Method for measuring curved plate profile of large hull based on three-dimensional imaging equipment

Abstract

The invention discloses a large-scale hull curved plate profile measurement method based on three-dimensional imaging equipment, and relates to the technical field of hull curved plate profile measurement, the method is applied to a large-scale hull curved plate profile measurement device, and the method comprises the following steps: controlling a carrying device to sequentially pass through all measurement points along the long edge direction of a hull curved plate to be measured, obtaining a plurality of original point cloud data; preprocessing each piece of original point cloud data to obtain multiple pieces of curved plate local point cloud data; determining a final transformation matrix corresponding to the local point cloud data of each curved plate, and splicing the point cloud data of the plurality of curved plate parts to obtain integral point cloud data of the curved plate; based on the angle relation between the point and the adjacent point on the projection plane, extracting a boundary point set of the hull curved plate to be measured from the overall point cloud data of the curved plate; and based on the overall distribution of the adjacent points, extracting the angular points of the to-be-measured hull curved plate from the boundary point set. By combining with a large hull curved plate profile measuring device, the precision and efficiency of large hull curved plate profile measurement can be improved.

Description

Technical Field

[0001] This application relates to the field of ship hull curved surface measurement technology, and in particular to a method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device. Background Technology

[0002] Hull curved plates are crucial structural components of ships, and their surface accuracy directly impacts the assembly workload during shipbuilding, the assembly stress of the hull structure, and the ship's hydrodynamic performance. Surface measurement accuracy is the basis and foundation for curved plate manufacturing accuracy. Traditional measurement methods utilize wooden templates and boxes or flexible iron templates for contact measurement, which suffers from drawbacks such as high tool manufacturing costs, heavy workload, poor measurement accuracy, and difficulty in digital representation. Therefore, vision-based non-contact measurement methods for hull curved plates are increasingly being explored for measurement. The main methods include:

[0003] 1. The acquisition of three-dimensional shape data of curved plates using a three-dimensional coordinate instrument has a measurement accuracy of up to ±0.068mm. Although it has accurate measurement results, it requires manual point-by-point measurement, resulting in incomplete data, low efficiency, and a lack of automation.

[0004] 2. Install a line structured light vision measurement system on a three-axis translation mechanism to measure the formed curved surface through stereo vision technology. This method has a large measurement range and a high degree of automation, but it requires high platform accuracy, can only measure one line at a time, has incomplete data, and is inefficient.

[0005] 3. The three-dimensional shape data of the hull curved plate was obtained by using a laser tracker. This method not only has high measurement accuracy but also has a large measurement range. However, the equipment used is too expensive and it still relies on manual operation. Therefore, due to cost and efficiency considerations, this method has not been widely used.

[0006] 4. The hull curved plate was reconstructed in three dimensions using binocular reconstruction technology to detect the forming state of the curved plate. This method improves the accuracy by 13% compared with the traditional measurement method, and the single measurement time can reach 2 seconds. However, its measurement range is small and it is difficult to measure large-sized hull curved plates.

[0007] Therefore, how to efficiently and quickly obtain the curved shape of the hull while meeting the precision requirements for hull plate manufacturing is an urgent problem to be solved. Summary of the Invention

[0008] The purpose of this application is to provide a method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device, which can improve the accuracy and efficiency of measuring the curved surface of a large ship hull.

[0009] To achieve the above objectives, this application provides the following solution:

[0010] In a first aspect, this application provides a method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device. The method is applied to a device for measuring the curved surface of a large ship hull, the device comprising:

[0011] Equipped with a device and multiple 3D imaging equipment;

[0012] The mounting device is equipped with a crossbeam; the crossbeam is perpendicular to the direction of movement of the mounting device.

[0013] Multiple three-dimensional imaging devices are equally spaced on the crossbeam;

[0014] Multiple measurement points are set at equal intervals along the long side of the curved plate of the hull to be tested;

[0015] When the mounting device is at adjacent measurement points, the field of view of the same three-dimensional imaging device overlaps; the field of view of the same three-dimensional imaging device at all measurement points covers the long side of the curved plate of the hull under test.

[0016] When the mounting device is at any measurement point, the fields of view of two adjacent three-dimensional imaging devices overlap; and the fields of view of all three-dimensional imaging devices cover the wide side of the curved plate of the ship under test.

[0017] The method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device includes:

[0018] Determine the horizontal and vertical transformation matrices;

[0019] The mounting device is controlled to pass through all measurement points sequentially along the long side of the curved plate of the hull under test, obtaining m×d original point cloud data; the i×j-th original point cloud data is acquired by the j-th three-dimensional imaging device when the mounting device is at the i-th measurement point; i = 1, 2, ..., m; m is the total number of measurement points; j = 1, 2, ..., d; d is the total number of three-dimensional imaging devices;

[0020] Each original point cloud data is preprocessed to obtain m×d local point cloud data of the curved plate;

[0021] Based on the horizontal transformation matrix and the vertical transformation matrix, the final transformation matrix corresponding to the local point cloud data of each curved plate is determined;

[0022] Based on multiple final transformation matrices, the point cloud data of m×d curved plate portions are stitched together to obtain the overall point cloud data of the curved plate.

[0023] Based on the angular relationship between a point and its neighboring points on the projection plane, the boundary point set of the curved hull under test is extracted from the overall point cloud data of the curved hull.

[0024] Based on the overall distribution of neighboring points, the corner points of the curved plate of the hull to be tested are extracted from the set of boundary points.

