Filtering Airborne LiDAR Data in Forested Environments Based on Multi-Directional Narrow Window and Cloth Simulation

: Ground ﬁltering is one of the essential steps for processing airborne light detection and ranging data in forestry applications. However, the performance of existing methods is still limited in forested areas due to the complex terrain and dense vegetation. To overcome this limitation, we proposed an improved surface-based ﬁlter based on multi-directional narrow window and cloth simulation. The innovations mainly involve two aspects as follows: (1) sufﬁcient and uniformly distributed ground seeds are identiﬁed by merging the lowest points and line segments from the point clouds within a multi-directional narrow window; (2) complete and accurate ground points are extracted using a cyclic scheme that includes incorrect ground point elimination using the internal force adjustment of cloth simulation, terrain reconstruction with moving least-squares plane ﬁtting, and ground point extraction based on progressively reﬁned terrain. The proposed method was tested in ﬁve forested sites with various terrain characteristics and vegetation distributions. Experimental results showed that the proposed method could accurately separate ground points from non-ground points in different forested environments, with the average kappa coefﬁcient of 88.51% and total error of 4.22%. Moreover, the comparative experiments proved that the proposed method performed better than the classical methods involving the slope-based, mathematical morphology-based and surface-based methods.


Introduction
Forests are the largest terrestrial ecosystem and play a pivotal role in balancing waterenergy-carbon cycles and containing biodiversity [1].With rising concerns about global climate change during the past decades, the ability of forests to absorb carbon dioxide and release oxygen through photosynthesis has received increasing attention [2].Many existing investigations have shown that forests are important carbon sinks and strongly beneficial to control warming [3].
The potential of forests to absorb carbon dioxide and promote carbon neutralization is highly related to their quantity, quality and dynamics [4].Accurate forest investigation is of great significance for understanding such information.As an important technology in forest ecosystem investigations, airborne light detection and ranging (LiDAR) has been widely applied to forest inventory and management due to its capability in providing precise and detailed three-dimensional (3D) information on forest structures [5].Researchers in this field mainly focus on individual tree segmentation [6,7], tree species classification [8][9][10], tree height measurement [11][12][13], canopy cover estimation [14,15] and others [16][17][18].In view of these existing publications, ground filtering (i.e., distinguishing ground points and non-ground points) has been recognized as one of the most fundamental but essential steps in processing raw LiDAR data.
The existing filtering methods have performed good availability and feasibility in distinguishing ground points and non-ground points from raw LiDAR data, and especially work well in forested environments with relatively flat terrain and sparse vegetation [47,[49][50][51].However, the filtering in complex forested environments, such as terrain discontinuities, highly rugged terrain, steep slopes, ridges and dense vegetation, is still facing great challenges [35,47,52,53].One vital limitation is the quality of ground seeds.Sufficient and evenly distributed ground seeds can provide a reliable reference for ground point extraction on various terrain details.Researchers have adopted multiple methods to improve the quality of ground seeds, e.g., identifying ground seeds based on segmentation [54][55][56], multi-scale mathematical morphology [47,48,57,58] and cloth simulation methods [42,59], etc.Although the filtering accuracy has increased by applying such methods, the filtering errors are still inevitable due to insufficient ground seeds identified on some terrain details, e.g., steep slopes and ridges.Another limitation is the extraction of ground points.In the process of detecting ground points precisely, researchers have tried to improve terrain surface accuracy through various interpolators such as the triangular irregular network [36], least-squares polynomial fitting [40] and thin plate spline [39].Although the improved terrain surfaces provide a more accurate reference for ground point extraction, inaccurate input data (i.e., ground points extracted in each iteration) may also limit the accuracy of terrain surfaces, even causing cumulative errors in subsequent iterations [47].In view of the previous studies, we found that this issue is rarely considered.
Against the aforementioned research backgrounds, we aimed to develop an improved surface-based filter for accurately extracting ground points in forested environments with complex terrain and dense vegetation.Compared with the existing ground filtering methods, the main contributions of the proposed method are as follows: (1) Sufficient and evenly distributed ground seeds are identified.In this step, we propose a ground seed identification method based on the multi-directional narrow rectangle window.The method can identify ground seeds in more positions and directions, obtaining more complete ground seeds on various terrain details than the common square window.Moreover, a line-segmentation-based ground seed enhancement method is developed to increase ground seeds on raised terrain.High-quality ground seeds provide a detailed basis for ground point extraction and therefore improve ground filtering accuracy in various forested environments.(2) Complete and accurate ground points are extracted.In this step, the ground points are extracted iteratively based on the updated terrain by executing three key procedures, i.e., incorrect ground point elimination, terrain reconstruction and ground point selection.The incorrect points among the extracted ground points can be eliminated by the internal force adjustment of cloth simulation, improving the accuracy of the terrain surface.The terrain surface is reconstructed through the moving least-squares plane fitting, which enhances the reliability of terrain due to it being terrain-adaptive.The two improvements provide guarantees for accurately extracting ground points in each iteration.Finally, ground points are extracted iteratively based on the progressively refined terrain, which ensures the extraction of complete ground points.
This proposed method is expected to efficiently filter out vegetation points while maintaining terrain details.Moreover, this method can perform stronger adaptability to various forested environments.The applicability and practicality of the proposed method is validated by comparing it with other widely used filtering methods.The paper is organized as follows: Section 2 presents the methodology, Section 3 introduces the experiments and results, Section 4 discusses the experimental results, and Section 5 summarizes the conclusions.

