Laser point cloud simplification method based on probability membership degree

Abstract

The invention provides a laser point cloud simplification method based on probability membership, and the method comprises the steps: carrying out the independent simplification of a feature point cloud to retain geometric features, and carrying out the simplification of remaining points; in the simplification process, a neighborhood curvature deviation model is designed to identify feature points, and probability membership is introduced in subsequent simplification to serve as the basis of point cloud sub-cluster division. For the sub-clusters, the invention provides a hierarchical simplification algorithm based on probability membership features, and aims to control the number of output points and realize uniform distribution at the same time. And finally, through average geometric error analysis and grid model reconstruction effect comparison, it is proved that geometric features are effectively reserved, and meanwhile uniform distribution of output points is kept. In addition, according to the method, the reduction rate and the function retention rate can be flexibly adjusted to meet the preference of the user.

Description

Technical Field

[0001] The present application belongs to the technical field of machine learning and computer vision, and specifically relates to a laser point cloud simplification method based on probability membership. Background Art

[0002] With the widespread application of LiDAR and 3D scanning technology, the amount of point cloud data generated is huge. Point cloud simplification can significantly reduce the amount of data and improve processing and storage efficiency. Especially in unmanned driving and robot navigation, real-time data processing is crucial, and point cloud simplification can help achieve faster decision-making and response speed.

[0003] From a topological point of view, solutions for point cloud simplification can be roughly divided into two categories: grid-based methods and point-based methods. In the past, grid-based methods were widely favored. However, these methods require mesh reconstruction, resulting in a large amount of computing resource utilization. Therefore, point-based simplification techniques are gradually gaining popularity when processing large amounts of point cloud data in contemporary scenarios.

[0004] In point-based simplification methods, it is crucial to preserve the geometric features of the point cloud. Martin et al. (mentioned in the literature P.Suchde, T.Jacquemin, and O.Davydov, "Point cloud generation for meshfreemethods: an overview," Archives of Computational Methods in Engineering, vol.30, no.2, pp.889-915, Sept.2022.) proposed a uniform grid downsampling method; however, this method does not consider the preservation of feature points. Therefore, the simplified point cloud may lose the complex details of the surface. To address this limitation, Lee et al. The literature KHLee, H.Woo, and T.Suk, "Point data reduction using 3D grids," TheInternational Journal of Advanced Manufacturing Technology, vol.18, pp.201-210, Aug.2001. introduced the use of normal deviation as feature information based on uniform grid partitioning. Similarly, Alexa et al. M.Alexa, J.Behr, D.Cohen-Or, S.Fleishman, D.Levin, and CTSilva, "Computing and rendering point set surfaces," IEEE Trans.Vis.Comput.Graphics, vol.9, no.1, pp.3-15, Jan. / Mar.2003. proposed a simplification method that relies on moving least squares fitting, but it also has shortcomings in preserving surface feature points. Song et al. in the literature H.Song and H.-Y.Feng, "A progressive pointcloud simplification algorithm with preserved sharp edge data," TheInternational Journal of Advanced Manufacturing Technology, vol.45, pp.583-592, Feb.2009. improved Alexa's method by introducing surface feature detection.

[0005] In recent years, researchers have introduced methods to simplify point clouds using graph Laplacian (e.g., C. Luo, X. Ge, and Y. Wang, “Uniformization and density adaptation for point cloud data via graph Laplacian,” Comput. Graph. Forum, vol. 37, no. 1, pp. 325-337, Feb. 2018. and J. Zeng, G. Cheung, M. Ng, J. Pang, and Y. Cheng, “3D point cloud denoising using graph Laplacian regularization of a low dimensional manifold model,” IEEE Trans. Image Process, vol. 29, pp. 3474-3489, Dec. 2019.). Although these methods achieve effective simplification, they usually have high computational complexity. Several deep learning-based point cloud simplification or sampling methods have been proposed for specific tasks such as classification, registration, and recognition (such as J. Yang et al, "Modeling point clouds with self-attention and Gumbel subset sampling," in Proc. IEEE / CVF Conf. Comput. Vis. Pattern Recognit. (CVPR), pp. 3323-3332, Jun. 2019. and E. Nezhadarya, E. Taghavi, R. Razani, B. Liu, and J. Luo, "Adaptive hierarchical down-sampling for point cloud classification," in Proc. IEEE / CVF Conf. Comput. Vis. Pattern Recognit. (CVPR), pp. 1295612964, Jun. 2020.) However, these methods still face challenges in balancing uniformity and feature preservation.