[0025] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0026] This application provides a method for measuring the surface shape of large ship hull curved plates based on a 3D imaging device, which can effectively solve the problem of high-precision and rapid measurement of the surface shape of large ship hull curved plates. A measurement device is constructed by mounting a 3D imaging device on a mounting device. To accommodate the size of the ship hull curved plate, at least two 3D imaging devices are used. The 3D imaging devices are positioned at a certain height above the ground to ensure that the measurement fields of adjacent 3D imaging devices overlap to a certain extent and cover the width of the plate. The device is photographed segment by segment by segment through the equidistant movement of a trolley to achieve coverage along the length of the plate. The captured point cloud is preprocessed (noise reduction is performed using a radius outlier filtering method; semantic segmentation of the point cloud is performed using a region growing algorithm to divide it into several subsets, and the point cloud belonging to the ship hull curved plate is extracted, removing the background). The measured point clouds are stitched together based on targets pasted on the curved plate. Finally, edge points and corner points are extracted based on the boundary point features and corner point features of the ship hull curved plate. The device of this invention is easy to construct, the measurement method is simple and easy to operate, the device does not require periodic calibration, and the measurement speed is fast, the accuracy is high, the data is complete, and the environmental adaptability is strong.

[0027] The large hull curved plate shape measurement device consists of one mounting device (mobile trolley (platform)) and two three-dimensional imaging devices. It has a simple structure, low cost, and is easy to operate. The device does not require pre-calibration and is not affected by the accuracy of the trolley's movement. It can better adapt to the vibration and lighting environment of the shipyard workshop. In addition to accurately obtaining the measurement point cloud of the curved plate (i.e., the overall point cloud data of the curved plate), it can also obtain accurate curved plate edges and corner points, which facilitates surface registration during subsequent shape comparison. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a schematic diagram of a large ship hull curved plate shape measuring device and its shooting field of view in one embodiment of this application;

[0030] Figure 2 This is a flowchart of a method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device in one embodiment of this application;

[0031] Figure 3This is a flow chart of the measurement process in one embodiment of this application;

[0032] Figure 4 This is a schematic diagram of the original point cloud in one embodiment of this application;

[0033] Figure 5 This is a schematic diagram of the point cloud before denoising in one embodiment of this application;

[0034] Figure 6 This is a schematic diagram of the denoised point cloud in one embodiment of this application;

[0035] Figure 7 This is a schematic diagram of the target head (front) point cloud data in one embodiment of this application;

[0036] Figure 8 This is a schematic diagram of target tail (rear) point cloud data in one embodiment of this application;

[0037] Figure 9 This is a schematic diagram of the coarse registration result of the target's first and last (front and back) point cloud data in one embodiment of this application;

[0038] Figure 10 This is a schematic diagram of point cloud projection onto a local projection plane in one embodiment of this application;

[0039] Figure 11 This is a schematic diagram of the angle features of a non-boundary point in one embodiment of this application;

[0040] Figure 12 This is a schematic diagram of the boundary point angle features in one embodiment of this application;

[0041] Figure 13 This is a schematic diagram of the corner angle features in one embodiment of this application;

[0042] Figure 14 This is a schematic diagram illustrating the principle of determining the optimal corner point in one embodiment of this application. Detailed Implementation

[0043] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0044] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0045] In one exemplary embodiment, a method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device is provided. The method is applied to a device for measuring the curved surface of a large ship hull, such as... Figure 1 As shown, the device includes: a mounting device and multiple 3D imaging devices; a crossbeam is mounted on the mounting device; the crossbeam is perpendicular to the movement direction of the mounting device; multiple 3D imaging devices are equally spaced on the crossbeam; multiple measurement points are equally spaced along the long side of the curved hull plate to be measured; when the mounting device is at adjacent measurement points, the field of view of the same 3D imaging device overlaps; the field of view of the same 3D imaging device at all measurement points covers the long side of the curved hull plate to be measured; when the mounting device is at any measurement point, the field of view of two adjacent 3D imaging devices overlaps; and the field of view of all 3D imaging devices covers the wide side of the curved hull plate to be measured.

[0046] Construction of the measuring equipment: The measuring equipment is a large-scale ship hull curved plate shape measuring device, including 3D imaging equipment and a moving trolley (or other moving fixture). Two 3D imaging devices are arranged on the crossbeam of the moving trolley, which is horizontally positioned and perpendicular to the direction of the trolley's movement. The 3D imaging devices are at a certain height above the ground to ensure that the measurement fields of view of the two 3D imaging devices overlap to a certain extent and cover the width of the plate. By moving the trolley at equal intervals, segment-by-segment imaging is performed to achieve coverage along the length of the plate. The imaging range of the 3D imaging devices is rectangular. The purpose of arranging two 3D imaging devices is that the field of view of a single 3D imaging device is insufficient; if a wider curved plate needs to be measured, the number of cameras can be increased.

[0047] like Figure 2 and Figure 3 As shown, the method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device includes:

[0048] Step 201: Determine the horizontal transformation matrix and the vertical transformation matrix.

[0049] Step 202: Control the mounting device to sequentially pass through all measurement points along the long side of the curved plate of the hull under test, obtaining m×d original point cloud data. The i×j-th original point cloud data is acquired by the j-th 3D imaging device when the mounting device is at the i-th measurement point; i = 1, 2, ..., m; m is the total number of measurement points; j = 1, 2, ..., d; d is the total number of 3D imaging devices.

[0050] Step 203: Preprocess each original point cloud data to obtain m×d local point cloud data of the curved plate.

[0051] Step 204: Based on the horizontal and vertical transformation matrices, determine the final transformation matrix corresponding to the local point cloud data of each curved plate.

[0052] Step 205: Based on multiple final transformation matrices, the point cloud data of the m×d curved plate portions are stitched together to obtain the overall point cloud data of the curved plate. The processed point cloud is a local point cloud of the curved plate, with different coordinate systems and partial overlap. It will be stitched together according to the target (circle or triangle) on the surface of the curved plate, first horizontally and then vertically.

[0053] Step 206: Based on the angular relationship between the point and its neighboring points on the projection plane, extract the boundary point set of the hull curved plate to be tested from the overall point cloud data of the curved plate.