Methods
This study aimed to develop an improved surface-based filter suitable for complex forested environments with diverse terrain and various vegetation conditions.We focused on the two major steps of ground filtering, i.e., the ground seed identification and ground point extraction, and tried to increase their effectiveness for performing ground filtering separately.The details are given as follows.

Ground Seed Identification
Sufficient numbers and uniform distribution of ground seeds are the prerequisites for accurate ground filtering [47].According to the prior knowledge that ground points are generally the local lowest in height, ground seeds are often identified by selecting the lowest points within each window, whose size should be larger than the largest non-ground objects in landscapes to prevent ground seeds from being selected in non-ground objects [39].In the existing research, the window shape has generally been set to square.However, such a window shape fails to identify enough ground seeds on irregular terrain [45].To address this problem, we developed a multi-directional narrow window-based method, which can identify ground seeds from more positions and directions.The multi-directional narrow window can accurately select ground seeds in multiple sub-regions corresponding to a square window, increasing the number of ground seeds.Figure 1 shows the conceptual diagrams of ground seed identification by using a traditional square window and a multi-directional narrow rectangle window.By searching the lowest points within each window, the square window identifies ground seeds at only one position (Figure 1a).However, when replacing the square window by three narrow rectangle windows in east-west (Figure 1b) or north-south (Figure 1c) directions, ground seeds at three positions are identified.Further, combining the narrow rectangle windows in both directions increases the number of ground seeds (Figure 1d).Based on the example, we speculate that the narrow rectangle window with infinite directions can identify more ground seeds.Nevertheless, this will inevitably increase the time cost.Therefore, to balance the number of ground seeds identified and the time cost in implementation, we constructed a multi-directional narrow rectangle window that includes east-west, north-south, southeast-northwest and northeast-southwest directions.
In addition to the window shape and direction, we also considered the influence of local terrain.Within each multi-directional narrow rectangle window, the raised terrain is generally the local highest [60].Thereby, ground points with lower heights may be identified as the ground seeds, while those in the raised terrain are mostly omitted (Figure 2a).To solve this problem, we adopted the random sample consensus (RANSAC) line segmentation method (Figure 2b).The RANSAC method has the advantage of being resistant to noise (i.e., non-ground points), and therefore lines are likely to be detected on ground.Ground seeds are identified by selecting the line primitives (Figure 3) [61].