[0006] The existing optimal point cloud simplification scheme needs to meet several key requirements: controllability of simplification ratio, preservation of geometric features, and uniform distribution of results. Early point cloud simplification schemes mainly focused on achieving uniform point distribution after simplification, while recent point cloud simplification methods tend to emphasize preserving point cloud geometric features. Since the controllability of the simplification ratio determines the versatility of the method, how to balance the three key requirements and improve the versatility of the scheme has become a technical problem that needs to be solved urgently. Summary of the invention

[0007] In order to solve the above problems existing in the prior art, the present application provides a laser point cloud simplification method based on probability membership. The technical problem to be solved by the present application is achieved through the following technical solutions:

[0008] A laser point cloud simplification method based on probability membership includes:

[0009] S100, obtaining an original point cloud, and extracting feature points from the original point cloud by combining a k-nearest neighbor algorithm and a PCA analysis algorithm;

[0010] S200, simplifying the feature points using a simplification algorithm to remove non-member points in the sub-cluster, and obtaining a simplified feature point result;

[0011] S300, taking non-feature points and non-member points in the original point cloud as residual points, and simplifying the features of the residual points using a simplification algorithm to obtain a simplified result of the residual points;

[0012] S400, fusing the simplified result of the feature points and the simplified result of the remaining points to obtain a simplified result of the original point cloud.

[0013] Beneficial effects:

[0014] This application proposes a laser point cloud simplification method based on probabilistic membership. First, the feature point cloud is independently simplified to retain the geometric features, and then the remaining points are simplified. During the simplification process, a neighborhood curvature deviation model is designed to identify feature points, and probabilistic membership is introduced in subsequent simplification as the basis for dividing the point cloud into subclusters. For subclusters, this application proposes a hierarchical simplification algorithm based on probabilistic membership features, which aims to control the number of output points while achieving uniform distribution. Finally, through the comparison of average geometric error analysis and mesh model reconstruction effects, it is confirmed that this application effectively retains geometric features while maintaining a uniform distribution of output points. In addition, this application can also flexibly adjust the reduction rate and function retention rate to meet user preferences.

[0015] The present application will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1It is a flowchart of a laser point cloud simplification method based on probability membership provided by the present application;

[0017] Figure 2 is a schematic diagram of the original point cloud and the extracted feature point cloud of the buuny model provided in this application;

[0018] Figure 3 This is a simplified result diagram of the Buuny model provided by this application;

[0019] Figure 4 is a schematic diagram of the average geometric errors of two models of different methods provided in this application;

[0020] Figure 5 It is a schematic diagram of a grid model of simplified results of each method provided in this application. DETAILED DESCRIPTION

[0021] The present application is further described in detail below in conjunction with specific embodiments, but the implementation methods of the present application are not limited thereto.

[0022] like Figure 1 As shown, the present application provides a laser point cloud simplification method based on probability membership, including:

[0023] S100, obtaining an original point cloud, and extracting feature points from the original point cloud by combining a k-nearest neighbor algorithm and a PCA analysis algorithm;

[0024] In order to preserve the geometric features of the point cloud, feature point clouds must be extracted from the original point cloud. This application chooses to use curvature measurement because it is a commonly used method. Considering the tight computing resources in the process of large-scale point cloud processing, K nearest neighbor (KNN) (literature Zhang, Shichao, et al, "Efficient kNN classification with different numbers of nearest neighbors," IEEE transactions on neural networks and learning systems, vol. 29, no. 5, pp. 1774-1785, 2017) search is used to obtain neighborhood information. Feature points are extracted by combining neighborhood information with principal component analysis (PCA) (literature M. Ringnér, "What is principal component analysis," Nat Biotechnol, vol. 26, no. 3, pp. 303-304, Mar. 2008).

