A global calibration method for multi-view tracking system based on high-reflective marker points

Abstract

This invention provides a global calibration method for a multi-view tracking system based on highly reflective markers, relating to the calibration field of multi-view tracking scanning measurement systems. The method includes the following steps: selecting an experimental site to deploy the multi-view tracking system; randomly affixing multiple circular highly reflective markers to a flat, rigid wall; using a laser tracker as a measuring device to measure the spatial position of the affixed highly reflective markers; synchronously acquiring the affixed highly reflective markers using the multi-view tracking system to determine the reflective point group that each group of binocular trackers can detect, and solving the transformation matrix of each group of binocular trackers relative to the global coordinate system; solving the transformation matrix between multiple groups of binocular trackers to complete the global calibration of the multi-view tracking system. The technical solution of this invention overcomes the problems of existing technologies that cannot overcome the physical limitations of the common viewing area and cannot eliminate the gradual accumulation of calibration errors.

Description

Technical Field

[0001] This invention relates to the field of calibration of large field-of-view multi-view tracking scanning measurement systems, and specifically to a global calibration method for multi-view tracking systems based on highly reflective marker points. Background Technology

[0002] With the rapid development of industrial manufacturing and other fields, the demand for inspection of large, complex free-form surface components is increasing. Wide field-of-view multi-view tracking scanning measurement systems are playing an increasingly important role in the three-dimensional topography measurement of large workpieces and non-contact non-destructive testing. Multi-view tracking systems typically consist of multiple binocular trackers distributed at different locations. To unify the local measurement data from each camera into the same spatial coordinate system, high-precision global calibration of the entire multi-view tracking system is essential.

[0003] Existing global calibration methods for multi-view tracking systems primarily rely on a common field of view among the cameras. This typically involves moving a calibration board or one-dimensional calibration object within the shared field of view of adjacent cameras to calculate their relative poses pairwise. However, in situations with large fields of view or complex industrial environments, ensuring a sufficient and high-quality common field of view among all adjacent cameras is extremely difficult due to limitations imposed by camera installation positions, shooting angles, and obstructions. This significantly restricts the deployment flexibility and applicability of multi-view tracking systems. Furthermore, existing pairwise serial derivation calibration methods suffer from severe error propagation. As the number of cameras in the system increases or the calibration link lengthens, small local calibration errors are amplified and accumulated at each level, making it difficult to meet the stringent requirements of high-precision large-scale spatial measurements in high-end manufacturing fields such as aerospace and automotive manufacturing.

[0004] Therefore, there is a need for a global calibration method for multi-view tracking systems based on highly reflective markers that can overcome the physical limitations of the common viewing area and effectively eliminate the stepwise accumulation of calibration errors. Summary of the Invention

[0005] The main objective of this invention is to provide a global calibration method for a multi-view tracking system based on highly reflective markers, in order to solve the problems in the prior art that cannot break the physical limitations of the common viewing area and cannot eliminate the stepwise accumulation of calibration errors.

[0006] To achieve the above objectives, this invention provides a global calibration method for a multi-view tracking system based on highly reflective markers, specifically including the following steps: S1. Select an experimental site to deploy a multi-view tracking system and randomly affix multiple circular, highly reflective markers to a flat, rigid wall.

[0007] S2, using a laser tracker as a measuring device to measure the spatial position of the posted highly reflective markers.

[0008] S3. Use a multi-view tracking system to synchronously collect the pasted highly reflective markers, determine the group of reflective points that each group of binocular trackers can detect, and solve the transformation matrix of each group of binocular trackers relative to the global coordinate system.

[0009] S4, solve for the transformation matrix between multiple sets of binocular trackers to complete the global calibration of the multi-view tracking system.

[0010] Furthermore, step S1 specifically includes the following steps: S1.1, The multi-view tracking system includes multiple sets of binocular trackers, each set of binocular trackers includes two industrial cameras, and the distance and optical axis angle between the two industrial cameras in each set of binocular tracking systems are set.

[0011] S1.2, set the diameter of the highly reflective markers and the distance between each highly reflective marker, and ensure that all highly reflective markers are within the field of view of the multi-view tracking system.

