Photon counting laser radar data denoising method based on point cloud main direction

Abstract

The invention discloses a photon counting laser radar data denoising method based on a point cloud principal direction. The method comprises the steps of S1, performing coarse denoising based on an elevation statistical histogram; s2, de-noising the data processed in the step S1 by adopting a photon data de-noising method based on a point cloud main direction; and S3, residual noise points of the data processed in the step S2 are removed based on an improved local statistical distance algorithm, and effective separation of signal photons and noise photons is realized. By calculating the principal direction characteristics of the point cloud space neighborhood, noise filtering is realized by using the principal direction difference between signal photons and noise photons, that is, starting from the point cloud neighborhood characteristics directly, when the signal photons and the noise photons are similar in density, distance or elevation, the traditional statistical method is not used any more, and the method is simple and practical. And based on the spatial distribution difference of noise and signal photons, effective denoising can be realized by using the difference of main directions in the neighborhood.

Description

Technical Field

[0001] The present application belongs to the technical field of denoising methods, and in particular, relates to a photon counting laser radar data denoising method based on the main direction of a point cloud. Background Art

[0002] Since photon counting lidar has the characteristics of high detection sensitivity and weak emission pulse signal, a large amount of solar radiation noise, atmospheric scattering noise and instrument noise will also enter the sensor, causing the returned photon signal to contain not only the required pulse signal, but also high background noise. Effective denoising is the basis and key to the application of ICESat-2 photon counting lidar data. It is difficult to carry out subsequent research on ICESat-2 data without denoising. In recent years, domestic and foreign scholars have carried out a lot of research on ICESat-2 photon counting lidar data denoising methods, and these research methods can be roughly summarized into three categories.

[0003] The first type is denoising based on image processing technology. This method first converts the profile point cloud into a raster image, and then uses image processing methods such as edge detection, median filtering, and region detection to identify noise, thereby indirectly achieving point cloud denoising. Although this type of method can remove noise photons to a certain extent, it will cause point cloud information loss during the point cloud rasterization and processing process.

[0004] The second type is denoising based on local statistical features. Noise photons and signal photons are different in spatial distribution, such as local distance, histogram, etc. Statistical algorithms can calculate the local information of each photon point cloud, and then set a certain threshold according to the difference between noise photons and signal photons to achieve denoising. This type of algorithm takes into account the difference in spatial distribution of noise photons and signal photons, and can separate noise photons from signal photons to a certain extent, but the selection of thresholds is not automated enough, and it is also the key to whether denoising can achieve good results.

[0005] The third category is denoising based on density clustering algorithms. The point cloud density of signal photons and noise photons is different. Generally, the density of signal photons is higher and the density of noise photons is lower. Therefore, there are also a lot of research based on this feature to achieve photon point cloud denoising. At present, there are roughly the following types of density clustering algorithms: photon point cloud denoising algorithm based on OPTICS (Ordering Points To Identify the Clustering Structure), DBSCAN (Density-Based Spatial Clustering of Applications with Noise) density clustering algorithm based on ellipse search shape, denoising method based on particle swarm optimization (PSO), and denoising method based on Bayesian decision theory. of Denoising method. This type of algorithm is basically to improve the traditional density clustering algorithm or use the density clustering algorithm and other The algorithm is combined to achieve photon point cloud denoising. This method is widely used and has high denoising accuracy, but the irregular distribution of noise usually affects the denoising effect.

[0006] It can be seen that there have been a lot of studies on photon counting lidar denoising algorithms, but they are basically based on three methods: rasterizing profile point clouds into images through image processing technology, denoising photon data by counting local features of point clouds, or denoising photon data based on point cloud density characteristics. These three methods still have certain defects, and a new photon point cloud denoising algorithm is urgently needed to make up for the shortcomings of current research. Summary of the invention

[0007] The purpose of this application is to utilize the obvious difference in the spatial distribution patterns of photon noise points and photon signal points, disclose a photon counting lidar data denoising method based on the main direction of the point cloud, and realize the effective separation of signal photons and noise photons.

