DENSITY-BASED METHOD FOR BUILDING DETECTION FROM LiDAR POINT CLOUD

: In this paper, a new building detection method based on a density of LIDAR point clouds is proposed. In this method, trees, vegetation, and any objects that have points in a vertical plane or column are removed. In the density-based method, a cube is utilized to calculate the density therein. For each point, the cube is used to determine the number of neighbouring points. The density is calculated in two cases: 3D and 2D space. In 3D space, the volumetric density is calculated using the cube. In 2D space, all points are projected onto the horizontal plane, and the surface density is calculated using a square. Next, the two densities are compared and the points with different values in both cases are removed. The method leads to promising results in the removal of vegetation and trees. Moreover, the results achieve more than 94% completeness and correctness at the per-area level.

One of the most important research fields in remote sensing and photogrammetry is building detection.In general, detecting the building from the LiDAR data depends on the removing of the other objects (Sajadian and Arefi, 2014, Awrangjeb and Siddiqui, 2017, Mahphood and Arefi, 2020b).The main objects that pose the greatest challenge to building detection are vegetation and ground.These objects have the greatest size in the dataset.For the removal of ground points, some studies have used DTM for this purpose (Dorninger and Pfeifer, 2008, Awrangjeb and Fraser, 2014, Awrangjeb et al., 2014, Awrangjeb and Siddiqui, 2017).Another study used a threshold as a flat plane.It is used if the region is flat (Sajadian and Arefi, 2014).However, for mountainous areas, the previous method cannot be carried out.Other studies have used commercial software (Ao et al., 2017).Some methods use the morphological method, which is not affected by the area type (Arefi andHahn, 2005, Cheng et al., 2013).Neidhart and Sester (2008) used a mathematical model (polynomial).Mahphood and Arefi (2020b) detected the buildings without handling the ground point filtering issue using the virtual first and last pulse method.For vegetation removal, most of the methods use features that are extracted using textural and spatial information to remove the vegetation points.These features are flatness, distribution of neighbourhood points, curvature, eigenvalue features, a variance of normal directions, etc. (Alharthy and Bethel, 2002, Forlani et al., 2006, Ekhtari et al., 2008, Maltezos and Ioannidis, 2015, Hui et al., 2016, Mahphood and Arefi, 2020b).The information of pulses has been used to remove the vegetation from LiDAR data (Alharthy and Bethel, 2002, Vögtle and Steinle, 2005, Tarsha-Kurdi et al., 2007, Niemeyer et al., 2011, Shiravi et al., 2012, Hui et al., 2016, Mahphood and Arefi, 2020b).This paper proposed a novel method to detect the buildings from the LiDAR point cloud by removing the vegetation, trees, and objects that have points located in the imaginary column.The proposed method used a volumetric shape (cubic) to detect the density for each point in two cases: 3D and 2D space.Depending on the density difference between the two cases, the points are removed or retained.

THE PROPOSED METHOD
Figure 1 explains the workflow of the proposed method.At first, the noise points are removed.Then, the ground points are filtered by the tornado method.After that, the vegetation and trees are removed by the density method.Finally, the resulting buildings are refined using some other filters.

Pre-processing
The noise points should be removed because they significantly affect the results of the proposed method, which depends on the points located in the imaginary column; therefore, the accuracy will be affected if the noise points are used in the other processing steps.The CloudCompare software is utilized to implement this step.It utilizes the statistical outlier removal method, which averages the distances between adjacent points to remove the noise points.Ground point filtering is considered one of the most important challenges in building detection because the ground points have the most significant number of points.This paper uses the tornado method for this purpose (Mahphood and Arefi, 2020a).This method simulates a realistic tornado for removing objects from the ground.A vertical cone models the tornado so its vertex is down and its base is up (Figure 2(a)).The cone moves on the ground surface using a series of points selected as vertices.Points that are inside the cone are classified as non-ground points and removed (Figure 2

Density-Based Method
After the previous step, the remaining objects are trees, vegetation, and small objects.For filtering these objects, the density of points in 3D and 2D space is used.First, the neighborhood density of each point is calculated using a cube (with dimensions: length l, width w, and height h as shown in Figure 3(a)) in the three-dimensional space (volumetric density).Then, these points are projected on a horizontal x-y plane, and the density of the points is calculated using the cube (surface density as shown in Figure 3(b)).Then, the points of the walls, power lines, trees, and vegetation are removed by comparing the two densities.In other words, all objects with points in the vertical plane or vertical column will be removed.Thus, the remaining points are related to the building and some small objects, which will be handled in the next step.
After obtaining the preliminary detected buildings, several sparse points have not been removed.Furthermore, the building outlines are affected due to the findings of the density method in the vegetation removal step.As a result, three filters are used to improve the results.

