Mahalanobis distance-based fuzzy clustering multi-parameter photon point cloud filtering method

Abstract

The invention provides a Mahalanobis distance-based fuzzy clustering multi-parameter photon point cloud filtering method, which comprises the following steps of: performing coordinate projection conversion on ICESat-2 / ATL03 photon point cloud data, and projecting three-dimensional coordinates of longitude, latitude and elevation to a two-dimensional section of along-rail distance-point cloud elevation; calculating feature parameters of each photon point in the photon point cloud data based on a local distance statistical method LDS; calculating feature parameters of each photon point in the photon point cloud data based on a local outlier factor (LOF) method; and fusing the two characteristic parameters of the LDS and the LOF through fuzzy clustering FCM-M based on mahalanobis distance. Automatic separation of signal photons and noise photons is realized through the membership matrix U; and precision evaluation: taking the ATL03 photon point cloud subjected to manual interpretation as a real signal photon point cloud, and carrying out quantitative comparison analysis on the real signal photon point cloud and signal photons identified based on a Mahalanobis distance fuzzy clustering filtering method. According to the method, high filtering precision can be shown in dense, tall and big forest regions and low and sparse forest regions under complex terrains.

Description

Technical Field

[0001] The invention provides a multi-parameter photon point cloud filtering method based on fuzzy clustering of Mahalanobis distance, belonging to the technical field of remote sensing. Background Art

[0002] In recent years, the new generation of satellite-borne lidar ICESat-2 has been widely used in many fields such as topography, ice sheet monitoring, forest measurement, and water body measurement due to its high precision, high density, and global coverage. However, there are a lot of noises in the ICESat-2 photon point cloud data, such as solar background noise, system noise, and atmospheric scattering noise. The photon point cloud data needs to be filtered before it can be used in production practice. Therefore, photon point cloud filtering is a key step in the practical application of ICESat-2 data.

[0003] The common single-parameter photon point cloud filtering method based on local statistics can accurately identify signal photons and noise photons, but the uncertainty of threshold selection and the lack of adaptability limit its application to a certain extent. The method based on multi-feature parameters can describe the characteristics of the spatial distribution of photon point clouds from a multi-dimensional perspective, which is a good supplement to the existing filtering methods. There are few studies on photon point cloud filtering methods based on multi-feature fusion. The main representative is that Chen Bowei et al. used machine learning methods to fuse 12 features related to photons to achieve the separation of signal photons and noise photons. Because this method introduces multiple feature parameters related to point clouds, noise photons can be removed more thoroughly, and there is no need to tune parameters, avoiding the influence of uncertainty in threshold selection. However, the method based on random forests requires prior information to be determined in advance, that is, training samples need to be selected, which increases the cost of manual training and the filtering results are greatly affected by samples. In addition, the photon point cloud filtering method based on random forests has not yet proven the reliability of its method in forest areas with complex terrain. Summary of the invention

[0004] In response to the above technical problems, the present invention proposes a multi-parameter photon point cloud filtering method based on fuzzy clustering of Mahalanobis distance. Among them, the fuzzy clustering method based on Mahalanobis distance belongs to unsupervised classification, which does not require the prior determination of training samples, and can automatically divide the photon point cloud data into two categories, namely signal photons and noise photons. In addition, the fuzzy clustering method based on Mahalanobis distance can adaptively adjust the geometric distribution of the data so that the distance between similar data points tends to be smaller. Therefore, compared with the random forest filtering method, it also has certain advantages in identifying noise photons adjacent to signals. In addition, the feature parameters selected by the present invention have been experimentally proven to better express the spatial distribution characteristics of the photon point cloud.

[0005] The specific technical solution is:

[0006] The multi-parameter photon point cloud filtering method based on fuzzy clustering of Mahalanobis distance (FCM-M) includes the following steps:

[0007] Step 1: Perform coordinate projection conversion on the ICESat-2 / ATL03 photon point cloud data, and project the three-dimensional coordinates of longitude, latitude, and elevation into a two-dimensional profile of along-track distance-point cloud elevation.