[0008] The purpose of this application is achieved through the following technical solutions:

[0009] A photon counting laser radar data denoising method based on the main direction of a point cloud, the photon counting laser radar data denoising method comprising:

[0010] S1: coarse denoising based on elevation statistical histogram;

[0011] S2: De-noising the data processed in step S1 using a photon data denoising method based on the main direction of the point cloud;

[0012] S3: For the data processed in step S2, the residual noise points are removed based on the improved local statistical distance algorithm to achieve effective separation of signal photons and noise photons.

[0013] According to a preferred embodiment, step S1 includes: preliminarily determining the elevation range of signal photons by establishing an elevation statistical histogram to achieve coarse denoising of the photon point cloud.

[0014] According to a preferred embodiment, step S1 specifically includes:

[0015] By dividing the grid, the original photons establish an elevation statistical histogram along the track based on the preset window size, and then the peak position of the histogram is used to determine the center of the signal photon;

[0016] Combined with the maximum height of the ground object, a threshold is set based on the center position of the signal photon to establish a buffer zone, and noise photons are filtered out by removing the photon point cloud outside the buffer zone.

[0017] According to a preferred embodiment, step S2 includes: calculating the main direction of the point cloud, obtaining the angle between the main direction and the along-track distance, and using a set angle threshold to achieve noise photon removal.

[0018] According to a preferred embodiment, the process of calculating the main direction of the point cloud includes:

[0019] According to the row and column information of the data, the profile photon point cloud is first converted into a three-dimensional point cloud. After calculating the covariance matrix within the k-neighborhood of the point cloud, the eigenvector corresponding to the maximum eigenvalue is the main direction of the corresponding point cloud.

[0020] According to a preferred embodiment, the noise photon removal process further includes:

[0021] When the surface type is irregular, when the number of points in the neighborhood that meet the threshold exceeds one-third, all photons in the neighborhood are considered to be signal photons.

[0022] According to a preferred embodiment, step S3 includes: searching for the nearest neighbor point through an ellipse and calculating the total distance, and statistically analyzing the frequency histogram of the local total distance to set a threshold to remove residual noise photons.

[0023] According to a preferred embodiment, the total distance is calculated as:

[0024]

[0025] Among them, x represents the distance along the track, h represents the elevation of the point cloud, a represents the semi-major axis value of the ellipse search area, and b represents the semi-minor axis value of the ellipse search area.

[0026] The aforementioned main scheme of the present application and its further options can be freely combined to form multiple schemes, all of which are schemes that can be adopted and claimed for protection in the present application. After understanding the scheme of the present application, those skilled in the art can understand that there are multiple combinations based on the prior art and common knowledge, all of which are technical schemes to be protected by the present application, and they are not exhaustively listed here.

[0027] Beneficial effects of this application:

[0028] Compared with the existing photon point cloud denoising algorithms, the main differences and advantages of the method of this application are: unlike statistical characteristics such as density, distance, and elevation, the main direction characteristics of the point cloud spatial neighborhood are calculated, and the main direction difference between the signal photons and the noise photons is used to filter out noise. That is, starting directly from the point cloud neighborhood characteristics, when the density, distance or elevation of the signal photons and the noise photons are similar, the traditional statistical methods are no longer useful. Based on the spatial distribution difference between the noise and signal photons, effective denoising can be achieved by using the difference in the main direction in the neighborhood. The method has a simple principle, few parameters, and is easy to implement, providing a new way for photon point cloud denoising. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 This is a flowchart of the photon point cloud denoising technology based on the main direction of this application;

[0030] Figure 2 It is a schematic diagram of experimental data Data1;

[0031] Figure 3 It is a schematic diagram of experimental data Data2;

[0032] Figure 4 It is a schematic diagram of experimental data Data3;

[0033] Figure 5 It is the first Sigma Space LiDAR data used for accuracy verification of denoising algorithms;

[0034] Figure 6 It is the second Sigma Space LiDAR data used for accuracy verification of denoising algorithms;

[0035] Figure 7 It is the third Sigma Space LiDAR data used for accuracy verification of denoising algorithms;

[0036] Figure 8 It is the first MATLAS data used to verify the accuracy of the denoising algorithm;

[0037] Fig. 9 It is the second MATLAS data used to verify the accuracy of the denoising algorithm;

[0038] Fig.10It is the third MATLAS data used for accuracy verification of denoising algorithms;

[0039] Fig.11 It is a schematic diagram of k neighboring points of signal points and noise points;