Building Boundary Refinement:
The points of the building boundaries are removed because of using the cubic for vegetation removal.Thus, the detected buildings should be refined.Therefore, the nearest neighbor method adds points from the removed points.Where the used threshold of the nearest neighbor is equal to half the cube width.

Area Threshold:
A few tiny regions are leftover from plants or objects that aren't recognized as buildings.As a result, an area threshold Ta is utilized to eliminate these regions.

Length Threshold:
Because of the use of the tornado method to filter the ground points, ground regions related to longitudinal objects, such as rivers, are not filtered well.As a result, a length threshold Tl is used to remove these regions.

Eigenvalue-Based
Feature: Some trees and vegetation are impenetrable.Therefore, their points cannot be removed using the density method.To handle this issue, the eigenvaluebased feature is utilized.Where the eigenvalues (λ1, λ2 and λ3) are extracted.The feature λ3 is used for this step (Ao et al., 2017, Mahphood andArefi, 2020b).

Data Description
To evaluate the results, the LiDAR point cloud of the 2015 IEEE GRSS dataset is used (Figure 4).The dataset contains an urban and harbour area in Zeebruges, Belgium.The point cloud density is 65 points/m².In other words, the point spacing is about 10 cm.

Evaluation System
The qualitative and quantitative assessments are described in this section.For the qualitative assessment, the detected buildings and other detected objects will be discussed visually.For the quantitative assessment, the metrics of CP completeness (%), CR correctness (%), and Q quality (%) (equations ( 1)-( 3)) are computed for the results on a per-object and per-area level (Rutzinger et al., 2009).Unfortunately, there is no reference data for the dataset.Thus, reference data is extracted manually using an orthophoto for the same areas.The main purpose of the density-based method is to remove vegetation and tree points.Therefore, the effect of the horizontal dimensions of the cube on the count of the removed points should be investigated.To evaluate these parameters and select the best values, nine sets of tree points are extracted manually from the data (Tr1,Tr2,Tr3,Tr4,Tr5,Tr6,Tr7,Tr8,and Tr9).After that, the density-based method is used for different width values (or length), and the removed points percentage is computed for each value and each set.The method is implemented for nine width values, so we start with a width equal to the mean density D. It is increased by the amount of density until we reach ten times the density.
Obviously, if the width increases, the removal percentage will increase (Table 1).The lowest width should be selected so that this width has a high removal ratio.The width should also be small because the greater width will affect the height (this effect is analyzed in the next step).Also, the removal percentage is higher for greater width.Therefore, the width at which the percentage is at least 99% is selected to ensure the best results.
From Figure 6, it can be seen that widths equal to 2.5D and more are the best widths that guarantee the previous percentage.Thus, a distance of 3D is utilized to ensure the best results.The results of mean values of the groups' results are shown in Table 1 and Figure 6(b).These results prove that this method has promising results for removing vegetation points from the LiDAR data.At the same time, this process is an essential step for detecting buildings.

Cube Height Analysis:
This method may remove roof points for the high-slope building roofs (Figure 7).From Figure 7(a), we see roof points inside the cube in the 2D space.But they are outside the cube in the 3D space (blue points).Therefore, the roof points will be removed.To handle this issue, the relationship between the cube height, cube width, and the largest inclination angle θ of the roof is found.From Figure 7(b), the relationship between the previous parameters can be expressed by equation ( 4) so that the roof points are not removed.The angle θ is assumed according to the knowledge of the roof slope of the existing buildings where it cannot be calculated accurately.
where θ = largest inclination angle of the roofs.hmin = the minimum height of cube.W = cube width. is the building roof.The red, green, and blue points represent the interest, the neighborhood, and the new points in 2D space, respectively.

