Long-distance imaging camera internal and external parameter separation calibration method based on precision three-axis turntable

Abstract

The application provides a long-distance imaging camera internal and external parameter separation calibration method based on a precision three-axis turntable. In the calibration process, two groups of light point sub-pixel coordinates are automatically collected through the precision three-axis turntable, and the corresponding relationship of the homonymic points under the pure rotation motion is constructed, so that the initial estimated value of the main internal and external parameters is linearly solved, and finally, all the camera internal and external parameters are iteratively optimized with the minimum homonymic point corresponding error as the target. In the solving process, the calibration point vector is eliminated without solving. The application is mainly applied to the high-precision calibration of long-distance and large-view-field imaging cameras in the aviation and aerospace fields before leaving the factory, and has important significance for realizing the high-precision visual measurement of the aviation and aerospace earth observation and celestial body sensing.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of aerospace measurement camera calibration, and particularly relates to a long-distance imaging camera internal and external parameter separation calibration method based on a precision three-axis turntable. BACKGROUND

[0002] Vision measurement applications represented by aerial photogrammetry and space celestial sensitive imaging calculate and obtain other information by imaging targets at several kilometers or even infinite distance. In order to realize high-precision measurement, the focal length, principal point, distortion and other imaging parameters of long-distance imaging cameras must be accurately calibrated in the ground environment before leaving the factory. The laboratory calibration method based on a high-precision turntable is widely used due to high precision and strong operability. In the calibration method based on a turntable, the method of using a single adjustable depth-of-field calibration point is simple in principle and convenient to operate. Ideally, the camera is installed on the turntable, the coordinate axes of the camera coordinate system are consistent with the coordinate axes of the turntable coordinate system, and the single calibration point (which can be constructed by a focus-adjustable collimator) is exactly on the imaging optical axis of the camera at the zero position of the turntable. However, in actual situations, the installation deviation between the camera coordinate system and the turntable coordinate system, and the installation deviation of the calibration point relative to the zero position of the turntable are inevitable. Removing these deviations through complex and delicate installation and alignment operations will bring huge cost and it is difficult to fully guarantee the precision, so it is of great significance to study a calibration method and algorithm that does not depend on manual adjustment.

[0003] The traditional calibration method based on integrated modeling of internal and external parameters adopts an integrated optimization method to simultaneously solve all internal and external parameters, and there is a coupling problem between the internal and external parameters, especially a strong coupling relationship between the deviation of the calibration point relative to the zero position of the turntable and the principal point of the camera. The result of this coupling is that only when all parameters are used together can high-precision measurement results be obtained, and when only part of the parameters or the parameters are used alone, the precision may be reduced. However, in most applications, the calibrated external parameters, especially the deviation of the calibration point relative to the zero position of the turntable, are not needed, and only the camera internal parameters are needed for measurement. Therefore, in order to ensure the measurement precision, a method capable of separating the internal and external parameters and mainly aiming at internal parameter calibration is of great significance. However, although the traditional internal and external parameter separation calibration method has achieved good calibration results, the process of solving the direction of the vector of the calibration point relative to the zero position of the turntable needs repeated fine adjustment, and human intervention is more during the process, so that the efficiency of the method is not high.

[0004] It can be seen that the traditional calibration method based on integrated modeling of internal and external parameters and the traditional internal and external parameter separation calibration method both have their own shortcomings, and it is difficult to balance the camera calibration efficiency and precision requirements. SUMMARY

[0005] Aiming at the calibration problem of the above-mentioned long-distance imaging camera, the purpose of the present application is to provide a long-distance imaging camera internal and external parameter separation calibration method based on a precision three-axis turntable, which is a three-step calibration method based on a precision three-axis turntable and a single calibration point, which does not require solving the vector relationship of the calibration point relative to the zero position of the turntable, and does not require manual adjustment during the calibration process.

