An als point cloud classification method based on random forest

Abstract

The present application relates to a kind of ALS point cloud classification methods based on random forest.The method uses the ground filtering algorithm of progressive triangulation to divide ALS point cloud into ground points and non-ground points, then calculates the element characteristics of each laser point of non-ground point: neighborhood average echo times, echo times, main direction, anisotropy, planarity, sphericity, linearity, neighborhood point spacing, height standard deviation, height kurtosis, height range, and the characteristics are used to train random forest classifier, finally the trained random forest classification model is used for ALS point cloud classification, and the ALS point cloud with semantic label is obtained.The present application has strong robustness to different scenes and point density, and can obtain good results in the area of sparse point cloud, unclear boundary and incomplete data, and can quickly and efficiently extract various ground objects in the scene, provide data support for building digital twin city, scene three-dimensional reconstruction, etc.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of computer vision and laser scanning data processing, and particularly relates to an ALS point cloud classification method based on a random forest. BACKGROUND

[0002] With the popularity of the "Digital Earth" and the rapid development of "Smart City", people's demand for comprehensive, accurate and real-time geographic information data, especially high-precision three-dimensional geographic information, is becoming more and more strong. Two-dimensional spatial data represented by maps and images has long been unable to meet people's needs for real three-dimensional spatial cognition. How to accurately and quickly obtain three-dimensional geographic information has become the fundamental task and urgent need of the field of surveying and geographic information. With the rapid development of laser scanning technology, three-dimensional laser scanning point cloud has become the third type of spatial data after maps and images, providing a new expression method for accurate portrayal of the real world.

[0003] Airborne laser point cloud is obtained by scanning and sampling the surface of ground objects by a laser radar carried by an aircraft. Airborne laser point cloud can obtain the three-dimensional coordinates and some attribute information of the surface of ground objects, such as echo intensity, time, etc. Airborne three-dimensional scanning system can quickly obtain the three-dimensional coordinates of large-scale, fine-grained urban ground elements by virtue of its top-down acquisition method, and visualize the ground structure of urban buildings, which plays a very important role in global change, smart city, global mapping, intelligent transportation and other national major needs.

[0004] The structure and planning of urban scenes are crucial to the layout and application of cities, and obtaining fine, timely updated various ground information is of great benefit to the work of urban management departments and government decision-making departments. Extraction and digital reconstruction of building, vegetation, ground and other elements can provide a large amount of data support for urban supervision, basic database updating, etc. At present, some satellite images or airborne images can be used as data sources for urban scene reconstruction, but two-dimensional image data will be disturbed by factors such as angle interference and spectral variation, making it difficult to extract various ground elements. Three-dimensional laser point cloud data can effectively make up for this deficiency, and effectively obtain the structure, height and other information of various ground elements through rich geometric structure information.

[0005] With the modernization of the city, the complexity of the city is increasing, so the semantic understanding and digital reconstruction of the city scene are also increasing. How to quickly, efficiently and automatically extract a large range of urban features has become the focus and difficulty of urban intelligent management and urban geographic database updating. At the same time, various urban features, such as buildings, low vegetation, trees, power lines, traffic signs, etc., can provide strong data support for city planning, urban traffic safety, illegal detection and other applications. Airborne laser scanning (ALS) point cloud can quickly and accurately capture the three-dimensional surface morphology and structural characteristics of ground objects, so it is an important data source for acquiring attribute information of urban feature elements.

[0006] Traditional urban feature extraction methods use images or manual annotation of point clouds. These methods consume a lot of manpower and material resources. In addition, the airborne point cloud classification method based on deep learning requires a large number of labeled data sets as training sets, and the classification effect of the trained model in other scenes is poor, and the model generalization ability is also weak. SUMMARY

[0007] The present application provides a random forest-based ALS point cloud classification method, comprising the following steps:

[0008] Step 1, noise removal of ALS point cloud, using progressive triangulation encryption ground filtering algorithm to screen out ground point cloud and non-ground point cloud;

[0009] Step 1.1, grid division of ALS point cloud, selecting the lowest point as the ground seed point;

