Filtering Airborne Lidar Data by Modified White Top-Hat Transform with Directional Edge Constraints

Transcription

1 Filtering Airborne Lidar Data by Modified White Top-Hat Transform with Directional Edge Constraints Yong Li, Bin Yong, Huayi Wu, Ru An, Hanwei Xu, Jia Xu, and Qisheng He Abstract A novel algorithm that employs modified white top-hat (MWTH) transform with directional edge constraints is proposed in this study to automatically extract ground points from airborne light detection and ranging (lidar) data. MWTH transform can effectively distinguish above-ground objects that are smaller than the window size and higher than the height difference threshold. Directional edge constraints significantly decrease omission errors from protruding ground features. Incorporating MWTH transform and directional edge constraints enables the simultaneous consideration of the size, height, and edge characteristics of lidar data for judging above-ground objects. Experimental results verify that the proposed algorithm exhibits promising performance and high accuracy in various complicated landscapes, even in areas with dramatic changes in elevation. The proposed algorithm has minimal omission and commission error oscillation for different test sites, thereby demonstrating its stability and reliability in a wide range of applications. Introduction Airborne light detection and ranging (lidar) technology has become a powerful and popular tool for rapid spatial data acquisition with acceptable spatial accuracy and large density (Filin and Pfeifer, 2006; Meng et al., 2009b; Shan and Sampath, 2005). Lidar can obtain three-dimensional (3D) coordinates of the surface of the Earth in a more convenient manner compared with traditional photogrammetric and field surveying methods. Lidar is also unaffected by external light conditions and requires few ground control points. These incomparable merits of lidar have attracted considerable attention from specialists and scholars in diverse fields. Although lidar systems have been widely utilized in various practical applications such as topographic surveying and environmental planning (Hill et al., 2000; Stoker et al., 2006; White and Wang, 2003), effectively processing raw data and accurately extracting useful information still remain a major challenge in complex situations, especially for areas with steep slopes or rough surfaces (Chen, 2007). Yong Li and Bin Yong are with the State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing , China (liyong@hhu.edu.cn; yongbin_hhu@126.com). Huayi Wu is with the State Key Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing, Wuhan University, Wuhan , China. Ru An, Hanwei Xu, Jia Xu, and Qisheng He are with the School of Earth Sciences and Engineering, Hohai University, Nanjing , China. Raw lidar data sets contain both ground and non-ground points such as buildings, vegetation, vehicles, and electrical wires. The first important step in digital terrain model generation and object extraction is to separate obtained point clouds into ground and non-ground points. This process is called filtering (Vosselman, 2000; Zhang et al., 2003). Manual classification and final quality control account for approximately 60 percent to 80 percent of total lidar data processing time because no efficient algorithms are available for filtering (Flood, 2001; Sithole and Vosselman, 2003). Considering the presence of complex and changeable landscapes in a surveyed field, lidar data filtering is difficult to automate in computers, especially for large areas with varying terrain characteristics (Bartels and Wei, 2010; Silvan-Cardenas and Wang, 2006; Sithole and Vosselman, 2004; Zhang and Whitman, 2005). Various approaches have been developed to filter lidar point clouds in recent decades (Bartels and Wei, 2010; Silvan-Cardenas and Wang, 2006; Sithole and Vosselman, 2004; Zhang and Whitman, 2005). These methods are mostly based on the assumption that most terrain surfaces have gradual elevation changes, whereas above-ground objects possess abrupt elevation changes compared with nearby ground (Bretar and Chehata, 2010). Moreover, the sizes of objects are within a limited range. Larger above-ground objects usually have more evident height differences, so a larger height threshold is necessary to filter the larger objects. The slope-based approach inspects slopes or height differences among nearby points. A predefined threshold is utilized for filtering based on the assumption that gradients between ground and nonground points are distinctively different (Shan and Sampath, 2005; Sithole, 2001; Vosselman, 2000; Wang and Tseng, 2010; Wang and Shan, 2009). The morphological approach involves a series of morphological operations, such as openings and closings, to separate objects and backgrounds (Chen et al., 2007; Li and Wu, 2009; Petzold et al., 1999; Wu et al., 2010; Zhang et al., 2003). The surface interpolation approach and triangular irregular network densification approach iteratively approximate the ground under strong angle and distance constraints (Axelsson, 1999 and 2000; Kraus and Pfeifer, 1998; Lee and Younan, 2003; Pfeifer et al., 2001; Sohn and Dowman, 2002). The directional scanning approach involves the calculation of slopes and elevation differences along a one-dimensional (1D) scan line in a specified direction and identifies ground points based on information along the scan line (Meng Photogrammetric Engineering & Remote Sensing Vol. 80, No. 2, February 2014, pp /14/ American Society for Photogrammetry and Remote Sensing doi: /PERS PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING February

