A method for solving the coordinates of the center of a space sphere based on monocular vision two-dimensional imaging

Abstract

The present invention relates to the field of aircraft digital assembly, and specifically to a method for solving the coordinates of the center of a space sphere based on monocular vision two-dimensional imaging, which includes the following steps: a. photographing a group of space spheres with a camera to obtain a two-dimensional image, where the space spheres appear as ellipses on the two-dimensional image; b. obtaining an ellipse boundary graphic through image recognition; c. solving the ellipse parametric equation based on the ellipse boundary graphic fitting; and d. solving the coordinates of the center of the space sphere using the ellipse parametric equation. This application requires minimal constraint information, is easy to meet, and has simple and fast calculation speeds. Compared with the traditional method of measuring the coordinates of the center of a space sphere using a laser tracker, this method can calculate and feedback the coordinates of the center of the sphere in real time, thereby improving the efficiency of aircraft attitude adjustment and alignment. Compared with the binocular vision measurement method, this method does not require calibration of internal and external parameters of the camera, has a large shooting angle, and a simple hardware structure.

Description

Technical Field

[0001] The present invention relates to the field of digital assembly of aircraft, and in particular to a method for solving the coordinates of the center of a space sphere based on monocular vision two-dimensional imaging. Background Art

[0002] The aircraft large component attitude adjustment and alignment system is a key process equipment that assists the assembly of aircraft sections into the entire structure. Traditional aircraft attitude adjustment and alignment is generally achieved by using a laser tracker in conjunction with a multi-degree-of-freedom mechanical attitude adjustment mechanism and a wheeled translation mechanism. This process mainly uses the laser tracker to measure the coordinates of the center of the space ball and feeds the center coordinates back to the assembly system. The system drives the ball socket on the assembly tool to move to the position of the space ball according to the center coordinates, achieving accurate and rapid docking of large aircraft components. The center coordinates of the space ball play a decisive role in the efficiency and accuracy of the attitude adjustment of large aircraft components. Figure 1 As shown in the figure. In actual operation, a single laser tracker cannot achieve rapid and automatic measurement of multiple reference points. Furthermore, laser obstruction is prone to occur during the laser tracker station establishment process. The laser tracker's proper position must be repeatedly determined so that its laser beam can fully cover the space sphere and thus obtain the coordinates of the space sphere's center. This process requires multiple adjustments to the laser tracker's position and station establishment, requiring the coordination of multiple people, resulting in low efficiency. Simultaneous measurement using multiple laser trackers is not only costly but also difficult to implement on-site. Therefore, a method for rapidly and automatically measuring the coordinates of the space sphere's center is urgently needed to improve the assembly efficiency and ensure assembly accuracy of the entire aircraft component. Summary of the Invention

[0003] To solve the above problems, the present invention provides a method for solving the coordinates of the center of a space sphere based on monocular vision two-dimensional imaging. The coordinates of the center of the space sphere are obtained using monocular vision, and the space sphere is photographed by a camera and projected as an ellipse on the image plane. The ellipse parametric equation is obtained by ellipse fitting, and then the ellipse parametric equation is used to solve the coordinates of the center of the space sphere in the camera coordinate system.

[0004] In order to achieve the above-mentioned invention objectives, the technical solutions provided by this application are as follows:

[0005] A method for solving the coordinates of the center of a space sphere based on monocular vision two-dimensional imaging includes the following steps:

[0006] a. Use a camera to shoot a group of space balls to obtain a two-dimensional image. The space balls appear as ellipses on the two-dimensional image.

[0007] b. Image recognition to obtain elliptical boundary graphics;

[0008] c. Solve the ellipse parametric equation based on the ellipse boundary figure fitting;

[0009] d. Use the parametric equation of the ellipse to solve the coordinates of the center of the space sphere.

[0010] Furthermore, the camera in step a is a monocular camera.

[0011] Furthermore, in step b, ellipse feature recognition and extraction technology is used to obtain the ellipse boundary graphic.

