Laser radar point cloud denoising method based on improved DBSCAN

Abstract

The application relates to a laser radar point cloud denoising method based on an improved DBSCAN, and relates to the technical field of laser radar data processing.The application is used to solve the problem that the adaptive denoising cannot be realized due to the existence of many differences in the neighborhood radius and the neighboring point threshold value in the DBSCAN algorithm.The laser radar point cloud denoising method based on the improved DBSCAN is used to calculate the neighborhood radius and the neighboring point threshold value according to a laser radar point cloud data set, to calculate the optimal neighborhood radius and the neighboring point threshold value according to a clustering evaluation index exponent, and to realize the laser radar point cloud denoising of the DBSCAN according to the optimal neighborhood radius and the neighboring point threshold value.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of laser radar data processing. BACKGROUND

[0002] Due to the influence of sensor errors, environmental interference and other factors, point cloud data often contains outliers and stray points and other noises, and the existence of these noises reduces the quality of subsequent data processing and analysis. Traditional denoising methods are mostly statistical filtering, bilateral filtering, radius filtering and other filtering algorithms based on method library. Inspired by one-dimensional and two-dimensional data clustering, the density-based noisy space clustering algorithm (Density-Based Spatial Clustering of Applications with Noise, DBSCAN) is also gradually applied to point cloud denoising.

[0003] Ma et al. proposed an algorithm combining DBSCAN and sea wave spectrum to successfully eliminate noise photons under the water surface; Wei Shuo et al. clustered and denoised point clouds by calculating point density; Zhao Kai et al. divided the point cloud data into voxel grids to reduce the search range of the DBSCAN algorithm, and Tao Zeyu et al. then used the grid network to find the maximum grid of point cloud density to find the clustering radius, completing the laser radar point cloud filtering; Zhang et al. proposed a DBSCAN model with an elliptical search area to improve the accuracy of ground height estimation; then Pan Chao et al. used DBSCAN with an elliptical search area combined with statistical filtering for denoising to obtain signal point cloud data.

[0004] However, these algorithms do not consider the selection of the two important parameters Eps (neighborhood radius) and Minpts (neighbor point threshold) in the DBSCAN algorithm, which are mainly selected manually or empirically. However, different experimental data denoising effects are different, and adaptive denoising cannot be achieved. SUMMARY

[0005] The present application is to solve the problem that the neighborhood radius and the neighborhood point threshold in the DBSCAN algorithm have many differences, which leads to the inability to achieve adaptive denoising. The present application provides a laser radar point cloud denoising method based on improved DBSCAN.

[0006] The laser radar point cloud denoising method based on improved DBSCAN comprises:

[0007] The neighborhood radius and the neighborhood point threshold are calculated according to the laser radar point cloud data set, the best neighborhood radius and the neighborhood point threshold are calculated according to the clustering evaluation index, and the laser radar point cloud denoising of DBSCAN is realized according to the optimal neighborhood radius and the neighborhood point threshold.

[0008] Further, the above calculating neighborhood radius according to the laser radar point cloud dataset comprises:

[0009] The laser radar point cloud dataset is expressed in the form of an n*m matrix, n is the total number of data points in the laser radar point cloud dataset, and m is the total number of features of the data points;

[0010] The Euclidean distance between each pair of data points is calculated respectively, and a distance distribution matrix is constructed using all the Euclidean distances;

[0011] The elements of each row and the elements of each column in the distance distribution matrix are sorted in ascending order in turn;

[0012] The serial number of the data points is taken as the abscissa, and the kth column element of the sorted distance distribution matrix is taken as the ordinate, to construct the kth distance curve, 1≤k≤n;

[0013] Each distance curve is fitted using the least squares method, and the goodness of fit value between the distance curve and the corresponding fitting curve is calculated, and then the optimal order of the fitting curve in the optimal range of the goodness of fit value is obtained, so as to obtain the optimal fitting curve;

[0014] The point with the largest change in the kth best fitting curve is taken as the inflection point, and the distance value of the inflection point in the kth distance curve is the kth neighborhood radius Eps k .

