A simple terrain relief index for tuning slope-related parameters of LiDAR ground filtering algorithms
Introduction
Airborne light detection and ranging (LiDAR) point clouds are widely used in topographic mapping (Brock et al., 2002), forest inventory (Hyyppä et al., 2008), 3D city modeling (Dorninger and Pfeifer, 2008), and ecosystem studies (Morsdorf et al., 2006). In almost all LiDAR applications, ground filtering is an essential prerequisite procedure to determine the ground and non-ground surface features (Axelsson, 1999). Distinguishing ground from non-ground is challenging in regions with high surface variability (Liu, 2008). Therefore, many ground filtering algorithms have been proposed to extract ground points from airborne LiDAR point clouds over the past two decades (Chen et al., 2007, Kraus and Pfeifer, 1998, Pingel et al., 2013, Vosselman, 2000, Zhang and Whitman, 2005, Zhang et al., 2016).
Generally, ground filtering algorithms can be categorized into three main groups: slope-based, morphology-based, and surface-based filters (Liu, 2008, Meng et al., 2010, Zhang et al., 2016). However, in spite of the different categories of filter algorithms, there remains a challenge when applying these algorithms using a manual configuration of a number of initial parameters. These parameters can be classified as “core” parameters and “auxiliary” parameters. The core parameters are always difficult to set based on a user’s experience because they relate to the characteristics of topography or objects, such as grid size, slope, and terrain relief amplitude, which can be subjective, time consuming, and prone to errors (Mongus and Žalik, 2012). The auxiliary parameters, such as the maximum iterative times, are determined by user’s demand, which are not the main goal and influencing factor for improving automation of a ground filtering algorithm. Almost all the “threshold-free” or “parameter-adaptive” algorithms we found in literatures are aiming for the core parameters. A comparison of ground filtering algorithms conducted by Sithole and Vosselman (2004) indicated that the selection of optimal filtering parameters mainly depends on the type of landscape and its complexity. Meanwhile, parameter tuning is heavily relies on the user’s experience; thus the parameters are not always optimally tuned (Yuan et al., 2009, Zhang et al., 2003). Automatic determination of landscape characteristics is a promising direction for the selection of the appropriate core parameters for filtering algorithms.
Over the past two decades, automatic parameter tuning has been widely studied. For example, to estimate the slope of the bare earth, Roggero (2001) proposed an algorithm to first extract the lowest point in each grid cell from the raw LiDAR points clouds to obtain a coarse digital terrain model (DTM), then determines the local slope using a local linear regression criterion. In the regression, each point has different weight according to the distance and height difference between the lowest point and each point. Roggero’s algorithm is a modification of the slope-based filtering algorithm developed by Vosselman (2000), which can adjust the slope threshold for each point according to the previously estimated local slope. Sithole (2001) adopted a similar strategy and directly calculated the local slope by using the lowest point in each grid. The algorithm proposed by Axelsson (2000) employed a method to tune the parameters inside the program. Axelsson’s algorithm first obtains the lowest point of each grid cell which forms a sparse triangular irregular network (TIN), and then iteratively adds points to the TIN according to a distance threshold and a slope threshold which are set by users. After each iteration, the thresholds are re-computed based on the latest TIN. The main idea of these algorithms is to form a rough terrain model from the raw LiDAR data by extracting the locally lowest points, and then the topographic information can be derived from the rough terrain model. However, the size of the grid cell or local neighborhood is difficult to determine (Zhang and Whitman, 2005). An inappropriate grid size is likely to lead to a biased estimation of the local slope and hence to a misclassification (Chen et al., 2007). Axelsson’s algorithm is more advanced because its parameters are updated after each iteration, so it has a wider tolerance to the size of grid cells. But Axelsson’s algorithm also needs appropriate slope-related parameters to generate an initial terrain model. Otherwise, the error may be accumulated (Liu, 2008).
Instead of generating rough terrain model by seed points, Kobler et al. (2007) presented an algorithm that first implements an initial filtering using existing algorithms, and then refines the DTM by a repetitive interpolation method. But the parameters still need to be set subjectively in the initial filtering stage. Employing the assumption that the elevation of the ground points is normally distributed, Bartels et al. (2006) proposed a parameter-free algorithm, Skewness Balancing, that iteratively labels the highest point as the object point until the distribution of the remaining points follows the normal distribution when the skewness equals 0. Further improvement of Skewness Balancing adopted other criteria, including the normal distribution of the normalized digital surface model (DSM) and the kurtosis of the distribution (Bao, 2008, Bartels and Wei, 2010). The assumption of Skewness Balancing is promising for parameter tuning in any other algorithm if it is widely verified in various types of landscape.