[0025] S200, simplifying the feature points using a simplification algorithm to remove non-member points in the sub-cluster, and obtaining a simplified feature point result;

[0026] S300, taking non-feature points and non-member points in the original point cloud as residual points, and simplifying the features of the residual points using a simplification algorithm to obtain a simplified result of the residual points;

[0027] In the simplification process using the simplification algorithm, the simplification rate is set to control the first ratio of the number of point clouds in the simplified result of the original point cloud to the original point cloud. In the simplification process using the simplification algorithm, the feature retention rate r is set f , to individually control the second ratio of the simplified result of feature points to the number of all feature points, and the third ratio of the simplified result of remaining points to the number of remaining points.

[0028] The input parameters of the simplification algorithm in this application mainly include the original point cloud, simplification rate and feature retention rate r f By adjusting r f , the user can effectively control the degree of feature retention. In addition, the simplification rate of the remaining point cloud can be calculated based on the simplification rate and feature retention rate.

[0029] S400, fusing the simplified result of the feature points and the simplified result of the remaining points to obtain the simplified result of the original point cloud.

[0030] As an optional implementation of the present application, S100 includes:

[0031] S110, obtaining an original point cloud;

[0032] S120, searching for a neighborhood matrix of each point cloud point in the original point cloud using a k-nearest neighbor algorithm;

[0033] S130, for each point cloud point, estimate the curvature of the point cloud point and the average curvature in the neighborhood according to the neighborhood matrix of the point cloud point and using the PCA analysis algorithm;

[0034] S140, selecting a feature point according to the curvature of each point cloud point and the average curvature in the neighborhood.

[0035] As an optional implementation of the present application, S140 includes:

[0036] S141, for each point cloud point, substituting the curvature of the point cloud point and the average curvature in the neighborhood into a Z-score model calculation formula to obtain a Z score for each point cloud point, where the Z score represents the standard deviation of the curvature of the point cloud point and the average curvature in the neighborhood;

[0037] The Z-score model calculation formula is expressed as:

[0038]

[0039] Where Z represents the Z score of the point cloud point, C represents the curvature of the point cloud point, μ is the average curvature in the neighborhood of the point cloud point, and δ is the standard deviation of the average curvature in the neighborhood.

[0040] S142, select the Z score greater than the predetermined deviation threshold Z th point cloud points, and select the point cloud points whose curvature is higher than the curvature threshold as feature points.

[0041] As an optional implementation of the present application, the simplified algorithm execution process includes:

[0042] a, obtain input points and simplification rates;

[0043] b. Clustering the input points using a minibatch k-means clustering algorithm to divide the input points into multiple subclusters to obtain a center matrix and multiple subclusters, and calculating the probability of the input points in each subcluster to belong to the center point of the subcluster; the center matrix represents the position of the center point of each subcluster;

[0044] This step includes: b1, clustering all feature points using the Kmeans clustering algorithm, dividing the feature points into k subclusters to obtain k subclusters and a center matrix; b2, for each subcluster, using the PCM calculation formula to calculate the probability membership of the member points in the subcluster to the center point of the subcluster.

[0045] The PCM calculation formula is expressed as:

[0046]

[0047]

[0048] In the formula, v j represents the center point of the jth subcluster, μ ij Represents the feature point p i For v j The probability membership of j Is a customizable constant.

[0049] c. For each sub-cluster, the member points in the sub-cluster are arranged from large to small according to the probability membership to obtain the arrangement result;

[0050] d, set the percentage threshold r of all sub-clusters out , and use the percentage threshold to determine the probability membership threshold;

[0051] e. For each sub-cluster, member points in the sub-cluster whose probability membership is not greater than the membership threshold are taken as external points;

[0052] f, for each sub-cluster, clustering the external points of the sub-cluster using the k-means clustering method and the simplification rate, and selecting the external point closest to the cluster center as the output point;

[0053] g, for each sub-cluster, take the non-external points in the sub-cluster as member points, and re-calculate df until the number of member points in the sub-cluster is no more than the predetermined number of member points to obtain a simplified sub-cluster;

[0054] h, for each simplified sub-cluster, re-cluster the simplified sub-cluster using the simplification rate described in the k-means clustering method, and select the external point closest to the cluster center as the output point;

[0055] i, simplify the result by treating all output points as input points.

