SCIENCE CHINA Information Sciences
. RESEARCH PAPER .
October 2013, Vol. 56 102314:1–102314:14 doi: 10.1007/s11432-012-4707-3
A mathematical morphology-based multi-level filter of LiDAR data for generating DTMs CHEN Dong, ZHANG LiQiang∗ , WANG Zhen & DENG Hao State Key Laboratory of Remote Sensing Science, Beijing Normal University, Beijing 100875, China Received July 5, 2012; accepted July 26, 2012; published online October 30, 2012
Abstract Light detecting and ranging (LiDAR) technology has become an effective way to generate highresolution digital terrain models (DTMs). To generate DTMs, point measurements from non-ground features, such as buildings, vegetation and vehicles, have to be identified and removed while preserving the terrain points. This paper proposes an efficient mathematical morphology-based multi-level filter to generate DTMs from airborne LiDAR data. Preliminary non-ground points are first identified with the characteristics of the multiecho airborne LiDAR data. The localized mathematical morphology opening operations are then immediately applied to the remaining points. By gradually increasing the window size of the filter and using a dynamic critical gradient threshold, the non-ground points are removed, while the ground points are preserved. Eight samples were chosen from eight sites provided with the ISPRS Commission III, Working Group 3, to evaluate the accuracy of our algorithm. Both the qualitative and quantitative experiment analyses show that our morphologybased multi-level filter method achieves promising results, not only in flat urban areas but also in rural areas, especially in preserving complex terrain details, while non-ground spatial objects are removed. Keywords
LiDAR, mathematical morphology, multi-level filter, DTMs
Citation Chen D, Zhang L Q, Wang Z, et al. A mathematical morphology-based multi-level filter of LiDAR data for generating DTMs. Sci China Inf Sci, 2013, 56: 102314(14), doi: 10.1007/s11432-012-4707-3
1
Introduction
As a data source for measuring elevation, LiDAR technology can provide dense and accurate threedimensional (3D) coordinates, multi-echo pulses and intensities with high horizontal and elevation accuracy. This technology has proven to be a rather powerful source for modeling buildings or trees, urban mapping, tourism and generation of digital city models and digital terrain models (DTMs). With the development of LiDAR technology, the LiDAR system is undergoing a complicated process of transitioning from single- to multi-echo and from full-waveform LiDAR to photon-counting LiDAR, which provides significant opportunities to extract detailed DTMs both in mountainous areas and urban areas. In addition, the point density of LiDAR data has improved greatly, reaching 10—20 points/m2 and even 50 points/m2 in some cases [1,2]. In this context, an unprecedented opportunity exists, using only LiDAR point clouds for generating DTMs, which are essential to many applications, such as road planning, flood modeling and landslide prediction. ∗ Corresponding
author (email:
[email protected])
c Science China Press and Springer-Verlag Berlin Heidelberg 2012
info.scichina.com
www.springerlink.com
Chen D, et al.
Sci China Inf Sci
October 2013 Vol. 56 102314:2
To generate high-resolution DTMs, non-ground point clouds (e.g., buildings, vegetation, pedestrians and vehicles) should be separated from ground point clouds (e.g., terrain points or bare-earth surfaces), while preserving the terrain details perfectly. Removing non-ground points from LiDAR datasets has proven to be a challenging task, especially in densely forested areas, steep terrain and highly varied terrain. Many algorithms have been developed for automatically or semi-automatically extracting DTMs from LiDAR point clouds in recent decades. Classification algorithms and the quality of the LiDAR data together determine the accuracy of the extracted DTMs. A reasonable filtering algorithm can adaptively tune its own parameters in real time based on terrain features and computational efficiency, thereby reducing Type I errors (i.e., rejecting ground points) and Type II errors (i.e., accepting non-ground points) effectively [3]. This paper presents an improved filtering algorithm based on the filtering methods proposed by [4,5]. To evaluate the performance of our proposed method, our method is compared with a benchmark study conducted by ISPRS Commission III/WG 3 [3], which tested eight filtering algorithms over sites ranging from urban to rural areas with different complexity. The remainder of this paper is organized as follows. Related works are presented in Section 2. Next, the workflow and methodology are presented in Section 3. In Section 4, the results are shown and discussed, and the main conclusions and perspectives are drawn in the final section.