[0012] Furthermore, step S2 specifically includes: The measurement coordinate system of the laser tracker is defined as the global world coordinate system, denoted as . Assuming a total of [number] sheets were pasted on a rigid wall surface. The first highly reflective marker point is defined as the... The three-dimensional coordinate vectors of the highly reflective markers are: ,in, : ; in,( , , ( ) represents the three-dimensional coordinates of the highly reflective marker points measured by the laser tracker.

[0013] Furthermore, step S3 specifically includes the following steps: S3.1, for any binocular tracker , , Let be the number of binocular tracker groups; assuming the binocular tracker detects a subset of points on the wall in its field of view, for the th in the subset of points... Using the intrinsic and extrinsic parameters obtained during the calibration process of each set of binocular trackers, the high reflectivity of each high reflectivity marker is calculated through triangulation. The three-dimensional coordinate vector in the local coordinate system, with the optical center of the left industrial camera as... The origin is denoted as : ; in,( , , ( ) represents the three-dimensional coordinates of the highly reflective markers detected by the binocular tracker.

[0014] S3.2, Describe the binocular tracker to the global world coordinate system The rotation matrix and translation vector are respectively and ,but: ; in, The true values ​​of the three-dimensional coordinates obtained by the laser tracker.

[0015] In order to find the optimal solution and Construct the least squares error function : .

[0016] S3.3, calculate the centroids of the point clouds in both coordinate systems: , ; in, Binocular tracker The total number of detected feature points, and The centroids of the point cloud are shown by a laser tracker and a binocular tracker, respectively.

[0017] Furthermore, step S3 also includes the following steps: S3.4, decentrifuge the two sets of point clouds: ; ; in, , These are the decentrifugated versions of the original text. and .

[0018] S3.5, Calculate the covariance matrix of the decentralized coordinates. : ; in, for The transpose of .

[0019] right Perform singular value decomposition: ; in, and It is an orthogonal matrix. It is a diagonal matrix. for The transpose of .

[0020] S3.6, Solve for the binocular tracker Rotation matrix to global coordinate system : ; Solve Translation vector to the global coordinate system : .

[0021] Furthermore, step S3 also includes the following steps: S3.7, obtained through singular value decomposition and As the initial value for nonlinear optimization, the pose parameters of each binocular tracker in the multi-view tracking system are transformed into Lie algebras. variables of the form The global calibration process is modeled as a factor graph, which includes variable nodes and factor nodes.

[0022] S3.8, with As variable nodes; the true values ​​of the three-dimensional coordinates obtained by the laser tracker. As a non-optimizable prior factor; the actual observed coordinates extracted by the binocular tracker on the two-dimensional pixel plane. As observation factors; construct a global reprojection error cost function based on the factor graph. : ; in, For the first The first in the group of binocular trackers The intrinsic parameter matrix of a Taiwanese industrial camera. These are the left and right cameras in a binocular tracker. for antisymmetric matrix, For the first Lie algebra variables corresponding to the pose of the binocular tracker For pose variables The generated rigid body transformation matrix.

[0023] S3.9, to minimize the global reprojection error cost function, is the Lie algebra perturbation of the error vector to the pose of the stereo tracker during iteration. Jacobian matrix The derivation is as follows: ; in, , Focal length This refers to the three-dimensional coordinates of the target point in the local coordinate system of the binocular tracker under the current iterative pose.

[0024] Furthermore, step S3 also includes the following steps: S3.10, Based on the global reprojection error cost function constructed in step S3.8 and the Jacobian matrix obtained in step S3.9, construct the pose increment equation in the manifold space: ; in, This is the reprojection error vector for the current iteration. Let be the Jacobian matrix of the error vector with respect to the pose Lie algebra perturbation. Let the pose increment be the one to be solved. For the trust region radius, This is a function that takes the minimum value.