[0056] In the above process, this application chooses to stick to k-means clustering because of its high efficiency and reliable performance. In addition, before each iteration begins, the number of output points must be pre-calculated in order to effectively adjust the simplification rate.

[0057] As an optional implementation of the present application, after S400, the laser point cloud simplification method based on probability membership further includes:

[0058] Meshing the simplified result of the original point cloud;

[0059] The average value of the minimum Euclidean distance from the original point cloud to the corresponding grid is calculated, and the average value is used as an evaluation index for evaluating the simplification of the original point cloud.

[0060] In point cloud simplification, the commonly used evaluation index is the average geometric error (reference Y. Miao, R. Pajarola, J. Feng, Curvature-aware adaptive re-sampling for point sampled geometry, Comput.-Aided Des. 41 (6) (2009) 395-403). The calculation formula is as follows:

[0061]

[0062] Where d(p,S') represents the minimum Euclidean distance from point p in the original point cloud S to the simplified point cloud mesh surface S', (H. Song, H.-Y. Feng, A global clustering approach to point cloud simplification with a specified data reduction ratio, Comput.-Aided Des. 40(3)(2008) 281-292. Its meaning is specifically introduced). The mesh surface S' is constructed by the crust surface reconstruction algorithm implemented in MATLAB (refer to L. Di Angelo, P. Di Stefano, L. Giaccari, A new mesh-growing algorithm for fast surface reconstruction, Comput.-Aided Des. 43(6)(2011) 639-650.). The average geometric error often indicates the uniformity of the simplified result, because the more uniform the result, the more consistent the reconstruction result of the flat area is with the original point cloud. In addition, due to the lack of indicators to evaluate the degree of feature preservation, subsequent experimental studies will compare the reconstructed models of the simplified results to analyze the ability of the algorithm to restore the original model.

[0063] This application proposes a point cloud simplification method based on probabilistic membership. The method uses a Z-score model to standardize the curvature of the point cloud, which is conducive to the evaluation of feature information. After the scoring process, the point cloud is divided into feature subsets and non-feature subsets. Subsequently, k-means and Possibilistic C-Means (PCM) are used to sub-cluster the two point clouds and obtain probabilistic membership. Based on probabilistic membership, this application develops a hierarchical subcluster simplification scheme. The simplified results of all subclusters are combined to produce the final output. While maintaining the detailed features of the point cloud and the consistency of the simplified results, the proposed algorithm allows the user to adjust the level of point cloud reduction and geometric feature retention.

[0064] The effect of this application can be further illustrated by the following simulation experiment.

[0065] 1. Simulation conditions

[0066] In this study, the proposed method was applied, data visualization was performed, and errors were estimated, all of which were programmed using MATLAB. All experimental datasets were from the point cloud dataset constructed by Stanford University.

[0067] In the following, this application will provide a simplified example to illustrate the proposed method. This application also conducts a comparative analysis of various downsampling methods to evaluate the effectiveness of the proposed algorithm. The compared methods include random downsampling (RD), uniform grid downsampling (UG) (introduced in P.Suchde, T.Jacquemin, and O.Davydov, "Point cloud generation for meshfree methods: an overview," Archives of Computational Methods in Engineering, vol.30, no.2, pp.889-915, Sept.2022.), Laplacian graph (LG) (reference J.Qi, W.Hu, and Z.Guo, "Feature preserving and uniformitycontrollable pointcloud simplification on graph," in 2019IEEE International Conference on Multimedia and Expo (ICME), pp.284-289, Jul.2019.) and simplification algorithm based on partition strategy (PS) (reference S.Wang et al, "A new point cloud simplification method with feature and integrity preservation by partition strategy,” Measurement, vol. 197, p. 111173-111189, Jun. 2022.). Next, this application analyzes the performance of the method from two aspects of simplified results: surface reconstruction model and average geometric error.

[0068] In the experiments of this application, the proposed algorithm involves multiple stages, each of which involves specific parameter values. These parameters and their experimental values ​​are listed in Table 1.