[0010] Step 1.2, constructing a TIN triangular net for the selected ground seed point;

[0011] Step 1.3, calculating the angle and distance of each non-ground point to the triangle;

[0012] Step 1.4, if the angle and distance of the non-ground point to the triangular net patch are less than the set threshold, then it is included in the ground point;

[0013] Step 1.5, repeat steps 1.2-1.4 until no new point is included in the ground point set;

[0014] Step 2, according to the geometric information and attribute information of each laser point in the non-ground point cloud, calculating the geometric features, attribute features and height features of each laser point in the non-ground point cloud;

[0015] Step 3, using the three types of features of each laser point in the non-ground point cloud calculated in step 2 to train the random forest classifier;

[0016] Step 4, using the random forest classifier trained in step 3, classify the ALS point cloud test set.

[0017] Furthermore, in step 1.1, the denoised ALS point cloud is divided into a grid according to the size of the N1m×N1m×N1m cubic grid, the minimum value of the z coordinate of all laser points in each grid in the spatial rectangular coordinate system is calculated, and the laser point with the minimum z coordinate value is selected as the lowest point in the grid, which is recorded as the ground seed point. The spatial rectangular coordinate system takes any laser point as the coordinate origin, the Z axis is vertically upward, and the X, Y and Z axes are orthogonal to each other.

[0018] Furthermore, in step 1.2, Delauney algorithm is used to construct triangular mesh for the selected ground seed points. These triangular meshes are composed of a series of connected but non-overlapping triangles, and the circumcircle of these triangles does not contain any other points in the face domain.

[0019] Furthermore, in step 1.3, for each laser point of the ALS point cloud that is not a ground seed point, the angle between the line segment from the point to the three vertices of the nearest triangle and the triangle face is calculated, and the vertical distance from the laser point to the nearest triangle face is calculated.

[0020] Furthermore, in step 1.4, the three angle calculation values and one distance calculation value of all laser points are counted, and the median of the three angles and the distance is calculated as the threshold value of this round of iteration. For each laser point, compare the three angle calculation values and one distance calculation value calculated by the laser point with the threshold value of this round of iteration. If they are all less than the threshold value, the point is included in the ground seed point set and participates in the construction of the next round of triangular mesh.

[0021] Furthermore, in step 2, the ALS point cloud is defined as:

[0022] ρ k (x k , y k , z k , I k , RN k ), k ∈ [1, K] (1)

[0023] In the formula, K is the number of laser points in the airborne laser scanning point cloud, ρ k (x k , y k , z k ) is the kth point in the ALS point cloud, I k is the reflection intensity information of the kth point, RN k is the return number information of the kth point, x k , y k , z kThe coordinate value of the kth point on the X, Y, and Z axes of a spatial rectangular coordinate system.

[0024] The geometric feature of the laser point refers to a principal direction feature, and the principal direction feature of each laser point is composed of three feature values obtained by performing principal component analysis on the covariance matrix of the laser point; the i th laser point in the non-ground point cloud of the ALS point cloud is taken as an example i The spherical neighborhood with a radius of R s is constructed with the center being the sphere center All laser points in the spherical neighborhood are used to construct the covariance matrix M i of the i th laser point in the non-ground point cloud, and the specific calculation method is as follows:

[0025]

[0026] In the formula, is the number of neighborhood laser points in the spherical neighborhood corresponding to the i th laser point, t is a laser point in the neighborhood of the i th laser point, ρ i，t is a vector from the coordinate origin to the neighborhood laser point in the spatial rectangular coordinate system, ρ i，t = [x i，t , y i，t , z i，t ], x i，t is the x coordinate value of the t th neighborhood laser point, y i，t is the y coordinate value of the t th neighborhood laser point, and z i，t is the z coordinate value of the t th neighborhood laser point, is a vector composed of the average values of the spatial coordinates of all laser points in the spherical neighborhood of the i th laser point, is the average value of the x coordinate values of all laser points in the spherical neighborhood of the i th laser point, is the average value of the y coordinate values of all laser points in the spherical neighborhood of the i th laser point, is the average value of the z coordinate values of all laser points in the spherical neighborhood of the i th laser point.

