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Light detection and ranging (lidar)-derived elevation data are commonly subjected to outliers due to the boundaries of occlusions, physical imperfections of sensors, and surface reflectance. Outliers have a serious negative effect on the accuracy of digital elevation models (DEMs). To decrease the impact of outliers on DEM construction, we propose a robust interpolation algorithm of multiquadric (MQ) based on a regularized least absolute deviation (LAD) technique. The objective function of the proposed method includes a regularization-based smoothing term and an LAD-based fitting term, respectively, used to smooth noisy samples and resist the influence of outliers. To solve the objective function of the proposed method, we develop a simple scheme based on the split-Bregman iteration algorithm. Results from simulated data sets indicate that when sample points are noisy or contaminated by outliers, the proposed method is more accurate than the classical MQ and two recently developed robust algorithms of MQ for surface modeling. Real-world examples of interpolating 1 private and 11 publicly available airborne lidarderived data sets demonstrate that the proposed method averagely produces better results than two promising interpolation methods including regularized spline with tension (RST) and gridded data-based robust thin plate spline (RTPS). Specifically, the image of RTPS is too smooth to retain terrain details. Although RST can keep subtle terrain features, it is distorted by some misclassified object points (i.e., pseudooutliers). The proposed method obtains a good tradeoff between resisting the effect of outliers and preserving terrain features. Overall, the proposed method can be considered as an alternative for interpolating lidar-derived data sets potentially including outliers. [ABSTRACT FROM AUTHOR]

Data pits commonly appear in lidar-derived canopy height models (CHMs) owing to the penetration ability of airborne light detection and ranging (lidar) into tree crowns. They have a seriously negative effect on the quality of tree detection and subsequent biophysical measurements. In this study, we propose an algorithm based on robust locally weighted regression and robust z-scores for the construction of a pit-free CHM. A significant advantage of the new algorithm is that it is parameter free, which makes it efficient and robust for practical applications. Simulated and airborne lidar-derived data sets are employed to assess the performance of the new method for CHM construction, and its results are compared to those of three classical methods, namely the natural neighbor (NN) interpolation of the highest point method (HPM), mean filter, and median filter. The results from the simulated data set demonstrate that our algorithm is more accurate compared to the three classical methods for generating pit-free CHMs in the presence of data pits. CHM construction using the lidar-derived data set shows that, compared to the classical methods, the new method has a better ability to remove data pits as well as preserving the edges, shapes, and structures of canopy gaps and crowns. Moreover, the proposed method performs better compared to the classical methods in deriving plot-level maximum tree heights from CHMs. Thus, the new method shows high potential for pit-free CHM construction. [ABSTRACT FROM AUTHOR]

Light detection and ranging (LiDAR) technique is currently one of the most important tools for collecting elevation points with a high density in the context of digital elevation model (DEME) construction. However, the high density data always leads to serious time and memory consumption problems in data processing. In this paper, we have developed a thin plate spline (TPS)-based feature-preserving (TPS-F) method for LiDAR-derived ground data reduction by selecting a certain amount of significant terrain points and by extracting geomorphological features from the raw dataset to maintain the accuracy of constructed DEMs as high as possible, while maximally keeping terrain features. We employed four study sites with different topographies (i.e., flat, undulating, hilly and mountainous terrains) to analyze the performance of TPS-F for LiDAR data reduction in the context of DEME construction. These results were compared with those of the TPS-based algorithm without features (TPS-W) and two classical data selection methods including maximum z-tolerance (Max-Z) and the random method. Results show that irrespective of terrain characteristic, the two versions of TPS-based approaches (i.e., TPS-F and TPS-W) are always more accurate than the classical methods in terms of error range and root means square error. Moreover, in terms of streamline matching rate (SMR), TPS-F has a better ability of preserving geomorphological features, especially for the mountainous terrain. For example, the average SMR of TPS-F is 89.2% in the mountainous area, while those of TPS-W, max-Z and the random method are 56.6%, 34.7% and 35.3%, respectively. [ABSTRACT FROM AUTHOR]

Remote-sensing-derived elevation data sets often suffer from noise and outliers due to various reasons, such as the physical limitations of sensors, multiple reflectance, occlusions and low contrast of texture. Outliers generally have a seriously negative effect on DEM construction. Some interpolation methods like ordinary kriging (OK) are capable of smoothing noise inherent in sample points, but are sensitive to outliers. In this paper, a robust algorithm of multiquadric method (MQ) based on an Improved Huber loss function (MQ-IH) has been developed to decrease the impact of outliers on DEM construction. Theoretically, the improved Huber loss function is null for outliers, quadratic for small errors, and linear for others. Simulated data sets drawn from a mathematical surface with different error distributions were employed to analyze the robustness of MQ-IH. Results indicate that MQ-IH obtains a good balance between efficiency and robustness. Namely, the performance of MQ-IH is comparative to those of the classical MQ and MQ based on the Classical Huber loss function (MQ-CH) when sample points follow a normal distribution, and the former outperforms the latter two when sample points are subject to outliers. For example, for the Cauchy error distribution with the location parameter of 0 and scale parameter of 1, the root mean square errors (RMSEs) of MQ-CH and the classical MQ are 0.3916 and 1.4591, respectively, whereas that of MQ-IH is 0.3698. The performance of MQ-IH is further evaluated by qualitative and quantitative analysis through a real-world example of DEM construction with the stereo-images-derived elevation points. Results demonstrate that compared with the classical interpolation methods, including natural neighbor (NN), OK and ANUDEM (a program that calculates regular grid digital elevation models (DEMs) with sensible shape and drainage structure from arbitrarily large topographic data sets), and two versions of MQ, including the classical MQ and MQ-CH, MQ-IH has a better ability of maximally reducing the impact of outliers, while faithfully preserving terrain features. Theoretically, MQ-IH is not a promising interpolation method, and some side effects can be found from its simulation results. For example, the contours of MQ-IH are coarser than ANUDEM in some locations of the real-world study site, and its hill shade may not strictly agree with the real-world surface at rough terrain. Furthermore, the computing cost of MQ-IH is much bigger than that of the classical interpolation methods. However, compared with the classical interpolation methods, MQ-IH has significant potential for interpolating remote-sensing-derived elevation data sets. [ABSTRACT FROM AUTHOR]