[0012] Furthermore, the camera coordinate system O is established c -X c Y c Z c , image plane coordinate system O1-X1Y1, world coordinate system O w -X w Y w Z w ,Since the positional relationship between the camera and the world coordinate system remains unchanged, the coordinates of the center of the space circle can be solved only in the camera coordinate system;

[0013] Furthermore, let the coordinates of a point P on the space sphere in the camera coordinate system be (X c ,Y c ,Z c ), the corresponding image coordinate p is (X, Y), according to the pinhole imaging principle, on the normalized focal plane

[0014]

[0015] Where f is the focal length of the camera.

[0016] Furthermore, according to the imaging principle, the radius of the space sphere is R0, and the projection of the space sphere on the image plane is an ellipse. When the projection is a circle, it is considered to be a special form of the ellipse. At the same time, with the origin of the camera coordinate system as the vertex, the camera optical center and the space sphere form a cone. Let the image ellipse equation be:

[0017] aX 2 +bY 2 +cXY+dX+eY+h=0(2)

[0018] Where a, b, c, d, e, h are constants in the ellipse formula;

[0019] Substituting the camera normalized imaging model (1) into the ellipse equation (2) yields the equation for the space cone:

[0020]

[0021] Formula (3) can be written in the form of matrix product, expressed as:

[0022] (X c ,Y c ,Z c )Q(Xc ,Y c ,Z c ) T =0, where

[0023] Furthermore, the coordinates of the center of the space ball are solved:

[0024] The projection of the space ball on the image plane is an ellipse, and the radius of the space ball is R0. To solve the position of the space circle, in order to simplify the solution process, a new coordinate system O0-X0Y0Z0 is established, where O0 is the same as the camera coordinate system O c Coincident, the cone axis Z0 axis coincides with the camera optical center, X0 and Y0 axes are arbitrarily set, and after the result is obtained in this new coordinate system, it is transformed back to the camera coordinate system to obtain the coordinates of the center of the camera coordinate system space ball; the camera coordinate system O c -X c Y c Z c The new coordinate system O0-X0Y0Z0 satisfies the R, T relationship, where T is zero because the origins of the two coordinate systems coincide. That is,

[0025] (X c ,Y c ,Z c ) T =R(X0,Y0,Z0) T (5)

[0026] The left side of equation (3) is a quadratic polynomial, which can be written as a quadratic form. Q is a 3x3 symmetric matrix. According to matrix theory, a third-order symmetric matrix must have an orthogonal matrix R that can diagonalize Q, that is,

[0027] R -1 QR=Diag(α1,α2,α3) (6)

[0028] Then transform formula (4) into the standard cone equation and substitute formula (5) into formula (4) to obtain:

[0029] {R[X0,Y0,Z0] T} T QR[X0,Y0,Z0] T =0 (7)

[0030] Transformation yields:

[0031] [X0,Y0,Z0]RQR[X0,Y0,Z0] T =0 (8)

[0032] Then we can get a standard elliptical cone with the rotation axis Z0, such as Figure 3 shown

[0033]

[0034] Among them, {α1, α2, α3} are the eigenvalues of Q. According to the expression of the standard cone, there must be two values of α1, α2, and α3 with the same sign and a different sign from the other one; Figure 3 Point O0 is the center of the space sphere in the O0-X0Y0Z0 coordinate system, so the coordinates of the center are (0, 0, O0O), let x0 = k(|α1|) -1 / 2 y0=k(|α2|) -1 / 2 z0=k(|α3|) -1 / 2 , where k is a non-zero constant; since the cone is a right cone, let α r =α1=α2, so let u r =x0=y0=k(|α r |) -1 / 2 , so by Figure 3 The geometric relationship is obtained.

[0035]

[0036] Therefore, the coordinates of the center of the space ball in the O0-X0Y0Z0 coordinate system are

[0037] Finally, the desired result must be converted to the camera coordinate system:

[0038] (X c ,Y c ,Z c ) T =R(X0,Y0,Z0) T

[0039] That is to solve the coordinates of the center of the space ball (X c ,Y c ,Z c ).

[0040] The advantages of the present invention are:

[0041] This patent only uses the principle of monocular vision two-dimensional imaging and proposes an algorithm for solving the coordinates of the center of a space sphere based on monocular vision two-dimensional imaging. This method requires minimal constraint information, the conditions are easy to meet, the calculation is simple, and the calculation speed is fast. Compared with the traditional laser tracker method of measuring the coordinates of the center of a space sphere, this method can calculate and feedback the coordinates of the center of the sphere in real time, thereby improving the efficiency of aircraft attitude adjustment. Compared with the binocular vision measurement method, this method does not require calibration of the internal and external parameters of the camera, has a large shooting angle, and a simple hardware structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is the principle of attitude adjustment for traditional aircraft.