[0006] In order to achieve the above-mentioned purpose and achieve the above-mentioned technical effect, the technical scheme adopted by the present application is as follows:

[0007] A long-distance imaging camera internal and external parameter separation calibration method based on a precision three-axis turntable, which realizes high precision of calibration by using a precision three-axis turntable, and realizes high efficiency of calibration by using a long-distance imaging camera internal and external parameter separation calibration model, involves automatic acquisition of two groups of light point sub-pixel coordinates by a precision three-axis turntable, a long-distance imaging camera perspective projection model and a distortion model, and initial estimation of main internal parameters and external parameters and joint optimization of all internal and external parameters based on the L-M method with the minimum corresponding error of the same name point as the target.

[0008] The automatic acquisition of two groups of light point sub-pixel coordinates by the precision three-axis turntable is realized by setting the rotation angle value file of the middle frame and the outer frame, manually adjusting the inner frame to 0° or 90°, and the turntable automatically rotating to collect the corresponding light point sub-pixel coordinates of the rotation angle value.

[0009] The long-distance imaging camera internal and external parameter separation calibration method based on the precision three-axis turntable of the present application comprises the following steps:

[0010] Step a, based on the rotation of the precision three-axis turntable and the camera calibration system composed of a single light point formed by an adjustable focusing collimator, under the condition that the inner frame rotates at different angles, the camera automatically collects two groups of light point sub-pixel coordinates of the imaging of the calibration points through a series of rotations of the middle frame and the outer frame; the single light point of the collimator is the calibration point, and the focusing position of the collimator is basically the same as the measurement position of the measurement camera;

[0011] Step b, according to the two groups of light point sub-pixel coordinates of the imaging of the calibration points in step a, the corresponding relationship of the same name points under two groups of pure rotation is established, so as to linearly solve the initial estimation value of the main internal parameters of the long-distance imaging camera, the main internal parameters including the focal length a x , a y and the pixel coordinates u0, v0 of the image principal point;

[0012] Step c, for the corresponding relationship of the same name points constructed in step b, a constraint equation about the external parameters is constructed, so as to linearly solve the initial estimation value of the camera external parameters, the camera external parameters being , i.e. the conversion matrix from the turntable coordinate system to the camera coordinate system;

[0013] Step d, according to the initial estimated value of the main intrinsic parameter and the initial estimated value of the camera extrinsic parameter solved in step b and step c, iteratively optimize all camera intrinsic and extrinsic parameters with the minimum corresponding point pair error as the optimization goal, to obtain the optimal estimated value of the camera intrinsic and extrinsic parameters.

[0014] Further, in step a, the camera is a long-distance imaging camera, which is placed at the center of a precise three-axis turntable, and a collimator is placed in front of the turntable to simulate a single calibration point at a long distance; under the conditions that the inner frame of the turntable is rotated by 0° and 90°, the middle frame and the outer frame are rotated by setting a series of fixed rotation angle values, and the camera automatically collects two groups of light point images of the imaging of the calibration points, and the light point sub-pixel coordinates are obtained according to the light point centroids, wherein the rotation angle range of the middle frame and the outer frame can be generally set to -10° to 10°, and the rotation angle interval is 2°; however, due to the limitation of the field of view of the camera, when the rotation angles of the middle frame and the outer frame are (±10°±10°), (±10°±8°) and (±8°±10°), the camera cannot collect light point images, so these 12 groups of rotation angle values are filtered out, and there are a total of 109 groups of rotation angle values.

[0015] Further, in step a, for each rotation of the middle frame relative to the outer frame, the next rotation position also maintains a fixed rotation angle relative to the previous position. Since the calibration point is at a long distance, the next position of the middle frame rotation direction relative to the current position is a fixed pure rotation motion.