2
Related work
Recently, many filtering algorithms have been developed to automatically extract ground features from airborne LiDAR point clouds [6–15], which are mainly classified into three categories: interpolationbased methods (i.e., linear prediction methods)[8], slope-based filtering methods [9–12] and mathematical morphology-based methods [5,13–15]. 2.1
Interpolation-based filtering methods
This type of method was first proposed by University of Vienna, Austria, Kraus and Pfeifer [8]. The basic principle is that the elevation of non-ground points is higher than that of terrain points. A rough approximation of the terrain surface is calculated first with equal weights for all points. This estimated surface is an averaging surface between ground points and non-ground points. The residuals (i.e., the oriented distances from the surface to the points) are then calculated. The non-ground points usually obtain positive or small negative residuals while the ground points are more likely to have negative residuals [16]. The weights of each point are then calculated according to weight function determined by their corresponding residuals. The process is iterated until the trend surface approaches the real terrain surface, and meanwhile the classification results are obtained. Interpolation-based filtering methods were originally used in forest areas and later extended to urban areas [17]. Although promising results were obtained in these environments, these methods are not applicable to terrain with breaklines, steep terrain and highly variable terrain [18]. In addition, it is a challenge for users to tune the complicated parameters of the algorithms, and large areas of dense shrubs as well as buildings cannot always be filtered completely. To overcome the aforementioned problems, Lee and Younan [18], based on the study of Kraus [8,19] and Pfeifer et al. [16,20], replaced the least squares method with a normalized least squares method called adaptive line enhancement (ALE). Encouraging results were achieved, especially in the areas with steep slopes and high terrain variation. The implementation of ALE requires a priori knowledge of a number of parameters, such as delay factors, adaptation parameters and filter orders. In another study, Brandtberg et al. [21] utilized iterative regression to derive digital elevation models (DEMs) in forest areas and promising results were obtained. 2.2
Slope-based filtering methods
A slope-based filtering method was first proposed by Vosselman [9]. It identifies whether a LiDAR survey point is a ground point as a function of the maximum slope value between it and its neighbors. This method relies on the premise that the gradient of the natural slope of terrain is distinctly different from
Chen D, et al.
Sci China Inf Sci
October 2013 Vol. 56 102314:3
the slope of non-ground objects [11]. A LiDAR point is identified as a ground point if the maximum value of slope between this point and its neighbors is less than the predefined threshold; otherwise it is a non-ground point. Thus, the slope threshold plays a critical role. The smaller the threshold, the more LiDAR points are classified as bare earth. A reasonable slope threshold may be obtained from training datasets. Additionally, any prior knowledge and other multi-resource datasets of the study area can also be incorporated to determine the slope threshold. Because the training datasets cannot possess all of the features of the entire study area, it is difficult to determine an optimal and reliable slope threshold. In practice, this threshold is set to a fixed value derived from the training dataset, or it can be dynamically tuned by the distance between the current point and its nearby neighbors to obtain a reasonable predefined slope threshold [5]. Generally, slope-based filtering methods work well in fairly flat terrains but become more difficult as the slope of the terrain increases [3], especially in a steep forested landscape. To overcome this limitation, Sithole [11] proposed a modified approach in which the threshold varies with the slope of the terrain and obtained a high filtering accuracy, especially in complicated terrain environments. 2.3
Morphological filtering methods
A morphological filter for LiDAR data processing is based on mathematical morphology methods that have been used to identify objects in grayscale images by using morphological operations such as opening and closing [4,22]. As the elevation values of non-ground object points are higher than those of nearby ground points, the grey tones in the grayscale image of the terrain are very different. The point clouds of LiDAR data can be converted into a grayscale image based on their corresponding elevation values. Therefore, mathematical morphology can be adapted to classify LiDAR point clouds [23]. Kilian [4] performed an opening operation to filter the LiDAR point clouds. In their method, a point with the lowest elevation within a current window is detected as a ground point. Other points that fall within a band (determined by the average point density of the LiDAR data) above the lowest elevation are also classified as ground points. Thereafter, the filtering window moves over the whole dataset. In this process, it is critical to select an optimal window size. On the one hand, if a small window size is used, the terrain details can be preserved well. However, large buildings in urban areas cannot be filtered completely, leading to high Type II errors. On the other hand, a large window can remove large objects completely, but if the window is too large, the terrain details are often “chopped off”, leading to high Type I errors. Thus, the optimal window size of the morphological operation should be small enough to preserve the terrain details, and large enough to filter large-sized building complexes. To solve this problem, Killian applied the operations iteratively with different window sizes to the LiDAR data, starting with the smallest window size. Each point classified as ground is assigned a weight related to the window size. The larger the window size is, the higher the weight. Points that are likely part of the terrain are assigned progressively higher weights than non-ground points. In the end, the terrain surface is extracted according to the value of point weights. Zhang et al. [5] presented a progressive morphological filter to remove non-ground points while preserving ground points by gradually increasing window sizes and using dynamic elevation thresholds between two successive filtered surfaces. In this method, the terrain details were kept well, while the non-ground objects were removed effectively. Moreover, this method provided quantitative equations relating the elevation thresholds to window size as an additional output. Chen et al. [14] expanded Zhang et al.’s method from one dimension to two dimensions, with operations based on the cut areas. In addition, Chen et al.’s method did not require the assumption of a constant slope variable in advance. Although this method represented a dramatic improvement in accuracy, obtaining the optimal parameters is difficult. Chen et al. [15] further presented an edge-based morphological method, which reduced the prior seven parameters to two parameters.
