A high-precision calibration method for zoom binocular vision measurement system

Abstract

The invention provides a high-precision calibration method for a zoom binocular vision measurement system, wherein the zoom binocular vision measurement system comprises a circular checkerboard target and two fixedly placed industrial cameras; the high-precision calibration method comprises moving the circular checkerboard target, using two industrial cameras to collect images of the circular checkerboard target from different angles; using two industrial camera image matching points and matching points before and after zooming of the two industrial cameras to estimate two types of homography matrices; calculating the internal and external parameters of the two industrial cameras after zooming according to a zoom mathematical model and a homography matrix; nonlinearly optimizing the internal and external parameters of the two industrial cameras using a Levenberg-Marquardt algorithm; and performing three-dimensional measurement of a large-sized object according to the optimized internal and external parameters. The actual measurement accuracy of large-sized objects is effectively improved.

Description

Technical Field

[0001] The invention belongs to the technical field of visual measurement, and in particular relates to a high-precision calibration method for a zoom binocular vision measurement system. Background Art

[0002] The research and development and production capabilities of large aircraft are important indicators of the level of a country's aviation industry and an important reflection of a country's comprehensive strength. The development of large aircraft is of great significance to improving my country's independent innovation capabilities and enhancing the country's core competitiveness.

[0003] In the process of intelligent manufacturing of aerospace, conventional auxiliary measurement technologies used for precise positioning, assembly and intelligent guidance of large parts cannot meet the accuracy requirements. High-precision three-dimensional measurement of large-sized objects puts higher requirements on vision-based and optical measurement methods, that is, to meet the requirements of a larger measurement field of view while ensuring high measurement accuracy.

[0004] Abdel-Aziz proposed a direct linear transformation method based on the perspective principle, but due to the lack of constraints between parameters and consideration of lens distortion, the calibration accuracy is not high. Tsai proposed a two-step method that takes radial distortion into consideration; J. Weng added consideration of tangential distortion on the basis of the two-step method, which is suitable for occasions with severe distortion. The most representative research on fixed-focus camera calibration in China is a method that uses a plane chessboard as a calibration object, which is called Zhang Zhengyou's plane calibration method. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention provides a high-precision calibration method for a zoom binocular vision measurement system.

[0006] The present invention provides a high-precision calibration method for a zoom binocular vision measurement system, wherein the zoom binocular vision measurement system comprises a circular checkerboard target and two fixedly placed industrial cameras; the high-precision calibration method comprises:

[0007] Move the circular checkerboard target and use two industrial cameras to collect images of the circular checkerboard target from different angles;

[0008] Two types of homography matrices are estimated using the matching points of two industrial camera images and the matching points of two industrial cameras before and after zooming;

[0009] According to the zoom mathematical model and homography matrix, the internal and external parameters of the two industrial cameras after zoom are calculated;

[0010] The Levenberg-Marquardt algorithm is used to perform nonlinear optimization of the internal and external parameters of two industrial cameras;

[0011] Perform three-dimensional measurement of large-sized objects based on optimized internal and external parameters.

[0012] Furthermore, the method of using the matching points of the two industrial camera images and the matching points of the two industrial cameras before and after zooming to estimate two types of homography matrices includes:

[0013] Get a single image captured by two industrial cameras; there are multiple matching points on the single image;

[0014] Construct the optimized homography matrix:

[0015]

[0016] Where n is the total number of matching points on a single image; and They are the kth matching points on the single images captured by the two industrial cameras respectively; there is a homography matrix H with a dimension of 3×3 between the single images captured by the two industrial cameras, m1=Hm2.

[0017] Furthermore, the calculation of the internal and external parameters of the two industrial cameras after zooming according to the zoom mathematical model and the homography matrix includes:

[0018] Get the spatial points on the image before zooming and the spatial points on the image after zooming of a single industrial camera;

[0019] The zoom factor of a single industrial camera is calculated according to the following formula:

[0020]

[0021] Among them, r u 、r v and r f are the zoom factors of a single industrial camera, r u =r v =r f ; It is the principal point coordinates of a single industrial camera before zooming; is the coordinate of the principal point of a single industrial camera after zooming; f 1 is the focal length of a single industrial camera before zooming; f 2 is the focal length of a single industrial camera after zooming; i is the i-th spatial point; m spatial points generate m matching points;

[0022] Get the intrinsic parameter matrix of a single industrial camera at the initial position and after zooming;

[0023] Construct the homography matrix between the intrinsic parameter matrix at the initial position and the intrinsic parameter matrix after zooming:

[0024] K 2 =H12 K 1

[0025] in,

[0026] A point in space is converted between the imaging points on the four image planes before and after zooming of two industrial cameras, satisfying:

[0027]

[0028]

[0029]

[0030] Among them, M1 is the external parameter of the two industrial cameras before zooming; M1 = [R1|t1]; R1 and t1 are the rotation matrix and translation vector between the two industrial cameras before zooming; M2 is the external parameter of the two industrial cameras after zooming; M2 = [R2|t2]; R2 and t2 are the rotation matrix and translation vector between the two industrial cameras after zooming; are the optical centers of two industrial cameras at the initial positions; They are the optical centers of two industrial cameras after zooming; are the image points after zoom The homogeneous coordinates of ; Respectively represent the transformation matrices of the optical centers of two industrial cameras; I = diag(1, 1, 1).

[0031] Furthermore, the nonlinear optimization of the internal and external parameters of the two industrial cameras using the Levenberg-Marquardt algorithm includes:

[0032] The internal and external parameters of the two industrial cameras are nonlinearly optimized according to the following formula:

[0033]

[0034] Among them, α x With α y is the normalized focal length of a single industrial camera; K is the internal parameter matrix of a single industrial camera; R, t are both the external parameter matrices of one of the industrial cameras, that is, the transformation relationship between the camera coordinate system of one of the industrial cameras and the world coordinate system established on the target plane; (x mi ,y mi ) is the theoretical physical coordinate of the i-th space point; (u mi ,v mi )、(u i ,v i) are the theoretical pixel coordinates and actual pixel coordinates of the ith spatial point respectively; (u0, v0) are the pixel coordinates of the principal point of one of the industrial cameras;

[0035] Let x k For the current solution, construct the following formula:

[0036]

[0037] Where J(x k ) is the Jacobian matrix; a positive definite matrix Ω k E added to (J(x k )) T J(x k ), becomes a positive definite matrix, and the step size of the Levenberg-Marquardt algorithm is:

[0038] d k =-((J(x k )) T J(x k )+Ω k E) -1 J(x k )F(x k );

[0039] Where E is the identity matrix; Ω is the parameter of the Levenberg-Marquardt algorithm. When Ω→∞, d k Tends to the steepest descent method, when Ω→0, d k tends to Gauss-Newton method;

[0040] The internal and external parameters obtained by direct linear transformation are used as initial values, and the initial values ​​of k1, k2, p1, and p2 are set to 0. Iterative calculation is performed. The algorithm steps are as follows:

[0041] a) Input the initial value x0, the initial parameter Ω=0.01, and the setting accuracy ε=1×10- 7 ;

[0042] b) Calculation J(x);

[0043] c) Calculate d k , then x k+1 =x k +d k ;

[0044] d) If And ||d k ||<ε, stop iteration and output the result; otherwise, set Ω=Ω / 10 and go to step b);

[0045] e) If Let Ω = 10Ω and recalculate d k , return to step d).

[0046] The invention provides a high-precision calibration method for a zoom binocular vision measurement system, wherein the zoom binocular vision measurement system comprises a circular checkerboard target and two fixedly placed industrial cameras; the high-precision calibration method comprises moving the circular checkerboard target, using two industrial cameras to collect images of the circular checkerboard target from different angles; using two industrial camera image matching points and matching points before and after zooming of the two industrial cameras to estimate two types of homography matrices; calculating the internal and external parameters of the two industrial cameras after zooming according to a zoom mathematical model and the homography matrix; nonlinearly optimizing the internal and external parameters of the two industrial cameras using a Levenberg-Marquardt algorithm; and performing three-dimensional measurement of a large-sized object according to the optimized internal and external parameters. The actual measurement accuracy of large-sized objects is effectively improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the technical solution of the present invention, the drawings required for use in the embodiments are briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0048] Figure 1 A flowchart of a high-precision calibration method for a zoom binocular vision measurement system provided by an embodiment of the present invention;

[0049] Figure 2 A schematic diagram of visual measurement with a zoom binocular camera provided in an embodiment of the present invention;

[0050] Figure 3 A schematic diagram of two homography matrix conversions in a zooming process provided by an embodiment of the present invention;

[0051] Figure 4 A schematic diagram of binocular extrinsic parameter solution provided by an embodiment of the present invention;

[0052] Figure 5 A reference diagram of the usage status of the zoom binocular camera vision measurement system provided by an embodiment of the present invention during actual measurement. DETAILED DESCRIPTION

[0053] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0054] like Figure 1 As shown, an embodiment of the present invention provides a high-precision calibration method for a zoom binocular vision measurement system, wherein the zoom binocular vision measurement system includes a circular checkerboard target and two fixedly placed industrial cameras; the high-precision calibration method includes:

[0055] Step 101, move the circular checkerboard target, and use two industrial cameras to collect images of the circular checkerboard target from different angles.