[0040] Fig.12 This is a schematic diagram of extracting the main direction of Data1 data;

[0041] Fig.13 This is a schematic diagram of the main direction extraction of Data3 data;

[0042] Fig.14 is the frequency histogram of the sum of distances of all points;

[0043] Fig.15 This is a schematic diagram of ICESat-2 / ATLASData1 data denoising results;

[0044] Fig.16 This is a schematic diagram of ICESat-2 / ATLASData2 data denoising results;

[0045] Fig.17 This is a schematic diagram of ICESat-2 / ATLASData3 data denoising results;

[0046] Fig.18 This is a schematic diagram comparing the ATL08 data product and the main direction-based denoising algorithm Data2 data results;

[0047] Fig.19 This is a schematic diagram comparing the ATL08 data product and the Data3 data results based on the main direction denoising algorithm;

[0048] Fig. 20 It is a comparison of the results of ATL03 photons with different confidence levels and the denoising algorithm based on the main direction;

[0049] Fig.21 It is the comparison of the denoising algorithm result based on the main direction when the confidence level is 2;

[0050] Fig. 22 It is the comparison between the denoising algorithm result based on the main direction when the confidence level is 3;

[0051] Fig.23 It is the comparison between the denoising algorithm result based on the main direction when the confidence level is 4;

[0052] Fig.24 It is a quantitative evaluation result statistic based on manually annotated verification data. DETAILED DESCRIPTION

[0053] The following describes the embodiments of the present application through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the contents disclosed in this specification. The present application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0054] refer to Figure 1 As shown in the figure, a photon counting lidar data denoising method based on the main direction of the point cloud is shown. The method of the present application first divides the point cloud into grids and constructs an elevation statistical histogram to remove obvious noise photon points. Then, the main direction of the point cloud is calculated to obtain the angle between the main direction and the distance along the track. The set angle threshold is used to achieve precise denoising. Finally, the residual noise points are removed based on the improved local statistical distance algorithm to achieve effective separation of signal photons and noise photons.

[0055] The differences in photon point cloud data are mainly determined by the observation time and terrain characteristics. In order to verify the stability and adaptability of the point cloud main direction denoising algorithm, night and daytime ATL03 data of different terrains are selected for experiments, as shown in Table 1 and Figure 2 , 3 , as shown in Figure 4.

[0056] Table 1 ICESat-2 / ATLAS data used for denoising experiments

[0057]

[0058]

[0059] The satellite-borne photon point cloud MATLAS data and the airborne photon point cloud Sigma Space LiDAR (SPL) data are used to verify the accuracy of the denoising algorithm proposed in the study, because the signal points and noise points of these two types of data have been marked. Among them, MATLAS data is a simulation of the flight data of the Multiple altimeter beam experimental LiDAR (MABEL) by NASA based on the parameter configuration of the ATLAS system on the satellite. It is the data that is closest to the actual satellite situation that can be publicly obtained from the official. Table 2 and Figure 5 , 6 , 7, 8, 9, and 10 show the MATLAS and Sigma Space LiDAR data used in this study to evaluate the accuracy of the denoising algorithm.

[0060] Table 2 SPL and MATLAS data used for accuracy verification in denoising algorithm

[0061]

[0062] The present application provides a method for denoising photon-counting lidar data based on the main direction of a point cloud, comprising the following steps.

[0063] 1. Coarse denoising based on elevation statistical histogram

[0064] By establishing an elevation statistical histogram, the elevation range of the signal photons can be preliminarily determined, and the photon point cloud coarse denoising can be achieved to remove most of the noise photons, greatly reducing the amount of data processing for fine denoising. The steps include: by dividing the grid, the original photons establish an elevation statistical histogram in the along-track direction based on a certain window size, and then use the histogram peak position to determine the center of the signal photon; combined with the maximum height of the ground object, the threshold is set based on the center position of the signal photon to establish a buffer zone, and most of the noise photons are filtered out by removing the photon point cloud outside the buffer zone.