3
Methodology
In this paper, we propose a mathematical morphology-based multi-level filter for generating DTMs. Our
Chen D, et al.
Figure 1
Sci China Inf Sci
October 2013 Vol. 56 102314:4
Framework of the mathematical morphology-based multi-level filter.
method is related to the methods proposed by Kilian [4] and Zhang et al. [5] and is mainly composed of the following three steps and is illustrated in Figure 1. (1) Extraction of preliminary non-ground points. Based on multi-echo characteristics of the LiDAR data, the reliable preliminary non-ground points (e.g., vegetation and building edge points) are extracted in advance, which improves the accuracy of the subsequent filtering method and dramatically reduces the computational complexity due to the diminished point clouds. (2) Rasterization of remaining point clouds. Our method is implemented based on raster data structures because of their efficiency and ease of implementation. The remaining point clouds are rasterized and prepared for the subsequent filtering algorithm. The raster grid cell size, point assignment and empty data-filling strategies are resolved in the process of rasterization. (3) Mathematical morphology-based multi-level filtering. The mathematical morphology-based multi-level filtering method is designed to identify and eliminate non-ground objects, while the terrain details are preserved. In our method, the mathematical opening
Chen D, et al.
Figure 2
Sci China Inf Sci
October 2013 Vol. 56 102314:5
Extraction of preliminary non-ground points in the lower right of Site 1. (a) The tree, understory shrub and
building edge points are preserved when the elevation difference of the two returns satisfies T0 =3.0 m; (b) only points located on the high tree canopy and high building edges are preserved when the elevation difference of the two returns satisfies T0 =12.0 m.
operations are employed only in local approximate object regions, which avoids smoothing the terrain as much as possible. Meanwhile, our modified filtering method is less sensitive to parameter tuning than the method proposed by Zhang et al. Encouraging results are obtained through the sample parameter tuning in our method.
3.1
Extraction of preliminary non-ground points
Using multi-echo LiDAR point clouds, reliable preliminary points can be extracted based on multi-echo characteristics. Usually, when a laser beam contacts high or sparse leaves, tree branches or building edges (i.e., step edges and ridge edges), at least two echoes are generated: one echo returns from the tree or building edges, and the other returns from the ground. In contrast, if a laser beam contacts the ground or building rooftops, only one return echo exists. Generally, if one laser beam generates N return echoes, the previous N − 1 return echoes may originate from vegetation and building edges, while the last return echo may reflect from the ground. As mentioned above, in the pre-extraction process, the echoes that are obtained at the previous N − 1 return echoes are marked as the preliminary non-ground points. Specifically, the datasets used in our extraction of preliminary non-ground points only include the first and the last return echoes. We can obtain a coarse digital surface model (DSM) of the study area, called DSMfirst , by the first return echo, and a fine DSM, called DSMlast , by the last return echo. There is a large elevation difference between the two return echoes, which means that the first return echo P is most likely reflected from vegetation or building edges, if two echo returns per pulse satisfy the following inequality: DSMfirst − DSMlast > T0 .
(1)
The preliminary non-ground points are extracted by tuning the parameter T0 . As shown in Figure 2(a), when T0 is set to a relatively small value (e.g., 3.0 m), some understory shrubs in forested regions are classified as preliminary non-ground points. When T0 is set to a relatively large value (e.g., 12.0 m), only some points located on high vegetation canopies and building edges are discriminated as preliminary non-ground points (see Figure 2(b)). In practice, the optimal threshold of T0 can be derived from the wavelength of the LiDAR pulse (i.e., range resolution). Although some vegetation points are extracted in advance, many vegetation points remain in dense forested regions because the pulse cannot penetrate the dense vegetation and the two return echoes have almost exactly the same elevation value. After the extraction of preliminary non-ground points, the remaining point clouds are gathered into the set Sremain, which provides input data for the subsequent operations.
Chen D, et al.