Ground Point Extraction
Ground points were extracted iteratively based on three major procedures, i.e., incorrect ground point elimination, terrain reconstruction and ground point selection.
We eliminated the incorrect ground points using the internal force adjustment of cloth simulation, which simulates the process of cloth reshaping and smooths out areas with large gradients caused by non-ground points [42].As shown in Figure 4, the k-nearest neighbors of a point are selected among the extracted ground points to construct a cloth model, which consists of cloth particles (i.e., ground points) and springs (Figure 4a).We compared the height difference between the two particles that form each spring one by one, and moved the two particles by the same distance in the opposite direction (Figure 4b).The height differences of points before and after internal force operations were calculated, and the points with height differences larger than a threshold were removed.The retained ground points were used to update the terrain, and new ground points continued to be extracted based on the updated terrain.Terrain reconstruction was performed by using the moving least-squares plane fitting method, which is a terrain-adaptive reconstruction method.Different from the horizontal buffers of ground seeds, which cannot characterize steep slopes [48], the moving leastsquares plane fitting method can generate adaptive terrain that is characterized by locally fitted planes [44].As shown in Figure 5a, only points inside the horizontal buffers are recognized as ground points, and other points on steep slopes are ignored due to lying outside the horizontal buffers (red rectangles).By adopting the moving least-squares plane fitting method, the locally fitted planes are closer to the reality, thereby the ground points on steep slopes are correctly labeled (points inside the ellipses). .

Implementation
Figure 6 shows the workflow of the proposed method for filtering airborne LiDAR data in forested environments.There are three major steps, including data preprocessing, ground seed identification and ground point extraction.The detailed description of each step are as follows.Step 1: Data preprocessing Data denoising: the LiDAR point clouds include outliers due to LiDAR system errors and multipath reflex [62].These outliers may be misidentified as ground seeds because they may also have low height.They negatively affect ground point extraction and thus reduce filtering accuracy.We removed outliers using a statistics-based method.A height frequency histogram of the point cloud was constructed, and then points in the tails of the histogram distribution were eliminated [43].Finally, non-removed and falsely removed outliers generated by the automatic method were manually corrected.
Data gridding: the LiDAR point cloud is massive and has no adjacency relationship, which limits the efficiency of subsequent ground seed identification because it involves the selection of neighboring points.To solve the problem, the point cloud was organized into the grid composed of cells.Only the lowest point remained in each cell, since the point was more likely to be ground seeds than other points [28].The adjacency relationship between cells was determined according to their indexes (id) using Equation (1): where int is the operation keeping only integer bits of a number; x min and y min are the minimum x and y coordinates of the point cloud, respectively; (x, y) and (r, c) are the x and y coordinates, and the row and column coordinates of a point from the point cloud, respectively; cs is cell size; and c total is number of columns.
Step 2: Ground seed identification Window cell extraction: a window was slid over the grid to identify ground seeds cell by cell.The cells within the window in four directions were extracted using Equation (2): where Id north-south , Id southeast-northwest , Id southeast-northwest and Id northeast-southwest represent the indexes of cells within the window in east-west, north-south, southeast-northwest and northeast-southwest directions, respectively; and i is the number of offset cells.
Lowest point calculation and line segmentation: the points corresponding to all cells within the window in each direction were extracted.Based on the extracted points, lowest point calculation and RANSAC line segmentation were performed, and lowest points and line segments were regarded as ground seeds.The ground seeds and other points were labeled as ground and unclassified points for the point cloud, respectively.
Step 3: Ground point extraction Incorrect ground point elimination: the cloth models were constructed based on ground points, and the height of each ground point was adjusted by internal force operations.The height differences before and after internal force adjustment were calculated for each ground point.The attributes of the ground points were modified as unclassified points if their height differences were greater than a threshold.
Terrain reconstruction: the local terrain corresponding to each unclassified point was reconstructed by the moving least-squares plane fitting method based on the k-nearest ground points.
Ground point selection: we calculated the height of each unclassified point to the local terrain.The unclassified points were marked as ground points if their heights were less than a threshold.
Incorrect ground point elimination, terrain reconstruction and ground point selection were repeated until no ground points were found any more.

Experimental Setup
The details of the experiments, including data description, accuracy metrics, comparative methods and parameter settings are given in this section.The experiments were carried out on a laptop computer with 40 GB RAM and an AMD Ryzen 7 5800H with Radeon Graphics @ 3.20 GHz.