[0027] According to the covariance matrix M i of the i th laser point in the non-ground point cloud of the ALS point cloud, the first feature value λ 1，i , the second feature value λ 2，i , and the third feature value λ 3，i corresponding to the i th laser point in the ALS non-ground point cloud are obtained by using the principal component analysis method, and thus the principal direction of the i th laser point in the ALS non-ground point cloud is obtained.

[0028] The attribute characteristics include echo count, neighborhood average echo count, anisotropy, planarity, sphericity, linearity, and neighborhood point spacing. Among these, the echo count is one of the measurements automatically acquired by the airborne lidar when scanning ground features. The formula for calculating the neighborhood average echo count is:

[0029]

[0030] In the formula, RN is the average number of echoes in the neighborhood. i For the number of echoes, The spherical neighborhood corresponding to the i-th laser point ρi in the ALS non-ground point cloud. The number of neighboring points within.

[0031] Anisotropic characteristics, planar characteristics, spherical characteristics, and linear characteristics can all be calculated using the principal direction:

[0032]

[0033]

[0034]

[0035]

[0036] In the formula, A λ，i For each heterogeneous characteristic, P λ，i As a planar characteristic, S λ，i As a spherical characteristic, L λ，i For linear characteristics, λ 1，i Let λ be the first eigenvalue. 2，i λ is the second eigenvalue. 3，i It is the third eigenvalue.

[0037] Neighborhood point spacing D i The calculation method is as follows:

[0038]

[0039] In the formula, Let ρ be the i-th laser point in the ALS non-ground point cloud. i Corresponding spherical neighborhood The number of neighborhood points within d i For the i-th laser point ρ i To neighboring areas The distance between all laser points within.

[0040] Height features are derived from the cylindrical neighborhood. Elevation range H within d，i Standard deviation of elevation H STD，iand elevation kurtosis H skw，i The specific calculation is as follows:

[0041] H d，i = z max，i -z min，i (9)

[0042]

[0043]

[0044] In the formula, represents the number of neighborhood laser points in the cylindrical neighborhood of the i-th laser point p i with ALS non-ground point cloud as the center of the cylinder, the radius is R S , the vertical height is L C , represents the number of neighborhood laser points in the cylindrical neighborhood of the i-th laser point p , z i is the coordinate value of the i-th point on the Z-axis in the spatial rectangular coordinate system, z max，i is the maximum value of the Z-axis coordinate value corresponding to all laser points in the cylindrical neighborhood of the i-th laser point p , z min，i is the minimum value of the Z-axis coordinate value corresponding to all laser points in the cylindrical neighborhood of the i-th laser point p , is the average value of the Z-axis corresponding to all laser points in the cylindrical neighborhood of the i-th laser point p .

[0045] Moreover, the non-ground points calculated in step 2 in step 3 are divided into a training set and a test set, the training set data is used to train the random forest classifier, and the test set data is used to verify the classification effect of the random forest classification model. The class label, echo number, neighborhood average echo number, principal direction, anisotropy, planarity, sphericity, linearity, neighborhood point spacing, elevation standard deviation, elevation kurtosis, and elevation range of each laser point in the training set data are input into the random forest classifier to train the random forest classifier. The training strategy is as follows: the maximum possible depth of the decision tree of the random forest classification model is set to 10, the minimum sample size of the decision tree node is set to 10, and the termination criterion of the regression tree is set to 0.01; the random forest is not set to establish an alternative split point, and the maximum cluster number is set to 15; the prior class probability array is not set, and the random initialization method is adopted; in the random forest classifier, the importance of the calculated variables is selected, and the size of the feature subset randomly selected by the decision tree node is 2.