2 et al., 2009a and 2009b; Shan and Sampath, 2005; Sithole, 2001; Sithole and Vosselman, 2005). Current approaches are generally suitable for flat terrains. However, obtaining reliable results for complex landscapes remain difficult, particularly in steeply sloping terrains (Meng et al., 2009b; Mongus and Žalik, 2012). Most filtering algorithms are adapted to various circumstances by tuning the adopted parameters. The proposed algorithm aims to remove above-ground objects as well as preserve terrain features by incorporating modified white top-hat (MWTH) transform and directional edge constraints. The morphological approach is a commonly used approach among existing approaches (Silvan-Cardenas and Wang, 2006). Several researchers have developed a number of filters based on mathematical morphology, which can remove object points efficiently (Arefi and Hahn, 2005; Chen et al., 2007; Kobler et al., 2007; Zhang et al., 2003). Adapting the size of the window used is necessary to ensure that certain terrain points belong to the window, thereby eliminating non-ground objects of different sizes. Protruding terrain features are flattened when a large window for morphological operators is utilized to remove large objects, such as buildings. Several researchers have gradually expanded window size to remove non-ground objects of different sizes and avoid mislabeling of ground points (Vosselman, 2000; Zhang et al., 2003; Zhang and Whitman, 2005). Zhang et al. (2003) identified non-ground points by comparing elevation differences from a morphological opening with a predefined threshold, which was actually MWTH transform (Bai et al., 2010). However, differentiation between ground and objects, particularly when a large window is used on abrupt surfaces, is an unresolved issue because of the similar characteristics of ground and non-ground objects (Bartels and Wei, 2010; Liu, 2008; Meng et al., 2009b; Mongus and Žalik, 2012; Sithole and Vosselman, 2004). A novel algorithm that incorporates MWTH transform with directional edge constraints is proposed in this study for the efficient filtering of lidar data. Two main steps are employed in differentiating non-ground points from terrain points at each time of iteration. MWTH transform is first utilized to extract potential above-ground objects. The objects are then determined by directional edge constraints imposed on potential objects. The size, height, and edge characteristics of objects are simultaneously considered in judging above-ground points. The experimental test results are compared with the results of other publicized filtering algorithms tested by the International Society for Photogrammetry and Remote Sensing (ISPRS) Commission III/WG3 (Sithole and Vosselman, 2003) to evaluate the performance of the proposed algorithm. The results reveal the robustness and practicality of the proposed method. This paper is organized as follows. A detailed description of the method is provided in the next section, followed by a description and discussion of Experiments. Summarizing remarks and conclusions finalize the paper. Methodology The proposed algorithm identifies above-ground objects based on the size, height, and edge characteristics of point clouds caused by various objects (e.g., buildings, vegetation, or vehicles). First, a grid index structure is created for efficient point cloud organization. Morphological gradients are calculated to analyze the elevation changes in the lidar point cloud. Low outliers are eliminated to prevent them from affecting subsequent gradient analysis. Second, small and low objects near the ground surface are removed by MWTH transform and directional edge constraints with a small window size and height difference threshold. Finally, MWTH transform and directional edge constraints are iterated with increased window size and height difference threshold to eliminate large objects. This step is repeated until the utilized window becomes larger Figure 1. Flowchart of the complete methodology. than the largest object. The flowchart of the proposed algorithm is shown in Figure 1. This section is divided into three subsections to explain the methodology. Three preprocessing steps, namely, grid index creation, morphological gradient calculation, and outlier removal, are presented in the first subsection. The subsequent subsections respectively illustrate MWTH transform and directional edge constraints. Preprocessing Three preprocessing steps must be performed prior to filtering above-ground objects in raw lidar point clouds. The steps are grid index creation, morphological gradient calculation, and outlier removal. A lidar strip generally contains several million of 3D laser points, which require efficient point cloud organization. Interpolating irregularly distributed points into a regular grid is favorable for the use of digital image processing techniques (Chen et