[0025] The pose increment equation is solved iteratively using the trust region optimization method. In each iteration, the Gauss-Newton direction and the steepest descent direction are determined based on the current reprojection error vector and the Jacobian matrix, respectively, and the pose increment for the current iteration is determined by these two directions under the trust region constraint. Then, it is applied to the current pose matrix through exponential mapping to achieve the first... Pose update of the binocular tracker group: ; in, Indicates the first During the nth iteration The pose transformation matrix of the binocular trackers relative to the global world coordinate system; This represents the updated pose transformation matrix; Indicates the first Group of binocular trackers in the first Pose increment in the next iteration.

[0026] Repeat the iterative process of step S3.10 until the change in global reprojection error, pose increment norm, or number of iterations meets the preset convergence condition, and obtain the optimized pose parameters of each binocular tracker.

[0027] S3.11, When the optimization iteration satisfies the convergence condition, the optimal rotation matrix is ​​extracted from the optimized state variables. With the optimal translation vector The optimal high-precision absolute transformation matrix is ​​obtained as follows: .

[0028] Furthermore, step S4 specifically includes: For solving binocular trackers To binocular tracker coordinate transformation matrix A point in space coordinates below Transform to global coordinates: ; Global coordinate transformation to In coordinate system: ; Obtain a binocular tracker To binocular tracker coordinate transformation matrix : ; Similarly, a binocular tracker is obtained. To binocular tracker coordinate transformation matrix .

[0029] The present invention has the following beneficial effects: This invention breaks away from the strict dependence of traditional multi-view tracking systems on a common field of view of cameras during calibration. By introducing a high-precision laser tracking measurement device to establish a unique global world coordinate system, even if the highly reflective marker points observed by each group of binocular trackers have no overlap, their absolute poses in the global coordinate system can still be solved separately. This allows for the derivation of spatial transformation relationships between camera groups, greatly reducing the difficulty of setting up and calibrating multi-view tracking systems in complex field environments. Furthermore, this invention effectively eliminates the error accumulation and propagation effects caused by traditional multi-view tracking cameras using pairwise overlapping field-of-view calibration. This ensures that the pose of each camera in the system is directly traced back to the high-precision measurement true value of the laser tracker, significantly improving the global positioning accuracy and measurement stability of the large field-of-view multi-view tracking scanning measurement system. Attached Figure Description

[0030] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings: Figure 1 This diagram illustrates the process of measuring the three-dimensional coordinates of each point using a laser tracker during the global calibration of a multi-view tracking system, as described in this invention.

[0031] Figure 2This diagram illustrates the components and their relative positions during the global calibration process of the multi-view tracking system in this invention.

[0032] Figure 3 This diagram illustrates the coordinate relationship transformation process during the global calibration of the multi-view tracking system in this invention.

[0033] Figure 4 The diagram shows the positional relationship between four industrial cameras and wall markers in the global world coordinate system.

[0034] Figure 5 It shows Figure 4 Top view.

[0035] Figure 6 The diagram shows local 3D points reconstructed by each set of binocular trackers using the method provided by this invention.

[0036] Figure 7 The vector diagram of the residuals on the wall surface is shown.

[0037] Figure 8 The three-dimensional registration residual plot is shown.

[0038] Figure 9 This illustrates the correction of the nearest point error in image reprojection.

[0039] The reference numerals in the above figures are: 1. Rigid wall; 2. Laser tracker; 3. Field of view of multi-view tracking system; 4. First binocular tracker; 5. Second binocular tracker; 6. Third binocular tracker. Detailed Implementation

[0040] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0041] A global calibration method for a multi-view tracking system based on highly reflective markers includes the following steps: S1. Select an experimental site to deploy a multi-view tracking system and randomly affix multiple circular, highly reflective markers to a flat, rigid wall.

[0042] S2, using a laser tracker as a measuring device to measure the spatial position of the posted highly reflective markers.

[0043] S3. Use a multi-view tracking system to synchronously acquire the pasted highly reflective markers, determine the group of reflective points that each group of binocular trackers can detect, and solve the transformation matrix of each group of cameras relative to the global coordinate system.

[0044] S4, solve for the transformation matrix between multiple sets of binocular trackers to complete the global calibration of the multi-view tracking system.