[0054] Step 207: Based on the overall distribution of neighboring points, extract the corner points of the curved plate of the hull to be tested from the set of boundary points.

[0055] Step 201 specifically includes:

[0056] Select any measurement point as the current measurement point.

[0057] Determine any two adjacent 3D imaging devices as the first and last 3D imaging devices.

[0058] The device is driven to the current measurement point, and the first target is placed in the overlapping area of ​​the fields of view of the first and last 3D imaging devices.

[0059] The first and last raw point cloud data were acquired. The first raw point cloud data was acquired using a first 3D imaging device. The last raw point cloud data was acquired using a last 3D imaging device.

[0060] The original point cloud data is segmented by a target to obtain the target first point cloud data.

[0061] The original point cloud data of the tail is segmented by a target to obtain the target tail point cloud data.

[0062] Outlier points in the target's first and last point cloud data are removed using a radius-based outlier filtering method.

[0063] Obtain the coordinates of multiple first target points in the target head cloud data and target tail cloud data, and obtain the coordinate pair corresponding to each first target point.

[0064] Based on the coordinate pairs corresponding to multiple first target points, the lateral coarse registration matrix of the first and last 3D imaging device coordinate systems is determined. Examples of coarse registration before and after are shown below. Figures 7 to 9 As shown. Figure 7 and Figure 8 In the diagram, (R0, A0), (R1, A1), (R2, A2), and (R3, A3) are the coordinate pairs corresponding to different (circular) target points.

[0065] The coarse horizontal registration matrix is ​​determined as the initial horizontal transformation matrix.

[0066] Based on the initial lateral transformation matrix, calculate the nearest corresponding point between the first and last original point cloud data.

[0067] Update the initial lateral transformation matrix using the nearest corresponding point, and return to the step "Calculate the nearest corresponding point between the first and last original point cloud data based on the initial lateral transformation matrix" until the initial lateral transformation matrix meets the error requirement or the number of iterations exceeds the preset number of iterations, and determine the initial lateral transformation matrix as the lateral transformation matrix.

[0068] The horizontal stitching involves determining the transformation matrix M between the two cameras, since the two cameras on the trolley's crossbar are fixed relative to each other. x This allows for the horizontal stitching of two point clouds from the same acquisition location. x The process of obtaining is as follows:

[0069] (1) First, place a circular or triangular target in the common field of view of the two cameras on the left and right, and collect a point cloud from each of the two cameras.

[0070] (2) Target segmentation is performed on the two collected point clouds. Then, in order to eliminate the influence of noise on the splicing result, radius outlier filtering is also required to denoise the target point cloud.

[0071] (3) Manually select the corresponding points between the targets, and use the corresponding points to calculate the transformation matrix M between the two targets. xr .

[0072]

[0073] Where b i For the left camera target, is the corresponding point; for the right camera target, is the corresponding point; n is the number of corresponding points; R and T represent the rotation and translation matrices of the tail camera point cloud transformation to the left camera coordinate system.

[0074] Since the corresponding points are manually selected, the calculated transformation matrix has some error, but it can achieve a rough stitching between point clouds. The process of obtaining this result is called coarse registration of point clouds, and the resulting transformation matrix M xr This is called the coarse registration matrix.

[0075] (4) Coarse registration has low accuracy and requires M to be re-registered. xr After optimization, a fine registration matrix M with smaller error is obtained. xc This process, called fine registration, uses the ICP (Iterative Closest Point) algorithm for fine registration. This algorithm will use M... xrAs the initial transformation matrix, calculate the nearest corresponding points between two point clouds, then solve for a new transformation matrix using these corresponding points. Use the resulting matrix to calculate new corresponding points, and repeat this process to iterate the transformation matrix until the iterative matrix meets the error requirement or exceeds the specified number of iterations. Finally, obtain the precise registration matrix M. xc And let the horizontal splicing matrix M x =M xc .

[0076] Longitudinal stitching: Since the trolley moves a fixed distance for data acquisition, and the displacement accuracy is within 1mm, the longitudinal transformation matrix between adjacent shooting positions can be considered fixed. Therefore, the longitudinal stitching matrix M is calculated. y And to obtain the horizontal splicing matrix M x The process is basically the same, the only difference is that the target is placed in the common field of view of the left camera's front and rear shooting positions, and stitched together according to the target point cloud, but the process is the same.

[0077] Identify any 3D imaging device as the current 3D imaging device.

[0078] Determine any two adjacent measurement points as the previous measurement point and the next measurement point.

[0079] The second target is placed in the overlapping area of ​​the field of view of the current 3D imaging device, with the mounting device positioned at the front and rear measurement points.

[0080] Acquire the preceding and following raw point cloud data. The preceding raw point cloud data is acquired by the 3D imaging device when the mounted device is at the preceding measurement point. The following raw point cloud data is acquired by the 3D imaging device when the mounted device is at the following measurement point.

[0081] The original point cloud data is segmented into targets to obtain the point cloud data in front of the targets.

[0082] The original point cloud data is segmented by a target to obtain the target-based point cloud data.

[0083] Outlier points in the point cloud data before and after the target are removed using a radius outlier filtering method.

[0084] The coordinates of multiple second target points in the point cloud data in front of and behind the target are obtained, and the coordinate pairs corresponding to each second target point are obtained.

[0085] Based on the coordinate pairs corresponding to multiple second target points, the longitudinal coarse registration matrix of the front three-dimensional imaging device coordinate system and the rear three-dimensional imaging device coordinate system is determined.

[0086] The longitudinal coarse registration matrix is ​​determined as the initial longitudinal transformation matrix.

[0087] Based on the initial longitudinal transformation matrix, the nearest corresponding points between the previous and subsequent original point cloud data are calculated.