[0015] Further, the distance distribution matrix expression is as follows:

[0016] D n*n ={d(i,j)|1≤i≤n,1≤j≤n},

[0017] Where d(i,j) represents the Euclidean distance between the ith data point and the jth data point.

[0018] Further, each distance curve is fitted using the least squares method, comprising:

[0019]

[0020] Where L is the fitting loss function, y k represents the kth distance curve function, f(x) represents the fitting curve function corresponding to the kth distance curve function, and has:

[0021] f(x)=θ0+θ1x+θ2x 2 +…+θ q x q ,

[0022] Where x is the variable of the fitting curve function, and θ λis the coefficient of the th term, λ = 0, 1, 2,..., q, q is the polynomial order of f(x).

[0023] Further, the calculation of the proximity point threshold according to the laser radar point cloud dataset comprises:

[0024] The proximity point threshold is calculated according to the following formula:

[0025]

[0026] wherein Minpts k is the th proximity point threshold, 1 ≤ k ≤ n, β is a noise suppression threshold, and 0 ≤ β < 1, P α is the number of data points contained in the range of the th neighborhood radius Eps k of the th data point in the laser radar point cloud, 1 ≤ α ≤ n.

[0027] Further, the calculation of the best neighborhood radius and proximity point threshold according to the clustering evaluation index comprises:

[0028] The corresponding neighborhood radius and proximity point threshold Minpts k are brought into the DBSCAN algorithm for clustering, and the clustering evaluation index of the DBSCAN algorithm is calculated,

[0029] The pair of neighborhood radius and proximity point threshold corresponding to the highest value of the clustering evaluation index is selected as the best neighborhood radius and proximity point threshold.

[0030] Further, the clustering evaluation index is calculated according to the following formula:

[0031]

[0032] wherein CH is the clustering evaluation index, c is the total number of classes of clustering, B is the inter-class dispersion, and W is the intra-class dispersion.

[0033] Further, the expression of the inter-class dispersion B is as follows:

[0034]

[0035] wherein a j is the number of samples in the th cluster, c j is the center point of the th cluster, j = 1, 2,..., c, and b is the global centroid.

[0036] Further, the expression of the intra-class dispersion W is as follows:

[0037]

[0038] wherein D jFor the sample set in the jth cluster, γ is the sample point in D j .

[0039] The laser radar point cloud denoising method based on the improved DBSCAN determines the parameters suitable for point cloud DBSCAN denoising through the fitting curve of the distance matrix and the clustering evaluation index. In order to verify the effectiveness of the algorithm, it is applied to simple and complex scenes, and the denoising effect is comprehensively evaluated from the denoising accuracy, noise recall rate, and origin retention rate. Simulation experiments show that the present application can effectively cluster noise and signal in point cloud models and complex scenes, and the denoising accuracy, noise recall rate, and origin retention rate can be maintained above 90%, and the target point cloud can be effectively retained, which makes up for the defects of manual parameter adjustment and inability to switch parameters according to point cloud transformation when using DBSCAN for denoising, reducing manpower and time. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 The flowchart of the laser radar point cloud denoising method based on the improved DBSCAN;

[0041] Figure 2 The distance curve and fitting curve graph when k = 100;

[0042] Figure 3 The neighborhood radius curve graph when k = 100, where (a) represents the rabbit point cloud, (b) represents the pony point cloud, (c) represents the elephant point cloud, and (d) represents the residential point cloud;

[0043] Figure 4 The noisy point cloud graph, where (a) represents the rabbit point cloud, (b) represents the pony point cloud, (c) represents the elephant point cloud, and (d) represents the residential point cloud;

[0044] Figure 5 The denoised point cloud graph, where (a) represents the rabbit point cloud, (b) represents the pony point cloud, (c) represents the elephant point cloud, and (d) represents the residential point cloud. DETAILED DESCRIPTION

[0045] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application. It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0046] Specific implementation one: refer to Figure 1To illustrate the present embodiment, the laser radar point cloud denoising method based on improved DBSCAN in the present embodiment first calculates a standby neighborhood radius and a proximity point threshold according to a point cloud set; then calculates optimal parameters according to a clustering evaluation index; and finally realizes DBSCAN clustering denoising according to the obtained optimal parameters. The specific process is as follows.