[0065] 2. Photon data denoising algorithm based on the main direction of point cloud

[0066] The rough denoising method based on elevation statistical histogram can remove most of the photon noise points, but there are still many noise points remaining. In order to further remove the noise points, it is necessary to perform fine denoising on them. The study constructed a fine denoising algorithm based on the main direction of the point cloud. The core of the algorithm is to remove noise photons by extracting the local geometric features of the point cloud according to the difference in the distribution of signal photons and noise photons. It includes:

[0067] 2.1 Calculate the main direction of the point cloud

[0068] The photon data profile point cloud only has two-dimensional information. According to the data row and column information, the profile photon point cloud is first converted into a three-dimensional point cloud. The main direction of each point in the point cloud data can be obtained by calculating its covariance matrix within a certain range. If a point in the point cloud data set (P) is point p i (i=1,2,3…n), then point p i and its k-neighborhood ( Fig.11 ) is shown in formula (1). After calculating the covariance matrix in the k-neighborhood of the point cloud, the eigenvector corresponding to the maximum eigenvalue is the main direction of the point.

[0069]

[0070] In the formula, k is p i The number of neighboring points represents the geometric center of the k-neighborhood point, j represents the number of eigenvectors and eigenvalues, e j and λ j Denote the corresponding eigenvectors and eigenvalues ​​respectively.

[0071] 2.2 Extracting the main direction of the point cloud

[0072] After calculating the covariance matrix in the k-neighborhood of the point cloud, the eigenvector corresponding to the maximum eigenvalue is the main direction of the photon point cloud. Signal photons are usually arranged in a regular direction with an upward direction, while the main direction of noise photons is generally chaotic and has no regular pattern. Therefore, denoising can be performed by the difference in the main directions of signal photons and noise photons ( Fig.12 , 13 ).

[0073] Based on this principle, when the angle (θ) between the main direction of the photon and the normal vector (0,1,0) along the track distance direction is almost perpendicular, the photon is considered to be a signal photon. However, there are also special cases, and signal photons can be extracted by two methods: First, when the surface type is irregular, only the photon point cloud when the main direction is perpendicular to the track distance direction is selected as the signal point, there will be a serious lack of signal photons. In order to solve this problem, the study takes the case that when the number of points that meet the threshold in the neighborhood exceeds one-third, all photons in the neighborhood are considered to be signal photons; the second is to observe the angle (θ) between the normal vector (0,1,0) in the main direction and the track distance direction, and adjust the angle threshold to achieve signal and noise separation.

[0074] 3. Photon point cloud denoising based on improved local statistical distance

[0075] After completing the above two denoising, most of the solar radiation noise has been basically removed, but there are still a small number of noise photons below the ground, in the air, near the canopy surface and near the ground. In order to further remove noise points, the study selected an improved local statistical distance algorithm to remove the remaining noise points.

[0076] First, the photon point cloud has obvious differences in the horizontal and vertical directions. The circular search cannot effectively distinguish signal photons from noise photons. The nearest neighbor point is searched through the ellipse and the total distance is calculated (Formula 2). Secondly, the frequency histogram of the local total distance is statistically analyzed ( Fig.14 ), set the threshold to remove residual noise photons.

[0077]

[0078] Where x represents the distance along the track, h represents the elevation of the point cloud, a represents the semi-major axis value of the ellipse search area, and b represents the semi-minor axis value of the ellipse search area.

[0079] Denoising results

[0080] Fig.15 , 16 , 17 are the data denoising results. Fig.15Shows the denoising effect of daytime photon data in a woodland area. Fig.16 The denoising effect of daytime photon data on construction land and water areas is shown. Fig.17 The denoising effect of night photon data in woodlands, bare land and waters is shown. It can be seen that the denoising algorithm based on the main direction can effectively identify signal photons and noise photons, whether it is daytime data or nighttime data, whether in flat areas or steep areas, and whether it is data with high or low signal-to-noise ratio.

[0081] Accuracy Assessment

[0082] The algorithm is evaluated from both qualitative and quantitative aspects to verify its stability and adaptability. The qualitative evaluation mainly includes comparison with the ATL08 algorithm and ATL03 photons with different confidence levels.