[0056] The binocular camera vision system consists of two industrial cameras, one for the left camera and the other for the right camera, which are fixedly placed. The two industrial cameras have a large field of view and high optical imaging accuracy. The circular checkerboard target is precisely made and has circular geometric features that can be identified and measured by the binocular camera vision system. The binocular camera vision system is fixedly installed in one position and the circular checkerboard target is within the visible range of the binocular camera vision system. The circular checkerboard target is a plane checkerboard, which is composed of regularly arranged circular geometric features. The distance between the centers of the circles is a standard value with extremely high accuracy and can be used as a standardized reference for the calibration of the vision system. The binocular camera vision system is fixedly placed, the circular checkerboard target is continuously moved, the circular checkerboard target is photographed from different angles, and the image of the circular checkerboard target is collected using the binocular camera vision system.

[0057] Step 102 , using the image matching points of two industrial cameras and the matching points before and after zooming of two industrial cameras, two types of homography matrices are estimated.

[0058] like Figure 2 As shown in the figure, the zoom lens is approximately regarded as a pinhole imaging model with a movable optical center. The relative position between the left camera and the right camera is fixed. Adjusting the zoom value of the zoom camera can enlarge or reduce the camera's measurement range. Figure 2 In the initial position, the camera coordinate systems of the left camera and the right camera are and and is the projection point of a point P in space on the imaging plane of the left and right cameras. After changing the Zoom value and automatically focusing, the optical center of the left camera Pan to Optical center of right camera Pan to The projection point of a point P in space on the left and right imaging planes and By using the parallax principle, when the internal and external parameters of the binocular camera vision system are known, the location of point P can be reconstructed. Coordinate system and Three-dimensional coordinates in the coordinate system. When visual measurement is performed using a binocular camera, the internal and external parameters need to be calibrated again after the optical center position changes.

[0059] In this step, two single images captured by industrial cameras are obtained, namely image I1 and image I2; there are multiple matching points on a single image, that is, there are multiple corresponding matching points on image I1 and image I2

[0060] Construct the optimized homography matrix:

[0061]

[0062] Where n is the total number of matching points on a single image; and They are the kth matching points on the single images captured by the two industrial cameras respectively; there is a homography matrix H with a dimension of 3×3 between the single images captured by the two industrial cameras, m1=Hm2.

[0063] exist Figure 2 There are two types of homography matrices in the measurement model shown, one is the homography matrix between the images of the left camera and the right camera, and the other is the homography matrix between the images of the same camera before and after zooming.

[0064] Step 103, calculating the internal and external parameters of the two industrial cameras after zooming according to the zoom mathematical model and the homography matrix.

[0065] In this step, the spatial points on the image before zooming and the spatial points on the image after zooming of a single industrial camera are obtained;

[0066] The zoom factor of a single industrial camera is calculated according to the following formula:

[0067]

[0068] Among them, r u 、r v and r f are the zoom factors of a single industrial camera, r u =r v =r f ; It is the principal point coordinates of a single industrial camera before zooming; is the coordinate of the principal point of a single industrial camera after zooming; f 1 is the focal length of a single industrial camera before zooming; f 2 is the focal length of a single industrial camera after zooming; i is the i-th spatial point; m spatial points generate m matching points;

[0069] Get the intrinsic parameter matrix of a single industrial camera at the initial position and after zooming;

[0070] Construct the homography matrix between the intrinsic parameter matrix at the initial position and the intrinsic parameter matrix after zooming:

[0071] K 2 =H 12 K 1

[0072] in,

[0073] like Figure 3 As shown, in order to describe the homography matrix during the zooming process, it is assumed that the image planes of the left and right cameras move before and after zooming, while the position of the optical center remains unchanged.

[0074] Taking the left camera as an example, solve the intrinsic parameters of the camera after zooming. The corresponding points of the spatial point P on the two images before and after zooming are and If there are m pairs of correct matching points generated by m spatial points, the zoom factor r can be defined as u 、r v and r f The details are as follows:

[0075]

[0076] are the principal point coordinates of the left camera before zooming; are the principal point coordinates of the left camera after zooming. is the focal length of the left camera before zooming; is the focal length of the left camera after zooming. i represents the i-th spatial point.