[0047] The laser radar point cloud data set is represented as a matrix D n*m , where each row of the matrix D n*m represents a data point in the laser radar point cloud data set, each column represents a feature of the data point, n is the total number of data points in the laser radar point cloud data set, and m represents the total number of features of a data point.

[0048] The Euclidean distance between each pair of data points is calculated, and the distance distribution matrix D n*n is:

[0049] D n*n = {d(i,j) | 1≤i≤n, 1≤j≤n},

[0050] where d(i,j) represents the Euclidean distance between the ith data point and the jth data point.

[0051] The elements in each row of the distance distribution matrix D n*n are sorted in ascending order, and the first column of the sorted matrix is the distance of each data point to itself, i.e. d(i,i) = 0. Then, the elements in each column are sorted in ascending order.

[0052] The sequence number Index of the data point is taken as the horizontal coordinate, and the elements in the kth column are taken as the vertical coordinate to construct the kth distance curve, where 1≤k≤n and 1≤Index≤n. In the kth distance curve, when the horizontal coordinate Index takes the value i, the vertical coordinate is the distance value of the ith row in the kth column.

[0053] Each distance curve is fitted by using the least squares method, and the calculation method of the least squares method is as follows:

[0054]

[0055] where L is the fitting loss function, y k represents the kth distance curve function, and f(x) represents the fitting curve function, and has:

[0056] f(x) = θ0+ θ1x + θ2x 2 + … + θ q x q ,

[0057] where x is the fitting function variable, and θ λis the coefficient of the λth term, λ = 0, 1, 2,..., q, q is the polynomial order of f(x).

[0058] Calculate the goodness of fit value R between each fitted curve and the corresponding distance curve 2 , according to the set goodness of fit value R 2 The optimal range further finds the most suitable order in the fitted curve function, so as to obtain the best fitted curve. The optimal range of the goodness of fit value in the embodiment is R 2 ≥ 0.99.

[0059] The point with the largest change in the kth best fitted curve is taken as the inflection point, and the corresponding distance value of the inflection point in the kth distance curve is the kth neighborhood radius Eps k .

[0060] Calculate the number of data points contained in the neighborhood radius range of each inflection point in the laser radar point cloud, and use mathematical expectation to generate the neighbor point threshold:

[0061]

[0062] Where Minpts k is the kth neighbor point threshold; β is the noise suppression threshold, and has 0 ≤ β < 1 (β is set to 0.5 in the experiment); P α is the number of data points contained in the kth neighborhood radius Eps k range of the αth data point in the laser radar point cloud, 1 ≤ α ≤ n.

[0063] The clustering evaluation index (CH) index evaluates the clustering quality by calculating the consistency within the cluster (i.e. the closeness between the points in the same cluster) and the separation between the clusters (i.e. the distance between the centers of different clusters). After Eps k and Minpts k are generated, Eps k and Minpts k are brought into the DBSCAN algorithm for clustering. The higher the CH index, the better the clustering result. When selecting the DBSCAN parameters, the CH indexes of different parameter combinations can be compared. By calculating the CH indexes under different neighborhood radius and neighbor point threshold combinations, the clustering effect of each combination can be quantitatively evaluated, so as to select the parameter combination with the highest CH index, and the corresponding Eps k and Minpts k are the optimal, and finally realize the laser radar point cloud denoising.

[0064] The expression for calculating the CH index is:

[0065]

[0066] Where c is the total number of clusters.

[0067] B is the inter-class scatter, defined as:

[0068]

[0069] a j Let c be the number of samples in the j-th cluster. j Let b be the centroid of the j-th cluster, where j = 1, 2, ..., c, and b is the global centroid, which is the average value of all samples.

[0070] W is the within-class dispersion (within-class variance), defined as:

[0071]

[0072] Among them, D j Let γ be the set of samples in the j-th cluster, and let D be the value of D. j The sample points in the data.