[0083] The quantitative evaluation mainly includes the evaluation of manually annotated ICESat-2 / ATLAS data using confusion matrix and overall accuracy (OA); the evaluation of Sigma Space Lidar (SPL) and MATLAS data using three statistical indicators: recall (Recall, R), precision (Precision, P), and the harmonic mean of recall and precision (F) (Formula 3-6). Among them, the recall rate is the ratio of the number of valid signal photons correctly extracted to the total number of original signal photons, and the precision rate is the ratio of the number of valid signal photons correctly extracted to the total number of valid signal photons extracted.

[0084]

[0085]

[0086] In the formula, TP represents the number of signal photons that are correctly identified, TN represents the number of noise photons that are correctly identified, FP represents the number of noise photon points that are mistakenly classified as signal photon points, and FN represents the number of signal photons that are not correctly identified.

[0087] Qualitative Assessment

[0088] Fig.18 , 19 A comparison of the denoising results of the ATL08 data product and the principal direction-based denoising algorithm is shown. Fig.18 This is a partial enlarged picture of Data2. Fig.19This is a partial enlarged image of Data3. The black photon points are the denoising results of the ATL08 algorithm, the green photon points are the denoising results of this algorithm, and the areas marked by red circles and red rectangular boxes are the noise points remaining in the ATL08 denoising algorithm. It can be seen that whether it is daytime data or nighttime data, flat areas or terrain undulating areas, data with low or high signal-to-noise ratio, the denoising results of the denoising algorithm based on the main direction are better than those of the ATL08 denoising algorithm. In particular, from the denoising effect of daytime data, the denoising algorithm based on the main direction is significantly better than the ATL08 denoising algorithm and can more effectively extract signal photons.

[0089] Fig. 20 , 21 , 22, and 23 show the comparison between the main direction-based denoising algorithm and ATL03 photons with different confidence levels, taking the local magnified image of Data1 as an example. Fig. 20 This algorithm is compared with data with medium, high and low confidence (Conf = 2 / 3 / 4). Fig.21 To compare this algorithm with data with low confidence (Conf=2), Fig. 22 To compare this algorithm with the data in confidence level (Conf=3), Fig.23 The algorithm is compared with data with high confidence (Conf = 4). Fig. 20 It can be found that the photons with medium, high and low confidence levels do not contain all signals, such as Fig. 20 In the black circle area, the denoising results based on the main direction are basically consistent with the photons with medium, high and low confidence levels in the ATL03 data. Comparing the denoising results based on the main direction with the photons with different confidence levels, it is found that there is a certain inconsistency between the denoising algorithm based on the main direction and the photons with low confidence levels, such as Fig.21 The middle black circle area is because some of the photons with low confidence are noise photons near the canopy surface and near the ground. Fig. 22 and Fig.23 It can be seen that the denoising results based on the main direction are highly consistent with the data with medium and high confidence levels, indicating that the denoising results of the denoising algorithm based on the main direction are reliable.

[0090] Quantitative evaluation

[0091] (1) Quantitative evaluation of manually annotated ICESat-2 / ATLAS data

[0092] Due to the lack of ground-truth data, the verification data were manually annotated. By comparing the manual interpretation with the denoising results, the points below the terrain line and the points that are obviously discrete in space are recorded as noise (0), and the rest are marked as signals (1). In order to minimize the subjective error of manual interpretation, the statistical average of the three interpretations is taken as the true value.

[0093] Taking Data1 as an example, according to Table 3 and Fig.24 It can be seen that the accuracy of secondary denoising is (18620+41337) / 63606=94.26%. The secondary denoising results of the three groups of experimental data are all better than 90%, with the highest reaching 97.17%. The tertiary denoising results are all better than 94%, with the highest reaching 97.43%. Data2 has low accuracy in both secondary and tertiary denoising, because the data is daytime data, the signal-to-noise ratio is low, the visual distinction of the data is poor, and the data also has construction land and water areas with serious noise density blocks, so the overall accuracy is slightly poor. Data3 has high accuracy in both secondary and tertiary denoising, all above 97%, because the data is nighttime data, the signal and noise are quite different in arrangement and distribution, the distinction is good, and the overall accuracy is high.

