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

Abstract

Airborne light detection and ranging (LiDAR) datasets with a large volume pose a great challenge to the traditional interpolation methods for the production of digital terrain models (DTMs). Thus, a fast, global interpolation method based on thin plate spline (TPS) is proposed in this paper. In the methodology, a weighted version of finite difference TPS is first developed to deal with the problem of missing data in the grid-based surface construction. Then, the interpolation matrix of the weighted TPS is deduced and found to be largely sparse. Furthermore, the values and positions of each nonzero element in the matrix are analytically determined. Finally, to make full use of the sparseness of the interpolation matrix, the linear system is solved with an iterative manner. These make the new method not only fast, but also require less random-access memory. Tests on six simulated datasets indicate that compared to recently developed discrete cosine transformation (DCT)-based TPS, the proposed method has a higher speed and accuracy, lower memory requirement, and less sensitivity to the smoothing parameter. Real-world examples on 10 public and 1 private dataset demonstrate that compared to the DCT-based TPS and the locally weighted interpolation methods, such as linear, natural neighbor (NN), inverse distance weighting (IDW), and ordinary kriging (OK), the proposed method produces visually good surfaces, which overcome the problems of peak-cutting, coarseness, and discontinuity of the aforementioned interpolators. More importantly, the proposed method has a similar performance to the simple interpolation methods (e.g., IDW and NN) with respect to computing time and memory cost, and significantly outperforms OK. Overall, the proposed method with low memory requirement and computing cost offers great potential for the derivation of DTMs from large-scale LiDAR datasets.

Accuracy of Ground Surface Interpolation from Airborne Laser Scanning (ALS) Data in Dense Forest Cover

“…There are no widely accepted guidelines for establishing the percentage of initial observations to be used for validation. As an example, we find that [42] uses 4 percent of input data for validation, while [38] uses 3 percent of data for the same purpose, [45] uses 0.1 percent of input data (but also carries out external validation using independent data) and [47] uses 10 percent of initial data to test a newly-developed method of DTM interpolation from LiDAR data.…”

“…However, when comparing previous research, one has to take into account the source of altimetry data. The accuracy of interpolation can be assessed using synthetic [41,47] or real data. The main sources of elevation data are: digital stereo-matching [42], topographical maps with isolines [46] and ground surveys carried out using topographical equipment [43,44], GNSS receivers [48] or LiDAR sensors [38,45,49].Regarding the influence of external factors on DTM quality, the consensus is relatively better.…”

Multi-Level Interpolation-Based Filter for Airborne LiDAR Point Clouds in Forested Areas

“…The interpolation-based filters first produce a reference surface using certain interpolation method [21], [22] and then gradually select more and more ground points. For example, Axelsson [23] proposed a progressive triangulated irregular network (TIN) densification (PTD) filtering method, where a point with the angle and distance to the corresponding triangle less than the thresholds is labeled as the ground point.…”

Determination of Terrain Profile from TLS Data by Applying Msplit Estimation

“…Depending on the type of platform, there is airborne laser scanning (ALS), terrestrial laser scanning (TLS), satellite laser scanning (SLS) and mobile laser scanning (MLS) [1,2]. All types of laser scanning have a wide range of applications, e.g., terrain surface and vegetation cover measurements and digital terrain model (DTM) generation [3][4][5][6][7], building detection and their condition diagnosis [8][9][10][11][12], displacement detection [13][14][15], modeling of cultural heritage sites or object structures [2,13,16], registration roads, railways or power lines [17,18], monitoring coastal zones [19], mining damages and ground disasters [20,21].…”

“…Such a separation might be done by segmentation, e.g., region-based methods, Hough transform and Random Sample Consensus (RANSAC) [11,17,[25][26][27]. Obviously, there are also other different methods of point cloud filtering, e.g., surface-based adjustment, morphology-based filtering, Triangulated Irregular Network (TIN)-based refinement or adaptive TIN (ATIN)-based refinement [1,5,7,28]. Another possible approach to such a separation is the application of M split estimation [1].…”