[0088] Update the initial longitudinal transformation matrix using the nearest corresponding point, and return to the step "Calculate the nearest corresponding point between the previous original point cloud data and the subsequent original point cloud data based on the initial longitudinal transformation matrix" until the initial longitudinal transformation matrix meets the error requirement or the number of iterations exceeds the preset number of iterations, and determine the initial longitudinal transformation matrix as the longitudinal transformation matrix.

[0089] Step 203 specifically includes:

[0090] Select any original point cloud data as the current original point cloud data.

[0091] Outlier points in the original point cloud data are removed using a radius-based outlier filtering method, resulting in the denoised point cloud data. The original point cloud and a comparison image before and after denoising are shown below. Figures 4 to 6 As shown.

[0092] A region growing algorithm is used to perform background segmentation on the current denoised point cloud data to obtain the local point cloud data of the current curved board.

[0093] Update the current original point cloud data and return to the step "Use the radius outlier filtering method to delete outliers in the current original point cloud data to obtain the current denoised point cloud data", until all original point cloud data are traversed to obtain m×d local point cloud data of the curved plate.

[0094] Specifically, the radius outlier filtering method is used to remove outliers from the original point cloud data to obtain the current denoised point cloud data, which includes:

[0095] Using a preset length R as the radius, construct a sphere corresponding to each three-dimensional point in the current original point cloud data, with each three-dimensional point in the current original point cloud data as the center.

[0096] Outliers are defined as three-dimensional points within a sphere whose number of points is less than a threshold N.

[0097] Remove outliers from the current original point cloud data to obtain the current denoised point cloud data.

[0098] Point cloud denoising: To address the noise present in the original point cloud captured by the 3D imaging device, a radius outlier filtering method is used to remove it, resulting in a denoised point cloud. A spherical space with radius R is set with each 3D point as the center, and the number of 3D points n in this space is searched. If n is less than a threshold N, the center point is identified as an outlier and removed.

[0099] Specifically, a region growing algorithm is used to perform background segmentation on the current denoised point cloud data to obtain the local point cloud data of the current curved board, including:

[0100] Construct an empty set as a partitioned array L.

[0101] Construct an empty set as the seed sequence Q.

[0102] Let the iteration number i = 1.

[0103] Construct an empty set as a three-dimensional point set C.

[0104] The point with the smallest curvature in the current denoised point cloud data is used as the seed and added to the seed sequence Q.

[0105] Determine any seed in the seed sequence Q as the current seed.

[0106] Obtain all neighboring points of the current seed from the current denoised point cloud data to form a neighboring point set.

[0107] All points in the neighborhood point set whose normal angle with the current seed is less than the smoothing threshold T are added to the 3D point set C as undetermined seeds.

[0108] Points in the undetermined seed whose curvature is less than the curvature threshold U are used as seeds and added to the seed sequence Q.

[0109] Remove the current seed from the current denoised point cloud data and seed sequence Q, and return to step "determine any seed in seed sequence Q as the current seed" until seed sequence Q is an empty set. Then, use the 3D point set C as the i-th subset C of the segmentation array L. i Add it to the partition array L.

[0110] Subset C i Remove from the current denoised point cloud data, increment the iteration count i by 1, and return to the step "Construct an empty set as a 3D point set C" until the current denoised point cloud data has been traversed.

[0111] Determine the centroid coordinates of each subset in the partition array L.

[0112] Based on multiple centroid coordinates, the expected value of each subset in the segmented array L is determined.

[0113] The subset corresponding to the maximum expected value in the segmented array L is determined as the local point cloud data of the current curved board.

[0114] Expected value:

[0115]

[0116] in,

[0117]

[0118] In the formula, Ei δ is the expected value of the i-th subset in the partition array L; i θ is the weight of the i-th height. i This is the weight of the i-th x-axis; Pz is the weight of the i-th y-axis; n) is the number of subsets in the partition array L; i Px represents the percentage of the z-coordinate of the centroid of the i-th subset in the segmented array L. i To determine the percentage of the centroid x-coordinate of the i-th subset in the partition array L; Py i The proportion of the centroid y-coordinate of the i-th subset in the segmented array L; {X i ,Y i Z i} represents the centroid coordinates of the i-th subset in the partition array L.

[0119] Background segmentation: The point cloud is semantically segmented using a region growing algorithm, dividing it into several subsets, and the point cloud belonging to the hull curved plate is extracted from them, and the background is removed.

[0120] The content of the region growing algorithm is as follows:

[0121] (1) The point cloud is sorted according to the curvature value of each point. Since the point with the minimum curvature is the smoothest region, the number of segmented segments can be reduced during growth to increase the efficiency of the algorithm. Therefore, the point with the minimum curvature is used as the seed point for growth.

[0122] (2) Set an empty three-dimensional point set C, an empty seed sequence Q, and a partition array L.

[0123] (3) Determine the initial seed point, add it to the sequence Q, and search for the neighboring points of the point. Calculate the normal angle between each neighboring point and the seed point. If the angle is less than the threshold T (called the smoothing threshold), add the neighboring point to the set C. At the same time, determine whether the curvature of the point is less than the curvature threshold U. If it is less, add it to the seed sequence Q. After all the neighboring points of the seed point have been determined, delete it.

[0124] (4) Select seed points in Q and repeat step 3 until all seed points in Q are deleted. Then the growth of the three-dimensional point set C of a region is completed and added to the segmentation array L.

[0125] (5) For the remaining point cloud, continue to generate a new set C according to steps (1)-(4) and add it to the array L until all regions of the point cloud are segmented. At that time, L = {C1, C2, ... C} n}, where n is the number of regions to be divided.

[0126] The semantic segmentation content is:

[0127] (1) For the segmented point cloud array L={C1,C2,…C n}, calculate each subset C i The barycentric coordinates G of (i∈n) i ={X i ,Y i Z i}

[0128] (2) Calculate the centroid coordinates Z of the i-th subset. i X i The proportion of the total Pz i Px i If the point cloud was acquired at the start or end position, the centroid Y also needs to be calculated according to Equation 2. i The proportion of the total Py i , where X is eliminated i With Y i To determine the impact of positive and negative values ​​on the total calculation, an exponential transformation must be performed before calculating the weight, and Z... i Since all values ​​are positive, no transformation is needed.