[0094] Table 3. Quantitative evaluation results of confusion matrix based on manually annotated validation data

[0095]

[0096] (2) Quantitative evaluation of SPL and MATLAS data

[0097] It can be seen from Table 4 that when the SPL data noise level is '0.5MHz', the denoising algorithm based on the main direction can well remove noise photon points. The reason may be that at low noise levels, the density difference between noise photon points and signal photon points is significant, and the main direction is easy to distinguish. However, when the noise level is '5MHz', the R, P and F values ​​are greatly reduced. The reason may be that at high noise levels, the difference between the density of noise photon points and the density of signal points is small, and some noise points are distributed inside the vegetation canopy, and the main direction is difficult to distinguish, making it difficult to remove noise points. For MATLAS data, the denoising algorithm based on the main direction can well remove noise photon points and obtain higher R, P and F values. In general, the average R value of the denoising algorithm based on the main direction is 0.940, the P value is 0.941, and the F value is 0.939, and the denoising effect is good.

[0098] The algorithm can process data with different signal-to-noise ratios during the day and at night, and the denoising accuracy can reach more than 96% in various terrain structures, especially for night data, the denoising accuracy can reach 97.43%. The denoising results of the algorithm are consistent with the photons with medium, high and low confidence levels (Conf=2 / 3 / 4) of ATL03, and the denoising accuracy is better than that of ATL08 product data. Based on the quantitative evaluation of SPL and MATLAS data, the average values ​​of R, P and F are 0.940, 0.941 and 0.939, respectively.

[0099] The present invention combines the denoising algorithm of the main direction of the point cloud to achieve a good denoising effect, can process data with different signal-to-noise ratios during the day and at night, and can achieve a denoising accuracy of more than 96% in various terrain structures. The denoising results of the present invention are consistent with the photons of ATL03 with medium, high and low confidence (Conf=2 / 3 / 4), and the denoising accuracy is better than that of ATL08 product data. The present invention can provide technical support for the rapid and accurate denoising of ICESat-2 photon counting lidar data, and provide data guarantee for subsequent applications of ICESat-2.

[0100] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. A photon counting lidar data denoising method based on the main direction of point cloud, characterized in that: The photon counting laser radar data denoising method comprises: S1: coarse denoising based on elevation statistical histogram; S2: De-noising the data processed in step S1 using a photon data denoising method based on the main direction of the point cloud; S3: For the data processed in step S2, the residual noise points are removed based on the improved local statistical distance algorithm to achieve effective separation of signal photons and noise photons.

2. The photon counting laser radar data denoising method according to claim 1, characterized in that: Step S1 includes: preliminarily determining the elevation range of signal photons by establishing an elevation statistical histogram to achieve coarse denoising of the photon point cloud.

3. The photon counting laser radar data denoising method according to claim 1, characterized in that: Step S1 specifically includes: By dividing the grid, the original photons establish an elevation statistical histogram along the track based on the preset window size, and then the peak position of the histogram is used to determine the center of the signal photon; Combined with the maximum height of the ground object, a threshold is set based on the center position of the signal photon to establish a buffer zone, and noise photons are filtered out by removing the photon point cloud outside the buffer zone.

4. The photon counting laser radar data denoising method according to claim 1, characterized in that: Step S2 includes: calculating the main direction of the point cloud, obtaining the angle between the main direction and the distance along the track, and using a set angle threshold to achieve noise photon removal.

5. The photon counting laser radar data denoising method according to claim 4, characterized in that: The process of calculating the main direction of the point cloud includes: According to the row and column information of the data, the profile photon point cloud is first converted into a three-dimensional point cloud. After calculating the covariance matrix within the k-neighborhood of the point cloud, the eigenvector corresponding to the maximum eigenvalue is the main direction of the corresponding point cloud.

6. The photon counting laser radar data denoising method according to claim 4, characterized in that: The noise photon removal process also includes: When the surface type is irregular, when the number of points in the neighborhood that meet the threshold exceeds one-third, all photons in the neighborhood are considered to be signal photons.

7. The photon counting laser radar data denoising method according to claim 1, characterized in that: Step S3 includes: searching for the nearest neighbor point through the ellipse and calculating the total distance, and statistically analyzing the frequency histogram of the local total distance to set a threshold to remove residual noise photons.

8. The photon counting laser radar data denoising method according to claim 7, characterized in that: The total distance is calculated as: Among them, x represents the distance along the track, h represents the elevation of the point cloud, a represents the semi-major axis value of the ellipse search area, and b represents the semi-minor axis value of the ellipse search area.

Images