[0077] According to the constraint that the image planes are parallel before and after zooming, r can be determined Lu =r Lv =r Lf , and the principal point remains unchanged. Assume that the internal parameter matrix of the initial position is The internal parameter matrix after zooming is Then the homography matrix between the internal parameter matrices can be determined Make

[0078]

[0079] in:

[0080]

[0081] Solve the intrinsic parameters of the right camera after zooming. The corresponding points of the spatial point P on the two images before and after zooming are and If there are m pairs of correct matching points generated by m spatial points, the zoom factor r can be defined as u 、r v and r f The details are as follows:

[0082]

[0083] are the principal point coordinates of the right camera before zooming; are the principal point coordinates of the right camera after zooming. is the focal length of the right camera before zooming; is the focal length of the right camera after zooming. i represents the i-th spatial point.

[0084] According to the constraint that the image planes are parallel before and after zooming, r can be determined Ru =r Rv =r Rf , and the principal point remains unchanged. Assume that the internal parameter matrix of the initial position is The internal parameter matrix after zooming is Then the homography matrix between the internal parameter matrices can be determined Make

[0085]

[0086] in:

[0087]

[0088] The homography matrix before and after zooming contains internal parameter information such as principal distance and principal point, so by finding the correct matching points of the images before and after zooming, the internal parameters of the camera after zooming can be estimated based on the internal parameters of the initial position.

[0089] like Figure 4 As shown, is the optical center of the left and right cameras at the initial position, It is the optical center of the left and right cameras after zooming.

[0090] At position I, the external parameters of the left and right cameras before zooming are M1 = [R1|t1], where R1 and t1 are the rotation matrix and translation vector between the left and right cameras before zooming; at position II, the external parameters of the left and right cameras after zooming are M2 = [R2|t2], where R2 and t2 are the rotation matrix and translation vector between the left and right cameras after zooming. A point P in space can be converted between the imaging points on the four image planes before and after binocular zooming, that is, it satisfies

[0091]

[0092] in, They are the image points after zoom at position II. The homogeneous coordinates of Represent the transformation matrix of the optical center of the left camera and the right camera respectively.

[0093]

[0094] Right now

[0095]

[0096] in, I = diag (1, 1, 1). We get

[0097]

[0098] The above formula shows that the binocular rotation matrix does not change after zooming, but the optical center position undergoes relative translation. This is consistent with the actual situation. According to the zooming process, under absolutely ideal conditions, the optical centers of the left and right cameras only undergo translation transformation but no rotation transformation.

[0099] Step 104: Use the Levenberg-Marquardt algorithm to perform nonlinear optimization on the internal and external parameters of the two industrial cameras.

[0100] In this step, the internal and external parameters obtained by the zoom binocular vision calibration method based on the homography matrix are used as initial values, and the internal and external parameters of the camera when the root mean square error of the distance between the theoretical point and the actual point is the smallest are iteratively solved as the optimal solution.

[0101] The internal and external parameters of the two industrial cameras are nonlinearly optimized according to the following formula:

[0102]

[0103] Among them, α x With α y is the normalized focal length of a single industrial camera; K is the internal parameter matrix of a single industrial camera; R, t are both the external parameter matrices of one of the industrial cameras, that is, the transformation relationship between the camera coordinate system of one of the industrial cameras and the world coordinate system established on the target plane; (x mi ,y mi ) is the theoretical physical coordinate of the i-th space point; (y mi ,v mi )、(u i ,v i ) are the theoretical pixel coordinates and actual pixel coordinates of the ith spatial point respectively; (u0, v0) are the pixel coordinates of the principal point of one of the industrial cameras;

[0104] Let x k For the current solution, construct the following formula:

[0105]

[0106] Where J(x k ) is the Jacobian matrix; a positive definite matrix Ω k E added to (J(x k )) T J(x k ), becomes a positive definite matrix, and the step size of the Levenberg-Marquardt algorithm is:

[0107] d k =-((J(x k )) T J(x k )+Ω k E) -1 J(x k )F(x k );

[0108] Where E is the identity matrix; Ω is the parameter of the Levenberg-Marquardt algorithm. When Ω→∞, d k Tends to the steepest descent method, when Ω→0, d k tends to Gauss-Newton method;

[0109] The internal and external parameters obtained by direct linear transformation are used as initial values, and the initial values ​​of k1, k2, p1, and p2 are set to 0. Iterative calculation is performed. The algorithm steps are as follows:

[0110] a) Input the initial value x0, the initial parameter Ω=0.01, and the setting accuracy ε=1×10 -7 ;

[0111] b) Calculation J(x);

[0112] c) Calculate d k , then x k+1 =x k +d k ;

[0113] d) If And ||d k ||<ε, stop iteration and output the result; otherwise, set Ω=Ω / 10 and go to step b);

[0114] e) If Let Ω = 10Ω and recalculate d k , return to step d).