[0073] Specific Implementation Method Two: Refer to Figure 3 to Figure 2 This embodiment describes a lidar point cloud noise reduction method based on an improved DBSCAN. Taking the Stanford rabbit point cloud model as an example, it uses a distance matrix calculation method to measure the distance between points in the point cloud set. Specifically:

[0074] The point cloud dataset is represented as a matrix D. n*3 Then, Euclidean distance is used to calculate the distance between each pair of data points in the dataset, resulting in the distance distribution matrix dist. n*n For the distance distribution matrix dist n*n Sort the data (both rows and columns in ascending order) to obtain the distance curve for each column. Fit each distance curve using the least squares method, and calculate the goodness-of-fit R-squared to evaluate the model's performance. 2 , obtain R 2 The optimal term k, R when ≥0.99 2 The calculation expression is as follows:

[0075]

[0076] Among them, SS resid Sum of squared residuals, representing the sum of squares of the differences between the actual observed values ​​and the fitted values; SS total The total sum of squares represents the sum of squares of the differences between the actual observed values ​​and their mean.

[0077] Figure 2 The distance curve and fitted curve corresponding to the 100th data point are shown. At this point, R... 2= 0.9901. Next, the stationary point on the fitted curve is calculated, according to Figure 2 the middle distance curve, the data point where the change begins is near Index = 10000, then the point selected into the neighborhood radius list is the maximum inflection point in 0-10000, as shown in Figure 3 .

[0078] After generating Eps k and Minpts k , they are brought into the DBSCAN algorithm for clustering, when the calculated CH index is the highest, the parameters at this time are defined as the optimal parameters.

[0079] Based on the above evaluation index of the denoising effect, the embodiment can complete the denoising task without multiple parameter tests, and can improve the noise recall rate to a certain extent.

[0080] Experimental verification

[0081] The experiment first uses the rabbit, pony and elephant point cloud models in the Stanford database for simulation analysis, adds Gaussian noise points with a mean of 0 and a standard deviation of 0.1 to the original point cloud to form a noisy point cloud. Then the public real residential area point cloud provided by NSF (National Science Foundation) is tested. In the experiment, the point cloud data only includes position information. Based on the above point cloud data, the optimal parameter set calculated according to the method described in the embodiment is as shown in Table 1.

[0082] Table 1 Optimal neighborhood radius and adjacent point threshold value given by the method

[0083]

[0084] After setting the above optimal parameters, the DBSCAN denoising effect of the rabbit, pony and elephant point cloud models is as shown in Figure 5 . From the results shown in Figure 5 , it is obvious that the method can accurately filter noise and leave clear target objects.

[0085] The introduction of the denoising precision P d , the noise recall rate R d , and the original point retention rate R oTo quantitatively compare the denoising degree of the filtering algorithm. The denoising precision refers to the proportion of points that are actually noise among the points correctly marked as noise by the algorithm, reflecting the accuracy of the algorithm in identifying noise. The noise recall rate refers to the proportion of all true noise points that are correctly marked as noise by the algorithm, measuring the ability of the algorithm to identify noise. The original point retention rate refers to the proportion of points in the original data that are not marked as noise and are correctly retained in the clustering results, measuring the ability of the algorithm to retain original information while denoising. By considering these indicators comprehensively, the performance of the algorithm can be more comprehensively evaluated. The calculation formulas of each indicator are as follows:

[0086]

[0087] In the formula, N q is the number of filtered noise; N g is the total number of noise; N y is the total number of filtered point clouds; N o is the number of signal points in the remaining point cloud; N f is the number of remaining points after filtering. The number of N q , N g , N y , N o , N f after denoising is shown in the table, where N is the total number of point clouds.

[0088] Table 2 Results after denoising

[0089]

[0090] The evaluation indicators after denoising of the present embodiment are as follows:

[0091] Table 3 Evaluation indicators after denoising

[0092]

[0093] The denoising precision, noise recall rate, and original point retention rate of the present embodiment in the point cloud model are all maintained at a high level. However, due to the complexity of the target object and environmental information in the residential scene, noise is easily mixed with the main object, resulting in a slight decrease in denoising precision and noise recall rate, but the overall effect remains good.

[0094] While the application has been described with reference to particular embodiments thereof, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present application. It will be apparent to those skilled in the art that numerous modifications can be made within the scope of the present application as defined by the appended claims. It is intended that all such modification fall within the spirit and scope of the present application. It will be understood that the features described in connection with one embodiment can be used in connection with another embodiment.