[0043] Figure 2 This is a flowchart of the application.

[0044] Figure 3 Create a schematic diagram of the coordinate system for this application.

[0045] Figure 4 Schematic diagram of two-dimensional solution of O0-X0Y0Z0 coordinate system.

[0046] Figure 5 Optimized aircraft attitude adjustment principle. DETAILED DESCRIPTION

[0047] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are intended to explain the present invention rather than to limit the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0048] The specific implementation method of the present invention is described below with reference to the accompanying drawings and examples, but the present invention is not limited to this embodiment.

[0049] Example 1

[0050] A method for solving the coordinates of the center of a space sphere based on monocular vision two-dimensional imaging includes the following steps:

[0051] a. Use a camera to shoot a group of space balls to obtain a two-dimensional image. The space balls appear as ellipses on the two-dimensional image.

[0052] b. Image recognition to obtain elliptical boundary graphics;

[0053] c. Solve the ellipse parametric equation based on the ellipse boundary figure fitting;

[0054] d. Use the parametric equation of the ellipse to solve the coordinates of the center of the space sphere.

[0055] This patent only uses the principle of monocular vision two-dimensional imaging and proposes an algorithm for solving the coordinates of the center of a space sphere based on monocular vision two-dimensional imaging. This method requires minimal constraint information, the conditions are easy to meet, the calculation is simple, and the calculation speed is fast. Compared with the traditional laser tracker method of measuring the coordinates of the center of a space sphere, this method can calculate and feedback the coordinates of the center of the sphere in real time, thereby improving the efficiency of aircraft attitude adjustment. Compared with the binocular vision measurement method, this method does not require calibration of the internal and external parameters of the camera, has a large shooting angle, and a simple hardware structure.

[0056] Example 2

[0057] A method for solving the coordinates of the center of a space sphere based on monocular vision two-dimensional imaging includes the following steps:

[0058] a. Use a camera to shoot a group of space balls to obtain a two-dimensional image. The space balls appear as ellipses on the two-dimensional image.

[0059] b. Image recognition to obtain elliptical boundary graphics;

[0060] c. Solve the ellipse parametric equation based on the ellipse boundary figure fitting;

[0061] d. Use the parametric equation of the ellipse to solve the coordinates of the center of the space sphere.

[0062] Furthermore, the camera in step a is a monocular camera.

[0063] Furthermore, in step b, an ellipse feature recognition and extraction technique is used to obtain an ellipse boundary graphic. This algorithm is very mature and can be used directly.

[0064] Furthermore, the camera coordinate system O is established c -X c Y c Z c , image plane coordinate system O1-X1Y1, world coordinate system O w -X w Y w Z w ,Since the positional relationship between the camera and the world coordinate system remains unchanged, the coordinates of the center of the space circle can be solved only in the camera coordinate system;

[0065] Furthermore, let the coordinates of a point P on the space sphere in the camera coordinate system be (X c ,Y c ,Z c ), the corresponding image coordinate p is (X, Y), according to the pinhole imaging principle, on the normalized focal plane

[0066]

[0067] Where f is the focal length of the camera.

[0068] Furthermore, according to the imaging principle, the radius of the space sphere is R0, and the projection of the space sphere on the image plane is an ellipse. When the projection is a circle, it is considered to be a special form of the ellipse. At the same time, with the origin of the camera coordinate system as the vertex, the camera optical center and the space sphere form a cone. Let the image ellipse equation be:

[0069] aX 2 +bY 2 +cXY+dX+eY+h=0(2)

[0070] Where a, b, c, d, e, h are constants in the ellipse formula;

[0071] Substituting the camera normalized imaging model (1) into the ellipse equation (2) yields the equation for the space cone:

[0072]

[0073] Formula (3) can be written in the form of matrix product, expressed as:

[0074] (X c ,Y c ,Z c )Q(X c ,Y c ,Z c ) T =0, where

[0075] Furthermore, the coordinates of the center of the space ball are solved:

[0076] The projection of the space ball on the image plane is an ellipse, and the radius of the space ball is R0. To solve the position of the space circle, it can be understood that the space ball with a radius of R0 can be uniquely determined to be tangent to the known right circular cone. Since the expression of the cone is very complicated when calculated directly in the camera coordinate system space, in order to simplify the solution process, a new coordinate system O0-X0Y0Z0 is established, where O0 is tangent to the camera coordinate system O c Coincident, the cone axis Z0 axis coincides with the camera optical center, the X0 and Y0 axes are arbitrarily set, and must satisfy the right-hand rule. After obtaining the result in this new coordinate system, it is transformed back to the camera coordinate system to obtain the coordinates of the center of the camera coordinate system space ball; the camera coordinate system O c -X c Y c Z c The new coordinate system O0-X0Y0Z0 satisfies the R, T relationship, where T is zero because the origins of the two coordinate systems coincide. That is,

[0077] (X c ,Y c ,Z c ) T =R(X0,Y0,Z0) T (5)

[0078] The left side of equation (3) is a quadratic polynomial, which can be written as a quadratic form. Q is a 3x3 symmetric matrix. According to matrix theory, a third-order symmetric matrix must have an orthogonal matrix R that can diagonalize Q, that is,

[0079] R -1 QR=Diag(α1,α2,α3) (6)

[0080] Then transform formula (4) into the standard cone equation and substitute formula (5) into formula (4) to obtain:

[0081] {R[X0,Y0,Z0] T} T QR[X0,Y0,Z0] T =0 (7)

[0082] Transformation yields:

[0083] [X0,Y0,Z0]RQR[X0,Y0,Z0] T =0 (8)

[0084] Then we can get a standard elliptical cone with the rotation axis Z0, such as Figure 3 shown

[0085]

[0086] Among them, {α1, α2, α3} are the eigenvalues of Q. According to the expression of the standard cone, there must be two values of α1, α2, and α3 with the same sign and a different sign from the other one; Figure 3 Point O0 is the center of the space sphere in the O0-X0Y0Z0 coordinate system, so the coordinates of the center are (0, 0, O0O), let x0 = k(|α1|) -1 / 2 y0=k(|α2|) -1 / 2 z0=k(|α3|) -1 / 2 , where k is a non-zero constant; since the cone is a right cone, let α r =α1=α2, so let u r =x0=y0=k(|α r |) -1 / 2 , so by Figure 3 The geometric relationship is obtained.

[0087]

[0088] Therefore, in the O0-X0Y0Z0 coordinate system, the coordinates of the center of the space ball (X0, Y0, Z0) = (0, 0,

[0089] Finally, the desired result must be converted to the camera coordinate system:

[0090] (X c ,Y c ,Z c ) T =R(X0,Y0,Z0) T

[0091] That is to solve the coordinates of the center of the space ball (Xc ,Y c ,Z c ).

[0092] Figure 5 To optimize the aircraft attitude adjustment diagram, Figure 1 Compared with removing the laser tracker, each target ball is equipped with a camera for shooting, and the coordinates of the center of the ball are obtained through the algorithm of this patent. The coordinates are fed back to the alignment system in real time, and the auxiliary system completes the aircraft attitude adjustment alignment.

[0093] This patent only uses the principle of monocular vision two-dimensional imaging and proposes an algorithm for solving the coordinates of the center of a space sphere based on monocular vision two-dimensional imaging. This method requires minimal constraint information, the conditions are easy to meet, the calculation is simple, and the calculation speed is fast. Compared with the traditional laser tracker method of measuring the coordinates of the center of a space sphere, this method can calculate and feedback the coordinates of the center of the sphere in real time, thereby improving the efficiency of aircraft attitude adjustment. Compared with the binocular vision measurement method, this method does not require calibration of the internal and external parameters of the camera, has a large shooting angle, and a simple hardware structure.