[0046] Moreover, the step 4 inputs the test set point cloud into the random forest classifier trained in step 3 for testing to obtain the classification results of the test set. The ALS point cloud of the test set is without any annotation information, and the average echo number of the neighborhood of each laser point of the ALS point cloud, the echo number, the main direction, the anisotropy, the planarity, the sphericity, the linearity, the point spacing of the neighborhood, the height standard deviation, the height kurtosis, and the height range are input into the trained random forest classifier. The decision trees and tree nodes in the random forest classifier will calculate and classify the features, and the features will be shunted to the child nodes and leaf nodes until a label value is calculated for each laser point. Finally, the non-ground points are marked as building points, vegetation points, tree points, power line points, cable tower points or other points.

[0047] Compared with the prior art, the present application has the following advantages:

[0048] 1) The present application uses the point cloud obtained by the airborne laser radar scanning, and obtains the point-by-point semantic label through the feature calculation and random forest classification method. Under the premise of the existing training model, the annotation cost of the sample can be greatly saved for other test data.

[0049] 2) The method proposed in the present application has strong robustness to different scenes and point densities, and good results can be achieved in areas with sparse point clouds, unclear boundaries and incomplete data.

[0050] 3) The method proposed in the present application can quickly and efficiently extract various ground objects in the scene, and provides data support for the construction of digital twin cities and scene three-dimensional reconstruction. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 The technical flowchart of the embodiment of the present application.

[0052] Figure 2 The schematic diagram of the progressive triangulation encryption ground filtering algorithm of the embodiment of the present application.

[0053] Figure 3 The schematic diagram of the laser point cloud random forest classification process of the embodiment of the present application. DETAILED DESCRIPTION

[0054] This invention provides an ALS point cloud classification method based on random forest. It uses a progressive triangulation-encrypted ground filtering algorithm to divide the ALS point cloud into ground points and non-ground points. Then, it calculates the feature characteristics of each laser point in the non-ground points: neighborhood average echo count, echo count, principal direction, anisotropy, planarity, sphericity, linearity, neighborhood point spacing, elevation standard deviation, elevation kurtosis, and elevation range. These features are then used to train a random forest classifier. Finally, the trained random forest classification model is used for testing on the ALS point cloud to obtain ALS point clouds with semantic labels.

[0055] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0056] like Figure 1 As shown, the process of this embodiment of the invention includes the following steps:

[0057] Step 1: Noise removal is performed on the ALS point cloud. The ground filtering algorithm with progressive triangulation encryption is used to filter out the ground point cloud and non-ground point cloud.

[0058] Step 1.1: Divide the ALS point cloud into a grid and select the lowest point as the ground seed point.

[0059] The denoised ALS point cloud is divided into grids of 50m×50m×50m cube size. The minimum z-coordinate of all laser points within each grid is calculated in a Cartesian coordinate system. The laser point with the minimum z-coordinate is selected as the lowest point within that grid and denoted as the ground seed point. The Cartesian coordinate system has any laser point as its origin, with the Z-axis pointing vertically upwards, and the X, Y, and Z axes being pairwise orthogonal.

[0060] Step 1.2: Construct a TIN triangulation network for the selected ground seed points.

[0061] The Delauney algorithm is used to construct triangulations from the selected ground seed points. These triangulations consist of a series of connected but non-overlapping triangles, and the circumcircles of these triangles do not contain any other points in the region. The constructed initial triangulations are used for subsequent iterations.

[0062] Step 1.3: Calculate the angle and distance from each non-ground point to the triangle.

[0063] For each laser point that is not a ground seed point in the ALS point cloud, calculate the angle between the line segment from that point to the three vertices of the nearest triangle and the triangle face, and calculate the perpendicular distance from that laser point to the nearest triangle face.

[0064] Step 1.4: If the angle and distance from a non-ground point to a triangular mesh are both less than the set threshold, then include it as a ground point.

[0065] The three angle calculation values and one distance calculation value of all laser points are counted, and the median of the three angles and the distance is calculated as the threshold of this round of iteration. For each laser point, compare the three angle calculation values and one distance calculation value calculated by the laser point with the threshold of this round of iteration, if all are less than the threshold, the point is included in the ground seed point set and participates in the construction of the next round of triangular net.

[0066] Step 1.5, repeat steps 1.2-1.4 until no new point is included in the ground point set.