3.2
Sci China Inf Sci
October 2013 Vol. 56 102314:6
Rasterization
After the aforementioned preprocessing, the LiDAR point set Sremain includes discrete three-dimensional point clouds. To improve computational efficiency and reduce spatial complexity, the set Sremain is converted to raster format. The following five factors must be taken into consideration during the conversion: (1) Grid cell size. The cell size is limited to the average point density of the raw LiDAR data. The principle of setting the cell size is to map as many points of set Sremain as possible into the grids in the premise of storage efficiency. Assuming there are n points in the study region with area of A, the optimal cell size C is defined as follows: A . (2) C= n (2) Point cloud assignment strategy. The number of columns and rows of the grids can be calculated by the minimum bounding rectangle of the LiDAR data and grid cell size. Each point is then mapped into its corresponding grid cell by its projection coordinates. During this process, the approximate projection coordinates can lead to mapping multiple points into the same grid cell, especially in cases of multiple return echoes of the same pulse. In these cases, the point with minimum elevation value will be preserved in the current grid cell. (3) Filling of empty grid cells. Small areas of missing data are mainly caused by the nonuniform distribution of the raw LiDAR data. When the point clouds are distributed nonuniformly, the distance between two LiDAR points is often greater than the average point density. Therefore, some grid cells often do not contain LiDAR point clouds during the rasterization. To fill these isolated empty cells, the Kriging interpolation algorithm was employed. However, terrain artifacts will appear when this approach is used to larger regions of contiguous empty cells, which are usually caused by errors in the laser range finder, gap errors between adjacent strips or water absorption. It is necessary to enhance the interpolation results for these large continuous empty regions. We first need to determine the locations of these regions. The grayscale raster image is converted into a binary image (see Figure 3(a)) where 0 (i.e., white grid cells) stands for cells that have values and 1 (i.e., black grid cells) for cells with no data. Next, the morphological closing operations denoted by ϕB (f ) = εB˘ [δB (f )]
(3)
are applied to the binary image using the corresponding structuring elements (e.g., cross or square structuring elements). Small empty regions are filled and large regions of missing data are discovered (see Figure 3(b)). We then filled the large empty regions with the minimum elevation of their boundary points, which are obtained by subtracting the value of dilation of the binary image from the binary image. After the process of interpolation and data filling, the enhanced raster dataset is marked as Gridinitial . In this paper, to eliminate the low outliers, a filtering window with size 3 × 3 is applied to Gridinitial using the closing operation denoted by Eq.(3). Then, the new derived raster dataset is recorded as Gridlast , which is the final input dataset for the subsequent filtering method mentioned in Subsection 3.3. In Eq.(3), the closing of an image f by a structuring element B is denoted by ϕB (f ) and is defined as the dilation of f with a structuring element B followed by the erosion with the reflected structuring ˘ element B. 3.3
Mathematical morphology-based multi-level filtering
In Zhang et al.’s progressive morphological filtering method, they compared the elevation difference between the two successive surfaces after morphological opening operations using the following equation: γB (f ) = δB˘ [δB (f )]
(4)
Chen D, et al.
Figure 3
Sci China Inf Sci
October 2013 Vol. 56 102314:7
Assignment of point clouds and strategies for filling missing data. (a) The binary image of Site 1; (b) employing
the closing operation to (a) with 3 × 3 square structuring element, with blank areas highlighted; (c) the final boundaries of the empty regions; (d) employing the closing operation to (a) with 3 3 cross structuring element; (e) the generated DTM after employing the Kriging interpolation of Site 1; (f) the enhanced DTM.
with successively increased window sizes. If the elevation difference of a point is less than dhT,k , the LiDAR point is classified into a ground point. Otherwise, it is a non-ground point. The elevation threshold dhT,k is determined by terrain slope; however, the author assumed that the slope over a study area is constant. The assumption of a constant slope is not always realistic, especially for complex terrains, which will lead to an increase in Type I errors. In our study, our approach has been developed based on the aforementioned methods proposed by Kilian [4] and Zhang et al. [5]. The negative effects of parameter dhT,k have been minimized, and the mathematical opening operations are employed only in localized areas nearby non-ground points, which improves the computational efficiency dramatically. In Eq.(4), the opening γ of an image f by a structuring element B is denoted by γB (f ) and is defined ˘ as the erosion of f by B followed by the dilation with the reflected structuring element B. As shown in Figure 4, region A only contains LiDAR ground points; region B contains the LiDAR points of large buildings; region C contains the points of small buildings; and region D is an area covered by vegetation (e.g., trees and understory shrubs). In our method, while the window size is increased, we only perform opening operations in non-ground point regions (e.g., regions B, C and D in Figure 4) and avoid doing such operations for terrain regions (e.g., region A in Figure 4) whenever possible. How to approximately determine regions B, C and D will be discussed later. Next, the elevation difference between two successive filtering surfaces is compared with the threshold HT,k . If the difference is larger than HT,k , then they are identified as non-ground points; otherwise, they are identified as ground points. How to set the value of HT,k will be discussed later. The filtering method described here has the following advantages: (1) It avoids errors in the process for calculating the dynamic threshold dhT,k , reducing the risk of Type I error, and also preserves terrain details. Here, we introduce another dynamic threshold HT,k with lower sensitivity, which simplifies pa-
Chen D, et al.