[0069] Table 1 Simulation parameters

[0070]

[0071] 2. Simulation content

[0072] 1) Simulation Example

[0073] exist Figure 2 In this paper, the original point cloud and the extracted feature point cloud of the bunny model are shown. When the simplification rate is 10%, the paper compares the different r fThe simplified result of Figure 3 In the left side, r f The value of is 0.4, and the r on the right f The value of is 0.1. Figure 3 From the analysis, it is clear that the image on the left has a higher r f The right image depicts the overall distribution more. Users can freely set r as needed. f value.

[0074] 2) Comparative analysis

[0075] This application uses the Buuny and Horse model to evaluate the proposed method and the above methods. Four reduction rates (10%, 20%, 30%, and 40%) are used for comparative analysis. Due to the limitations of UG and PS in controlling the reduction rate, this application must constantly adjust the parameters to approach the desired reduction rate. The average geometric error of each method is shown in Figure 4 As shown. After analyzing the figure, the present application found that the average geometric error of the proposed method was significantly lower than that of other methods at different reduction rates. Specifically, when the reduction rate is low, methods such as PS and LG that can retain features show poor performance. This can be attributed to their inability to fully control the proportion of feature points, resulting in excessive retention of feature points, thus affecting the uniformity of the results. This observation indirectly emphasizes the substantial advantage of the algorithm of the present application in achieving uniform results. Similarly, the UG method pays more attention to ensuring the uniform distribution of the simplified point cloud. However, when the simplification rate is high and the generated point cloud contains a sufficient number of points, the description of fine details becomes more critical, and the advantage of UG becomes less obvious.

[0076] In order to evaluate the degree of feature preservation, this application uses the above method to simplify the armadillo model at a reduction rate of 20%. Subsequently, the mesh model is reconstructed using the simplified point cloud. The results are shown in Figure 2. Figure 5As shown. Through comparative analysis of the original point cloud reconstructed model, this application found that RD's reconstruction performance was insufficient. This is due to its emphasis on speed, which leads to a lack of detail and uniformity in the simplified results. As for UG, its focus is on ensuring the consistency of the simplified results, resulting in a relatively smooth reconstructed model, but the details of the armadillo's leg muscles appear blurred. PS uses curvature as feature information, allowing the reconstructed model to better retain sharp features, such as the curve of the armadillo's forehead. However, the details of the thigh are still not clear enough. LG performs well in retaining details, but shows obvious roughness in flat areas. The reconstructed model of this method is superior to other methods in feature retention. In addition, it shows good smoothness in flat areas. In summary, the method described in this study provides a flexible and controllable reduction rate, which effectively ensures the uniform distribution and retention of features in the reduction results. In addition, the method of this application allows parameters to be adjusted to modify the level of feature retention in the point cloud to meet different requirements. These advantages are particularly evident in the comparative experiments.

[0077] It is worth noting that the terms "first" and "second" in this application are used for descriptive purposes only and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of this application, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0078] Although the present application is described herein in conjunction with various embodiments, in the process of implementing the claimed application, those skilled in the art may understand and implement other variations of the disclosed embodiments by reviewing the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality of components or steps.

[0079] The above content is a further detailed description of the present application in combination with specific preferred implementation methods, and it cannot be determined that the specific implementation of the present application is limited to these descriptions. For ordinary technicians in the technical field to which the present application belongs, several simple deductions or substitutions can be made without departing from the concept of the present application, which should be deemed to fall within the scope of protection of the present application.

Claims

1. A laser point cloud simplification method based on probability membership, characterized in that: include: S100, obtaining an original point cloud, and extracting feature points from the original point cloud by combining a k-nearest neighbor algorithm and a PCA analysis algorithm; S200, simplifying the feature points using a simplification algorithm to remove non-member points in the sub-cluster, and obtaining a simplified feature point result; S300, taking non-feature points and non-member points in the original point cloud as residual points, and simplifying the features of the residual points using a simplification algorithm to obtain a simplified result of the residual points; S400, fusing the simplified result of the feature points and the simplified result of the remaining points to obtain a simplified result of the original point cloud.