[0045] Specifically, step S1 includes the following steps: S1.1, The multi-view tracking system includes multiple sets of binocular trackers, each set of binocular trackers includes two industrial cameras, and the distance and optical axis angle between the two industrial cameras in each set of binocular tracking systems are set.

[0046] like Figure 1 As shown, a multi-view tracking system was deployed at the selected experimental site. Multiple circular, highly reflective markers were randomly affixed to a flat, rigid wall 1. The multi-view tracking system consisted of three sets of binocular trackers: a first binocular tracker 4, a second binocular tracker 5, and a third binocular tracker 6. Two industrial cameras were used, one for the left eye and one for the right eye. In each set of binocular trackers, the optical center distance between the two industrial cameras was 500 mm, and the angle between their optical axes was 45°. The three sets of binocular trackers were arranged parallel to each other in the same direction, with a center-to-center distance of 500 mm between adjacent sets. The experimental site was an 8 m × 6 m constant temperature and humidity laboratory. The distance between each highly reflective marker on the wall was no less than 300 mm, and it was ensured that all markers were within the field of view of the multi-view tracking system.

[0047] S1.2, set the diameter of the highly reflective markers and the distance between each highly reflective marker, and ensure that all highly reflective markers are within the field of view of the multi-view tracking system.

[0048] The markers are highly reflective with a diameter of 30mm, and the distance between each marker is no less than 300mm. At the same time, it is ensured that all markers are located in the field of view 3 of the multi-view tracking system.

[0049] Specifically, step S2 is as follows: The measurement coordinate system of laser tracker 2 is defined as the global world coordinate system, denoted as . Assuming a total of [number] sheets were pasted on a rigid wall surface. The first highly reflective marker point is defined as the... The three-dimensional coordinate vectors of the highly reflective markers are: ,in, : ; in,( , , ( ) represents the three-dimensional coordinates of the highly reflective marker point measured by the laser tracker. For example... Figure 2 The laser tracker was set up in the experimental space to measure the three-dimensional coordinates of the highly reflective markers.

[0050] Specifically, step S3 includes the following steps: S3.1, for any binocular tracker , , Let be the number of binocular tracker groups; assuming the binocular tracker detects a subset of points on the wall in its field of view, for the th in the subset of points... Using the intrinsic and extrinsic parameters obtained during the calibration process of each set of binocular trackers, the high reflectivity of each high reflectivity marker is calculated through triangulation. The three-dimensional coordinate vector in the local coordinate system, with the optical center of the left industrial camera as... The origin is denoted as : ; in,( , , ( ) represents the three-dimensional coordinates of the highly reflective markers detected by the binocular tracker.

[0051] S3.2, as can be seen from S2 and S3, regarding... The detected local point set now has two sets of three-dimensional coordinates: the ground truth provided by the laser tracker. and the measurement values ​​detected by the binocular tracker Record the binocular tracker to the global world coordinate system. The rotation matrix and translation vector are respectively and ,but: ; in, The true values ​​of the three-dimensional coordinates obtained by the laser tracker.

[0052] In order to find the optimal solution and Construct the least squares error function : .

[0053] S3.3, calculate the centroids of the point clouds in both coordinate systems: , ; in, Binocular tracker The total number of detected feature points, and The centroids of the point cloud are shown by a laser tracker and a binocular tracker, respectively.

[0054] Specifically, step S3 also includes the following steps: S3.4, decentrifuge the two sets of point clouds: ; ; in, , These are the decentrifugated versions of the original text. and .

[0055] S3.5, Calculate the covariance matrix of the decentralized coordinates. : ; in, for The transpose of .

[0056] right Perform singular value decomposition (SVD): ; in, and It is an orthogonal matrix. It is a diagonal matrix. for The transpose of .

[0057] S3.6, Solve for the binocular tracker Rotation matrix to global coordinate system : .

[0058] Solve Translation vector to the global coordinate system : .

[0059] like Figure 3 As shown, the coordinate transformation matrices between the global coordinate system and the camera coordinate system, and between cameras, are solved to achieve the solution of the overall transformation relationship.