Overall Results and Evaluation:
The results of the proposed method for detecting the building are shown in Figure 8, with some advantages and disadvantages.
For qualitative assessment, it can be seen from Figure 8 that small, large, residential, and complex buildings (Figure 8(f)) are successfully detected.According to Figure 8(f), the method detects the buildings that contain sloping, flat, and hipped roofs.Also, the buildings which have one or a block of buildings are detected (Figure 8(f)).This is an advantage of our method.Also, we see that all trees and vegetation are removed successfully using the density-based method.As an initial vision, the results are excellent, especially with regard to removing vegetation points and detecting different shapes of buildings.Our method achieves promising results.However, some problems arose during the procedure.
Some buildings (Figure 8(e)) are not fully detected because trees surround some parts of the building.These parts are occluded areas that are not detected by this method.Also, we note from Figure 8(f) that the building boundaries (inner and outer) that have height displacement were removed.This is because the points of the outer and inner walls and the neighbouring points were removed.Where the density of each point was different between 3D and 2D space.For vegetation, some vegetative walls are not removed, shown in Figure 8(c).They have a flat surface and are non-penetrated.The cars are removed.But some are not removed (Figure 8(d)).Because they are behind each other and considered as a large object.Figure 8(b) shows that some ground points are not filtered.This problem is due to the ground filtering step.The cone (tornado) did not remove the river points completely.This is because these points have a high slope.
For quantitative assessment, the metrics: completeness, correctness, and quality are computed and listed in Table 2 for the IEEE 2015 data.From Table 2, our method obtains 94.17% completeness, 94.66% correctness, and 89.44% quality at the perarea level and 91.53% completeness, 82.63% correctness, and 76.75% quality at the per-object level.Also, it obtains the completeness of 100%, correctness, and quality of 96.4% for the buildings whose areas are larger than 50 m 2 .As a result, the density-based method provides promising results, especially at the per-area level, where the completeness and correctness are more than 94%.Also, these results provide promising results for completeness metrics for all levels.Also, these results are very good for buildings whose areas are larger than 50 m 2 .Correctness is relatively low due to the presence of unfiltered ground points.2. The results of the building detection.

Parameters Analysis:
There are two important parameters that affect the results.The first one is the cube width.This parameter was analyzed previously.The second one is the slope angle of the building roof to calculate the cube height.This angle is set to 70 degrees.The area threshold Ta is set to 9 m 2 , as most buildings in the IEEE 2015 data are interconnected and large.For the length threshold, Tl is set to 200 m, as most buildings are less than 100 m.The eigenvalue λ3 shows the spatial difference in the vertical direction.Thus, √ 3 is used as the standard deviation and set to 5 cm.

CONCLUSION
A novel method has been proposed for tress and vegetation removal by using the density inside a cube in 2D and 3D space to detect the buildings from the LiDAR point cloud.The densitybased method used a cube with dimensions related to the point cloud density and the maximum roof slope.The results achieve the completeness of 94.17%, correctness of 94.66%, and quality of 89.44% for the per-area level.Also, the method provides promising results for completeness metrics for all levels.The small, large, and complex buildings are detected well.In other words, the type or size of roofs does not affect the results of the proposed method.Also, the trees and vegetation are removed perfectly.This is an essential step for the methods of building detection.
Finally, our method is very good for detecting buildings with different shapes, sizes, and heights.But the building boundaries are affected slightly.Also, the method cannot extract the occluded areas of the buildings surrounded by trees.This issue is considered the major disadvantage of our method.

Figure 1 .
Figure 1.Workflow of the proposed method.

Figure 2 .
Tornado method.a) The vertical cone, and b) the procedure of point removal.In(Mahphood and Arefi, 2020a) Density-based method.a) The used cube dimensions to detect the neighborhood of each point, b) detecting the point neighborhood in 3D and 2D space.The red and green points represent the interest points and the points inside the cube, respectively.

Figure 5 .
FP, and FN indicate a true positive, a false positive, and a false negative, respectively.3.3 Density-Based Method Evaluation3.3.1 Horizontal Dimensions Analysis of the Cube (length l and width w):To analyze the horizontal dimensions of a cube, we see from Figure5(a) that the minimum width and length must be greater than the point cloud density.Because if the dimensions are less than the density, the density inside the cube is not found at any point (red point), and the method becomes meaningless (Figure5(b)).Also, in this cube, the length is always equal to the width.The cube dimensions are greater than density (a) or less than density (b).The green points are the points inside the cube.The black points are the points outside the cube.

Figure 6 .
Figure 6.The relationship between the cube width and the removal percentage.a) Results of nine tree sets, b) Average results.

Figure 7 .
Issue of the building roof with a steep slope.a) The difference between the number of neighborhood points in the 3D and 2D space, b) The relationship between the minimum height, width, and the inclination angle of the roof.The red line