[0008] The basic information read from ICESat-2 is the along-track time (delta_time), longitude (lon_ph), latitude (lat_ph), and elevation (h_ph) of the photon point, which requires data preprocessing. At present, the commonly used data preprocessing method is the coordinate system conversion method, which is to convert the three-dimensional spatial information composed of longitude, latitude, and elevation into a two-dimensional profile of along-track distance and elevation.

[0009] The specific steps are as follows:

[0010] (1.1) Project the longitude and latitude in geographic coordinates to plane coordinates in the UTM coordinate system through Gaussian calculation, i.e., formulas (1) to (3);

[0011] (1.2) Take the photon point at the location of the minimum x value as the initial point, and use formula (4) to calculate the distance of the photon point along the track;

[0012] (1.3) Establish a two-dimensional coordinate profile of the point cloud elevation along the track.

[0013]

[0014] Among them, B and L represent the latitude and longitude of the photon point respectively, L0 is the longitude of the central meridian, N is the radius of curvature of the meridian, X0 and X are the meridian length and the distance along the track respectively, x and y are the plane coordinates of the photon point in UTM coordinates, and x1 and y1 are the plane coordinates of the initial point in UTM coordinates.

[0015] Step 2: Calculate the characteristic parameters of each photon point in the photon point cloud data based on the local distance statistics method (LocalDistanceSum, LDS). The LDS parameter calculation method is shown in the following formula:

[0016]

[0017] In the formula, x represents the distance along the track, h represents the point cloud elevation, and m represents the number of the nearest points. The present invention sets m=50.

[0018] Step 3, calculate the characteristic parameters of each photon point in the photon point cloud data based on the local outlier factor method (Local Outlier Factor, LOF).

[0019] LOF parameter calculation method:

[0020] (3.1) Define the ellipse search shape as shown below:

[0021]

[0022] In the formula, x represents the distance along the track, h represents the elevation of the point cloud, a and b represent the major semi-axis and the minor semi-axis of the ellipse respectively, and the present invention sets a:b=6:1.

[0023] (3.2) Calculate the reachable distance of each photon point. The reachable distance from point p to point q is defined as the maximum value of the KNN distance of point q and the distance from point p to point q, as shown in the following formula:

[0024] reachdist(p, q)=max{dist_k(q), dist(p, q)} (7)

[0025] In the formula, k represents the neighborhood range, and the present invention sets k=30 meters.

[0026] (3.3) Calculate the local accessibility density. The local accessibility density of point p is the inverse of the average local accessibility density within the neighborhood of point p, as shown in the following formula:

[0027]

[0028] In the formula, Indicates that q is a point in the k-neighborhood of p, N k (p) represents the number of points in the neighborhood.

[0029] (3.4) Calculate the LOF score. The LOF score is defined as: the average local accessibility density within the neighborhood of point p divided by the local accessibility density of point p itself, as shown in the following formula:

[0030]

[0031] Step 4: The two characteristic parameters of LDS and LOF are fused by fuzzy clustering based on Mahalanobis distance (FCM-M). Finally, the automatic separation of signal photons and noise photons is realized by the membership matrix U.

[0032] The fuzzy clustering method based on Mahalanobis distance (FCM-M) is used, and the objective function is:

[0033]

[0034] The Lagrangian operator of formula (10) is:

[0035]

[0036] Minimize the Lagrangian operator, that is, for α i 、u ij ,∑ i Find the partial derivative and get the extreme value condition:

[0037]

[0038] The specific steps of the FCM-M method are as follows:

[0039] (4.1) Initialization: Determine the number of cluster categories c, 2≤c≤n, n is the number of data points, set the iteration termination threshold δ and the iteration initial value b=0, and initialize the cluster center matrix A (0) .

[0040] (4.2) Calculate or update the membership matrix U according to equations (14) and (15): (b) .