Data Description
Airborne LiDAR data in five 300 × 300 m forested sites were used to test the performance of the proposed method.The data in each site were collected using different sensors and settings, as listed in Table 1.The point density of these sites varies from 1.63 to 25.45 points/m 2 .The terrain and vegetation conditions of each site are summarized in Table 2. Various terrain features are included such as gentle slopes, steep slopes, ridges, valleys and break lines.The average terrain slope changes from 18.3 to 33.14 • .Moreover, vegetation status varies greatly.The average canopy cover ranges between 8.74 and 84.45%, and average canopy height changes from 11.5 to 23.61 m.The different point densities, terrains and vegetation conditions make the five forested sites ideal study areas to evaluate the adaptability and applicability of the proposed method comprehensively.Additionally, the reference data were acquired through human interaction.As shown in Figure 7, reference ground and non-ground points were rendered in brown and green, respectively.  "ave" is the average values of height, slope, canopy cover and canopy height, respectively. 2"sd" is the standard deviation of height, slope, canopy cover and canopy height, respectively.°m

Accuracy Metrics
We applied four metrics to assess the accuracy of the proposed method quantitatively, i.e., type I, type II, total errors and kappa coefficient [63,64].A type I error indicates the proportion of ground points being misclassified into non-ground points (Equation (3)).A type II error represents the proportion of the opposite condition (Equation ( 4)).Total error is the proportion of all misclassified points (Equation ( 5)).The kappa coefficient is an alternative measure of the overall classification accuracy that subtracts the effect of chance agreement and quantifies how much better a particular classification is, as compared with a random classification (Equation ( 6)) [39].The four metrics were calculated based on the cross-matrix of filtering results, as shown in Table 3.
Type II error = c c + d (4) Table 3. Cross-matrix of filtering results.

Reference
Ground points a b Non-ground points c d

Existing Methods Applied to Do Comparison
Three well-known ground filtering methods, namely maximum slope filter (MSF) [22], progressive morphology filter (PMF) [27] and cloth simulation filter (CSF) [42], were selected to do a comparison with the proposed method.MSF is a typical slope-based ground filtering method, which extracts ground points by calculating the slope differences between the points and their neighbors.We implemented MSF using C++ language.PMF is a modified morphology-based method.This method removes non-ground points using the open operations with multi-scale windows.It was implemented through C++ language and point cloud library (https://pointclouds.org/ (accessed on 15 November 2022)).CSF is a famous surface-based filtering method developed in recent years, which identifies ground points by simulating the physical process of cloth touching terrain.CSF was executed in CloudCompare software (https://www.danielgm.net/cc/(accessed on 15 November 2022, v2.11.3)).

Parameter Settings
The proposed method has four key user-defined parameters, namely, cell size (cs), window size (ws), ground point identification height (h gi ) and incorrect ground point elimination height difference (h gr ).All parameters use the same settings in all sites, which can demonstrated the generalizability of the proposed method.Parameter cs controls the level of detail of the initial terrain.The smaller the cs, the higher the level of detail of the initial terrain, but it leads to higher time cost and invalid selection of ground seeds.We set the parameter as 1 m, considering that the terrain change within each square meter is not significant.Parameter ws is the extent for identifying ground seeds, which should be larger than the largest non-ground object in a landscape to prevent the ground seeds from being located in the non-ground objects.It was set to 10 m, which can accurately identify ground seeds in each site.Parameter h gi determines the ground point extraction.This parameter was set to 0.5 m empirically, considering that non-ground objects are usually higher than 0.5 m relative to terrain.Parameter h gr controls the removal of incorrectly extracted ground points.This parameter was set to 0.8 m empirically.

Results of the Proposed Method
Figure 8 shows the digital terrain models (DTMs) and the 3D transects of the proposed method.Details of the comparison illustrated that various terrain features were completely preserved, such as the gentle slopes in Site 1 (Figure 8a), valleys in Site 2 (Figure 8b), ridges in Site 3 (Figure 8c), break lines in Site 4 (Figure 8d) and steep slopes in Site 5 (Figure 8e).Meanwhile, vegetation with different cover and height values was effectively filtered out.However, the proposed method tended to misclassify the ground points on highly steep slopes as non-ground points, as denoted by the blue ellipses in Figure 8b,d.Table 4 shows the type I, type II, total errors and kappa coefficients of the proposed method in five selected forested sites.The proposed method achieved low type I errors in all sites, indicating that most ground points could be correctly extracted and thus the terrain was fully preserved.The type II errors of the proposed method were large (>10%) for Sites 4 and 5.This was not due to a limitation of the proposed method, but because the number of non-ground points was small, and misclassification of only a few non-ground points produced a large type II error.The average kappa coefficient and total error of the proposed method were 88.51% and 4.22%, respectively, with standard deviations of 6.74% and 2.25%, respectively.It indicated a good applicability and availability in diverse terrain and vegetation conditions. 1 "ave" represents the average value of four accuracy metrics, respectively. 2"sd" represents the standard deviation of the four accuracy metrics, respectively.