al., 2007; Lloyd and Atkinson, 2006; Meng et al., 2009b; Mongus and Žalik, 2012; Zhang et al., 2003). However, interpolation methods cause information loss and artificial error (Liu, 2008; Shan and Sampath, 2005). Directly processing raw irregular point clouds (Elmqvist, 2002; Shan and Sampath, 2005; Sithole and Vosselman, 2005; Zhang and Whitman, 2005) can prevent errors introduced by interpolation but requires complex neighbor search methods (Meng et al., 2009b). In this study, a grid index structure that maximizes the simplicity of a regular grid and maintains the accuracy of raw data without interpolation is utilized to manage irregular point clouds. The input point cloud is arranged into a predefined index grid G with equal-sized cells. Each grid cell stores an array of lidar points. Empty cells are ignored during the remaining steps of the algorithm. During spatial searching and processing of each lidar point, the relevant cell is first determined. The contained points are then selected for calculation. The cell size that can accurately represent neighborhood relationships among lidar points depends on the density of the point clouds. The average point spacing of raw point clouds is a relatively suitable reference for grid-cell size. For instance, if point spacing ranges from 1 m to 2 m, then grid-cell size is set to 2 m 2 m. 134 February 2014 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

3 The next preprocessing step is to calculate the morphological gradients of point clouds to analyze the elevation changes. Mathematical morphology, which was developed based on geometry and set theory, is a powerful tool for spatial feature extraction and analysis (Soille, 2003). Erosion and dilation are two fundamental morphological operations that work with a roving two-dimensional window superimposed upon the original data set. The window, also referred to as the structuring element (SE), specifies the reference neighborhood of a considered point. The elevation of point l(x, y) of set f after being eroded by SE B is denoted as [f B ( f )](x, y) and defined as follows: [f B ( f )](x, y) = min{f(x+i, y+j) i,j [-w, w]; (x+i), (y+j) D f }, (1) where D f is the domain of f, and the size of SE B is (2w + 1) (2w + 1). Erosion presents the lowest elevation within the neighborhood defined by SE B, whereas dilation presents the highest elevation of the highest point within the neighborhood defined by SE B. The elevation of point l(x, y) of set f after being dilated by SE B is denoted as [d B ( f )](x, y) and defined as follows: [d B ( f )](x, y) = max{f(x+i, y+j) i,j [-w, w]; (x+i), (y+j) D f }. (2) The gradients of each point indicate the elevation changes in the close neighborhood of that point. The elevation changes of non-ground objects are different from the elevation changes of ground points; thus, gradients can be utilized to analyze nonground lidar points. The gradients can be expressed numerically by morphological operations in several ways (Soille, 2003). Two types of morphological gradients are employed in the proposed algorithm, namely, internal and external gradients. Internal gradients are operators that represent the extent of descent of a point elevation in a neighborhood determined by SE as shown in Figure 2b. The internal gradient of the considered point l is defined as the difference between the original and eroded values by elementary SE B (3 3 square), which is denoted by t : t B = f f B. (3) Similarly, external gradients represent the extent of the ascent of a point elevation in a neighborhood determined by SE, as shown in Figure 2c. External gradient t + is defined as the difference between the dilated and original values: t + B = d B f. (4) The last preprocessing step involves the removal of low outliers in the point clouds. Low outliers are commonly caused by laser returns that are reflected several times or by the malfunction of a laser rangefinder (Sithole and Vosselman, 2004). The distinctive characteristic of low outliers is that these points are unrealistically lower than the surrounding points, thereby resulting in inconsistencies in gradient analysis for filtering. Therefore, low outliers must be eliminated beforehand. A lidar point is identified as belonging to a low outlier based on two conditions: (a) external gradient t + is larger than the predefined threshold, which means that the point is located extremely low in a local region, and (b) the number of neighboring points close to the point is small, indicating that the point is rare and scattered. The threshold of t + and the number of close points in a 3 3 neighborhood of a low outlier, which are set by trial and error, are 5 m and two points, respectively, for the data sets tested in this study. MWTH Transform for Filtering Lidar Data Above-ground objects possess abrupt elevation changes compared with the surrounding ground surface. This fact is the basis for filtering algorithms, as presented in the Introduction Section. Terrains are often uneven in reality; thus, global threshold techniques are generally unsatisfactory. Morphological top-hat transform can mitigate terrain relief and probe local height contrast. White top-hat (WTH) transform is widely utilized to extract image components that are brighter