Claims

1. A laser radar point cloud denoising method based on an improved DBSCAN, characterized in that, The application relates to a method for calculating a neighborhood radius and a neighboring point threshold value according to a laser radar point cloud data set, calculating an optimal neighborhood radius and a neighboring point threshold value according to a clustering evaluation index, and realizing laser radar point cloud noise reduction by DBSCAN according to the optimal neighborhood radius and the neighboring point threshold value. The method comprises the following steps: The method comprises the following steps: The laser radar point cloud data set is expressed in the form of an n*m matrix, wherein n is the total number of data points in the laser radar point cloud data set, and m is the total number of features of the data points. The Euclidean distances between two data points are calculated respectively, and a distance distribution matrix is constructed by using all the Euclidean distances. The elements in each row and the elements in each column of the distance distribution matrix are sequentially sorted in ascending order. The serial numbers of the data points are taken as the horizontal coordinates, and the kth column elements of the sorted distance distribution matrix are taken as the vertical coordinates, so that the kth distance curve is constructed, wherein 1<=k<=n. The least square method is used to fit each distance curve respectively, and the goodness-of-fit values between the distance curves and the corresponding fitting curves are calculated, so that the optimal order of the fitting curve in the optimal goodness-of-fit value range is obtained, and the optimal fitting curve is obtained. The point with the largest change in the kth best fitting curve is taken as the inflection point, and the distance value corresponding to the inflection point in the kth distance curve is the kth neighborhood radius Eps k ; The method comprises the following steps: corresponding neighborhood radius and the neighboring point threshold Minpts k are brought into the DBSCAN algorithm for clustering, and the clustering evaluation index of the DBSCAN algorithm is calculated, A pair of neighborhood radius and neighboring point threshold value corresponding to the highest clustering evaluation index value is selected as the optimal neighborhood radius and the neighboring point threshold value.

2. The improved DBSCAN-based LiDAR point cloud denoising method according to claim 1, wherein, The distance distribution matrix is expressed as follows: D n*n = {d(i,j) | 1≤i≤n, 1≤j≤n}, Wherein d(i,j) represents the Euclidean distance between the ith data point and the jth data point.

3. The improved DBSCAN-based LiDAR point cloud denoising method according to claim 1, wherein, The least square method is used to fit each distance curve respectively, and the goodness-of-fit values between the distance curves and the corresponding fitting curves are calculated, so that the optimal order of the fitting curve in the optimal goodness-of-fit value range is obtained, and the optimal fitting curve is obtained. wherein L is a fitting loss function, y k represents the kth distance curve function, f(x) represents a fitting curve function corresponding to the kth distance curve function, and has: f(x) = θ0+ θ1x + θ2x2 2 +…+θ q x q , where x is a variable of the fitting curve function, θ λ is the coefficient of the λth term, λ = 0, 1, 2,..., q, q is the polynomial order of f(x).

4. The improved DBSCAN-based LiDAR point cloud denoising method according to claim 1, wherein, The method comprises the following steps: The neighboring point threshold value is calculated according to the following formula: wherein Minpts k is the kth neighborhood point threshold, 1≤k≤n, β is a noise suppression threshold, and has 0≤β<1, P α is the number of data points contained in the kth neighborhood radius Eps k range of the αth data point in the laser radar point cloud, 1≤α≤n.

5. The improved DBSCAN based LiDAR point cloud denoising method according to claim 1, wherein, The clustering evaluation index is calculated according to the following formula: Wherein CH is the clustering evaluation index, c is the total number of classes, B is the inter-class dispersion, and W is the intra-class dispersion.

6. The improved DBSCAN-based LiDAR point cloud denoising method according to claim 5, characterized in that, The expression of the inter-class dispersion B is as follows: where a j is the number of samples in the jth cluster, c j is the center point of the jth cluster, j = 1, 2,..., c, and b is the global centroid.

7. The improved DBSCAN-based LiDAR point cloud denoising method according to claim 5 or 6, characterized in that, The expression of the intra-class dispersion W is as follows: where D j is the set of samples in the jth cluster, and γ is the sample point in D j .

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