[0115] After obtaining the initial values ​​of the internal and external parameters of the camera linear model by Zhang’s calibration method, nonlinear optimization is performed. Taking the left camera as an example, optimizing the internal and external parameters is to solve the objective function Minimum:

[0116]

[0117] Here: α Lx With α Ly is the normalized focal length of the left camera; K L is the intrinsic parameter matrix of the left camera; R L , t L is the external parameter matrix of the left camera, that is, the transformation relationship between the left camera coordinate system and the world coordinate system (established on the target plane); (x Lmi ,y Lmi ) is the theoretical physical coordinate of the i-th space point; (u Lmi ,v Lmi )、(u Li ,v Li ) are the theoretical pixel coordinates and actual pixel coordinates of the ith spatial point respectively; (u L0 ,v L0 ) is the pixel coordinate of the principal point of the left camera.

[0118] This paper uses the Levenberg-Marquardt algorithm to solve the optimization problem. The Levenberg-Marquardt algorithm is one of the classic algorithms for solving nonlinear optimization problems, combining the advantages of the Gauss-Newton method and the steepest descent method.

[0119] Let x k is the current solution, and the trial step of the Gauss-Newton method to solve the problem is:

[0120]

[0121] Where J(x k ) is the Jacobian matrix. The Gauss-Newton method requires the Jacobian matrix to be of full row rank, so it cannot be used to solve singular problems of nonlinear equations.

[0122] The Levenberg-Marquardt algorithm improves the Gauss-Newton method by converting a positive definite matrix Ω k E added to (J(x k )) T J(x k ) to make it a positive definite matrix, and the step size of the Levenberg-Marquardt algorithm is

[0123] d k =-((J(x k )) T J(x k )+Ω k E) -1 J(x k)F(x k );

[0124] Where: E is the unit matrix; Ω is the parameter of the Levenberg-Marquardt algorithm. When Ω→∞, d k Tends to the steepest descent method, when Ω→0, d k Approaching the Gauss-Newton method.

[0125] The internal and external parameters obtained by direct linear transformation are used as initial values, and the initial values ​​of k1, k2, p1, and p2 are set to 0. Iterative calculation is performed. The algorithm steps are as follows:

[0126] a) Input the initial value x0, the initial parameter Ω=0.01, and the setting accuracy ε=1×10 -7 ;

[0127] b) Calculation J(x);

[0128] c) Calculate d k , then x k+1 =x k +d k ;

[0129] d) If And ||d k ||<ε, stop iteration and output the result; otherwise, set Ω=Ω / 10 and go to step b);

[0130] e) If Let Ω = 10Ω and recalculate d k , return to step d).

[0131] Step 105 , performing three-dimensional measurement on the large-sized object to be measured according to the optimized internal and external parameters.

[0132] By using the calibrated internal and external parameters of the binocular camera vision system, high-precision three-dimensional measurement of large-sized objects can be performed to achieve a complete expression of the geometric quantities of the measured objects.

[0133] When actually measuring Figure 5 As shown, the binocular camera vision system and the object to be measured are fixedly placed, and the binocular camera vision system is used to collect the image of the object to be measured. High-precision three-dimensional measurement of large-sized objects is performed to achieve complete expression of the geometric quantity of the measured object.

[0134] The present invention first constructs a system calibration platform, calibrates the binocular vision measurement system, finds a suitable circular chessboard target placement position, and changes its position in sequence. Thus, the binocular vision measurement system can be used to measure the target plate from different angles, fit the circular contour to obtain its center coordinates, and then obtain the internal and external parameters of the left and right cameras respectively through homography matrix transformation. Then, the Levenberg-Marquardt algorithm is used for iterative optimization to obtain an accurate solution for the internal and external parameters. Finally, the calibrated binocular vision measurement system is used to perform high-precision three-dimensional measurement of the object.