than the background in gray-scale image processing. This technique can be utilized to extract objects higher than the surrounding ground in lidar filtering. WTH is the difference between original set f and its opening c B ( f ) that is defined as erosion followed by dilation (Soille, 2003): c B ( f ) = d B [f B ( f )]. (5) WTH transformation of set f by SE B as denoted by WTH B ( f ) is defined as: WTH B ( f ) = f c B ( f ). (6) As illustrated in Figure 3, the WTH returns a subset of objects smaller than SE and higher than the surrounding regions. WTH with a flat isotropic SE functions as a high-pass filter (Soille, 2003). Thus, WTH with a specified neighborhood window size can be utilized to detect potential proportionally sized objects in point clouds. Figure 2. Example of morphological gradients of 1d lidar points: (a) objects A and B in original lidar data and the employed SE, (b) internal gradients, and (c) external gradients. PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING February

4 Figure 3. wth of 1d lidar points: (a) original data set f and its opening c B ( f ), and (b) outputs of WTH( f ) = f c B ( f ). Figure 4. Comparison of edge characteristics between protruding terrain and objects: (a) 1d lidar points, and (b) outputs of mwth. Aside from abrupt elevation changes in objects, moderate relief also commonly occurs on terrains in actual landscapes. Morphological opening changes most of the elevation values of the original data set, and all the changed regions produce outputs in the resulting set of WTH. Thus, the resulting set of WTH has numerous ground regions except for object regions. Potential object regions are not necessarily non-zero regions but regions with significant elevation changes in the outputs of WTH. Thus, a height difference threshold can be imported into WTH to differentiate between potential object region and slow varied ground based on the elevation changes of these regions. MWTH with a height difference threshold can be expressed as follows (Bai et al., 2010): MWTH B (x, y) = max(f(x, y) c B (x, y), t) t, (7) where t is the height difference threshold. By accurately specifying t, MWTH can be employed to mark high regions with elevation change larger than t, which suppresses most terrain relief (e.g., Part B in Figure 4). During the processing of lidar data by MWTH, the morphology of the objects to be extracted from a raw point cloud depends on two parameters, namely, height difference threshold t and utilized SE size of (2w + 1) (2w + 1). Above-ground objects are categorized into two groups. The first group includes small and low objects near the ground surface such as isolated vegetation points, shrubs, road signs, and fences. This group of objects can be removed by employing a special small w and t, which are set as follows: w = 1, t = pointspacing/3, (8) where pointspacing refers to the average point spacing utilized to create the grid index in the Preprocessing Subsection. The second group of objects contains large objects such as buildings, which have to be removed progressively by iteratively increasing w and t. In the iterative filtering process, w and t are determined by the following equation: w = ½i a/pointspacing½, t = i, (9) where i [1, 2,, n] and a is a coefficient orienting the filter toward removing objects or preserving terrain features; a is set as 3 for the data set tested in this study. Directional Edge Constraints The primary challenge for morphological filters is to avoid the removal of protruding terrain features when the SE must be large for removing large objects such as buildings (Chen et al., 2007). Although terrain features can be maintained to a certain extent by setting a height difference threshold in top-hat transform, omission errors may still occur when the utilized window covers a large-scale terrain with abrupt elevation changes (see Figure 4). Component A of the protruding terrain is eliminated after employing a height difference threshold in MWTH (see Figure 4b). The internal gradients of the edges of the continuous regions can be utilized to determine if the extracted top hats belong to the ground or to an object. The examples in Figure 4 indicate that the internal gradients of edge points a1 and a2 of the protruding ground component, which are extracted by MWTH, are distinctly smaller than the internal gradients of edge points b1 and b2 of object C. Discontinuity occurs only on one side although terrain discontinuities (e.g., cliffs) may have dramatically large internal gradients similar to those of objects. Therefore, internal gradients along a scan line in a specified direction can be employed to determine whether components extracted by MWTH belong to above-ground objects. 136 February 2014 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