[0041] (4.3) Update the cluster center matrix A according to formula (13) (b+1) .

[0042] (4.4) If ||A (b) -A (b+1) ||<δ, the method ends and outputs the membership matrix U and cluster center A, otherwise let b=b+1 and repeat steps (4.2) to (4.4).

[0043] The present invention sets c=2, δ=0.5, and ||·|| represents the second normal form.

[0044] Step 5, precision assessment, the ATL03 photon point cloud that has been manually interpreted is used as the real signal photon point cloud, and a quantitative comparative analysis is performed with the signal photons identified based on the Mahalanobis distance fuzzy clustering filter method. The quantitative analysis indicators used include recall rate R (Recall), accuracy rate P (Precision) and comprehensive indicator F (F-Measure). BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flow chart of the method of the present invention;

[0046] Figure 2 The distribution of signal photons and noise photons after filtering in the La Rioja Autonomous Region of the embodiment;

[0047] Figure 3 The signal photons after filtering for the embodiment of the Autonomous Region of La Rioja;

[0048] Figure 4 This is a photon point cloud filtering result diagram in the left channel of the Washington State experimental area of ​​the embodiment;

[0049] Figure 5 This is a photon point cloud filtering result diagram in the middle channel of the Washington State experimental area of ​​the embodiment;

[0050] Figure 6 This is a photon point cloud filtering result diagram in the right channel of the Washington State experimental area of ​​the embodiment;

[0051] Figure 7 This is a result diagram of signal photons in the left channel of the Washington State experimental area of ​​the embodiment;

[0052] Figure 8 This is a result diagram of signal photons in the middle channel of the Washington State experimental area of ​​the embodiment;

[0053] Fig. 9 This is a result diagram of signal photons in the right channel of the Washington State experimental area of ​​the embodiment;

[0054] The red dots on the graph represent signal photons, and the black dots represent noise photons. DETAILED DESCRIPTION

[0055] The present invention proposes a photon point cloud filtering method based on fuzzy c-means algorithm based on Mahalanobis distance (FCM-M). The technical route is as follows: Figure 1 As shown, the blue dashed box represents the general workflow of FCM-M.

[0056] In order to verify the reliability of the multi-parameter photon point cloud filtering method based on fuzzy clustering of Mahalanobis distance, this embodiment selects the local distance (LDS) and local outlier factor (LOF) as the input feature parameters of fuzzy clustering based on Mahalanobis distance for comparison with the corresponding filtering methods, aiming to illustrate the superiority of the combined multi-feature parameters in distinguishing signal photons from noise photons over the single-parameter filtering method. At the same time, the DBSCAN filtering method, which is also a clustering method, is selected for comparison, aiming to illustrate the advantages of the fuzzy clustering method based on Mahalanobis distance in photon point cloud filtering. In addition, the number of clustering categories c=2 is set, namely, signal photons and noise photons.

[0057] The experimental areas selected in this embodiment are located in La Rioja Autonomous Region, Spain and Washington State, USA.

[0058] 1. Filtering results for the Autonomous Region of La Rioja;

[0059] Figure 2 and Figure 3The filtering result diagram of the multi-parameter filtering method based on fuzzy clustering of Mahalanobis distance in La Rioja Autonomous Region is shown. It can be seen from the figure that the method of the present invention can effectively distinguish the signal photons from the noise photons in the forest area. At the same time, Table 1 can quantitatively show that compared with the three classic methods of DBSCAN, LDS, and LOF, the method of the present invention can not only better identify the signal photons, but also accurately eliminate the noise photons. Therefore, the comprehensive index F achieved by the method of the present invention is better than the other three filtering methods. In addition, compared with the filtering methods corresponding to the single characteristic parameters LDS and LOF alone, the filtering method based on multiple characteristic parameters can better reflect the distribution characteristics of the photon point cloud, which is specifically manifested in that it can better balance the denoising strength of the characteristic parameters LDS and LOF, thereby resulting in the multi-parameter filtering method based on fuzzy clustering of Mahalanobis distance to achieve the highest F value.