[0129] (3) Find Pz i Px i With Py i Then, different weights are assigned to calculate the expectation. For the point cloud captured by the left camera, its θ i Px i The sign at the beginning is negative, and vice versa for the sign on the right camera; at the same time, for the point cloud collected at the starting point, The preceding sign is negative, and conversely, the sign of the point cloud collected at the end is positive. Therefore, the highest expected value E in the point cloud array L is... max The corresponding point set C max That is, the point cloud of the hull curved plate C. s Since height is a prominent positional feature of the hull's curved plates, the height weight δ i A larger value should be assigned to the characteristic weights θ of the xy axes. i and By assigning a smaller value, the curved point cloud can be filtered out.

[0130] Get M y With M x Then, following the stitching order of first horizontal and then vertical, the point clouds of 2×m hull curved plates (where m is the number of point cloud segments acquired from the hull curved plates) are stitched together. Because all point clouds need to be transformed to the coordinate system of the first camera at the end acquisition position, the non-end point clouds will affect the vertical stitching matrix M. y Perform cumulative multiplication, M iS M iW Let E be the final transformation matrix corresponding to the point clouds of the first and last cameras in the i-th acquisition segment, and let E be the identity matrix. In step 204, when the total number of 3D imaging devices d is 2, the final transformation matrix is:

[0131]

[0132] In the formula, M iW M is the final transformation matrix corresponding to the local point cloud data of the i×j-th curved plate when j=2, that is, the final transformation matrix corresponding to the point cloud of the lower tail camera of the i-th acquisition segment; y M is the vertical transformation matrix; x M is the horizontal transformation matrix; iS E is the final transformation matrix corresponding to the local point cloud data of the i×j-th curved plate when j=1; E is the identity matrix, that is, the final transformation matrix corresponding to the point cloud of the lower tail camera in the i-th acquisition segment.

[0133] When stitching multiple devices horizontally, one device is used as the reference, and the devices are stitched sequentially according to the final transformation matrix when the total number of 3D imaging devices, d, is 2. For example, if there are four devices numbered 1, 2, 3, and 4 horizontally distributed, using device 1 as the reference, the stitching can be completed sequentially as 2-1, 3-2-1, and 4-3-2-1.

[0134] Step 206: Search the point cloud and determine whether a point is a boundary point based on the angular relationship between a point and its neighboring points on the projection plane. This specifically includes:

[0135] Determine any point in the overall point cloud data of the curved board as the first target point.

[0136] Search for the k nearest neighbors of the first target point in the overall point cloud data of the curved plate.

[0137] The least squares method is used to fit the first target point and its k nearest neighbors to obtain the optimal plane F. opti .

[0138] According to the optimal plane F opti The normal vector is defined as the local projection plane F passing through the first target point. p .

[0139] Project all k nearest neighbors onto the local projection plane F. p Above, on the local projection plane F p The direction vectors between the projected point of the first target point and the projected points of each neighboring point are calculated. The point cloud is projected onto the local projection plane as follows: Figure 10 As shown.

[0140] Based on the maximum angle θ between adjacent direction vectors max The boundary recognition result of the first target point is determined.

[0141] Update the first target point and return to the step "search for the k nearest neighbor points of the first target point from the overall point cloud data of the curved plate" until the overall point cloud data of the curved plate is traversed to obtain the boundary point set of the curved plate of the ship to be tested.

[0142] Based on the maximum angle θ between adjacent direction vectors max The boundary recognition result of the first target point is determined, specifically including:

[0143] Determine the maximum angle θ between adjacent direction vectors max Is it greater than the first angle threshold θ? bnd Thus, the first judgment result was obtained.

[0144] If the first judgment result is yes, then the first target point is determined to be the boundary point of the curved plate of the hull to be tested. The angular characteristics of the boundary point are as follows: Figure 12 As shown.

[0145] If the first judgment result is negative, then the first target point is determined to be a non-boundary point of the curved plate of the hull under test. The angular characteristics of the non-boundary point are as follows: Figure 11 As shown.

[0146] The point cloud is searched, and a point is determined as a boundary point based on the angular relationship between it and its neighboring points on the projection plane.

[0147] (1) Take the target point p in the point cloud, search for its k nearest neighbors, and fit the optimal plane F using the least squares method through the k+1 points. opti , with F opti The normal vector is defined as the plane F passing through point p. p F p Let F be the local projection plane of point p, and project the neighboring points of p onto F. p superior.

[0148] (2) Calculate the direction vectors between point p and each neighboring point on the local projection plane, and calculate the angle θ between adjacent vectors. i If point p is not an edge point, it is surrounded by neighboring points, so the maximum angle θ between adjacent vectors is... max The angle will not be too large; if point p is an edge point, since its neighboring points are only distributed on one side, the maximum angle between adjacent vectors will be relatively large. Based on this characteristic, an angle threshold θ is set. bnd θ max >θ bnd The points are classified as boundary points.

[0149] Step 207 involves evaluating each boundary point individually, starting from the overall distribution of neighboring points, to find the optimal corner point. This specifically includes:

[0150] Determine any point in the boundary point set as the second target point.

[0151] Search for the k nearest neighbors of the second target point in the overall point cloud data of the curved plate.

[0152] Determine the vectors of the second target point and each second target point, and normalize them to obtain a set of normalized vectors.

[0153] The normalized vector groups are used to construct a 3D point cloud, and Euclidean clustering is used to divide the 3D point cloud into a first cluster point set E1 and a second cluster point set E2.

[0154] The mean point of the first cluster point set E1 is determined as the first mean point.