Figure 4
Sci China Inf Sci
October 2013 Vol. 56 102314:8
Filtering process for identifying terrain and non-ground objects. The horizontal axis stands for horizontal
distance. The vertical axis stands for elevation. Region A represents the terrain; Region B represents a large building. Region C represents a small building; Region D represents an area of sparse vegetation. HB is the elevation of the large building B and HC is the elevation of the building C. HA is the maximum elevation difference between two successive surfaces after opening operations.
rameter adjustment. (2) The opening operation is only performed in approximate non-ground regions, which improves computational efficiency, and meanwhile, can retain the terrain details, such as region A illustrated in Figure 4. To determine regions B, C and D, two definitions are given as follows: (1) Critical gradient: the value of elevation difference yielded by subtracting the original elevation of the image f from the result of dilation by the structuring element B. It is defined as HG = [δB (f )](x) − f (x),
(5)
where [δB (f )](x) = maxb∈B f (x + b) represents the dilation of image f using the structuring element B. (2) Critical points: The terrain points located near the non-ground objects within the current filtering window. The critical gradient is defined for all grid points, while the critical points are defined only for certain points (HG > HG,k ). If the current LiDAR points’ critical gradients are larger than the threshold HG,k , which is related to the window size Wk , these points are most likely critical points. As shown in Figure 4, when the filtering window has size Wk = 3, the critical gradients of points B1 and B3 satisfy HG > HG,3 . Therefore, the points B1 and B3 are identified as the critical points corresponding to the building B when the window has size Wk =3. When Wk = 5, the points B1 , B2 , B3 and B4 satisfy HG > HG,5 . According to the definition of the critical points, B1 , B2 , B3 and B4 are the critical points corresponding to building B when Wk = 5. Generally, if the points around the building B satisfy HG > HG,max in the window size of Wmax , the LiDAR points that are within a distance of Wmax /2 from the edge of building B are identified as the critical points. The critical points corresponding to building C and vegetation D are determined in the same way. The opening operation is immediately applied to the current window with a small size W0 centered at the critical points and the two successive filtered surfaces are compared. If the elevation difference is larger than HT,0 , then the points are identified as non-ground points. Otherwise, they are ground points. Vegetation points in region D are removed by setting a proper threshold HT,0 ; however, the buildings B and C cannot be removed as the window size W0 is smaller than the size of these buildings. We gradually increase the window size Wk and still apply the opening operations to the current window centered at critical points, and we compare the elevation difference of the two successive filtered surfaces with a proper threshold HT,k . If the elevation difference is larger than the threshold HT,k , the small building C is removed. When Wk becomes larger than the size of big building B, then this big building will be removed. By dynamically tuning critical gradient HG,k , the critical points barely exist in prominent terrain features such as region A with a small window size, so the terrain details in region A will be preserved. However, as the window size is large, there will be fake critical points A1 and A2 when HA > HG,k . When we
Chen D, et al.
Sci China Inf Sci
October 2013 Vol. 56 102314:9
perform the opening operation in this window and compare the elevation differences, the differences are often smaller than the current threshold HT,k , so the terrain details such as the steep slope area A are still preserved when using the large window for filtering. By this multi-level filtering process, non-ground points can be removed and ground points are preserved perfectly. The selection of the elevation difference threshold HT,k and critical gradient threshold HG,k will affect the filtering results. The initial value of HG,k should be smaller than the height of the smallest building and should not be increased too fast, or else some buildings will be left out. The maximum value of HG,k should be smaller than the height of the highest building to guarantee that the highest building is removed. The method has a relatively low sensitivity to the elevation difference parameter HG,k . The increasing rate of HG,k should be matched with HT,k , meaning that HG,k is small/large when HT,k is small/large. Under this condition, when both HT,k and HG,k are small, we can remove some small objects such as cars, shrubs. When both HT,k and HG,k are increased gradually, we not only can filter big objects, such as large buildings and high trees, but also preserve the terrain details perfectly. In our method, the dynamic window size Wk increases exponentially and is defined as Wk = 2bk + 1,
(6)
where k = 1, 2, . . . , M, and b is the initial window.