[0060] Specifically, after obtaining the initial rigid body transformation of each binocular tracker relative to the global coordinate system, a global reprojection error optimization model based on factor graphs is further constructed, and the Powell dogleg trust region strategy is adopted. The pose increment on the manifold is solved iteratively. Step S3 also includes the following steps: S3.7, obtained through singular value decomposition and As the initial value for nonlinear optimization, the pose parameters of each binocular tracker in the multi-view tracking system are transformed into Lie algebras. variables of the form The global calibration process is modeled as a factor graph, which includes variable nodes and factor nodes.

[0061] S3.8, with As variable nodes; the true values ​​of the three-dimensional coordinates obtained by the laser tracker. As a non-optimizable prior factor; the actual observed coordinates extracted by the binocular tracker on the two-dimensional pixel plane. As observation factors; construct a global reprojection error cost function based on the factor graph. : ; in, For the first The first in the group of binocular trackers The intrinsic parameter matrix of a Taiwanese industrial camera. These are the left and right cameras in a binocular tracker. for antisymmetric matrix, For the first Lie algebra variables corresponding to the pose of the binocular tracker For pose variables The generated rigid body transformation matrix.

[0062] S3.9, to minimize the global reprojection error cost function, is the Lie algebra perturbation of the error vector to the pose of the stereo tracker during iteration. Jacobian matrix The derivation is as follows: ; in, , Focal length This refers to the three-dimensional coordinates of the target point in the local coordinate system of the binocular tracker under the current iterative pose.

[0063] Specifically, step S3 also includes the following steps: S3.10, Based on the global reprojection error cost function constructed in step S3.8 and the Jacobian matrix obtained in step S3.9, construct the pose increment equation in the manifold space: ; in, This is the reprojection error vector for the current iteration. Let be the Jacobian matrix of the error vector with respect to the pose Lie algebra perturbation. Let the pose increment be the one to be solved. For the trust region radius, This is a function that takes the minimum value.

[0064] The pose increment equation is solved iteratively using a trust region optimization method, with the Powell-Dogleg trust region algorithm being the preferred approach. In each iteration, the Gauss-Newton direction and the steepest descent direction are determined based on the current reprojection error vector and the Jacobian matrix, respectively. Under the trust region constraint, these two factors determine the pose increment for the current iteration. Then, through exponential mapping, Applying to the current pose matrix, to achieve the first Pose update of the binocular tracker group: ; in, Indicates the first During the nth iteration The pose transformation matrix of the binocular trackers relative to the global world coordinate system; This represents the updated pose transformation matrix; Indicates the first Group of binocular trackers in the first Pose increment in the next iteration.

[0065] Repeat the iterative process of step S3.10 until the change in global reprojection error, pose increment norm, or number of iterations meets the preset convergence condition, and obtain the optimized pose parameters of each binocular tracker.

[0066] S3.11, When the optimization iteration satisfies the convergence condition, the optimal rotation matrix is ​​extracted from the optimized state variables. With the optimal translation vector The optimal high-precision absolute transformation matrix is ​​obtained as follows: ; Thus, the solution has been found. , , Transformation matrix to global world coordinate system , , .

[0067] Specifically, step S4 is as follows: For solving binocular trackers To binocular tracker coordinate transformation matrix A point in space coordinates below Transform to global coordinates: .

[0068] Global coordinate transformation to In coordinate system: .

[0069] Obtain a binocular tracker To binocular tracker coordinate transformation matrix : .

[0070] Similarly, a binocular tracker is obtained. To binocular tracker coordinate transformation matrix .

[0071] This invention establishes a unique global world coordinate system, enabling each group of binocular trackers to independently solve for their absolute pose relative to the global coordinate system even without a sufficiently common field of view, and then derives the spatial transformation relationship between camera groups. Compared with traditional adjacent camera cascade calibration, this method reduces the difficulty of station deployment in complex environments and minimizes the cascading accumulation of errors, thereby improving the global positioning accuracy and stability of large field-of-view multi-camera tracking systems.

[0072] like Figure 4 and Figure 5 The diagram illustrates the positional relationships between four industrial cameras and wall markers within the same global world coordinate system. First, a global 3D point set of highly reflective wall markers is established. Then, each set of binocular trackers solves its absolute pose relative to the global coordinate system. Therefore, the multi-camera tracking system is no longer merely a local relationship between adjacent industrial cameras, but rather all industrial cameras are unified within the same global coordinate framework.