5 Figure 5. Edge constraints imposed on the outputs of mwth considering the end points of continuous point sequences along scan lines: (a) digital surface model generated from raw lidar data, and (b) directional scanning after mwth. For top hats extracted by MWTH, directional edge constraints are executed along scan lines whose directions are from left to right on every row of the index grid and from bottom to top on every column of the index grid as illustrated in Figure 5. The sequences of continuous points on every scan line are detected and judged one by one. A point sequence is judged as an object depending on the characteristics of the two end points. A sequence of points is considered as belonging to an object when the two end points of the sequence meet one of the following conditions: (a) the internal gradients are higher than the predefined threshold, (b) the end points lie on the boundary of the data set (i.e., large objects partially contained in the data set), and (c) the neighboring grid cell on the external side is empty. Results The practical performance of the proposed algorithm is assessed by the standard data set provided by the ISPRS Commission III/WG3 on its website ( filtertest/). The data set was acquired in the Vaihingen/Enz test field and Stuttgart City center with an Optech ALTM scanner. A total of 15 reference samples were selected from seven study sites and compiled by manual processing to provide ground-truth data to be utilized in testing the accuracy of filters (Sithole and Vosselman, 2004). Table 1 shows that the test data typically contain special features that challenge automatic filtering, including rugged terrain, complex buildings, dense vegetation, data gaps, bridges, vehicles, etc. (Sithole and Vosselman, 2003). Point spacing is between 1.0 m and 1.5 m for urban areas (Samples 11 to 42 in Plate 1) and between 2.0 m and 3.5 m for rural areas (Samples 51 to 71 in Plate 2). The threshold values of the data are made identical except for the grid-cell size of the grid index structure mentioned in Preprocessing Subsection to test the robustness of fixed parameters in the proposed algorithm. Grid-cell size depends on the density of the point cloud, thus preventing grid cells from containing too many points or none at all. In this study, the grid-cell size is set to be slightly higher than the average point spacing, namely, 1.5 m 1.5 m for urban data sets and 3.5 m 3.5 m for rural data sets. The proposed algorithm has promising and competitive results compared with other popular filtering algorithms tested by the ISPRS (Sithole and Vosselman, 2003; Sithole and Vosselman, 2004). Based on the average overall accuracy of all sample data (Figure 6), four algorithms are found to have average overall accuracy values larger than 90 percent. Axelsson (1999 and 2000) and Sohn and Dowman (2002) both analyzed ground surface through progressive densification of sparse TIN based on certain triangle and distance criteria. Pfeifer et al. (2001) adopted a hierarchical interpolation method to derive ground points. More comprehensive comparisons of the four algorithms are performed based on Type I and Type II errors (see Figures 7, 8, 9, and 10). Type I error refers to the percentage of ground points rejected as objects in all ground points, whereas Type II error is the percentage of object points accepted as ground in all object points. Figures 7, 8, and 9 show that the proposed method can simultaneously control the two error types at a relatively low level and can maintain balance between the two types of errors. Among the considered algorithms, the proposed algorithm has the smallest standard deviation for Type I and II errors (Figure 10), which means that the algorithm has the most stable response to diverse landscapes. This advantage is favorable to quality control of generating Location Site Sample Features Urban Rural Table 1. Features Of The Data Set Provided By Isprs For Algorithm Testing Steep slopes, mixture of vegetation and buildings on hillside, buildings on hillside, data gaps Large buildings, irregularly shaped buildings, road with bridge and small tunnel, data gaps Densely packed buildings with vegetation between them, building with eccentric roof, open space with mixture of low and high features, data gaps Railway station with trains (low density of terrain points), data gaps Steep slopes with vegetation, quarry, vegetation on river bank, data gaps 6 61 Large buildings, road with embankment, data gaps 7 71 Bridge, underpass, road with embankments, data gaps PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING February

6 Figure 6. Average overall accuracy of the considered algorithms. Figure 7. Type I error of the different algorithms for all samples. Figure 8. Type II error of the different algorithms for all samples. practical digital elevation model (DEM) for large-scale areas. Plates 1 and 2 present the error distributions of the proposed algorithm for each sample. Given that the proposed algorithm filters objects based on MWTH transform and subsequently suppresses omissions of terrain features through directional edge constraints, the algorithm can preserve the shapes of various terrain features with dramatic elevation changes (see Samples 22, 23, 51, 52, and 53 in Plates 1 and 2). For filtering steep slopes in dramatically rugged areas, various vegetation and complicated buildings are effectively extracted, and the main terrain features are well preserved (see Samples 11, 24, 51, 52, and 53 in Plates 1 and 2). Small objects (e.g., vehicles and shrubs) are distinguished by the small window size (see Sample 12 in Plate 1). Attached objects appear to be connected to the ground on one side while exhibiting a