2. The laser point cloud simplification method based on probability membership according to claim 1, characterized in that: S100 includes: S110, obtaining the original point cloud; S120, searching for a neighborhood matrix of each point cloud point in the original point cloud using a k-nearest neighbor algorithm; S130, for each point cloud point, estimate the curvature of the point cloud point and the average curvature in the neighborhood according to the neighborhood matrix of the point cloud point and using the PCA analysis algorithm; S140, selecting a feature point according to the curvature of each point cloud point and the average curvature in the neighborhood.

3. The laser point cloud simplification method based on probability membership according to claim 2, characterized in that: S140 includes: S141, for each point cloud point, substituting the curvature of the point cloud point and the average curvature in the neighborhood into a Z-score model calculation formula to obtain a Z score for each point cloud point, where the Z score represents the standard deviation of the curvature of the point cloud point and the average curvature in the neighborhood; S142, selecting point cloud points whose Z scores are greater than a predetermined deviation threshold, and selecting point cloud points whose curvatures are higher than the curvature threshold as feature points.

4. The laser point cloud simplification method based on probability membership according to claim 3 is characterized in that: The Z-score model calculation formula is expressed as: Where Z represents the Z score of the point cloud point, C represents the curvature of the point cloud point, μ is the average curvature in the neighborhood of the point cloud point, and δ is the standard deviation of the average curvature in the neighborhood.

5. The laser point cloud simplification method based on probability membership according to claim 1, characterized in that: The simplified algorithm execution process includes: a, obtain input points and simplification rates; b. Clustering the input points using a minibatch k-means clustering algorithm to divide the input points into multiple subclusters to obtain a center matrix and multiple subclusters, and calculating the probability of the input points in each subcluster to belong to the center point of the subcluster; the center matrix represents the position of the center point of each subcluster; c. For each sub-cluster, the member points in the sub-cluster are arranged from large to small according to the probability membership to obtain the arrangement result; d. Set the percentage threshold of all subclusters and use the percentage threshold to determine the probability membership threshold; e. For each sub-cluster, member points in the sub-cluster whose probability membership is not greater than the membership threshold are taken as external points; f, for each sub-cluster, clustering the external points of the sub-cluster using the k-means clustering method and the simplification rate, and selecting the external point closest to the cluster center as the output point; g, for each sub-cluster, take the non-external points in the sub-cluster as member points, and re-calculate df until the number of member points in the sub-cluster is no more than the predetermined number of member points to obtain a simplified sub-cluster; h, for each simplified sub-cluster, re-cluster the simplified sub-cluster using the simplification rate described in the k-means clustering method, and select the external point closest to the cluster center as the output point; i, simplify the result by treating all output points as input points.

6. The laser point cloud simplification method based on probability membership according to claim 5, characterized in that b include: b1, use Kmeans clustering algorithm to cluster all feature points, divide the feature points into k sub-clusters to obtain k sub-clusters and center matrix; b2, for each sub-cluster, use the PCM calculation formula to calculate the probability of membership of the member points in the sub-cluster to the center point of the sub-cluster.

7. The laser point cloud simplification method based on probability membership according to claim 6, characterized in that: The PCM calculation formula is expressed as: In the formula, v j represents the center point of the jth subcluster, μ ij Represents the feature point p i For v j The probability membership of j Is a customizable constant.

8. The laser point cloud simplification method based on probability membership according to claim 1, characterized in that: In the simplification process using the simplification algorithm, a simplification rate is set to control a first ratio of the number of point clouds in the simplified result of the original point cloud to the original point cloud.

9. The laser point cloud simplification method based on probability membership according to claim 1, characterized in that: In the simplification process using the simplification algorithm, the feature retention rate is set to individually control the second ratio of the simplified result of the feature points to the number of all feature points and the third ratio of the simplified result of the remaining points to the number of remaining points.

10. The laser point cloud simplification method based on probability membership according to claim 1, characterized in that: After S400, the laser point cloud simplification method based on probability membership further includes: Meshing the simplified result of the original point cloud; The average value of the minimum Euclidean distance from the original point cloud to the corresponding grid is calculated, and the average value is used as a simplification index for evaluating the simplification of the original point cloud.

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