4
Experimental results
The LiDAR data used in this paper are free sample data provided by ISPRS Commission III group 3. The LiDAR data were collected in the second phase of OEEPE (The European Organization for Experimental Photogrammetric Research) project on laser scanning [24]. These samples are located in the Vaihingen/Enz test field in south Germany and in Stuttgart city center, and they cover diverse feature contents (open fields, vegetation, buildings, roads, railroads, rivers, bridges, powerlines, water surfaces, etc.). The LiDAR data were collected with an Optech ALTM scanner, with first and last pulse and the intensities recorded simultaneously. The data for the sites were extracted from laser scanning data produced by FOTONOR AS. The datasets are in the Universal Transverse Mercator zone 32 (UTM 32) projection, based on the World Geodetic System 1984 (WGS84) Coordinate System. The average density of the point clouds is 1.0—1.5 m in urban sites (i.e., from Site 1 to Site 4), while it is 2.0—3.5 m in rural sites (i.e., from Site 5 to Site 8). Moreover, for each sample, the reference data were provided by semi-automatic filtering and manual editing with knowledge of the landscape and available aerial images. The detailed characteristics of the test sites are described in [24]. The experiments were performed on a personal computer with a 2.33 GHz Intel (R) Core (TM) CPU, 1 GB of main memory and an Intel (R) 82865G graphics controller card. Eight mainstream filtering algorithms were compared with our method. In the process of the extraction of preliminary non-ground points, the reliable non-ground objects, such as vegetation and building edges, were extracted based on the wavelength of the laser pulse, so we set the threshold T0 to 3.0 m. After the non-ground point extraction, 118 665 LiDAR point clouds were removed from the dataset of Site 1, which account for 8.68% of the raw point clouds. The cell size was set to 1.0 m during rasterization, which is less than the average spacing between LiDAR measurements at the urban sites, and therefore most of LiDAR points were retained in a raster grid. There are 26 987 points preserved after rasterization, which account for 70.99% of the total raw point clouds in Sample 11, and the number of grid cells is 40 468. For other urban samples, the points assigned to the grids amount to roughly 70% of the corresponding raw Sample point clouds. For the rural samples, the average density of the point clouds is 2.0—3.5 m, so nearly all of the points for each sample data were mapped into to the grids for the subsequent filtering algorithm. Considering that there are many complex buildings in urban areas and that the maximum window size should be larger than the size of the largest building, the maximum of Wk was set up to 150 m. HG,k was initialized as 0.6 m, which is approximately equal to the LiDAR measurement error, so that small non-ground objects could be removed. The rate of increase of HT,k was the same as HG,k , so
Chen D, et al.
Sci China Inf Sci
Table 1
October 2013 Vol. 56 102314:10
The parameters used in our method
Parameter
Value
T0
3.0 m
Size
1.0 m
W0
2.0 m
Wk
150.0 m
HG,k
0.6 m (Wk 5.0 m); 8.0 m (HG,k 8.0 m); HG,k = HG,k + 1 (Wk > 5.0 m)
HT,k
HG,k
they could match each other. The value of HT,k was small as the window was small; otherwise, HT,k would become larger. Details of these parameter settings are shown in Table 1. At least one sample was randomly selected from the corresponding eight sites to evaluate the accuracy of our method both qualitatively and quantitatively. The filtering results are given in Figure 5, using the parameters listed in Table 1. We did not evaluate our algorithm at Site 8, as ISPRS did not provide reference data for Site 8. As shown in Table 2, three types of errors were used to evaluate the performance of the classification algorithms. The Type I error rate is defined as b/(a + b), the Type II error rate is c/(c + d) and the total error rate is (b + c)/(a + b + c + d). Type I error rates, Type II error rates and the total error rates are important indices for evaluating various filtering methods. This paper has quantitatively evaluated the performance of our method, compared with the current eight filtering methods, based on the total error rates, and the results are shown in Table 3. As shown in Table 3, the total error rates in Samples 12, 21 and 31 produced by our method are slightly higher than the mean total error rates generated by other eight algorithms, which is mainly ascribed to the relative high Type I error rates. In spite of the relatively high Type I error rate, the accuracy of the generated DTMs was not dramatically affected by Type I error because these datasets were acquired from the urban areas and a few non-ground points missing have few impacts on DTMs generation. However, in the rural areas, e.g., Samples 11, 42, 51, 61 and 71, our method effectively reduces the risk of Type I error. Meanwhile, it maintains Type II error in a relatively low level. Therefore, a relatively low total error rate is maintained. Even though our results are not as good as those methods proposed by Sohn and Axelsson [3], our approach is less sensitive to parameter settings described in Table 1. Furthermore, it achieves high computational efficiency in generating DTM details both in complex rural environments and urban areas. In addition, our method was compared with the method proposed by Zhang et al. by the two representative datasets of urban Sample 21 and rural Sample 71 (see Figure 6). For the urban Sample 21,6798 LiDAR points were identified as terrain points, and 2403 points were classified as non-ground points. Type I and Type II error rates reached 10.17% and 12.99%, respectively, in Zhang et al.’s filtering algorithm. However, 7041 LiDAR points were identified as terrain points and 2160 points were identified as non-ground points in our method. The corresponding Type I error rates just account for 6.91%, while Type II error rate reaches as high as 16.48%. As shown in Figure 6, the filtering method proposed by Zhang et al. can effectively filter the nonground points but has no advantage in preserving terrain details, especially in rural Sample 71, which could explain why the total error reaches 11.35% in Zhang et al.’s method, while the total error of our method is only 8.17%. As shown in Figure 6 of Sample 71, the embankments of the roads and slopes on both sides of the bridge were obviously chopped off in Zhang et al.’s method. However, our method keeps these characteristics perfectly. In contrast, our method cannot filter the dense vegetation areas completely in Sample 21, but Zhang et al.’s method can. Generally, Zhang et al.’s method performs slightly better than our method in areas of fairly flat terrain. However, for greater terrain slope or in some areas of complex terrain, our method achieves more encouraging results.