[0067] Repeat the above triangular net construction, parameter threshold calculation and parameter comparison process to update the constructed triangular net until no new point is added in the next round of iteration, then the iteration is terminated.

[0068] After the above gradual triangular net encryption ground filtering algorithm, the ground points and non-ground points in the ALS point cloud can be screened out, and the screened ALS non-ground points can be used for feature calculation in step 2.

[0069] Step 2, according to the geometric information and attribute information of each laser point in the non-ground point cloud, the geometric features, attribute features and height features of each laser point in the non-ground point cloud are calculated.

[0070] Airborne Laser Scanning (ALS) point cloud is defined as:

[0071] ρ k (x k , y k , z k , I k , RN k ), k ∈ [1, K] (1)

[0072] In the formula, K is the number of laser points in the airborne laser scanning point cloud, ρ k (x k , y k , z k ) is the kth point in the ALS point cloud, I k is the reflection intensity information of the kth point, RN k is the return number information of the kth point, x k , y k , z k is the coordinate value of the kth point in the X, Y, Z axes of the space rectangular coordinate system.

[0073] The geometric feature of the laser point refers to the principal direction feature, and the principal direction feature of each laser point is composed of three feature values, which are obtained by principal component analysis on the covariance matrix of the laser point.

[0074] The i-th laser point ρ in the non-ground points of the ALS point cloud i With the center of the sphere as the center, construct a structure with radius R. s spherical neighborhood Utilizing spherical neighborhood Construct the covariance matrix M of the i-th laser point in the non-ground point cloud from all laser points within it. i The specific calculation method is as follows:

[0075]

[0076] In the formula, The spherical neighborhood corresponding to the i-th laser point The number of neighboring laser points, t is the number of laser points in the neighborhood of the i-th laser point, ρ i，t Let ρ be the vector from the neighborhood laser point to the origin in a Cartesian coordinate system. i，t =[x i，t y i，t , z i，t ], x i，t Let x be the x-coordinate of the t-th neighboring laser point, and y be the x-coordinate of the t-th neighboring laser point. i，t Let z be the y-coordinate of the t-th neighboring laser point. i，t Let z be the z-coordinate of the t-th neighboring laser point. For the spherical neighborhood of the i-th laser point The vector formed by the average spatial coordinates of all laser points within the area. For the spherical neighborhood of the i-th laser point The average of the x-coordinate values ​​of all laser points within the range. For the spherical neighborhood of the i-th laser point The average y-coordinate value of all laser points within the range. For the spherical neighborhood of the i-th laser point The average value of the z-coordinate of all laser points within the range.

[0077] Based on the covariance matrix M of the i-th laser point in the ALS point cloud (non-ground point cloud), i The first eigenvalue λ corresponding to the i-th laser point in the ALS non-ground point cloud is obtained using principal component analysis. 1，i The second eigenvalue λ 2，i and the third eigenvalue λ 3，i Thus, the principal direction of the i-th laser point in the ALS non-ground point cloud is obtained.

[0078] Using the coordinates and attribute values ​​of each laser point and the coordinates and attribute values ​​of laser points in its neighborhood, seven attribute characteristics are calculated: number of echoes, average number of echoes in the neighborhood, anisotropy, planarity, sphericity, linearity, and the distance between points in the neighborhood.

[0079] Wherein, the number of returns is one of the measurement values captured automatically by the airborne laser radar when scanning the ground object, and the calculation formula of the average number of returns in the neighborhood is:

[0080]

[0081] In the formula, is the average number of returns in the neighborhood, RN i is the number of returns, is the i-th laser point in the ALS non-ground point cloud ρ i The number of neighborhood points in the corresponding spherical neighborhood .

[0082] The anisotropy feature, the planarity feature, the sphericity feature and the linearity feature can be calculated by the principal direction:

[0083]

[0084]

[0085]

[0086]

[0087] In the formula, A λ，i is the anisotropy feature, P λ，i is the planarity feature, S λ，i is the sphericity feature, L λ，i is the linearity feature, λ 1，i is the first eigenvalue, λ 2，i is the second eigenvalue, λ 3，i is the third eigenvalue.