[0155] Determine the second target point and the first mean point The resulting vector is a single vector.

[0156] The mean point of the second cluster point set E2 is determined as the second mean point.

[0157] Determine the second target point and the second mean point. The resulting vector is a two-vector.

[0158] The angle between two vectors is determined as the corner point determination factor.

[0159] Based on the corner point determination quantity, the corner point recognition result of the second target point is determined.

[0160] Update the second target point and return to the step "Search for the k nearest neighbor points of the second target point from the overall point cloud data of the curved board" until the boundary point set is traversed to obtain the set of undetermined corner points.

[0161] The set of undetermined corner points is divided into D clusters using Euclidean clustering. D represents the actual number of corner points on the curved plate of the hull to be tested.

[0162] Determine the trace and ε in each cluster of undetermined corner points. sum The undetermined corner point corresponding to the minimum value is the optimal corner point. The principle for determining the optimal corner point is as follows: Figure 14 As shown. Based on the corner detection value, the corner recognition result of the second target point is determined, specifically including:

[0163] Determine if the corner detection value is less than the second angle threshold θ an Thus, the second judgment result is obtained.

[0164] If the second judgment result is negative, then the second target point is determined to be a non-corner point.

[0165] If the second judgment result is yes, then the second target point is determined to be a corner point to be determined. The corner point angle characteristics are as follows: Figure 13 As shown.

[0166] Construct the first matrix M based on the first cluster point set E1. E1 .

[0167] Calculate the first matrix M E1The covariance matrix is ​​the first covariance matrix.

[0168] The trace of the first covariance matrix is ​​calculated as the first covariance trace.

[0169] Determine the second cluster point set E2 and construct the second matrix M E2 .

[0170] Calculate the second matrix M E2 The covariance matrix is ​​the second covariance matrix.

[0171] The trace of the second covariance matrix is ​​calculated as the second covariance trace.

[0172] The sum of the first covariance trace and the second covariance trace is determined to be the trace ε of the second target point. sum .

[0173] The point cloud of the hull's curved plates is not sharply defined at the corners, and may even exhibit polygonal features, which could lead to incorrect corner extraction. To prevent incorrect corner extraction, the angle θ between the vectors of the target point and its neighboring points is no longer used. max Instead of using it as a basis, the optimal corner point is determined based on the overall distribution of neighboring points. The specific process is as follows:

[0174] (1) Find the vector between the target point p and its neighboring points q, where q∈E={q1,q1,q1,…q1} k}, and normalize the vectors to obtain a normalized vector set V = {v1, v2, v3…v}. k}

[0175]

[0176] (2) Construct a three-dimensional point cloud from the normalized vector set, and divide it into two clusters E1 and E2 using Euclidean clustering. Calculate the mean points of E1 and E2. The angle θ between the two E This serves as the basis for corner point determination. If the resulting included angle is less than the angle threshold θ, then... an It is then considered a corner point.

[0177]

[0178] In addition, the covariance traces ε1 and ε2 of the two clusters of point sets need to be calculated and summed to obtain ε. sum The calculation process is as follows, which serves as the basis for subsequent corner point selection:

[0179] Construct matrices M of type 3×k1 and 3×k2 using E1 and E2 respectively. E1 M E2 , where k1 and k2 are the number of points in the two point sets.

[0180]

[0181] Calculate the covariance matrix:

[0182]

[0183] Request covM E1 covM E2 Find the traces ε1 and ε2, and sum them to obtain ε. sum .

[0184] ε sum =tr(covM E1 )+tr(covM E2 ).

[0185] (3) Following the steps above, extract corner points from the boundary points of the hull curved plate. Multiple corner points are extracted at each corner location; these are called potential corner points. This effectively solves the problem of circled areas not being identified as corner points, increasing the likelihood of correct corner point selection. Since only one corner point is needed at each location, potential corner points must be filtered to obtain the optimal corner point.

[0186] (4) Based on the number n of corner points on the hull curved plate, the suspected corner points are divided into n clusters using Euclidean clustering. In each cluster, the calculated trace and ε of each point are compared. sum The corner point with the smallest trace sum is selected as the optimal corner point in the cluster. Because ε sum The smaller the value, the more concentrated the neighboring points are, and the more concentrated the neighboring points are, the more it conforms to the characteristics of a corner point.

[0187] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal. The computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is connected to the system bus via the I / O interfaces. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The I / O interfaces of the computer device are used for exchanging information between the processor and external devices. The communication interface of the computer device is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device.

[0188] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0189] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0190] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0191] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0192] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0193] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0194] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device, characterized in that, The method is applied to a large ship hull curved surface measuring device, the device comprising: Equipped with a device and multiple 3D imaging equipment; The mounting device is equipped with a crossbeam; the crossbeam is perpendicular to the direction of movement of the mounting device. Multiple three-dimensional imaging devices are equally spaced on the crossbeam; Multiple measurement points are set at equal intervals along the long side of the curved plate of the hull to be tested; When the mounting device is at adjacent measurement points, the field of view of the same three-dimensional imaging device overlaps; the field of view of the same three-dimensional imaging device at all measurement points covers the long side of the curved plate of the hull under test. When the mounting device is at any measurement point, the fields of view of two adjacent three-dimensional imaging devices overlap; and the fields of view of all three-dimensional imaging devices cover the wide side of the curved plate of the ship under test. The method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device includes: Determine the horizontal and vertical transformation matrices; The mounting device is controlled to pass through all measurement points sequentially along the long side of the curved plate of the hull under test, obtaining m×d original point cloud data; the i×j-th original point cloud data is acquired by the j-th three-dimensional imaging device when the mounting device is at the i-th measurement point; i = 1, 2, ..., m; m is the total number of measurement points; j = 1, 2, ..., d; d is the total number of three-dimensional imaging devices; Each original point cloud data is preprocessed to obtain m×d local point cloud data of the curved plate; Based on the horizontal transformation matrix and the vertical transformation matrix, the final transformation matrix corresponding to the local point cloud data of each curved plate is determined; Based on multiple final transformation matrices, the point cloud data of m×d curved plate portions are stitched together to obtain the overall point cloud data of the curved plate. Based on the angular relationship between a point and its neighboring points on the projection plane, the boundary point set of the curved hull under test is extracted from the overall point cloud data of the curved hull. Based on the overall distribution of neighboring points, the corner points of the curved plate of the hull to be tested are extracted from the set of boundary points.