5
Conclusions
Our morphology-based multi-level filter method achieves promising results, not only in flat urban areas
Chen D, et al.
Sci China Inf Sci
October 2013 Vol. 56 102314:11
Chen D, et al.
Figure 5
Sci China Inf Sci
October 2013 Vol. 56 102314:12
Filtering results. (a) The DSMs before filtering; (b) the referenced terrain provided by ISPRS; (c) our method
results. All of these shaded relief maps are derived by using Kriging interpolation in Surfer software. The grid size is 0.5 m. The searching radii for Samples 11, 12, 21, 31, 42, 51, 61 and 71 are 166.0 m, 167.0 m, 84.5 m, 119.0 m, 152.0 m, 244.0 m, 336.0 m and 226.0 m, respectively.
Table 2
Cross-matrices used to evaluate the risk of errors Filtered
Reference
Bare Earth (BE)
Object (Obj)
Bare Earth (BE)
a
b
Object (Obj)
c
d
but also in rural areas, especially when preserving complex terrain details, while removing non-ground spatial objects. The elimination of preliminary non-ground points can improve the accuracy of the filter-
Chen D, et al.
Table 3
Sci China Inf Sci
October 2013 Vol. 56 102314:13
The total error rate comparison of our algorithm against the eight mainstream algorithms (%)∗
Datasets
Elmq
Sohn
Axel
Pfei
Brov
Rogg
Wack
Sith
Our Method
Mean
Sample 11
22.40
20.49
10.76
17.35
36.96
20.80
24.02
23.25
18.25
21.11
Sample 12
8.18
8.39
3.25
4.50
16.28
6.61
6.61
10.21
7.95
7.53
Sample 21
8.53
8.80
4.25
2.57
9.30
9.84
4.55
7.76
8.97
6.43
Sample 31
5.34
6.39
4.78
1.80
12.92
2.14
2.21
3.15
6.95
4.44
Sample 42
3.68
1.78
1.62
2.64
6.38
4.30
3.54
3.85
2.60
3.33
Sample 51
23.31
9.31
2.72
3.71
22.81
3.01
11.45
7.02
8.03
9.51
Sample 61
35.87
2.99
2.08
6.91
21.68
18.99
13.47
21.63
9.13
13.96
Sample 71
34.22
2.20
1.63
8.85
34.98
5.11
16.97
21.83
8.71
14.31
* Elmq, Sohn, Axel, Pfei, Brov, Rogg, Wack and Sith are eight mainstream filtering algorithms presented by Elmqvist, Sohn, Axelsson, Pfeifer, Brovelli, Roggero, Wack and Sithole, respectively. For more details, please refer to [3].
Figure 6
Filtering method comparison. (a) The reference terrain supplied by ISPRS; (b) the results produced by the
method of Zhang et al.; (c) our generated results. All of these shaded relief maps are derived by Kriging interpolation in Surfer software. The grid size is 0.5 m. The searching radii for Sample 21 and Sample 71 are 84.5 m and 226.0 m, respectively.
ing and simultaneously guarantee the quality of the input LiDAR point clouds, which is critical for subsequent mathematical filtering. Moreover, the implementation of our mathematical opening operation is based on the nearby non-ground points within a localized region, which dramatically improves our computational efficiency compared with the method proposed by Zhang et al. Our method can be used to extract city models [25] and terrain models for visualization [26]. Although promising results are achieved, our method is based on raster data, which will inevitably lead to a loss of precision. In future studies, a more reasonable algorithm will be developed based on discrete point clouds, and other data sources or prior knowledge will be employed to acquire more accurate classification results. Additionally, full-waveform LiDAR data will be integrated into our work for better filtering.
Acknowledgements The authors would like to thank the editors and the anonymous reviewers for their valuable comments and suggestions which have helped us improve the context and the presentation of the paper. The work was supported by National Natural Science Foundation of China (Grant No. 60502008) and National High-Tech Program of China (863) (Grant No. 2011AA120302).
Chen D, et al.