clear distance from the ground on the other side. Attached objects such as bridges are successfully removed (see Samples 21, 22, and 71 in Plates 1 and 2). The morphological operations only consider neighbors within the specified window, thus data holes caused by water absorption or swath gaps have no effect on filtering (Samples 41, 51, 52, and 61 in Plates 1 and 2). A few low and large objects exceed the assumption defined by Equation 9, which results in commission errors such as those in Samples 11 and 42 in Plate 1. The proposed algorithm requires seconds to conduct filtering on Site 1 which contains 683,204 lidar points with an Intel Core i GHz processor, 2 GB RAM, and Microsoft Visual C MWTH and directional edge constraints are the main filtering steps utilized in the proposed algorithm as previously mentioned. MWTH can effectively remove above-ground objects smaller than the utilized neighborhood window size as shown in Plate 3b. However, several protruding terrain features may be eliminated in rugged areas (e.g., Sample 53 ). Plate 3d indicates that a rejected ground portion, which has discontinuities on one side and a steep slope on the other, exists in the center of Sample 53 in Plate 2. Plates 3b and 3e show that the protruding ground is filtered because the extent of ground protrusion exceeds the height difference threshold of MWTH. The retrieved protruding ground features (see Plates 3c and 3f) demonstrate the effectiveness of the directional edge constraints imposed on top hats obtained using MWTH. Figure 9. Mean of Type I and II errors for all samples. Figure 10. Standard deviation of Type I and II errors for all samples. Conclusions Filtering lidar point clouds is a significant research challenge because of varying terrain and complex objects. A novel algorithm that incorporates MWTH transform with directional edge constraints is proposed for lidar data filtering in this study. MWTH can effectively distinguish above-ground objects smaller than the utilized window size and higher than the height difference threshold. Directional edge constraints can significantly reduce the occurrence of omission errors from protruding ground features. Incorporating MWTH and directional edge constraints enables the algorithm to simultaneously consider the size, height, and edge characteristics of point clouds for judging above-ground points. Experimental results based on the standard test data of ISPRS confirm the effectiveness and practicality of the proposed algorithm. The competitive performance is achieved in comparison with the other typical filtering algorithms tested by ISPRS. The size and shape of non-ground objects have no significant influence on the performance of the proposed algorithm. The proposed algorithm is robust to various complicated scenes, indicating that the algorithm is reliable and can be applied extensively, particularly in areas with dramatic elevation changes. The minimal standard deviations of omission and commission errors denote the stable response of the proposed algorithm 138 February 2014 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

7 (c) (b) (a) (d) (f ) (e) (g) (h) (i) Plate 1. Error distribution for urban samples (11 to 42) displayed at a unique scale: (a) Sample 11, (b) Sample 12, (c) Sample 21, (d) Sample 22, (e) Sample 23, (f) Sample 31, (g) Sample 42, (h) Sample 24, and (i) Sample 41. to diverse landscapes, which is favorable to quality control of DEM products. This simple and efficient algorithm also has relatively fast processing speed which is helpful in surveying large-scale areas. However, the experimental results indicate that a few low and large objects may cause errors because the objects exceed the assumption defined by the empirical relation equation of window size and height difference threshold. The process of tuning parameters in a self-adaptive manner requires further investigation. PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING Acknowledgments This work was supported by the National Natural Science Foundation of China ( ; ; ; ; ), the 973 Program (2012CB719906) and the Fundamental Research Funds for the Central Universities (2011B06614). The authors thank three anonymous reviewers who helped to improve the earlier version of this paper. Fe b ruar y

8 (b) (a) (c) (d) (e) (f ) Plate 2. Error distribution for rural samples (51 to 71) displayed at a unique scale: (a) Sample 51, (b) Sample 52, (c) Sample 53, (d) Sample 54, (e) Sample 61, and (f) Sample 71. Plate 3. Processing point cloud of Sample 53: (a) digital surface model generated from raw data (the dotted line denotes profile position), (b) error distribution after mwth, (c) error distribution after edge constraints are imposed on mwth, (d) ground points along the profile in (a), (e) ground points along the profile in (b), and (f) ground points along the profile in (c). 140 Feb rua r y PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

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Whitman, Comparison of three algorithms for filtering airborne lidar data, Photogrammetric Engineering & Remote Sensing, 71(3): (Received 06 December 2012; accepted 21 August 2013; final version 24 August 2013) PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING February