An improved euclidean clustering-based industrial scene part instance segmentation method

Abstract

The application discloses an industrial scene part instance segmentation method based on improved Euclidean clustering, which comprises the following steps: firstly, the real industrial scene point cloud collected by a visual system and comprising multiple workpieces is preprocessed to remove a background work plane, background redundant points, outliers and workpiece contact point clouds; then, a Euclidean clustering algorithm is used on the preprocessed point cloud file to perform instance segmentation clustering of two-dimensional Euclidean distance and three-dimensional Euclidean distance respectively, the clustering results are fused to complete instance-level position division by using the position relationship of the point cloud, and single workpiece point cloud is segmented; finally, the removed contact point cloud is dynamically backfilled to the segmented workpiece point cloud, and workpiece instance segmentation in the industrial scene is completed. The application designs a high-stability and high-real-time instance segmentation method without requiring a large amount of training data, and solves the technical problem of segmenting a target scene part pile into a series of single workpieces which is urgently needed in the field of industrial robots.

Description

Technical Field

[0001] This invention relates to a method for segmenting industrial scene parts based on improved Euclidean clustering, belonging to the field of computer vision technology. Background Technology

[0002] In recent years, China's manufacturing industry has experienced rapid development. To promote the upgrading and transformation of the manufacturing sector, the goal is to drive it towards high-end and intelligent development, strengthen technological innovation and independent R&D capabilities, and promote the deep integration of industrialization and informatization. Against this backdrop, the integration of computer vision with industrial production has become an important research area, especially vision-based robotic grasping. By utilizing vision technology, it is possible to accurately detect and locate multiple scattered targets in industrial scenarios, thereby enabling intelligent grasping operations by robotic arms. The three key tasks in vision-based robotic grasping are target localization, target pose estimation, and grasping estimation, with target localization being a particularly hot research topic in recent years.

[0003] Specifically, target localization in visual localization includes classless target localization, target detection, and target instance segmentation. This task provides regions of target objects in the input data. Classless target localization only outputs the potential regions of the targets without knowing their categories; target detection provides the bounding boxes of the target objects and their categories; target instance segmentation further provides pixel-level or point-level regions of the target objects along their categories. Among these, target instance segmentation is one of the most challenging tasks in robot grasping. Target instance segmentation requires not only distinguishing different individuals of the same category but also providing pixel / point cloud-level segmentation masks, that is, labeling every pixel or point cloud of each target object. This is equivalent to combining semantic segmentation and target detection, greatly increasing the research difficulty of the algorithm.

[0004] Deep learning has achieved significant success in instance segmentation. By using deep neural networks, this method can automatically learn and predict object boundaries and pixel-level segmentation results in images. Its advantages include the ability to handle complex scenes and multiple object instances, and with sufficient training, it can achieve high accuracy. However, deep learning-based instance segmentation algorithms rely on large-scale labeled data to support the training of network parameters, creating a dilemma of "the more intelligence, the more manual (annotation)." In terms of acquiring industrial target data, the high cost of labeling training samples in real-world industrial scenarios further exacerbates this dilemma. Summary of the Invention

[0005] The technical problem solved by this invention is to address the high training cost of deep neural networks in instance segmentation algorithms, and to provide an industrial scene part instance segmentation method based on improved Euclidean clustering.

[0006] This invention is achieved using the following technical solution:

[0007] An industrial scene part instance segmentation method based on improved Euclidean clustering includes the following steps:

[0008] S1. Preprocess the real industrial scene point cloud collected by the vision system, which includes multiple workpieces, to remove redundant point sets, working planes, false edges, isolated noise points, and workpiece contact edge points from the real industrial scene point cloud image.

[0009] S2. Apply Euclidean clustering algorithm to the preprocessed point cloud file, perform instance segmentation and clustering using two-dimensional Euclidean distance and three-dimensional Euclidean distance respectively, fuse the clustering results and use the point cloud position relationship to complete the instance-level position division, and segment out the point cloud of a single workpiece.

[0010] S3. Dynamically refill the point cloud of the workpiece contact edge points removed in step S1 into the segmented workpiece point cloud to complete the workpiece instance segmentation in the industrial scene.

[0011] In an industrial scene part instance segmentation method based on improved Euclidean clustering of the present invention, step S1 further includes the following sub-steps:

[0012] S11. Use a binocular structured light 3D imaging system to acquire N point cloud images of the real industrial scene where the workpiece is located.

[0013] S12. Use the RANSAC method to fit the plane in the scene, and use the fitted plane parameters and the centroid coordinates of the plane point set to remove the redundant point set working plane of the scene point cloud image obtained in sub-step S11.

[0014] S13. Use statistical methods to filter out the outliers in the scene point cloud image obtained in sub-step S12, and remove false edges and isolated noise points from the outliers in the scene point cloud image.

[0015] S14. Calculate the surface normal vectors of the scene point cloud processed by sub-step S13 based on the principal component analysis method, and make consistency adjustments to the normal vectors to keep all normal vectors pointing outward from the surface.

[0016] S15. Using the scene point cloud normal vector obtained in sub-step S14, perform edge point culling optimization on the scene point cloud filtered in sub-step S13, distinguish between contact edge points and non-contact edge points, and remove the contact edge point cloud of the real industrial scene point cloud image where the workpiece is located.

[0017] In the industrial scene part instance segmentation method based on improved Euclidean clustering of the present invention, the specific process of sub-step S12 is as follows:

[0018] First, select several candidate point clouds with a sampling basis k>3 on the same plane in the point cloud space. Satisfy the following equations:

[0019]

[0020] Where θ1, θ2, θ3, and θ4 are the four parameters of the plane equation. and Represents candidate point cloud p 1 and p N In the three-dimensional coordinates of the point cloud space, the above equation can be transformed into matrix form as follows:

[0021]

[0022] θ is the plane fitting parameter vector, and A represents the plane fitting matrix. The plane fitting parameter vector θ is calculated using the following formula. * :

[0023]

[0024] Then, the remaining data points in the point cloud space are used to calculate the error of the calculated plane fitting parameter model. The fitting error in the plane fitting parameter model is defined as the distance from point p to the affine space, where the affine space... The definition of is:

[0025]

[0026] Solve for the relationship between each point and the Lagrange multiplier method. The solution;

[0027] The point p can be determined using the following formula. The fitting error on the x-axis, i.e., the squared distance of the orthogonal projection:

[0028]

[0029] The orthogonal projection squared distance is compared with a pre-set error threshold μ. Points smaller than the threshold μ are considered to be in-plane points. This process is repeated for each point cloud, and the corresponding θ is recorded. * The number of all interior points below;

[0030] Update the plane fitting parameter vector θ * Repeat the above process. If the number of points in the new plane is greater than the current maximum number of points, retain the updated plane equation parameters until the set maximum number of iterations, and retain the point cloud plane corresponding to the final updated plane equation parameters.

[0031] Calculate the coordinates (σ) of the centroid σ of the point cloud plane corresponding to the parameters of the final updated plane equation. x , σ y , σz Directly delete all values ​​less than σ in the z-axis direction. z +Z i The point cloud, Z i This is a set value for minute fluctuations.

[0032] In the industrial scene part instance segmentation method based on improved Euclidean clustering of the present invention, the specific process of sub-step S13 is as follows:

[0033] First, define the maximum distance threshold τ between the point cloud and its N nearest neighbors obtained in sub-step S12. For point cloud p with index i in the point cloud... i ∈P, where P represents the entire point cloud space, and the search is performed on the N nearest neighbor points in the point cloud M. n Calculate the relationship between each nearest neighbor and p using the following formula. i The Euclidean distance is calculated, and the average distance d is calculated. i ,

[0034]

[0035]

[0036] Where d(p) i M n ) represents the point cloud p i And neighboring point cloud M n Distance calculation value, For point cloud p i The three-dimensional coordinates For the nearest point cloud M n 3D coordinates;

[0037] If the average distance d i If p > τ, then p i Filter out outliers and retain outliers, repeating the above process to traverse each scene point cloud and remove outliers from all scene point cloud images.

[0038] In the industrial scene part instance segmentation method based on improved Euclidean clustering of the present invention, the specific process of sub-step S14 is as follows:

[0039] First, perform z-channel smoothing on the scene point cloud data in the camera coordinate system to obtain the smoothed point cloud. For each point cloud Calculate the z-axis mean μ of the k nearest neighbors. z ,if If the z-axis of that point is subtracted by a step size dρ, then... Just add a step size dρ, τ l and τ hIt is the set calibration threshold, and the step size dρ is 2 to 4 times the camera resolution;

[0040] Computational point cloud Given the point cloud normal vectors, calculate the covariance matrix ∑ of the point cloud using the following formula.

[0041]

[0042] Where k represents the number of neighboring points, p ij Represents the i-th point cloud The coordinates of the j-th neighboring point Represents the i-th point cloud The average of the coordinates of the neighboring points;

[0043] The covariance matrix Σ is decomposed to obtain the eigenvalues ​​and eigenvectors of the matrix. The eigenvector with the smallest eigenvalue is the point cloud normal vector. The point cloud normal vectors are calculated by traversing each point cloud.

[0044] Then, calculate the mean of all point cloud normal vectors, and for each point cloud, calculate the sum of the normal vectors of its q nearest neighbors to obtain the sum vector. Then Divide by the number of neighborhood points q to obtain the normal vector mean vector.

[0045] For each point, compute its original normal vector. With normal vector and mean vector The included angle β between them, if β is greater than the set threshold β max If the original normal vector and the neighborhood normal vector have different directions, then the original normal vector will be... Invert the values ​​and repeat the above process until the normal vectors of all point clouds are consistent.

[0046] In the industrial scene part instance segmentation method based on improved Euclidean clustering of the present invention, the specific process of sub-step S15 is as follows:

[0047] For the remaining points after removing outliers from all scene point cloud images and adjusting the point cloud normals, select radius r and construct point cloud p. b The point cloud p is calculated using the following arctangent function within the neighborhood of ∈P. b With another point p in the neighborhood j Angle between normal vectors:

[0048]

[0049] Where, θ bj For point cloud p b With another point p in the neighborhood jThe angle between the normal vectors, n b and n j p b and p j The normal vector is then used to calculate the point cloud p using the following formula. b The mean angle α between the normal vectors of the entire neighborhood of P.

[0050]

[0051] G represents the number of point clouds in the neighborhood, and ε represents the threshold value. th The following threshold comparison formula is used to distinguish whether a point cloud is a contact edge point cloud:

[0052]

[0053] For point clouds at contact edges, α>ε th Conversely, for other point clouds in the scene, α≤ε th ;

[0054] For all contact edge point clouds s i ∈CP con For each contact edge point s i Finding k n Find the nearest neighbor points and calculate the average distance μ from each nearest neighbor point to the contact edge point. i Determine the mean distance μ i With threshold μ th The size, if μ i <μ th This confirms that the point belongs to the contact edge point that needs to be removed. If μ i ≥μ th If the point is not a contact edge point, it is considered not to be removed.

[0055] The removed edge point cloud is stored in the edge point set P. e In the end, the preprocessed scene point cloud data S is obtained. sc .

[0056] In an industrial scene part instance segmentation method based on improved Euclidean clustering of the present invention, step S2 further includes the following sub-steps:

[0057] S21. Set the maximum point cloud distance threshold and the minimum number of point clouds M for a single instance workpiece. min and the maximum number of point clouds M max The scene point cloud file after continuous k-nearest neighbor dynamic search sub-step S15 processing is used to obtain the scene workpiece 3D point cloud instance segmentation and clustering results based on Euclidean clustering.

[0058] S22. Multiply the scene point cloud file processed in sub-step S15 by a scaling factor ω in the z-axis direction of the camera coordinate system, where 0 < ω < 1. Then perform the same Euclidean clustering calculation as in sub-step S21 to obtain the scene workpiece 2D point cloud instance segmentation and clustering results based on Euclidean clustering.

[0059] S23. Combine the segmentation and clustering results of the three-dimensional Euclidean clustering obtained in sub-step S21 and the two-dimensional Euclidean clustering obtained in sub-step S22 to realize the clustering selection of the combined selection strategy and obtain the final workpiece instance segmentation result in the scene.

[0060] In the industrial scene part instance segmentation method based on improved Euclidean clustering of the present invention, the specific process of sub-step S21 is as follows:

[0061] Initialize a distance threshold value r for a point cloud distance threshold. d Set the minimum number of point clouds M for each cluster of instance artifacts. min and the maximum number of point clouds M max And input scene point cloud data S sc Randomly select a starting point s0 as the current activity point and put it into the cluster subset Q. i ;

[0062] Find all pairs of objects whose distance is less than or equal to r within the k-neighborhood. d The points are collected into a point set. Set of points S ok All members are merged into cluster subset Q i In, and marked s q Processed in Q i Select the next unprocessed point s n As a new activity point, repeat the above process;

[0063] When clustering subset Q i All points in the cluster are marked as processed, or clustered into a subset Q. i The number of points exceeds the maximum number of point clouds M max At that time, Q i From scene point cloud S sc Remove from the middle and restart clustering the next subset Q. i+1 Repeated subsets and clustering;

[0064] After clustering all points in the point cloud, remove points whose number is less than the minimum point cloud number M. min The clustered subsets, and for any set Q i All satisfy the following formula:

[0065] Q i ={s j|d(s j ,s k ) <r d ,s j ,s k ∈Q i},

[0066] Where s j Let s be any point in the set. k For set s j Distance less than r d The point, s k The quantity must be at least 1.

[0067] In the industrial scene part instance segmentation method based on improved Euclidean clustering of the present invention, the specific process of sub-step S23 is as follows:

[0068] The scene point cloud data is subjected to three-dimensional (x,y,z) spatial Euclidean clustering in sub-step S21 and two-dimensional (x,y) spatial Euclidean clustering in sub-step S22, respectively. A maximum threshold δ for the number of point clouds is set during the three-dimensional Euclidean clustering. max In the case of two-dimensional Euclidean clustering, no maximum threshold is set. After obtaining the clustering results, the number of point clouds in each cluster is reduced by a ratio C. Then, all cluster subsets obtained from the two Euclidean clusterings are sorted from largest to smallest in terms of the number of point clouds. The cluster center of each cluster is calculated. The number of cluster combinations n is set according to the type of workpiece.

[0069] Select the cluster with the largest number of point clouds from the three-dimensional Euclidean clustering array as the current cluster, find the n cluster centers that are closest to the current cluster center, and merge the instances of these n clusters with the current cluster to form a new cluster;

[0070] The number of cluster points exceeds the maximum threshold δ of the point cloud. max The new clusters are then compared sequentially with the two-dimensional clusters in ascending order. The comparison metrics include the total number of point clouds and the Euclidean distance between the cluster centers on the (x,y,0) plane, calculated using the following formula:

[0071]

[0072] Where, N 3d N represents the number of points in a 3D Euclidean cluster. 2d C represents the number of points in a two-dimensional Euclidean cluster. 3d Let C be the coordinates of the center of the 3D Euclidean clustered point cloud. 2d Let σ be the coordinates of the center of the two-dimensional Euclidean clustered point cloud. N and σ D For hyperparameters, if the calculated ε value is less than the set threshold ε hIf the two-dimensional Euclidean cluster and the merged three-dimensional Euclidean cluster are considered to be in correspondence, undersegmentation occurred during the three-dimensional Euclidean cluster, the result of the merged cluster is adopted, and the corresponding two-dimensional cluster and the merged n three-dimensional clusters are removed from the array respectively.

[0073] Select the next 3D clustering result from the 3D clustering array and continue execution; after traversing the entire 3D clustering array, increment the value of n by 1 and start the loop again from the starting position until the array is empty or n exceeds the preset maximum value;

[0074] During the loop, when the clustered point cloud values ​​exceed the maximum threshold δ for the number of point clouds... max When the condition is met, it indicates that the two-dimensional segmentation has been oversegmented. In this case, the largest n clusters are gradually eliminated in order from farthest to nearest relative to the cluster center until the total number of point clouds meets the requirements. The retained clusters will be added to the result, and the corresponding points will be deleted from the two-dimensional cluster point cloud. After deleting the corresponding clusters in the three-dimensional cluster array, the loop continues.

[0075] In the industrial scene part instance segmentation method based on improved Euclidean clustering of the present invention, the specific process of step S3 is as follows:

[0076] For the edge point set P e For all edge points, perform a nearest neighbor search within a range R. If a non-edge point is found, classify it into the corresponding subset Y according to its non-edge point category. CN ;

[0077] Calculate subset Y according to the following formula. CN Each cluster center:

[0078]

[0079] Among them, C Y Here, x represents the coordinates of the cluster centers, m represents the number of point clouds in the cluster, and x represents the number of point clouds in the cluster. i For a single point cloud coordinate, then for each non-edge point p c Calculate the Euclidean distance between each edge point and each cluster center, assign it to the nearest cluster, and repeat the process for classifying all edge points. CN This continues until the category of all points no longer changes or the set iteration limit is exceeded.

[0080] This invention offers further advantages over existing target point cloud instance segmentation methods, which are typically based on classic algorithms and techniques in computer vision, such as edge detection, region growing, and graph cut. These methods do not require large amounts of training data and rely on hand-designed features and rules. Furthermore, instance segmentation methods may be more stable and reliable in certain scenarios because they are less susceptible to noise and complex backgrounds.

[0081] Meanwhile, compared with existing traditional segmentation methods based on Euclidean clustering, the advantages of this invention are as follows:

[0082] (1) This invention preprocesses point clouds by using the RANSAC plane fitting algorithm to remove the working plane and then uses statistical methods to remove background redundant points and outliers, thereby reducing the influence of speckle error from binocular structured light cameras.

[0083] (2) This invention addresses the segmentation misjudgment problem caused by shape discontinuities in contact point clouds. It calculates the point cloud normal vectors based on principal component analysis and adjusts their orientation, then selectively removes point clouds at scene contact edges using the arctangent function. Compared to traditional Euclidean clustering algorithms, which struggle to handle occlusion and adhesion, the addition of edge point removal improves the performance of the Euclidean clustering algorithm, increasing the accuracy by 40%.

[0084] (3) This invention proposes a combined strategy that integrates two-dimensional and three-dimensional Euclidean clustering segmentation results. The integrated two-dimensional and three-dimensional clustering results utilize the positional relationship of point clouds to complete the instance-level position division, segmenting individual workpiece point clouds, reducing the impact caused by imaging defects, and further improving the segmentation effect of Euclidean clustering algorithm by combining edge point removal.

[0085] In summary, this invention provides a method for segmenting industrial scene parts instances by fully utilizing 3D point cloud information acquired by a 3D camera in industrial scenarios where parts are stacked and partially occluded. It does not require a large amount of training data, can quickly obtain accurate target positioning, and robustly complete the unordered grasping task of the robot. It solves the technical problem of segmenting a stack of target scene parts into a series of individual workpieces in the field of industrial robots.

[0086] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0087] Figure 1 This is an overall flowchart of the present invention.

[0088] Figure 2 Flowchart of the sub-steps of step S1.

[0089] Figure 3a , 3bThe comparison images before and after filtering out redundant working planes show that... Figure 3a This is the point cloud map of the original workpiece scene. Figure 3b This is the point cloud image after removing redundant point sets from the working plane based on the RANSAC plane fitting algorithm.

[0090] Figure 4a , 4b The image shows a comparison before and after outlier removal, where... Figure 4a Point cloud map of the workpiece scene, Figure 4b This is a point cloud image after removing false edges and isolated noise points from the scene point cloud using a statistical method.

[0091] Figure 5 , 6 This is an example of comparing the point cloud processing of the contact edge of two workpieces before and after the embodiment.

[0092] Figure 7 This is a flowchart of the sub-steps of step S2.

[0093] Figure 8 The flowchart of Euclidean clustering calculation in this invention. Detailed Implementation

[0094] Example

[0095] The industrial scene part instance segmentation method of the present invention is based on an improved Euclidean clustering segmentation algorithm, and the overall process is as follows: Figure 1 As shown, S1, firstly, the point cloud of the real industrial scene collected by the vision system is preprocessed. This invention uses the RANSAC plane fitting algorithm to remove the working plane, and then uses statistical methods to remove redundant background points and outliers to reduce the influence of speckle error of the binocular structured light camera. At the same time, the point cloud normal vector is calculated and the normal vector direction is adjusted to remove redundant point sets, working planes, false edges and isolated noise points, and workpiece contact edge points in the real industrial scene point cloud image. S2, then the Euclidean clustering algorithm is used to perform two-dimensional Euclidean distance and three-dimensional Euclidean distance respectively. The two-dimensional and three-dimensional clustering results are fused to complete the instance-level position division using the positional relationship of the point cloud, and the individual workpiece point cloud is segmented. S3, the workpiece contact edge points removed in step S1 are dynamically added back to the segmented workpiece point cloud to complete the workpiece instance segmentation in the industrial scene and ensure the integrity of the data.

[0096] The above steps of the present invention will be described in detail below through an application example.

[0097] In this embodiment, the point cloud of the industrial parts scene was obtained by capturing images of a simulated industrial robot grasping environment using a Gocator3110 LED dual-monocular structured light 3D imaging sensor, containing 3D point cloud information of the industrial parts scene. As an application example, test results of a self-made dataset DB9-1000 with a nine-pin serial port model as the instance segmentation target are presented. The dataset contains 1000 real-world images of industrial parts scenes.

[0098] Step S1 involves preprocessing the collected industrial real-world scene point cloud, which includes multiple workpieces, and includes the following sub-steps:

[0099] Sub-step S11: 1000 point cloud images of a real industrial part scene are obtained by capturing images of a simulated industrial robot grasping environment using the Gocator3110 LED dual-monocular structured light 3D imaging sensor. Some of the point cloud images are shown below. Figure 3a As shown.

[0100] Sub-step S12: Fit the planes in the scene using the RANSAC method. Use the fitted plane parameters and the centroid coordinates of the plane point set to remove redundant point sets from the 1000 scene point cloud images obtained in sub-step S11. The partially filtered scene is shown below. Figure 3b As shown.

[0101] The specific filtering process in this step is as follows:

[0102] (1) Randomly select candidate point clouds p from the same plane in the point cloud space with a sampling basis k = 3. 1 p 2 p 3 Then the following equations are satisfied.

[0103]

[0104] Where θ1, θ2, θ3, and θ4 are the four parameters of the plane equation. Representing candidate point clouds p respectively 1 p 2 p 3 In the three-dimensional coordinates of the point cloud space, the above equation can be transformed into matrix form as follows:

[0105]

[0106] θ is the plane fitting parameter vector, and A is the plane fitting matrix. The plane fitting parameter vector θ is calculated using the following formula. * :

[0107]

[0108] (2) The remaining data points in the point cloud space are used to calculate the error of the calculated plane fitting parameter model. The fitting error is defined as the distance from point p to the affine space. The distance between them, where the affine space The definition of is:

[0109]

[0110] Solve for the relationship between each point and the Lagrange multiplier method. The solution is to find the point p in the following equation. The fitting error on the plane, i.e., the squared distance of the orthogonal projection.

[0111]

[0112] Simultaneously, this distance is compared with a pre-set error threshold μ. Points smaller than the set value are considered to be points within the plane. This process is repeated for each point cloud, and the corresponding θ is recorded. * The number of all interior points below.

[0113] (3) Repeat steps (1) and (2) above to update the plane fitting parameter vector θ. * If the new number of in-plane points is greater than the current maximum number of in-plane points, then the updated plane equation parameters are retained.

[0114] (4) Repeat steps (1)-(3) until the maximum number of iterations is 500, and retain the point cloud plane corresponding to the final updated plane equation parameters.

[0115] (5) Calculate the coordinates of the centroid σ of the point cloud plane corresponding to the final updated plane equation parameters (σ). x , σ y , σ z Directly delete all values ​​less than σ in the z-axis direction. z +Z i The point cloud, Z i The set value for minute fluctuations is 0.3 mm in this example.

[0116] Sub-step S13, scene point cloud as follows Figure 3b As shown, outliers in the scene point cloud file calculated in sub-step S12 are filtered out using statistical methods to remove false edges and isolated noise points. The scene point clouds before and after filtering are shown below. Figure 4a and Figure 4b As shown.

[0117] The specific process for removing false edges and isolated noise points from scene point clouds in this example is as follows:

[0118] (1) Define the number of nearest neighbors N = 50 and the maximum distance threshold τ = 4mm for the scene point cloud neighborhood obtained in sub-step S12.

[0119] (2) For point cloud p with index i in the point cloud i ∈P, search for the N nearest neighbor point cloud M. n Use the following formula to calculate the relationship between each nearest neighbor and p. i The Euclidean distance is calculated, and the average distance d is calculated. i ;

[0120]

[0121]

[0122] Where d(p) i M n ) represents the point cloud p i And neighboring point cloud M n Distance calculation value, For point cloud p i The three-dimensional coordinates For the nearest point cloud M n The three-dimensional coordinates.

[0123] (3) If the average distance d i If p > τ, then p i Filter out outliers, and retain outliers.

[0124] (4) Repeat steps (2) and (3) to traverse each point cloud and remove outliers from all scene point cloud images.

[0125] In this embodiment, the nearest neighbor search method used is the KD-Tree neighborhood query method.

[0126] Sub-step S14: Calculate the surface normal vector of the workpiece point cloud processed by sub-step S13 based on the principal component analysis method, and make consistency adjustment on the normal vector to keep all normal vectors pointing outward from the surface.

[0127] The specific process of calculation and adjustment is as follows:

[0128] (1) Perform a smoothing operation on the z-axis channel of the scene point cloud data in the camera coordinate system to obtain the smoothed point cloud. For each point cloud p i Calculate the z-axis mean μ of the k nearest neighbors for each of ∈P. z ,if Subtract a step size dρ from the z-axis of that point. Just add a step size dρ. Here, τ l and τ h It is a manually set calibration threshold, which is set to τ in this embodiment. l =0.05mm, τ h=0.15mm, the step size dρ is 2 to 4 times the camera resolution, and in this embodiment dρ =0.05mm.

[0129] (2) Calculate point cloud Given the point cloud normal vectors, calculate the covariance matrix ∑ of the point cloud using the following formula.

[0130]

[0131] Where k represents the number of neighboring points, p ij Represents the i-th point cloud The coordinates of the j-th neighboring point Represents the i-th point cloud The average value of the coordinates of the neighboring points.

[0132] The covariance matrix Σ is decomposed to obtain the eigenvalues ​​and eigenvectors of the matrix. The eigenvector with the smallest eigenvalue is the normal vector. The normal vector of all point clouds is calculated by traversing each point cloud.

[0133] (3) Calculate the mean of the normal vectors. For each point, calculate the sum of the normal vectors of all its nearest 100 points (q = 100 points) to obtain the sum vector. Then Dividing by the number of neighborhood points q = 100 yields the normal vector and the mean vector.

[0134] (4) For each point cloud p i ∈P, calculate its original normal vector With normal vector and mean vector The angle β between them. If β is greater than the set threshold β max =90°, meaning the original normal vector and the neighborhood normal vector have different directions, then the original normal vector... Invert.

[0135] (5) Repeat steps (3) and (4) until the normal vectors of all point clouds are consistent.

[0136] Sub-step S15: Using the scene point cloud normal vector obtained in sub-step S14, edge point culling optimization is performed on the scene point cloud filtered in sub-step 13. This distinguishes between contact edge points and non-contact edge points, and removes the contact point cloud of the workpiece. It also removes the contact edge point cloud of the actual industrial scene point cloud image where the workpiece is located. Two examples comparing the contact point cloud before and after culling are provided in this embodiment. Figure 5 and Figure 6 As shown.

[0137] The specific process of edge point cloud culling is as follows:

[0138] (1) For the remaining points after removing outliers from all scene point cloud images and adjusting the point cloud normal vectors, select radius r and establish point cloud p. b The neighborhood of ∈P. r is generally 20 times the camera resolution. The purpose is to obtain the neighboring point clouds within the radius r of the point cloud and calculate whether they are contact edge point clouds. In this embodiment, r = 1 mm.

[0139] (2) Calculate the point cloud p using the following arctangent function. b With another point p in the neighborhood j The angle between the normal vectors

[0140]

[0141] Where, θ bj For point cloud p b Another point in the field, cloud p j The angle between the normal vectors, n b and n j For p b With p j The normal vector is then used to calculate the point cloud p using the following formula. b The mean angle α between the normal vectors of the entire neighborhood of P.

[0142]

[0143] G represents the number of point clouds in the neighborhood.

[0144] (3) Set the judgment threshold ε th =36°, the following formula is used for threshold comparison to distinguish whether the point cloud is a contact edge point cloud.

[0145]

[0146] For point clouds at contact edges, α>ε th Conversely, for other point clouds in the scene, α≤ε th .

[0147] (4) For all contact point clouds s i ∈CP con For each contact edge point s i Finding k n =6 nearest neighbor points, and calculate the distance s from each nearest neighbor point to the contact edge point. i The mean distance μ i Determine the mean distance μ i With threshold μ th The size, in this embodiment, μ th =0.25mm, if μ i <μ th Then the point is considered to be a contact edge point, if μi ≥μ th If a point is not considered a contact edge point, it should not be removed. The removed edge point cloud is stored in the edge point set P. e In the end, the preprocessed scene point cloud data S is obtained. sc .

[0148] This completes the preprocessing of the real industrial scene point cloud acquired by the vision system in step S1. The RANSAC plane fitting algorithm was used to remove working planes, and statistical methods were employed to remove redundant and outlier points in the background, reducing the impact of speckle error from the binocular structured light camera. Simultaneously, principal component analysis was used to calculate the point cloud normal vectors and adjust their orientation. The arctangent function was then used to selectively remove point clouds at scene contact edges. This edge removal reduced workpiece occlusion and adhesion, improving the accuracy of the subsequent Euclidean clustering algorithm by 40%.

[0149] like Figure 7 As shown, step S2 in this embodiment segments the point cloud of a single workpiece by fusing instance segmentation clusters after performing two-dimensional Euclidean clustering and three-dimensional Euclidean clustering. Specifically, it includes the following sub-steps:

[0150] Sub-step S21: Manually set the maximum point cloud distance threshold r d Minimum number of point clouds for a single instance workpiece, M min and the maximum number of point clouds M max The point cloud file processed by the k-nearest neighbor dynamic search sub-step S15 continuously yields the scene workpiece 3D point cloud instance segmentation and clustering results based on Euclidean clustering.

[0151] See Figure 8 The Euclidean clustering process shown in this embodiment is as follows:

[0152] (1) Initialize a distance threshold value r d =0.325mm, set the minimum and maximum number of points for each cluster type to M. min =4500 and M max =27500, and input the point cloud data S of the scene. sc .

[0153] (2) In S sc A starting point s0 is randomly selected as the current activity point and placed into the cluster subset Q. i .

[0154] (3) Find all points in the k-neighborhood whose distance is less than or equal to r, and collect these points into a point set.

[0155] (4) Set S 0kAll members are merged into Q. i In the middle, s0 is marked as processed.

[0156] (5) In Q i Select the next unprocessed point s n As a new activity point, repeat steps (3) and (4).

[0157] (6) When the clustering subset Q i All points in the array have been marked as processed, or Q. i The number of points exceeds M max At that time, the clustering subset Q i From scene point cloud S sc Remove from the middle and restart clustering the next subset Q. i+1 Repeat steps (1)-(5).

[0158] (7) After completing the clustering of all points in the point cloud, remove points with a number less than M. min The clustered subsets, and for any set Q i All satisfy the following formula:

[0159] Q i ={s j |d(s j ,s k ) <r d ,s j ,s k ∈Q i}

[0160] Where s j Let s be any point in the set. k For set s j Distance less than r d The point, s k The quantity must be at least 1.

[0161] Sub-step S22: Multiply the processed scene point cloud file from sub-step 15 by a scaling factor ω in the z-axis direction. In this embodiment, ω = 0.1. Then perform Euclidean clustering in sub-step S21 to obtain the scene workpiece 2D point cloud instance segmentation and clustering results based on Euclidean clustering.

[0162] Sub-step S23 combines the segmentation results of two-dimensional Euclidean clustering and three-dimensional Euclidean clustering obtained from sub-steps S21 and S22 to achieve cluster selection using a combined selection strategy, thus obtaining the final instance segmentation result.

[0163] The specific process of implementing instance segmentation using the combination strategy in this embodiment is as follows:

[0164] (1) Perform three-dimensional (x,y,z) spatial Euclidean clustering in sub-step S21 and two-dimensional (x,y) spatial Euclidean clustering in sub-step S22 on the point cloud data of the scene respectively. Set the maximum threshold δ for the number of point clouds during three-dimensional Euclidean clustering. max In this embodiment, δ max =42000, no maximum threshold is set when performing two-dimensional Euclidean clustering.

[0165] (2) After obtaining the clustering results, the number of point clouds in each cluster is reduced by a ratio C. The impact of error is reduced by discretization. The ratio C is 0.05-0.2 depending on the number of target instances. In this embodiment, C = 0.1.

[0166] (3) Sort all the cluster subsets obtained by the two Euclidean clusterings in descending order of the number of point clouds, and calculate the cluster center of each cluster. Let the number of cluster combinations be n. When n is set to 1, it means that each cluster combination contains only one cluster result. In the industrial scenario of this embodiment, there are two kinds of workpieces, so the number of combinations n is set to 2.

[0167] (4) Select the largest cluster from the 3D clustering array as the current cluster. Find the two cluster centers closest to the current cluster center and merge the instances of these two clusters into a new cluster. If the number of points in the new cluster exceeds the maximum threshold δ of the point cloud, the process is repeated. max Then proceed to step (7) below.

[0168] (5) Compare the new clusters with the two-dimensional clusters in ascending order. The comparison metrics include the total number of point clouds and the Euclidean distance between the cluster centers on the (x,y,0) plane, calculated using the following formula.

[0169]

[0170] Where, N 3d N represents the number of points in a 3D Euclidean cluster. 2d C represents the number of points in a two-dimensional Euclidean cluster. 3d Let C be the coordinates of the center of the 3D Euclidean clustered point cloud. 2d Let σ be the coordinates of the center of the two-dimensional Euclidean clustered point cloud. N and σ D As a hyperparameter, σ in this embodiment N =0.25, σ D =1.

[0171] If the calculated ε value is less than the set threshold ε h If the two-dimensional Euclidean cluster and the merged three-dimensional Euclidean cluster are considered to be in correspondence, then undersegmentation occurred during the three-dimensional Euclidean cluster, with a threshold ε. hThe basis is to fine-tune it by half of the maximum number of parallel planes contained in the current type of workpiece, generally 2-4. In this embodiment, ε h =3.5. At this point, the results of the merged clusters are used, and the corresponding two-dimensional Euclidean clusters and the merged n three-dimensional Euclidean clusters are removed from the array respectively. Then, return to step (4) and select the next three-dimensional Euclidean cluster result to continue execution. The largest cluster in the three-dimensional Euclidean cluster array has already been selected as the current cluster, and the subsequent three-dimensional Euclidean cluster results are selected according to the largest cluster among the remaining clusters. If no matching item is found after traversing the entire two-dimensional Euclidean cluster array, then step (4) is executed in a loop.

[0172] (6) After traversing the entire three-dimensional Euclidean clustering array, increment the value of n by 1. Then, restart the loop from the beginning until the array is empty or n exceeds the preset maximum value n. max =2.

[0173] (7) When the number of cluster points exceeds the maximum threshold δ of the point cloud quantity max When the value is 0, it indicates that the two-dimensional segmentation has been oversegmented. In this case, the largest n clusters are gradually eliminated in order from farthest to nearest until the total number of points in the point cloud meets the requirements. The retained clusters will be added to the result, and the corresponding points will be deleted from the two-dimensional Euclidean cluster point cloud, rather than completely deleting the entire cluster. At the same time, the corresponding clusters are deleted from the three-dimensional Euclidean cluster array, and then the process returns to step (4) to continue.

[0174] This completes step S2, which involves segmenting the workpiece point cloud based on Euclidean clustering. By combining the segmentation results of two-dimensional and three-dimensional Euclidean clustering, the positional relationship of the point cloud is used to complete the instance-level position division, segmenting individual workpiece point clouds, reducing the impact of missing images, and further improving the segmentation effect of the Euclidean clustering algorithm by combining edge point removal.

[0175] In the final step S3, the contact point clouds removed in S1 are dynamically added back into the segmented workpiece point cloud. In this embodiment, step S3 uses the k-means clustering algorithm to process the final segmentation result, dynamically adding the removed contact edge point clouds back into the original point cloud. For the edge point set P... e For any edge point within the instance, the nearest non-edge point is found through nearest neighbor search. This non-edge point then becomes the instance represented by the edge point. This process is repeated for all edge points until a new point is found, thus completing the dynamic re-addition of the contact edge point cloud. The specific re-addition process is as follows:

[0176] (1) For the edge point set P eA large-scale nearest neighbor search (R = 2.35 mm) is performed on all edge points. If a non-edge point is found, it is assigned to the corresponding subset Y according to the non-edge point category. CN .