[0073] like Figure 6 The invention demonstrates that the local 3D points reconstructed by each set of binocular trackers, after transformation with a global calibration matrix, can be aligned with the global point set on the wall. This indicates that each set of binocular trackers only needs to see a subset of points in the wall's marked point set to independently register to the global coordinate system. Each set of binocular trackers does not need to strictly rely on a large common field of view, nor does it require the transfer of extrinsic parameters between adjacent industrial cameras. This invention reduces the difficulty of deploying multi-view tracking systems in complex environments and improves deployment flexibility.

[0074] like Figures 7-9As shown, this invention can unify the local calibration results of multiple camera groups into the same world coordinate system and use the wall marker point cloud for global registration and error correction, thereby obtaining a consistent multi-camera spatial layout, stable camera optical axis orientation, and small image reprojection error and 3D registration residual. Experimental results show that the root mean square error of the reprojection error of each camera's corrected image is approximately 0.20 px to 0.25 px, indicating that this invention can achieve sub-pixel level image geometric correction; in the 3D registration residual, the root mean square error of the cam34 combination is approximately 2.66 mm, and the root mean square error of the cam12 combination is approximately 7.82 mm, indicating that this invention can complete the 3D unified registration of wall marker points within a millimeter-level accuracy range.

[0075] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A global calibration method for a multi-view tracking system based on highly reflective marker points, characterized in that, Specifically, the steps include the following: S1. Select an experimental site to deploy a multi-view tracking system and randomly affix multiple circular, highly reflective markers to a flat, rigid wall. S2, using a laser tracker as a measuring device to measure the spatial position of the posted highly reflective markers; S3. Use a multi-view tracking system to synchronously collect the pasted highly reflective markers, determine the group of reflective points that each group of binocular trackers can detect, and solve the transformation matrix of each group of binocular trackers relative to the global coordinate system. S4, solve for the transformation matrix between multiple sets of binocular trackers to complete the global calibration of the multi-view tracking system.

2. The global calibration method of a multi-camera tracking system based on highly reflective markers according to claim 1, wherein, Step S1 specifically includes the following steps: S1.1, The multi-view tracking system includes multiple sets of binocular trackers, each set of binocular trackers includes two industrial cameras, and the distance and optical axis angle between the two industrial cameras in each set of binocular tracking systems are set; S1.2, set the diameter of the highly reflective markers and the distance between each highly reflective marker, and ensure that all highly reflective markers are within the field of view of the multi-view tracking system.

3. The global calibration method of multi-camera tracking system based on high-reflective marker points according to claim 1, wherein, Step S2 is as follows: The measurement coordinate system of the laser tracker is defined as the global world coordinate system, denoted as . Assuming a total of [number] sheets were pasted on a rigid wall surface. The first highly reflective marker point is defined as the... The three-dimensional coordinate vectors of the highly reflective markers are: ,in, : ； in,( , , ( ) represents the three-dimensional coordinates of the highly reflective marker points measured by the laser tracker.

4. The global calibration method of multi-camera tracking system based on high-reflective marker points according to claim 1, wherein, Step S3 specifically includes the following steps: S3.1, for any binocular tracker , , Let be the number of binocular tracker groups; assuming the binocular tracker detects a subset of points on the wall in its field of view, for the th point in the subset... Using the intrinsic and extrinsic parameters obtained during the calibration process of each set of binocular trackers, the high reflectivity of each high reflectivity marker is calculated through triangulation. The three-dimensional coordinate vector in the local coordinate system, with the optical center of the left industrial camera as... The origin is denoted as : ； in,( , , ( ) represents the three-dimensional coordinates of the highly reflective marker points detected by the binocular tracker; S3.2, Describe the binocular tracker to the global world coordinate system The rotation matrix and translation vector are respectively and ,but: ； wherein, true values of three-dimensional coordinates acquired by the laser tracker; To solve the optimal and , a least square error function is constructed ； S3.3, calculate the centroids of the point clouds in both coordinate systems: ， ； wherein, is a binocular tracker is the total number of detected feature points, and is the point cloud centroid under laser tracker and binocular tracker detection, respectively.