Mongus and Žalik (2012) presented a parameter-free algorithm that integrates several independent algorithms. The algorithm starts by selecting seed points with a regularly expanding window size, with only the lowest point within a grid cell being selected for the next level. Then a thin plate spline surface interpolation is implemented on each level, accompanied by a top-hat transformation and adaptive threshold, the remaining object points are removed. The threshold is derived from the standard deviation of the distribution of the offsets between the remaining points and the spline surface, according to the assumption of a normal distribution. The threshold is set by statistical theory, rather than landscape characteristics. Zhang et al. (2016) proposed an easy-to-use filtering method, called Cloth Simulation Filtering (CSF), for which only an integer and a Boolean parameter related to the landscape type need to be set. The CSF can be classified as a surface-based method and it has been widely used as a plugin of the CloudCompare software (Girardeau-Montaut, 2015) and presents superior precision in most landscape type. But it still has the potential to be a genuinely parameter-free algorithm if prior terrain information is available.
In summary, the existing threshold-adaptive approaches still need independent user-provided terrain information to achieve automatic parameter tuning. Parameter-free filtering algorithms always statistically estimate critical parameters by experiment. Ideally, the terrain characteristics can be automatically extracted and used to select the optimal parameters for a particular type of landscape (Sithole and Vosselman, 2004). In this paper, we propose a simple terrain relief index derived from raw airborne LiDAR data to quantify macro terrain relief and tune the topographic parameters in ground filtering algorithms. The terrain relief index is a ratio between the height of the entire point cloud and the maximum above ground level of non-ground points. The latter variable can be estimated as the maximum local height difference of raw airborne LiDAR data. We first validated the terrain relief index using the benchmark airborne LiDAR datasets provided by the International Society for Photogrammetry and Remote Sensing. Then we introduced the terrain relief index into two existing ground filtering algorithms: Cloth Simulation Filtering (CSF) and Progressive Morphological (PM) Filter. The PM filter is a traditional morphology-based algorithm. It has been widely used and many modifications have been based on it. The CSF is a newly proposed algorithm that has attracted attention recently because of its ease of use and good performance. We related the terrain relief index to the cloth rigidness of the CSF filter and the slope threshold of the PM filter. The two algorithms were chosen because their core parameters are related to the terrain relief amplitude; meanwhile, they have less auxiliary parameters, which can reduce the workload of manually parameter tuning and the interference from auxiliary parameters, thus makes the experiment more reliable. The filtering accuracy was quantificationally tested to validate the effectiveness of the terrain relief index for ground filtering algorithms.
Section snippets
Basic assumption
The idea of the terrain relief index in this study was inspired by the observation that the maximum above ground level (AGL) of objects usually accounts for more of the height difference for a point cloud in a relatively flat area. In contrast, in a mountainous area, the terrain relief amplitude usually accounts for a large part of the total height difference (Fig. 1). Based on this observation, it can be assumed that the proportion of the maximum AGL of the objects to the total height
Test data
Our methods were tested using the benchmark airborne LiDAR datasets provided by the International Society for Photogrammetry and Remote Sensing (ISPRS) Commission III/WG3 (http://www.commission3.isprs.org/wg3/). The datasets consist of eight sites, which were grouped into city sites and forest sites based on the land cover types. Fifteen samples with diverse typical features were abstracted from the eight sites. Each of the eight sites has a large geographic extent, and the fifteen samples have
Correlation between TRIc and the terrain relief amplitude
Table 3 shows the correlation between TRIc and the terrain relief amplitude. The correlation between them was strong in general with all sites and samples (r = 0.867). In large areas, the correlation was higher (r = 0.926) than in small areas (r = 0.861). And the correlations were higher in city areas (r = 0.911 to 0.993) than in forest areas (r = 0.848 to 0.905) regardless of the geographic extent.
Correlation and bias between TRIc and TRIp
Figs. 3 and 4 are the correlation and the mean bias between TRIc and TRIp of all sites and
Discussion
In this paper we have presented a novel and simple terrain relief index that is highly correlated with the terrain relief amplitude. The terrain relief index can be transformed into slope-related parameters that are vital to ground filtering algorithms. We tested the terrain relief index on two filtering algorithms: Cloth Simulation Filtering (CSF) and the Progressive Morphological (PM) Filter, by relating the terrain relief index to the cloth rigidness of the CSF and to the slope threshold of
Conclusion
We have proposed a novel and simple terrain relief index (TRI) in this study. The TRI was highly correlated with the terrain relief amplitude and can be transformed into different kinds of parameters that are vital to ground filtering algorithms, such as the cloth rigidness for the Cloth Simulation Filtering (CSF) and the slope threshold for the Progressive Morphological (PM) filter. With the TRI-derived parameters, these two filters achieved filtering accuracies comparable to the optimal
Acknowledgments
This work was supported by the National Natural Science Foundation of China Grant Nos. 41331171, 41671414 and 41171265. This work was also supported by the National Basic Research Program of China (973 Program) Grant No. 2013CB733402.
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