[0177] (2) For all Y CN Process the subset Y according to the following formula. CN Each of their respective cluster centers

[0178]

[0179] Among them, c Y Here, x represents the coordinates of the cluster centers, m represents the number of point clouds in the cluster, and x represents the number of point clouds in the cluster. i For a single point cloud coordinate, then for each non-edge point p c Calculate the Euclidean distance between it and each cluster center, and assign it to the category with the closest distance.

[0180] (3) Repeat step (2) until the category of all points no longer changes or the maximum number of iterations of 100 is exceeded.

[0181] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for segmenting parts instances in industrial scenarios based on improved Euclidean clustering, characterized in that, The steps include the following: S1. Preprocess the real industrial scene point cloud acquired by the vision system, which includes multiple workpieces, to remove redundant point sets, working planes, false edges, isolated noise points, and workpiece contact edge points from the real industrial scene point cloud image. This includes the following sub-steps: S11. Use a binocular structured light 3D imaging system to acquire N point cloud images of the real industrial scene where the workpiece is located. S12. Use the RANSAC method to fit the plane in the scene, and use the fitted plane parameters and the centroid coordinates of the plane point set to remove the redundant point set working plane of the scene point cloud image obtained in sub-step S11. S13. Use statistical methods to filter out outliers in the scene point cloud image obtained in sub-step S12, and remove false edges and isolated noise points from the outliers in the scene point cloud image. S14. Calculate the surface normal vectors of the scene point cloud processed by sub-step S13 based on the principal component analysis method, and make consistency adjustments to the normal vectors to keep all normal vectors pointing outward from the surface. S15. Using the scene point cloud normal vector obtained in sub-step S14, perform edge point culling optimization on the scene point cloud filtered in sub-step S13, distinguish between contact edge points and non-contact edge points, and remove the contact edge point cloud of the real industrial scene point cloud image where the workpiece is located. S2. Apply Euclidean clustering algorithm to the preprocessed point cloud file, performing instance segmentation and clustering using both 2D and 3D Euclidean distances. Merge the clustering results and utilize the point cloud positional relationships to complete instance-level positional partitioning, segmenting individual workpiece point clouds. This includes the following sub-steps: S21, set a maximum point cloud distance threshold and a minimum point cloud number M of a single instance workpiece min and a maximum point cloud number M max , continuously perform the k-nearest neighbor dynamic search sub-step S15 on the processed scene point cloud file to obtain a scene workpiece three-dimensional point cloud instance segmentation clustering result based on Euclidean clustering. S22. Multiply the scene point cloud file processed in sub-step S15 by a scaling factor ω in the z-axis direction of the camera coordinate system, where 0 < ω < 1. Then perform the same Euclidean clustering calculation as in sub-step S21 to obtain the scene workpiece 2D point cloud instance segmentation and clustering results based on Euclidean clustering. S23. Combine the segmentation and clustering results of the three-dimensional Euclidean clustering obtained in sub-step S21 and the two-dimensional Euclidean clustering obtained in sub-step S22 to realize the clustering selection of the combined selection strategy and obtain the final workpiece instance segmentation result in the scene. S3. Dynamically refill the point cloud of the workpiece contact edge points removed in step S1 into the segmented workpiece point cloud to complete the workpiece instance segmentation in the industrial scene.

2. The method for segmenting industrial scene parts based on improved Euclidean clustering according to claim 1, characterized in that, The specific process of sub-step S12 is as follows: First, select several candidate point clouds with a sampling basis k>3 on the same plane in the point cloud space. It satisfies the following equation: ， Where θ1, θ2, θ3, and θ4 are the four parameters of the plane equation. and Represents candidate point cloud and In the three-dimensional coordinates of the point cloud space, the above equation can be transformed into matrix form as follows: ， Let A be the plane fitting parameter vector, and let A be the plane fitting matrix. The plane fitting parameter vector is calculated using the following formula. : ， Then, the remaining data points in the point cloud space are used to calculate the error of the calculated plane fitting parameter model. The fitting error in the plane fitting parameter model is defined as the point... The distance to the affine space, where the affine space The definition of is: ， Solve for the relationship between each point and the Lagrange multiplier method. The solution; The point is obtained using the following formula. exist The fitting error on the x-axis, i.e., the squared distance of the orthogonal projection: ， The orthogonal projection square distance is compared with a pre-set error threshold. When compared, it is less than the set error threshold. Points are treated as points in the plane. Each point in the cloud is traversed, and its value is recorded. The number of all interior points below; Update the plane fitting parameter vector Repeat the above process. If the number of points in the new plane is greater than the current maximum number of points, retain the updated plane equation parameters until the set maximum number of iterations, and retain the point cloud plane corresponding to the final updated plane equation parameters. Calculate the centroid of the point cloud plane corresponding to the parameters of the final updated plane equation. coordinates ( ), directly delete all values ​​less than in the z-axis direction Point clouds, This is a set value for minute fluctuations.

3. The method for segmenting industrial scene parts instances based on improved Euclidean clustering according to claim 1, characterized in that, The specific process of sub-step S13 is as follows: First, define the maximum distance threshold between the scene point cloud neighborhood and the N nearest neighbors obtained in sub-step S12. For point cloud with sequence number Point clouds P represents the entire point cloud space, and the search term is for the N nearest neighbor points in the point cloud. Calculate the sum of the sums ... The Euclidean distance is calculated, and the average distance is calculated. , 、 ， in For point clouds Neighboring point clouds Distance calculation value, For point clouds The three-dimensional coordinates for 3D coordinates; If average distance Then see Filter out outliers and retain outliers, repeating the above process to traverse each scene point cloud and remove outliers from all scene point cloud images.

4. The method for segmenting industrial scene parts instances based on improved Euclidean clustering according to claim 1, characterized in that, The specific process of sub-step S14 is as follows: First, perform z-channel smoothing on the scene point cloud data in the camera coordinate system to obtain the smoothed point cloud. For each point cloud Calculate the z-axis mean of the k nearest neighbors. ,if Subtract a step size from the z-axis of that point. ,if Add a step size. , and It is the set calibration threshold, step size. Two to four times the camera resolution; Computational point cloud Given the point cloud normal vectors, calculate the covariance matrix of the point cloud using the following formula. , ， in, Indicates the number of neighboring points. Represents the i-th point cloud The coordinates of the j-th neighboring point Represents the i-th point cloud The average of the coordinates of the neighboring points; For the covariance matrix Decompose the matrix to obtain its eigenvalues ​​and eigenvectors. The eigenvector with the smallest eigenvalue is the point cloud normal vector. Traverse each point cloud and calculate all point cloud normal vectors. Then, calculate the mean of all point cloud normal vectors, and for each point cloud, calculate the sum of the normal vectors of its q nearest neighbors to obtain the sum vector. Then Divide by the number of neighborhood points q to obtain the normal vector mean vector. ; For each point, compute its original normal vector. with normal vector and mean vector The angle between ,if Greater than the set threshold If the original normal vector and the neighborhood normal vector have different directions, then the original normal vector will be... Invert the values ​​and repeat the above process until the normal vectors of all point clouds are consistent.