5. The global calibration method of a multi-camera tracking system based on highly reflective markers according to claim 4, wherein, Step S3 also includes the following steps: S3.4, decentrifuge the two sets of point clouds: ； ； in, , These are the decentrifugated versions of the original text. and ; S3.5, compute covariance matrix of decentralized coordinates : ； wherein is the transpose of To perform singular value decomposition: ； wherein and is an orthogonal matrix, is a diagonal matrix, is the transpose of S3.6, solving the binocular tracker rotation matrix to global coordinate system : ； solving out translation vector to global coordinate system : 。 6. The global calibration method of a multi-camera tracking system based on highly reflective markers according to claim 5, wherein, Step S3 also includes the following steps: S3.7, obtained through singular value decomposition and As the initial value for nonlinear optimization, the pose parameters of each binocular tracker in the multi-view tracking system are transformed into Lie algebras. variables of the form ; The global calibration process is modeled as a factor graph, which includes variable nodes and factor nodes. S3.8, with As variable nodes; the true values ​​of the three-dimensional coordinates obtained by the laser tracker. As a non-optimizable prior factor; the actual observed coordinates extracted by the binocular tracker on the two-dimensional pixel plane. As observation factors; construct a global reprojection error cost function based on the factor graph. : ； in, For the first The first in the group of binocular trackers The intrinsic parameter matrix of a Taiwanese industrial camera. These are the left and right cameras in a binocular tracker. for antisymmetric matrix, For the first Lie algebra variables corresponding to the pose of the binocular tracker For pose variables The generated rigid body transformation matrix; S3.9, for minimizing the global re-projection error cost function, the error vector to the binocular tracker pose Lie algebra perturbation quantity is the Jacobian matrix of is derived as follows: ； wherein, , is the focal length, is the three-dimensional coordinate of the target point converted to the local coordinate system of the binocular tracker at the current iteration pose.

7. The global calibration method of a multi-camera tracking system based on highly reflective markers according to claim 6, wherein, Step S3 also includes the following steps: S3.10, Based on the global reprojection error cost function constructed in step S3.8 and the Jacobian matrix obtained in step S3.9, construct the pose increment equation in the manifold space: ； in, This is the reprojection error vector for the current iteration. Let be the Jacobian matrix of the error vector with respect to the pose Lie algebra perturbation. Let the pose increment be the one to be solved. For the trust region radius, The function is for finding the minimum value; The pose increment equation is iteratively solved using a trust region optimization method. In each iteration, the Gauss-Newton direction and the steepest descent direction are determined based on the current reprojection error vector and the Jacobian matrix, respectively, and the pose increment for the current iteration is determined by these two directions under the trust region constraint. Then, it is applied to the current pose matrix through exponential mapping to achieve the first... Pose update of the binocular tracker group: ； in, Indicates the first During the nth iteration The pose transformation matrix of the binocular trackers relative to the global world coordinate system; This represents the updated pose transformation matrix; Indicates the first Group of binocular trackers in the first Pose increment in the next iteration; Repeat the iterative process of step S3.10 until the change in global reprojection error, pose increment norm, or number of iterations meets the preset convergence condition, and obtain the optimized pose parameters of each binocular tracker. S3.11, When the optimization iteration satisfies the convergence condition, the optimal rotation matrix is ​​extracted from the optimized state variables. With the optimal translation vector The optimal high-precision absolute transformation matrix is ​​obtained as follows: 。 8. The global calibration method of multi-camera tracking system based on high-reflective marker points according to claim 1, wherein, Step S4 is as follows: For solving binocular trackers To binocular tracker coordinate transformation matrix A point in space coordinates below Transform to global coordinates: ； Global coordinate transformation to Coordinate system under: ； Obtaining a binocular tracker To a binocular tracker Coordinate conversion matrix : ； Likewise, a binocular tracker is obtained to the binocular tracker coordinate conversion matrix .

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