[0060] Table 1 Comparison of filtering results in La Rioja experimental area

[0061]

[0062] 2. Filtering results for Washington State;

[0063] The three channel filtering results of the selected strips in the Washington State experimental area are as follows Figure 3 The quantitative analysis results are shown in Table 2. Comprehensive analysis of the above experimental results can draw the following conclusions:

[0064] (1) By Figures 4 to 6 As shown in FIG. 1 , the multi-parameter filtering method of the present invention can accurately remove noise photons in the left, middle and right channels. Figures 7 to 9 , there is no obvious noise photon remaining around the signal photon. At the same time, it can be seen that the filtering method of the present invention can show better performance in the forest area with high background noise and large terrain undulation.

[0065] (2) According to the characteristics of the forest area selected in Washington State and the experimental results, it can be found that the filtering method we proposed is also applicable to forest areas with tall and dense vegetation.

[0066] (3) As can be seen from Table 2, the quantitative analysis results are consistent with the qualitative analysis results. At the same time, we can further find that the filtering effect of the method of the present invention is significantly better than that of the other three filtering methods. This phenomenon also illustrates the application potential of the multi-parameter filtering method based on fuzzy clustering of Mahalanobis distance in distinguishing signal photons from noise photons.

[0067] At present, the mainstream photon point cloud filtering method is based on a single feature parameter. The fuzzy clustering method based on Mahalanobis distance proposed in the present invention is based on the fusion of multiple feature parameters, and is an attempt to fuse multiple feature parameters following random forest. Compared with the filtering method based on a single feature parameter, the method proposed in the present invention does not involve the selection of thresholds, and can effectively avoid the influence of terrain slope, surface cover type, photon point cloud density and statistical range on threshold selection. At the same time, compared with the photon point cloud filtering method based on random forest, the present invention does not need to select training samples in advance, which reduces the cost of manual training and can also achieve better filtering effects in forest areas with complex terrain.

[0068] Table 2 Filtering results and accuracy analysis of the Washington State experimental area

[0069]

[0070] 3. Summary

[0071] Most existing filtering methods rely on a single feature parameter to describe the spatial distribution characteristics of photon point clouds. However, a single feature parameter is difficult to accurately express the spatial distribution characteristics of photon point clouds. Therefore, the present invention proposes a multi-parameter photon point cloud filtering method based on fuzzy clustering of Mahalanobis distance. First, two typical feature parameters are selected according to the characteristics of the recognition ability of photon points by the existing single-parameter filtering method. Then, the two feature parameters LDS and LOF are fused using the fuzzy clustering method based on Mahalanobis distance. Finally, the photon point cloud is automatically divided into signal photons and noise photons according to the membership matrix U. At the same time, a comparative verification experiment was carried out with the three existing classic filtering methods. The experimental results show that the method of the present invention can show higher filtering accuracy whether in dense and tall forests under complex terrain or in low and sparse forests.

[0072] In addition, the filtering method proposed in the present invention does not need to rely on a threshold to separate noise photons from signal photons, thus avoiding the problem of uncertainty caused by threshold selection. At the same time, unlike random training, the method of the present invention does not require the prior determination of training samples, thus reducing the cost of manual training.

Claims

1. A multi-parameter photon point cloud filtering method based on fuzzy clustering of Mahalanobis distance, characterized in that: The following steps are involved: Step 1: Perform coordinate projection conversion on ICESat-2 / ATL03 photon point cloud data, and project the three-dimensional coordinates of longitude, latitude, and elevation into a two-dimensional profile of along-track distance-point cloud elevation; Step 2, calculating the characteristic parameters of each photon point in the photon point cloud data based on the local distance statistics method LDS; Step 3, calculating the characteristic parameters of each photon point in the photon point cloud data based on the local outlier factor method LOF; Step 4, the two characteristic parameters of LDS and LOF are fused through fuzzy clustering FCM-M based on Mahalanobis distance; finally, the automatic separation of signal photons and noise photons is realized through the membership matrix U; Step 5, accuracy assessment, takes the ATL03 photon point cloud that has been manually interpreted as the real signal photon point cloud, and conducts quantitative comparative analysis with the signal photons identified based on the Mahalanobis distance fuzzy clustering filtering method.