Claims

1. A method for solving the coordinates of the center of a space sphere based on monocular vision two-dimensional imaging, characterized by: The following steps are involved: a. Use a camera to shoot a group of space balls to obtain a two-dimensional image. The space balls appear as ellipses on the two-dimensional image. b. Image recognition to obtain elliptical boundary graphics; c. Solve the ellipse parametric equation based on the ellipse boundary figure fitting; d. Use the ellipse parametric equation to solve the coordinates of the center of the space sphere; Establish camera coordinate system O c -X c Y c Z c , image plane coordinate system O1-X1Y1, world coordinate system O w -X w Y w Z w ,Since the positional relationship between the camera and the world coordinate system remains unchanged, the coordinates of the center of the space circle can be solved only in the camera coordinate system; Assume that the coordinates of a point P on the space sphere in the camera coordinate system are (X c ,Y c ,Z c ), the corresponding image coordinate p is (X, Y), according to the pinhole imaging principle, on the normalized focal plane Where f is the focal length of the camera; According to the imaging principle, the radius of the space ball is R0, and the projection of the space ball on the image plane is an ellipse. When the projection is a circle, it is considered to be a special form of the ellipse. At the same time, with the origin of the camera coordinate system as the vertex, the camera optical center and the space ball form a cone. Let the image ellipse equation be: aX 2 +bY 2 +cXY+dX+eY+h=0(2) Where a, b, c, d, e, h are constants in the ellipse formula; Substituting the camera normalized imaging model (1) into the ellipse equation (2) yields the equation for the space cone: Formula (3) can be written in the form of matrix product, expressed as: Solve the coordinates of the center of the space sphere: The projection of the space ball on the image plane is an ellipse, and the radius of the space ball is R0. To solve the position of the space circle, in order to simplify the solution process, a new coordinate system O0-X0Y0Z0 is established, where O0 is the same as the camera coordinate system O c Coincident, the cone axis Z0 axis coincides with the camera optical center, X0 and Y0 axes are arbitrarily set, and after the result is obtained in this new coordinate system, it is transformed back to the camera coordinate system to obtain the coordinates of the center of the camera coordinate system space ball; the camera coordinate system O c -X c Y c Z c The new coordinate system O0-X0Y0Z0 satisfies the R, T relationship, where T is zero because the origins of the two coordinate systems coincide. That is, (X c ,Y c ,Z c ) T =R(X0,Y0,Z0) T (5) The left side of equation (3) is a quadratic polynomial, which can be written as a quadratic form. Q is a 3x3 symmetric matrix. According to matrix theory, a third-order symmetric matrix must have an orthogonal matrix R that can diagonalize Q, that is, R -1 QR=Diag(α1,α2,α3) (6) Then transform formula (4) into the standard cone equation and substitute formula (5) into formula (4) to obtain: {R[X0,Y0,Z0] T } T QR[X0,Y0,Z0] T =0 (7) Transformation yields: [X0,Y0,Z0]RQR[X0,Y0,Z0] T =0 (8) Then we can get a standard elliptical cone with the rotation axis Z0. Among them, {α1, α2, α3} are the eigenvalues of Q. According to the expression of the standard cone, there must be two values of α1, α2, and α3 with the same sign and a different sign from the other one. Point O0 is the center of the space sphere in the O0-X0Y0Z0 coordinate system, so the coordinates of the center are (0, 0, O0O). Let x0 = k(|α1|) -1 / 2 y0=k(|α2|) -1 / 2 z0=k(|α3|) -1 / 2 , where k is a non-zero constant; since the cone is a right cone, let α r =α1=α2, so let u r =x0=y0=k(|α r |) -1 / 2 , so from the geometric relationship, Therefore, the coordinates of the center of the space ball in the O0-X0Y0Z0 coordinate system are 2. The method for solving the coordinates of the center of a space sphere based on monocular vision two-dimensional imaging according to claim 1, characterized in that: The camera in step a is a monocular camera.

3. The method for solving the coordinates of the center of a space sphere based on monocular vision two-dimensional imaging according to claim 1, characterized in that: In step b, ellipse feature recognition and extraction technology is used to obtain the ellipse boundary graphic.

4. The method for solving the coordinates of the center of a space sphere based on monocular vision two-dimensional imaging according to claim 1, characterized in that: Convert the result to the camera coordinate system: (X c ,Y c ,Z c ) T =R(X0,Y0,Z0) T That is to solve the coordinates of the center of the space ball (X c ,Y c ,Z c ).

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