Comparisons between the Proposed Method and Existing Methods
The performance of the proposed method was further evaluated by comparing it with three well-known filtering methods, i.e., MSF, PMF and CSF. Figure 9 shows the ground filtering results of MSF, PMF, CSF and the proposed method compared with benchmark points in Site 4, where various complex terrain features were included, such as break lines, steep slopes and ridges.The visual assessment revealed that the proposed method was robust compared with MSF, CSF and PMF in terms of preserving break lines, steep slopes and ridges, although the ground points on highly steep slopes were still not extracted accurately by the proposed method, as shown with blue ellipses in Figure 9b-f.On average, the proposed method had the highest kappa coefficient of 88.51% and the smallest total error of 4.22% across all sites (Figure 10a,b).This illustrated that, under various forested environments and point densities, the proposed method had higher effectiveness and robustness than other existing methods.The type I errors of the proposed method were all below 5% in each site (Figure 10c).This meant that the proposed method could protect terrain better than the comparative methods.The proposed method obtained the optimal type II errors in three sites, and the results of the proposed method in the remaining sites were comparable to PMF and CSF (Figure 10d).This indicated that the performance of the proposed method was superior in terms of removing non-ground points.For the purpose of comparing the time consuming of the proposed method and the other three methods, we recorded their runtime in the five forested sites.Table 5 gives the runtime of different ground filtering methods in each site.MSF, PMF, PMF and the proposed method resulted in the average runtimes of 21.93 s, 61.41 s, 16.6 s and 19.26 s, respectively.The results indicated that the efficiency of the proposed method was acceptable due to the runtime being comparable to the fastest ground filtering method.