[0088] The neighborhood point spacing D i The calculation method is as follows:

[0089]

[0090] In the formula, is the i-th laser point in the ALS non-ground point cloud ρ i The number of neighborhood points in the corresponding spherical neighborhood , d i is the distance from the i-th laser point ρ i to all laser points in the neighborhood .

[0091] Take the i-th laser point in the ALS non-ground point cloud ρ i as the center of the cylinder, and construct a cylindrical neighborhood with a radius R S and a vertical height L C ​ The height feature consists of the elevation range H within the cylindrical neighborhood d，i , the elevation standard deviation H STD，i and the elevation kurtosis H skw，i , and the specific calculation method is as follows:

[0092] H d，i = z max，i - z min，i [[ID=1​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​

[0098] The construction method of the decision tree is as follows:

[0099] ①There are N samples in the training set T, N samples are randomly selected with replacement, the selected N samples are used to train the decision tree, and the decision tree is taken as the sample at the root node of the decision tree.

[0100] ②Suppose each sample has M attributes, when each node of the decision tree needs to be split, m attributes are randomly selected from the M attributes, satisfying the condition m << M, and one attribute is selected as the split attribute of the node from the m attributes by using a certain strategy (such as information gain).

[0101] ③Each node in the decision tree formation process is split according to step ② until it cannot be split any more. It is noted that no pruning is performed in the entire decision tree formation process.

[0102] ④A large number of decision trees are established according to steps ①-③ to form a random forest.

[0103] The numerous decision trees constitute a random forest, each decision tree will have a voting result, and the class with the most final voting result is the prediction result of the final random forest classification model. The training process of the random forest classifier is as shown in Figure 3 .

[0104] The non-ground points calculated in step 2 for geometric features, attribute features and height features are divided into a training set and a test set according to 8:2, the training set data is used to train the random forest classifier, and the test set data is used to verify the classification effect of the random forest classification model. The class label, echo number, neighborhood average echo number, principal direction, anisotropy, planarity, sphericity, linearity, point spacing of the neighborhood, height standard deviation, height kurtosis, and height range of each laser point in the training set data are input into the random forest classifier to train the random forest classifier. The training strategy is as follows: the maximum possible depth of the decision tree of the random forest classification model is set to 10, the minimum sample number of the decision tree node is set to 10, and the termination standard of the regression tree is set to 0.01; the random forest is not set to establish an alternative split point, and the maximum cluster number is set to 15; the prior class probability array is not set, and the random initialization method is used; in the random forest classifier, the importance of the calculated variables is selected, and the size of the feature subset randomly selected by the decision tree node is 2.

[0105] Step 4, using the random forest classifier trained in step 3, classifying the ALS point cloud test set.

[0106] The test set point cloud is input to the random forest classifier trained in step 3 for testing to obtain the classification results of the test set. The ALS point cloud of the test set is without any labeled information. The average number of echo times of the neighborhood of each laser point of the ALS point cloud, the number of echo times, the main direction, the anisotropy, the planarity, the sphericity, the linearity, the point spacing of the neighborhood, the height standard deviation, the height kurtosis, and the height range are input to the trained random forest classifier. The decision trees and tree nodes in the random forest classifier will calculate and classify the features, and the features will be divided into sub-nodes and leaf nodes until a label value is calculated for each laser point. Finally, the non-ground points are marked as building points, vegetation points, tree points, power line points, cable tower points, or other points.

[0107] The specific embodiments described herein are merely illustrative of the principles of this application. Numerous modifications or adaptations will be readily apparent to those skilled in the art of this application without departing from the spirit or scope of the application as defined by the following claims.

