dataset demonstrate that the proposed method is comparable to the smoothing RBF, and far superior to the exact RBF. Moreover, the first is much faster than the others. The proposed method with the RBF centers selected by the surface variation-based algorithm obviously outperforms that with the random selection of equal number. Real-world examples on one private and ten public datasets show that the surfaces of simple interpolation methods including inverse distance weighting, natural neighbor, linear and bicubic suffer from the problems of roughness, peak-cutting, discontinuity and subtle terrain feature loss, respectively. By contrast, the proposed method produces visually appealing results, keeping a good tradeoff between noise removal and terrain feature preservation. Additionally, the new method compares favorably with ordinary kriging (OK) for the generation of high-resolution DTMs in terms of interpolation accuracy, yet the former is much more robust to spatial resolution variation and terrain characteristics than the latter. More importantly, our method is about 4 times faster than OK. In conclusion, the proposed method has high potential for the interpolation of a large LiDAR dataset, especially when both interpolation accuracy and computational cost are taken into account.

Comparison of different spatial interpolation methods for historical hydrographic data of the lowermost Mississippi River

“…Our ultimate result shows both OK with anisotropic consideration (UK and OKA) and TPS (from RBF) interpolators have the best performance on the crosssectional data in LMR. This finding is similar to the conclusions from several above mentioned studies (Merwade, Maidment, and Goff 2006;Šiljeg, Lozić, and Šiljeg 2014;Chowdhury et al 2017;Chen et al 2018a). All these researches addressed that both geostatistical and deterministic interpolation methods have similar performance on generating bathymetric surface.…”

“…The concept of RBFs is to fit a smooth surface through the measured sample values while minimizing the curvature of the surface (Aguilar et al 2005;Xie et al 2011;Chen et al 2018aChen et al , 2018b. Talmi and Gilat (1977) first constructed the mathematical background of RBFs; as a rule, the variable Z in a prediction point x can be expressed as the sum of two components (Mitášová and Mitáš 1993):…”

“…Several studies evaluated the interpolation methods for generating DEM (Digital Terrain Model) with different algorithms (e.g., Erdogan 2009;Boreggio, Bernard, and Gregoretti 2018;Chen et al 2018a and b). For interpolating bathymetric data, in particular, past studies exhibited no consensus regarding which interpolation method performs the best in generating bathymetric surfaces.…”

A Fast Global Interpolation Method for Digital Terrain Model Generation from Large LiDAR-Derived Data

“…Castrillón-Candás et al [24] developed a discrete hierarchical basis to efficiently solve the RBF interpolation problem with variable polynomial degree. However, the aforementioned algorithms do not take the huge storage requirement into account [25].…”

Fast interpolation method for surfaces with faults by multi-scale second-derivative optimization

“…At each stage a least squares approximation of the data is computed which is quite efficient to approximate large amount of scattered data points (up to 300 000). More recently, huge amount of data come from Light Detection And Ranging (LiDAR) for the derivation of Digital Terrain Models (DTMs), a least squares Compactly Supported Radial Basis Function (CSRBF) interpolation method is quite efficient and four times faster compared with ordinary kriging (Chen et al, 2018a(Chen et al, , 2018b.…”