Discussion
Given the limitations of existing methods for ground filtering in forested environments with complex terrain and dense vegetation, we proposed an improved surface-based filter based on a multi-directional narrow window and cloth simulation in this study.The proposed method has two main contributions, as discussed in the Introduction.Experimental results in five selected forested sites proved that the proposed method could accurately separate ground points from non-ground points in different forested environments.Meanwhile, the proposed method performed better than the classical methods involving the slope-based, mathematical morphology-based and surface-based methods.Accordingly, we want to discuss three questions as follows.
(1) Is the proposed method effective for performing ground filtering?
Based on the analysis in Section 3.2, the effectiveness of the proposed method has been proven by evaluating its filtering results in five forested sites and doing comparisons with three classical filtering methods.However, the accuracy metrics were calculated based on the final filtering results.Here, we aim to discuss whether each contribution helped to improve the effectiveness for performing ground filtering in forested environments.
The first contribution of the proposed method was the improvement of ground seed identification via the synergistic application of a multi-directional narrow window and RANSAC line segmentation method.Figure 11 shows the ground seeds identified by performing different procedures.Figure 11a displays the benchmark ground points of Site 4. By searching the local lowest points within square windows, we just identified limited ground seeds.Thereby, the characterized terrain was relatively coarse and omitted many details (Figure 11b).The application of multi-directional narrow windows increased the number of identifying ground seeds, based on which, more terrain details were characterized (Figure 11c).By further adopting the line segmentation method, the completeness of ground seeds on raised terrain was further enhanced, as denoted by the ellipse in Fig- ure 11d.The quantitative assessment indicated that the kappa coefficients reached 74.1%, 76.43% and 77.53% when using a square window, a multi-directional window and adopting the line segmentation method, respectively.This indicated that the improvement of ground seed identification was helpful for performing ground filtering.The second contribution of the proposed method was the improvement of ground point extraction, which iteratively eliminated incorrect ground points and adaptively reconstructed terrain.Figure 12 shows the filtering results of performing different procedures.Figure 12a,b shows the 3D transect position in Site 4 and the benchmark filtering results, respectively.The incorrect ground points were significantly reduced, as denoted by the red ellipses in Figure 12b,c,e.Besides, the ground and non-ground points on steep slopes were distinguished more accurately due to adaptive terrain reconstruction improvement, as denoted by the blue ellipses in Figure 12b,d,e.The kappa coefficients of the three tests were 71.83%, 75.84% and 77.53%, respectively.The qualitative and quantitative results demonstrated that the improvement of ground point extraction was effective for performing ground filtering.
(2) Why is the proposed method effective for performing ground filtering?
In this study, we evaluated the effectiveness and robustness of the proposed method by comparing it with three well-known filtering methods, i.e., MSF, PMF and CSF.The three methods separately belong to the slope-based, morphology-based and surface-based ground filtering methods.The comparative results were illustrated in Section 3.2.2.Here, we aim to answer this question by discussing how they worked differently.Specifically, MSF identified ground seeds using square windows, and then extracted ground points based on the slope differences between the points and the terrain, which consisted of local horizontal planes.Different from MSF, the proposed method obtained higher quality ground seeds due to the application of a multi-directional narrow window, line segmentation and internal force adjustment of cloth simulation, as described in Section 2. In addition, the adaptive terrain for ground point extraction could be reconstructed by the moving least-squares plane fitting method.Thereby, the improvements made our method achieve better results (Figures 9 and 10).PMF tended to misclassify raised terrain as non-ground objects (Figure 9).Inaccurate referencing in ground point extraction led to poor filtering results on raised terrain.Compared with PMF, the proposed method provided a more accurate reference on raised terrain, where ground seeds were adequately identified by the line segmentation method (Figure 11d).Our method worked significantly better on raised terrain (Figure 9).CSF may have obtained inaccurate filtering results (Figures 9 and 10), due to the following two reasons.The cloth with fixed hardness may be not have been applicable for identifying ground seeds accurately in different areas of the landscape containing multiple terrain features.In addition, CSF extracted ground points based on the terrain composed of local horizontal planes.The proposed method could identify ground seeds as completely as possible on multiple terrain features, and the reconstructed terrain was terrain-adaptive, thus more accurate ground filtering results were obtained (Figures 9 and 10).Overall, these contributions made the proposed method more accurate and robust to various terrain and vegetation features.
(3) What improvements are needed in the proposed method?
The proposed method can accurately filter out vegetation points with different canopy coverage and height, and completely preserve various terrain features (such as gentle slopes, steep slopes, ridges and break lines).However, the method still has room for improvement in reducing the errors of ground points being misclassified as non-ground points on highly steep slopes (Figure 8b,d).The terrain had a slope close to 90 • , exhibiting a similar appearance to non-ground objects (such as building facades).This resulted in the ground seeds on the terrain not being adequately identified based on the assumption that ground seeds were the local minimum.The reference terrain constructed based on insufficient ground seeds was coarse, causing ground points to be misclassified as non-ground points.In the future, we will focus on the identification of highly steep slopes, and design a special method to identify ground seeds on the terrain to improve the filtering accuracy.

Conclusions
Ground filtering in forested environments with complex terrain and dense vegetation has been a challenge.To overcome this challenge, we proposed an improved surface-based filter for airborne LiDAR point clouds.The improved filter used a multi-directional narrow window to select ground seeds, which could be identified in more locations and directions than the common square window.Moreover, the ground seeds included not only the lowest points but also line segments within the windows, enhancing the integrity of the ground seeds on raised terrain.The two improvements in the ground seed identification step ensured that the ground seeds were identified as completely as possible on various terrain details, which provided a detailed basis for ground point extraction.The internal force adjustment of cloth simulation was applied to eliminate incorrectly extracted ground points, ensuring the accuracy of the terrain being determined in each iteration.In addition, the moving least-squares plane fitting method was adopted to reconstruct terrain, which could enhance the terrain adaptability.Finally, ground points were extracted iteratively based on the continuously refined terrain, assuring the completeness of ground points.These improvements in the ground point extraction step ensured that ground points were extracted accurately and completely.
We compared the proposed method with three types of classical ground-filtering methods (including slope-based, mathematical morphology-based and surface-based ground filtering methods) in five forested sites containing various terrain and vegetation conditions.The comparison results showed that the proposed method not only preserved terrain details more completely, but also filtered out vegetation points more accurately.Additionally, the proposed method obtained the lowest average total error and standard deviation across all sites, which demonstrated the effectiveness and robustness of the proposed method.Therefore, the proposed method can provide an important reference in airborne LiDAR data processing for forestry applications.