2. The method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device according to claim 1, characterized in that, Each original point cloud data point is preprocessed to obtain m×d local point cloud data points for the curved plate, specifically including: Select any raw point cloud data as the current raw point cloud data; The outlier in the original point cloud data is removed by using the radius outlier filtering method to obtain the current denoised point cloud data; The region growing algorithm is used to perform background segmentation on the current denoised point cloud data to obtain the local point cloud data of the current curved board; Update the current original point cloud data and return to the step "Use the radius outlier filtering method to delete outliers in the current original point cloud data to obtain the current denoised point cloud data", until all original point cloud data are traversed to obtain m×d local point cloud data of the curved plate.

3. The method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device according to claim 2, characterized in that, The radius-based outlier filtering method is used to remove outliers from the original point cloud data, resulting in the current denoised point cloud data. Specifically, this includes: With a preset length R as the radius, construct a sphere corresponding to each three-dimensional point in the current original point cloud data, with each three-dimensional point in the current original point cloud data as the center of the sphere; The three-dimensional points within the corresponding sphere whose number of three-dimensional points is less than the number threshold N are identified as outliers. Remove outliers from the current original point cloud data to obtain the current denoised point cloud data.

4. The method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device according to claim 3, characterized in that, The region growing algorithm is used to perform background segmentation on the current denoised point cloud data to obtain the local point cloud data of the current curved board, specifically including: Construct an empty set as a partitioned array L; Construct an empty set as the seed sequence Q; Let the iteration number i = 1; Construct an empty set as a three-dimensional point set C; The point with the smallest curvature in the current denoised point cloud data is used as the seed and added to the seed sequence Q. Determine any seed in the seed sequence Q as the current seed; Obtain all neighboring points of the current seed from the current denoised point cloud data to form a neighboring point set; All points in the neighborhood point set whose normal angle with the current seed is less than the smoothing threshold T are added as undetermined seeds to the three-dimensional point set C; Points in the undetermined seed with curvature less than the curvature threshold U are used as seeds and added to the seed sequence Q; Remove the current seed from the current denoised point cloud data and seed sequence Q, and return to step "determine any seed in seed sequence Q as the current seed" until the seed sequence Q is an empty set. Then, use the 3D point set C as the i-th subset C of the segmentation array L. i Add it to the partition array L; subset C i Remove from the current denoised point cloud data, increment the iteration count i by 1, and return to the step "Construct an empty set as a 3D point set C" until the current denoised point cloud data has been traversed; Determine the centroid coordinates of each subset in the partition array L; Based on the multiple centroid coordinates, the expected value of each subset in the segmented array L is determined respectively; The subset corresponding to the maximum expected value in the segmented array L is determined as the local point cloud data of the current curved board.

5. The method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device according to claim 4, characterized in that, The expected value is: in, In the formula, E i δ is the expected value of the i-th subset in the partition array L; i θ is the weight of the i-th height. i This is the weight of the i-th x-axis; Pz is the weight of the i-th y-axis; n) is the number of subsets in the partition array L; i Px represents the percentage of the z-coordinate of the centroid of the i-th subset in the segmented array L. i To determine the percentage of the centroid x-coordinate of the i-th subset in the partition array L; Py i The proportion of the centroid y-coordinate of the i-th subset in the segmented array L; {X i ,Y i Z i } represents the centroid coordinates of the i-th subset in the partition array L.

6. The method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device according to claim 1, characterized in that, Determining the horizontal and vertical transformation matrices specifically includes: Designate any measurement point as the current measurement point; Determine any two adjacent 3D imaging devices as the first 3D imaging device and the last 3D imaging device; The device is driven to the current measurement point, and the first target is placed in the overlapping area of ​​the fields of view of the first and last three-dimensional imaging devices. Acquire first and last raw point cloud data; the first raw point cloud data is acquired using a first 3D imaging device; the last raw point cloud data is acquired using a last 3D imaging device. The original point cloud data is segmented by a target to obtain the target first point cloud data; Target segmentation is performed on the raw point cloud data of the tail to obtain the target tail point cloud data; Outliers in the first and last point cloud data of the target are removed using a radius-based outlier filtering method. Obtain the coordinates of multiple first target points in the target head point cloud data and the target tail point cloud data, and obtain the coordinate pair corresponding to each first target point; Based on the coordinate pairs corresponding to multiple first target points, the lateral coarse registration matrix of the coordinate system of the first 3D imaging device and the coordinate system of the last 3D imaging device is determined. The coarse horizontal registration matrix is ​​determined as the initial horizontal transformation matrix; Based on the initial lateral transformation matrix, calculate the nearest corresponding point between the first original point cloud data and the last original point cloud data; The initial lateral transformation matrix is ​​updated using the nearest corresponding point, and the process returns to the step "Calculate the nearest corresponding point between the first original point cloud data and the last original point cloud data based on the initial lateral transformation matrix" until the initial lateral transformation matrix meets the error requirement or the number of iterations exceeds the preset number of iterations, and the initial lateral transformation matrix is ​​determined to be a lateral transformation matrix. Identify any 3D imaging device as the current 3D imaging device; Determine any two adjacent measurement points as the previous measurement point and the next measurement point; Place the second target in the overlapping area of ​​the field of view of the current 3D imaging device, with the device positioned at the front and rear measurement points; Acquire front raw point cloud data and back raw point cloud data; the front raw point cloud data is acquired by the current 3D imaging device when the mounted device is at the front measurement point; the back raw point cloud data is acquired by the current 3D imaging device when the mounted device is at the back measurement point. Target segmentation is performed on the raw point cloud data to obtain the point cloud data in front of the target; The original point cloud data is segmented by a target to obtain the target-segmented point cloud data. Outliers in the point cloud data before and after the target are removed using a radius-based outlier filtering method. Obtain the coordinates of multiple second target points in the point cloud data in front of and behind the target, and obtain the coordinate pair corresponding to each second target point; Based on the coordinate pairs corresponding to multiple second target points, the longitudinal coarse registration matrix of the front three-dimensional imaging device coordinate system and the rear three-dimensional imaging device coordinate system is determined; The longitudinal coarse registration matrix is ​​determined as the initial longitudinal transformation matrix; Based on the initial longitudinal transformation matrix, calculate the nearest corresponding point between the previous original point cloud data and the subsequent original point cloud data; The initial longitudinal transformation matrix is ​​updated using the nearest corresponding point, and the process returns to the step "Calculate the nearest corresponding point between the previous original point cloud data and the subsequent original point cloud data based on the initial longitudinal transformation matrix" until the initial longitudinal transformation matrix meets the error requirement or the number of iterations exceeds the preset number of iterations, at which point the initial longitudinal transformation matrix is ​​determined to be the longitudinal transformation matrix.