Claims

1. A high-precision calibration method for a zoom binocular vision measurement system, characterized in that: The zoom binocular vision measurement system includes a circular checkerboard target and two fixed industrial cameras; the high-precision calibration method includes: Move the circular checkerboard target and use two industrial cameras to collect images of the circular checkerboard target from different angles; Two types of homography matrices are estimated using the matching points of two industrial camera images and the matching points before and after the two industrial cameras are zoomed, including: Get a single image captured by two industrial cameras; there are multiple matching points on the single image; Construct the optimized homography matrix: Where n is the total number of matching points on a single image; and are the kth matching points on the single images captured by the two industrial cameras respectively; there is a homography matrix H with a dimension of 3×3 between the single images captured by the two industrial cameras, m1=Hm2; According to the zoom mathematical model and homography matrix, the internal and external parameters of the two industrial cameras after zoom are calculated, including: Get the spatial points on the image before zooming and the spatial points on the image after zooming of a single industrial camera; The zoom factor of a single industrial camera is calculated according to the following formula: Among them, r u 、r v and r f are the zoom factors of a single industrial camera, r u =r v =r f ; It is the principal point coordinates of a single industrial camera before zooming; is the coordinate of the principal point of a single industrial camera after zooming; f 1 is the focal length of a single industrial camera before zooming; f 2 is the focal length of a single industrial camera after zooming; i is the i-th spatial point; m spatial points generate m matching points; Get the intrinsic parameter matrix of a single industrial camera at the initial position and after zooming; Construct the homography matrix between the intrinsic parameter matrix at the initial position and the intrinsic parameter matrix after zooming: K 2 =H 12 K 1 in, A point in space is converted between the imaging points on the four image planes before and after zooming of two industrial cameras, satisfying: Among them, M1 is the external parameter of the two industrial cameras before zooming; M1 = [R1|t1]; R1 and t1 are the rotation matrix and translation vector between the two industrial cameras before zooming; M2 is the external parameter of the two industrial cameras after zooming; M2 = [R2|t2]; R2 and t2 are the rotation matrix and translation vector between the two industrial cameras after zooming; are the optical centers of two industrial cameras at the initial positions; They are the optical centers of two industrial cameras after zooming; are the image points after zoom The homogeneous coordinates of ; Respectively represent the transformation matrices of the optical centers of two industrial cameras; I = diag(1,1,1); The Levenberg-Marquardt algorithm is used to perform nonlinear optimization of the internal and external parameters of two industrial cameras; Perform three-dimensional measurement of large-sized objects based on optimized internal and external parameters.

2. The high-precision calibration method according to claim 1, characterized in that: The Levenberg-Marquardt algorithm is used to perform nonlinear optimization on the internal and external parameters of two industrial cameras, including: The internal and external parameters of the two industrial cameras are nonlinearly optimized according to the following formula: Among them, α x With α y is the normalized focal length of a single industrial camera; K is the internal parameter matrix of a single industrial camera; R, t are both the external parameter matrices of one of the industrial cameras, that is, the transformation relationship between the camera coordinate system of one of the industrial cameras and the world coordinate system established on the target plane; (x mi ,y mi ) is the theoretical physical coordinate of the i-th space point; (u mi ,v mi )、(u i ,v i ) are the theoretical pixel coordinates and actual pixel coordinates of the ith spatial point respectively; (u0, v0) are the pixel coordinates of the principal point of one of the industrial cameras; Let x k For the current solution, construct the following formula: Where J(x k ) is the Jacobian matrix; a positive definite matrix Ω k E added to (J(x k )) T J(x k ), becomes a positive definite matrix, and the step size of the Levenberg-Marquardt algorithm is: d k =-((J(x k )) T J(x k )+Ω k E) -1 J(x k )F(x k ) Where E is the identity matrix; Ω is the parameter of the Levenberg-Marquardt algorithm. When Ω→∞, d k Tends to the steepest descent method, when Ω→0, d k tends to Gauss-Newton method; The internal and external parameters obtained by direct linear transformation are used as initial values, and the initial values ​​of k1, k2, p1, and p2 are set to 0. Iterative calculation is performed. The algorithm steps are as follows: a) Input the initial value x0, the initial parameter Ω=0.01, and the setting accuracy ε=1×10 -7 ; b) Calculation J(x); c) Calculate d k , then x k+1 =x k +d k ; d) If And ∥d k ∥<ε, stop iteration and output the result; otherwise, set Ω=Ω / 10 and go to step b); e) If Let Ω = 10Ω and recalculate d k , return to step d).

Images