Figure 1 .
Figure 1.Conceptual diagrams of ground seed identification by using different windows: (a) square window; (b) narrow rectangle window in east-west direction; (c) narrow rectangle window in north-south direction; (d) multi-directional narrow rectangle window.Parallelogram boxes represent windows, and red pentagrams are ground seeds that are identified by selecting the lowest points within the windows.

Figure 2 .
Figure 2. Ground seed enhancement with line segmentation.Ground seeds identified only using the method (a) without and (b) with line segmentation.Ground seeds can be supplemented on raised terrain, where it is difficult for ground seeds to be identified by selecting the lowest points within the windows.Black lines and red pentagrams represent line primitives and ground seeds, respectively.

Figure 3 .
Figure 3. Ground seed identification on raised terrain by using the RANSAC line segmentation method.Brown points, green points, red points and black lines represent ground points, vegetation points, ground seeds and line primitives, respectively.

Figure 4 .
Figure 4. Schematic illustration of (a) cloth model and (b) cloth simulation.

Figure 5 .
Figure 5. Ground point extraction based on the terrain consists of (a) horizontal and (b) locally fitted planes.The ground points on the steep slope can be correctly recognized based on the locally fitted planes, as shown in the ellipses.Red pentagrams, black points and red rectangles represent ground seeds, ground points and terrain buffers for extracting ground points, respectively.

Figure 6 .
Figure 6.Workflow of the proposed method for filtering airborne LiDAR data in forested environments.

Figure 7 .
Figure 7. LiDAR point clouds of five forested sites: (a) Site 1, (b) Site 2, (c) Site 3, (d) Site 4 and (e) Site 5. Ground and non-ground points were colored brown and green, respectively.

Figure 8 .
Figure 8. DTMs of the proposed method in all sites: (a) Site 1, (b) Site 2, (c) Site 3, (d) Site 4 and (e) Site 5.The red lines indicate the positions of cross sections, and the content inside the blue ellipses is the terrain details ignored by the proposed method.

Figure 9 .
Figure 9. Qualitative comparison of ground filtering results in Site 4. (a) The 3D transect position (white line) in Site 4. The 3D transects of ground filtering results obtained by (b) human interaction, (c) MSF, (d) PMF, (e) CSF and (f) proposed method.Brown and green points represent ground and non-ground points, respectively.The content inside the blue ellipses indicates the terrain details ignored by the proposed method.

Figure 10 .
Figure 10.Accuracy assessment of four filtering methods in five forested sites: (a) kappa coefficient, (b) total error, (c) type I error and (d) type II error.

Figure 11 .
Figure 11.Validation results for the contribution in the ground seed identification step.(a) Benchmark ground points.The ground seeds identified through selecting the lowest points of the point clouds within (b) square and (c) multi-directional narrow windows.(d) The enhanced ground seeds after line segmentation.Ground seeds were identified more completely by multi-directional narrow windows, and the line segmentation could further improve the completeness of ground seeds on raised terrain.The content inside the ellipses indicates the differences in ground seeds on raised terrain.

Figure 12 .
Figure 12.Validation results for the contribution in the ground point extraction step.(a) The 3D transect position (white line) in Site 4. The 3D transects of ground filtering results obtained by (b) human interaction and the methods (c) without incorrect ground point elimination and adaptive terrain reconstruction, (d) with incorrect ground point elimination, and (e) with incorrect ground point elimination and adaptive terrain reconstruction.Ground points were extracted more accurately after incorrect ground point elimination, and the adaptive terrain reconstruction could further improve the accuracy of ground filtering on steep slopes.The content inside the ellipses indicates typical filtering errors.

Table 1 .
Data collection summaries of the five forested sites.

Table 2 .
Descriptions and statistics of the five forested sites.

Table 4 .
Errors and kappa coefficients of the proposed method in all sites (%).

Table 5 .
Runtime of four filtering methods in five forested sites (s).