2. The multi-parameter photon point cloud filtering method based on fuzzy clustering of Mahalanobis distance according to claim 1 is characterized in that: Step 1 includes the following sub-steps: (1.1) Project the longitude and latitude in geographic coordinates to plane coordinates in the UTM coordinate system through Gaussian calculation, i.e., formulas (1) to (3); (1.2) Take the photon point at the location of the minimum x value as the initial point, and use formula (4) to calculate the distance of the photon point along the track; (1.3) Establish a two-dimensional coordinate profile of distance along the track and point cloud elevation; n=(int(L) / 6+31 (1) Where B and L represent the latitude and longitude of the photon point, respectively. L0 is the longitude of the central meridian, N is the radius of curvature of the meridian, X0 and X are the meridian length and the distance along the track, respectively. x and y are the plane coordinates of the photon point in UTM coordinates, respectively. x1 and y1 are the plane coordinates of the initial point in UTM coordinates, respectively.

3. The multi-parameter photon point cloud filtering method based on fuzzy clustering of Mahalanobis distance according to claim 1 is characterized in that: The LDS parameter calculation method in step 2 is as follows: In the formula, x represents the distance along the track, h represents the point cloud elevation, and m represents the number of nearest points.

4. The multi-parameter photon point cloud filtering method based on fuzzy clustering of Mahalanobis distance according to claim 1 is characterized in that: LOF parameter calculation method in step 3: (3.1) Define the ellipse search shape as shown below: In the formula, x represents the distance along the track, h represents the point cloud elevation, a and b represent the major and minor semi-axis of the ellipse respectively; (3.2) Calculate the reachable distance of each photon point. The reachable distance from point p to point q is defined as the maximum value of the KNN distance of point q and the distance from point p to point q, as shown in the following formula: reachdist(p, q)=max{dist_k(q), dist(p, q)} (7) In the formula, k represents the neighborhood range; (3.3) Calculate the local accessibility density. The local accessibility density of point p is the inverse of the average local accessibility density within the neighborhood of point p, as shown in the following formula: In the formula, Indicates that q is a point in the k-neighborhood of p, N k (p) represents the number of points in the neighborhood; (3.4) Calculate the LOF score. The LOF score is defined as: the average local accessibility density within the neighborhood of point p divided by the local accessibility density of point p itself, as shown in the following formula:

5. The multi-parameter photon point cloud filtering method based on fuzzy clustering of Mahalanobis distance according to claim 1 is characterized in that: In step 4, the fuzzy clustering method based on Mahalanobis distance (FCM-M) is used, and the objective function is: The Lagrangian operator of formula (10) is: Minimize the Lagrangian operator, that is, for α i 、u ij ,∑ i Find the partial derivative and get the extreme value condition: The specific steps of the FCM-M method are as follows: (4.1) Initialization: Determine the number of cluster categories c, 2≤c≤n, n is the number of data points, set the iteration termination threshold δ and the iteration initial value b=0, and initialize the cluster center matrix A( 0 ); (4.2) According to equations (14) and (15), calculate or update the membership matrix U( b ); (4.3) Update the cluster center matrix A( b+1 ); (4.4) If ||A (b) -A (b+1) ||<δ, the method ends and outputs the membership matrix U and cluster center A, otherwise let b=b+1 and repeat steps (4.2) to (4.4).

6. The multi-parameter photon point cloud filtering method based on fuzzy clustering of Mahalanobis distance according to claim 1 is characterized in that: In step 5, the quantitative analysis indicators used include recall rate R, precision rate P and comprehensive index F.

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