7. The method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device according to claim 1, characterized in that, When the total number of 3D imaging devices, d, is 2, the final transformation matrix is: In the formula, M iW M is the final transformation matrix corresponding to the local point cloud data of the i×j-th curved plate when j=2; y M is the vertical transformation matrix; x M is the horizontal transformation matrix; iS The final transformation matrix corresponding to the local point cloud data of the i×jth curved plate when j=1; E is the identity matrix.

8. The method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device according to claim 1, characterized in that, Based on the angular relationship between a point and its neighboring points on the projection plane, the boundary point set of the curved hull under test is extracted from the overall point cloud data of the curved hull, specifically including: Determine any point in the overall point cloud data of the curved board as the first target point; Search for the k nearest neighbors of the first target point in the overall point cloud data of the curved board; The least squares method is used to fit the first target point and its k nearest neighbors to obtain the optimal plane F. opti ; According to the optimal plane F opti The normal vector is defined as the local projection plane F passing through the first target point. p ; Project all k nearest neighbors onto the local projection plane F. p Above, on the local projection plane F p Calculate the direction vectors between the projection points of the first target point and the projection points of each neighboring point. Based on the maximum angle θ between adjacent direction vectors max Determine the boundary recognition result of the first target point; Update the first target point and return to the step "search for the k nearest neighbor points of the first target point from the overall point cloud data of the curved plate" until the overall point cloud data of the curved plate is traversed to obtain the boundary point set of the curved plate of the ship to be tested; Based on the maximum angle θ between adjacent direction vectors max The boundary recognition result of the first target point is determined, specifically including: Determine the maximum angle θ between adjacent direction vectors max Is it greater than the first angle threshold θ? bnd The first judgment result is obtained; If the first judgment result is yes, then the first target point is determined to be the boundary point of the curved plate of the hull to be tested; If the first judgment result is negative, then the first target point is determined to be a non-boundary point of the curved plate of the hull to be tested.

9. The method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device according to claim 1, characterized in that, Based on the overall distribution of neighboring points, the corner points of the curved plate of the hull under test are extracted from the boundary point set, specifically including: Determine any point in the boundary point set as the second target point; Search for the k nearest neighbors of the second target point in the overall point cloud data of the curved plate; Determine the vectors of the second target point and each second target point, and normalize them to obtain a set of normalized vectors; The unitized vector groups are used to construct a 3D point cloud, and Euclidean clustering is used to divide the 3D point cloud into a first cluster point set E1 and a second cluster point set E2. The mean point of the first cluster point set E1 is determined as the first mean point. Determine the second target point and the first mean point The resulting vector is a single vector; The mean point of the second cluster point set E2 is determined as the second mean point. Determine the second target point and the second mean point. The resulting vector is a two-vector; The angle between two vectors is determined as the corner point determination factor; Based on the corner point determination quantity, determine the corner point recognition result of the second target point; Update the second target point and return to the step "Search for the k nearest neighbor points of the second target point from the overall point cloud data of the curved board" until the boundary point set is traversed to obtain the set of undetermined corner points; Euclidean clustering is used to divide the set of undetermined corner points into D clusters; D is the actual number of corner points on the curved plate of the hull to be tested. Determine the trace and ε in each cluster of undetermined corner points. sum The undetermined corner point corresponding to the minimum value is the optimal corner point; D optimal corner points are determined as the corner points of the curved plate of the hull to be tested.

10. The method for measuring the curved surface of a large ship hull based on a three-dimensional imaging device according to claim 9, characterized in that, Based on the corner detection value, the corner recognition result of the second target point is determined, specifically including: Determine if the corner detection value is less than the second angle threshold θ an The second judgment result is obtained; If the second judgment result is negative, then the second target point is determined to be a non-corner point; If the second judgment result is yes, then the second target point is determined to be an undetermined corner point; Construct the first matrix M based on the first cluster point set E1. E1 ; Calculate the first matrix M E1 The covariance matrix is ​​the first covariance matrix; The trace of the first covariance matrix is ​​calculated as the first covariance trace; Determine the second cluster point set E2 and construct the second matrix M E2 ; Calculate the second matrix M E2 The covariance matrix is ​​the second covariance matrix; The trace of the second covariance matrix is ​​calculated as the second covariance trace; The sum of the first covariance trace and the second covariance trace is determined to be the trace ε of the second target point. sum .

Images