Sci China Inf Sci
October 2013 Vol. 56 102314:14
References 1 Vosselman G. Analysis of planimetric accuracy of airborne laser scanning surveys. Int Archiv Photogramm Rem Sens Spat Inf Sci, 2008, 37: 99–104 2 H¨ ofle B, Hollaus M, Hagenauer J. Urban vegetation detection using radiometrically calibrated small-footprint fullwaveform airborne LiDAR data. ISPRS J Photogramm Rem Sens, 2012, 67: 134–147 3 Sithole G, Vosselman G. Experimental comparison of filter algorithms for bare earth extraction from airborne laser scanning point clouds. ISPRS J Photogramm Rem Sens, 2004, 59: 85–101 4 Kilian J, Haala N, Englich M. Capture and evaluation of airborne laser scanner data. Int Archiv Photogramm Rem Sens Spat Inf Sci, 1996, 31: 383–388 5 Zhang K Q, Chen S C, Whitman D, et al. A progressive morphological filter for removing nonground measurements from airborne LiDAR data. IEEE Trans Geosci Rem Sens, 2003, 41: 872–882 6 Silv´ an-C´ ardenas J L, Wang L. A multi-resolution approach for filtering LiDAR altimetry data. ISPRS J Photogramm Rem Sens, 2006, 61: 11–22 7 Kobler A, Pfeifer N, Ogrinc P, et al. Repetitive interpolation: A robust algorithm for DTM generation from aerial laser scanner data in forested terrain. Rem Sens Envir, 2007, 108: 9–23 8 Kraus K, Pfeifer N. Determination of terrain models in wooded areas with airborne laser scanner data. ISPRS J Photogramm Rem Sens, 1998, 53: 193–203 9 Vosselman G. Slope based filtering of laser altimetry data. Int Archiv Photogramm Rem Sens Spat Inf Sci, 2000, 33: 935–942 10 Roggero M. Airborne laser scanning: clustering in raw data. Int Archiv Photogramm Rem Sens Spat Inf Sci, 2001, 34: 227–232 11 Sithole G. Filtering of laser altimetry data using a slope adaptive filter. Int Archiv Photogramm Rem Sens Spat Inf Sci, 2001, 34: 203–210 12 Shan J, Sampath A. Urban DEM generation from raw LiDAR data: A labeling algorithm and its performance. Photogramm Engin Rem Sens, 2005, 71: 217–226 13 Zhang K Q, Whitman D. Comparison of three algorithms for filtering airborne LiDAR data. Photogramm Engin Rem Sens, 2005, 71: 313–324 14 Chen Q, Gong P, Baldocchi D, et al. Filtering airborne laser scanning data with morphological methods. Photogramm Engin Rem Sens, 2007, 73: 175–185 15 Chen Q. Improvement of the edge-based morphological (EM) method for LiDAR data filtering. Int J Rem Sens, 2009, 30: 1069–1074 16 Pfeifer N, Reiter T, Briese C, et al. Interpolation of high quality ground models from laser scanner data in forested areas. Int Archiv Photogramm Rem Sens Spat Inf Sci, 1999, 32: 31–36 17 Pfeifer N, Stadler P, Briese C. Derivation of digital terrain models in the SCOP++ environment. In: Proceedings of OEEPE Workshop on Airborne Laser scanning and Interferometric SAR for Digital Elevation Models, Stockholm, 2001 18 Lee H S, Younan N H. DTM extraction of LiDAR returns via adaptive processing. IEEE Trans Geosci Rem Sens, 2003, 41: 2063–2069 19 Kraus K. A new method for surface reconstruction from laser scanner data. Int Archiv Photogramm Rem Sens Spat Inf Sci, 1997, 32: 80–86 20 Pfeifer N, Kostli A, Kraus K. Interpolation and filtering of laser scanner data-implementation and first results. Int Archiv Photogramm Rem Sens Spat Inf Sci, 1998, 32: 153–159 21 Brandtberg T, Warner T A, Landenberger R E, et al. Detection and analysis of individual leaf-off tree crowns in small footprint, high sampling density LiDAR data from the eastern deciduous forest in North America. Rem Sens Envir, 2003, 85: 290–303 22 Lohmann P, Koch A, Schaeffer M. Approaches to the filtering of laser scanner data. Int Archiv Photogramm Rem Sens Spat Inf Sci, 2000, 33: 540–547 23 Haralick R M, Shapiro L G. Computer and Robot Vision. New York: Addison-Wesley, 1992 24 Petzold B, Axelsson P. Results of the OEEPE Working Group on laser data acquisition. Int Archiv Photogramm Rem Sens, 2000, 33: 718–741 25 Chen D, Zhang L Q, Li J. Urban building roof segmentation from airborne lidar point clouds. Int J Rem Sens, 33: 6497–6515 26 Yang L, Zhang L Q, Kang Z Z, et al. An efficient rendering method for large vector data on large terrain models. Sci China Inf Sci, 2010, 53: 1122–1129