Claims

1. An ALS point cloud classification method based on random forest, characterized in that, Includes the following steps: Step 1: Noise removal is performed on the ALS point cloud, and the ground point cloud and non-ground point cloud are filtered out using a progressive triangulation encryption ground filtering algorithm. Step 1.1: Divide the ALS point cloud into a grid and select the lowest point as the ground seed point; Step 1.2: Construct a TIN triangulation network for the selected ground seed points; Step 1.3: Calculate the angle and distance from each non-ground point to the triangle; Step 1.4: If the angle and distance from a non-ground point to a triangular mesh patch are both less than a set threshold, then include it as a ground point. Step 1.5, repeat steps 1.2-1.4 until no new points are added to the ground point set; Step 2: Based on the geometric and attribute information of each laser point in the non-ground point cloud, calculate the geometric features, attribute features, and height features of each laser point in the non-ground point cloud; ALS point cloud is defined as: （1） In the formula, K represents the number of laser points in the airborne laser scanning point cloud. For the k-th point in the ALS point cloud, For the reflection intensity information at the k-th point, Information on the number of callbacks for the k-th point. Let x be the coordinates of the k-th point on the X, Y, and Z axes of the Cartesian coordinate system. The geometric features of a laser point refer to its principal direction features. Each laser point's principal direction feature consists of three eigenvalues, obtained through principal component analysis of the laser point's covariance matrix. Taking the i-th laser point in the ALS point cloud's non-ground points as an example... With the center of the sphere as the center, construct a circle with a radius of 1. spherical neighborhood Utilizing spherical neighborhood Construct the covariance matrix of the i-th laser point in the non-ground point cloud from all laser points within the cloud. The specific calculation method is as follows: （2） In the formula, The spherical neighborhood corresponding to the i-th laser point The number of neighboring laser points within the i-th laser point, where t is the number of laser points in the neighborhood of the i-th laser point. Let be the vector from the neighborhood laser point to the origin in a spatial rectangular coordinate system. , Let x be the x-coordinate of the t-th neighboring laser point. Let y be the y-coordinate of the t-th neighboring laser point. Let z be the z-coordinate of the t-th neighboring laser point. For the spherical neighborhood of the i-th laser point The vector formed by the average spatial coordinates of all laser points within the area. , For the spherical neighborhood of the i-th laser point The average of the x-coordinate values ​​of all laser points within the range. For the spherical neighborhood of the i-th laser point The average y-coordinate value of all laser points within the range. For the spherical neighborhood of the i-th laser point The average z-coordinate value of all laser points within the range; Based on the covariance matrix of the i-th laser point in the ALS point cloud (non-ground point cloud) Principal component analysis was used to obtain the first eigenvalue corresponding to the i-th laser point in the ALS non-ground point cloud. Second eigenvalue and the third eigenvalue Thus, the principal direction of the i-th laser point in the ALS non-ground point cloud is obtained; Attribute characteristics include echo count, neighborhood average echo count, anisotropy, planarity, sphericity, linearity, and neighborhood point spacing. Among them, the echo count is one of the measurements automatically captured by the airborne lidar when scanning ground features. The formula for calculating the neighborhood average echo count is: （3） In the formula, The average number of echoes in the neighborhood. For the number of echoes, Let i be the i-th laser point in the ALS non-ground point cloud. Corresponding spherical neighborhood The number of neighboring points within; Anisotropic characteristics, planar characteristics, spherical characteristics, and linear characteristics are all calculated using the principal directions: （4） （5） （6） （7） In the formula, For each opposite sex characteristic, It is a planar feature. It has spherical characteristics. It is a linear feature. The first eigenvalue, The second eigenvalue, It is the third eigenvalue; Neighborhood point spacing The calculation method is as follows: （8） In the formula, Let i be the i-th laser point in the ALS non-ground point cloud. Corresponding spherical neighborhood The number of neighboring points within, For the i-th laser point To neighboring areas The distance between all laser points within; Step 3: Train the random forest classifier using the three-class features of each laser point in the non-ground point cloud calculated in Step 2; Step 4: Use the random forest classifier trained in Step 3 to classify the ALS point cloud test set.

2. The ALS point cloud classification method based on random forest as described in claim 1, characterized in that: In step 1.1, according to The cube-shaped mesh size is used to divide the denoised ALS point cloud into meshes. The minimum z-coordinate value of all laser points in the spatial rectangular coordinate system is calculated. The laser point with the minimum z-coordinate value is selected as the lowest point in the mesh and is denoted as the ground seed point. The spatial rectangular coordinate system takes any laser point as the origin, the Z-axis is vertically upward, and the X, Y, and Z axes are pairwise orthogonal.