5. The method for segmenting industrial scene parts instances based on improved Euclidean clustering according to claim 1, characterized in that, The specific process of sub-step S15 is as follows: For the remaining points after removing outliers from all scene point cloud images and adjusting the point cloud normals, select radius r to construct the point cloud. Calculate the point cloud in the neighborhood of using the following arctangent function. With another cloud in the neighborhood Angle between normal vectors: ， in, For point clouds With another cloud in the neighborhood The angle between the normal vectors and They are respectively and The normal vector is then used to calculate the point cloud using the following formula. Mean angle between the normal vectors of the entire neighborhood , ； G represents the number of point clouds in the neighborhood, and a threshold value is set. The following threshold comparison formula is used to distinguish whether a point cloud is a contact edge point cloud: ， For contact edge point clouds Conversely, for other point clouds in the scene, then ; For all contact edge point clouds For each contact edge point Searching Find the nearest neighbor points and calculate the average distance from each nearest neighbor point to the contact edge point. Determine the mean distance With threshold The size, if This confirms that the point is a contact edge point that needs to be removed. If the point is not a contact edge point, it is considered not to be removed. The removed edge point cloud is stored in the edge point set. In the end, the preprocessed scene point cloud data is obtained. .

6. The method for segmenting industrial scene parts instances based on improved Euclidean clustering according to claim 1, characterized in that, The specific process of sub-step S21 is as follows: Initialize a distance threshold value for a point cloud distance threshold. Set the minimum number of point clouds for each cluster of instance artifacts. and maximum number of point clouds Input scene point cloud data Randomly select a starting point As the current activity point, it is placed into the cluster subset. ; Find all pairs of objects whose distance is less than or equal to k-neighborhood. The points are collected into a point set. ϵ , set of points All members are merged into a cluster subset. In, and marked It has been processed. Select the next unprocessed point. As a new activity point, repeat the above process; When clustering subsets All points in the data are marked as processed, or as a cluster subset. The number of points exceeds the maximum number of point clouds. At that time, From scene point cloud Remove from the middle and restart clustering the next subset. Repeated subsets and clustering; After clustering all points in the point cloud, remove points whose number is less than the minimum number of points. Cluster subsets, and for any set All satisfy the following formula: ， Where s j Let s be any point in the set. k For set s j Distance less The point, s k The quantity must be at least 1.

7. The method for segmenting industrial scene parts instances based on improved Euclidean clustering according to claim 6, characterized in that, The specific process of sub-step S23 is as follows: The scene point cloud data is subjected to three-dimensional (x,y,z) spatial Euclidean clustering in sub-step S21 and two-dimensional (x,y) spatial Euclidean clustering in sub-step S22, respectively. A maximum threshold δ for the number of point clouds is set during the three-dimensional Euclidean clustering. max In the case of two-dimensional Euclidean clustering, no maximum threshold is set. After obtaining the clustering results, the number of point clouds in each cluster is reduced by a ratio C. Then, all cluster subsets obtained from the two Euclidean clusterings are sorted from largest to smallest in terms of the number of point clouds. The cluster center of each cluster is calculated. The number of cluster combinations n is set according to the type of workpiece. Select the cluster with the largest number of point clouds from the three-dimensional Euclidean clustering array as the current cluster, find the n cluster centers that are closest to the current cluster center, and merge the instances of these n clusters with the current cluster to form a new cluster; The number of cluster points exceeds the maximum threshold δ of the point cloud. max The new clusters are then compared sequentially with the two-dimensional clusters in ascending order. The comparison metrics include the total number of point clouds and the Euclidean distance between the cluster centers on the (x, y, 0) plane, calculated using the following formula: ， Where, N 3d N represents the number of points in a 3D Euclidean cluster. 2d C represents the number of points in a two-dimensional Euclidean cluster. 3d Let C be the coordinates of the center of the 3D Euclidean clustered point cloud. 2d The coordinates of the center of the two-dimensional Euclidean clustered point cloud are: and For hyperparameters, if the calculated ε value is less than the set threshold... If the two-dimensional Euclidean cluster and the merged three-dimensional Euclidean cluster are considered to be in correspondence, undersegmentation occurred during the three-dimensional Euclidean cluster, the result of the merged cluster is adopted, and the corresponding two-dimensional cluster and the merged n three-dimensional clusters are removed from the array respectively. Select the next 3D clustering result from the 3D clustering array and continue execution; after traversing the entire 3D clustering array, increment the value of n by 1 and start the loop again from the starting position until the array is empty or n exceeds the preset maximum value; During the loop, when the clustered point cloud values ​​exceed the maximum threshold δ for the number of point clouds... max When the condition is met, it indicates that the two-dimensional segmentation has been oversegmented. In this case, the largest n clusters are gradually eliminated in order from farthest to nearest relative to the cluster center until the total number of point clouds meets the requirements. The retained clusters will be added to the result, and the corresponding points will be deleted from the two-dimensional cluster point cloud. After deleting the corresponding clusters in the three-dimensional cluster array, the loop continues.

8. The method for segmenting industrial scene parts instances based on improved Euclidean clustering according to claim 1, characterized in that, The specific process of step S3 is as follows: For edge point set For all edge points, perform a nearest neighbor search within a range R. If a non-edge point is found, it is assigned to the corresponding subset according to the non-edge point category Y. ; Calculate the subset according to the following formula. Each cluster center: ， in, Here, x represents the coordinates of the cluster centers, m represents the number of point clouds in the cluster, and x represents the number of point clouds in the cluster. i For a single point cloud coordinate, then for each non-edge point... Calculate the Euclidean distance between each edge point and each cluster center, assign it to the nearest cluster, and repeat the process for classifying all edge points. This continues until the category of all points no longer changes or the set iteration limit is exceeded.

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