3. The ALS point cloud classification method based on random forest as described in claim 1, characterized in that: In step 1.2, the Delauney algorithm is used to construct a triangulation network for the selected ground seed points. This triangulation network consists of a series of connected but non-overlapping triangles, and the circumcircles of these triangles do not contain any other points in this region.

4. The ALS point cloud classification method based on random forest as described in claim 1, characterized in that: In step 1.3, for each laser point that is not a ground seed point in the ALS point cloud, calculate the angle between the line segment from that point to the three vertices of the nearest triangle and the triangle face, and calculate the perpendicular distance from that laser point to the nearest triangle face.

5. The ALS point cloud classification method based on random forest as described in claim 1, characterized in that: In step 1.4, the calculated values ​​of the three angles and one distance of all laser points are counted, and the median of the three angles and distance is calculated as the threshold for this round of iteration. For each laser point, the calculated values ​​of the three angles and one distance of the laser point are compared with the threshold for this round of iteration. If they are all less than the threshold, the point is included in the ground seed point set and participates in the construction of the next round of triangulation.

6. The ALS point cloud classification method based on random forest as described in claim 1, characterized in that: In step 2, the height feature is determined by the cylindrical neighborhood. Elevation range within Standard deviation of elevation and elevation kurtosis The composition and specific calculation method are as follows: （9） （10） （11） In the formula, Represents the i-th laser point in the ALS non-ground point cloud. The center of the cylinder is and the radius is . Vertical height The cylindrical neighborhood, Represents the cylindrical neighborhood corresponding to the i-th laser point. The number of laser points in the inner neighborhood Let be the Z-axis coordinate of the i-th point in the spatial rectangular coordinate system. The cylindrical neighborhood corresponding to the i-th laser point The maximum value of the Z-axis coordinate corresponding to all laser points within the area. The cylindrical neighborhood corresponding to the i-th laser point The minimum Z-axis coordinate value corresponding to all laser points within the area. The cylindrical neighborhood of the i-th laser point The average value of the Z-axis corresponding to all laser points within the area.

7. The ALS point cloud classification method based on random forest as described in claim 6, characterized in that: In step 3, the non-ground points for which geometric features, attribute features, and height features were calculated in step 2 are divided into training and testing sets. The training set data is used to train the random forest classifier, and the testing set data is used to test the classification performance of the random forest classification model. The category label, echo count, neighborhood average echo count, principal direction, anisotropy, planarity, sphericity, linearity, neighborhood point spacing, elevation standard deviation, elevation kurtosis, and elevation range of each laser point in the training set data are input into the random forest classifier to train the random forest classifier. The training strategy is as follows: the maximum possible depth of the decision tree in the random forest classification model is set to 10, the minimum number of samples per decision tree node is set to 10, and the termination criterion for the regression tree is set to 0.01; the random forest is set not to establish alternative split points, and the maximum number of clusters is set to 15; no prior class probability array is set, and random initialization is used; in the random forest classifier, the importance of the variables is selected for calculation, and the size of the feature subset randomly selected by the decision tree node is 2.

8. The ALS point cloud classification method based on random forest as described in claim 7, characterized in that: In step 4, the test set point cloud is input into the random forest classifier trained in step 3 for testing, and the classification results of the test set are obtained. The test set ALS point cloud has no labeling information. The average echo count, echo count, principal direction, anisotropy, planarity, sphericity, linearity, neighborhood point spacing, elevation standard deviation, elevation kurtosis, and elevation range of each laser point in the ALS point cloud are input into the trained random forest classifier. The decision tree and tree nodes in the random forest classifier will calculate and classify the features, and distribute the features to child nodes and leaf nodes until a label value is calculated for each laser point. Finally, the non-ground points are labeled as building points, vegetation points, tree points, power line points, cable tower points, or other points.

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