[0016] Further, step a comprises:

[0017] The single calibration point forms two groups of light point sub-pixel coordinates under a series of rotations of the turntable, and the perspective projection model of the long-distance imaging camera is as follows:

[0018]

[0019] Wherein:

[0020]

[0021] Wherein, ρ is a proportional coefficient, m = [u (i,j) v (i,j) 1] T is the pixel coordinate of the calibration point under the camera image, R v0is the vector of the calibration point when the turntable is at zero position in the turntable coordinate system, C v (i,j) is the vector of the calibration point in the camera coordinate system after the turntable is rotated, and K is the camera intrinsic parameter matrix, which is determined by the main intrinsic parameters a x , a y , u0, v0, a x , a y ​These are the normalized focal lengths on the x-axis and y-axis, respectively, and u0 and v0 are the pixel coordinates of the principal point of the image. R R (i,j) It is the rotation angle of the turntable's outer frame. Mid-frame rotation angle ψ (j) The rotation matrix, It is the transformation matrix from the turntable coordinate system to the camera coordinate system, i.e., the camera extrinsic parameters;

[0022] The camera distortion model is as follows:

[0023]

[0024] Among them, (x u ,y u ) and (x d ,y d ) represents the coordinates of the distorted and undistorted pixels, and r is the coordinate of (x... u ,y u The physical distance from the principal point (u0, v0) is given by k1 and k2, which are the first two radial distortion coefficients of the camera, and p1 and p2 are the first two tangential distortion coefficients of the camera.

[0025] Further, step b includes: the turntable rotates to form a series of imaging points on a single calibration point in front, equivalent to a single imaging of a cluster of virtual calibration points on the image plane; for the first set of rotations, the middle frame and outer frame rotate n times, equivalent to an array of n points; for each rotation of the middle frame relative to the outer frame, the next rotation position always maintains a fixed rotation angle Δ relative to the previous position, according to the perspective projection model of a long-distance imaging camera, we have:

[0026]

[0027] in, R v (i,j) yes R The rotation angle of vector v0 on the outer frame of the turntable Mid-frame rotation angle ψ (j) The calibration point vector in the turntable coordinate system is then used. R v (i,j+1) yes R The rotation angle of vector v0 on the outer frame of the turntable Mid-frame rotation angle ψ (j) The calibration point vector R in the turntable coordinate system after +Δ. Δ for:

[0028]

[0029] Equation (4) shows that, at any calibrated position, the next position of the middle frame rotation direction is a fixed pure rotation relative to the current position;

[0030] Let m1 and m2 be the projection points of the calibration points on the camera image at the previous position and the next position of the middle frame rotation respectively, according to formula (1) and formula (4), we have:

[0031]

[0032] wherein, ρ1 and ρ2 are homogeneous coefficients, R v (i,j) is the vector of the calibration points in the coordinate system of the turntable after the rotation of the turntable; formula (6) shows that m1 and m2 are corresponding homologous points under pure rotation, and therefore all point arrays are divided into two groups of homologous points in the direction of the middle frame rotation;

[0033] The second group of rotations rotates the inner frame by 90° on the basis of the rotation of the middle frame and the outer frame, and rotates the two groups of homologous points in the first group of rotations by 90° as a whole, and the corresponding equation of the homologous points under the second group of rotations is as follows:

[0034]

[0035] wherein, R 90o is the rotation angle of the inner frame, and the expression is as follows:

[0036]

[0037] According to formula (6) and (7), the homologous point correspondence equation is further derived; by eliminating R v (i,j) , we have:

[0038] ρm2=H k ·m1,k=1,2 (9)

[0039] wherein, ρ=ρ2 / ρ1 is a homogeneous coefficient, H k,k＝1,2 is a homography matrix corresponding to the two groups of pure rotation, and the homography matrix corresponding to the two groups of pure rotation is:

[0040]

[0041] wherein, the upper index -1 on the right side of the formula represents the inverse operation of the matrix. H1 and H2 are solved through the homologous point correspondence, and then the known homography matrix H k,k＝1,2 is used to solve the intrinsic matrix K;

[0042] Let ω=(KK T ) -1 be the image of the absolute conic, ω * =KK T is the dual of the absolute conic image ω, then according to formula (10), the irrelevant rotation matrix is eliminated, and H k,k＝1,2 is normalized by determinant, and ω * and Hk,k＝1,2 Constraint relationship of ω

[0043]

[0044] where ω * is a 3x3 symmetric matrix, only containing 6 elements, then equation (11) constitutes 6 linear constraint equations about 6 unknowns; let the 6 unknown elements of ω * be x, then equation (11) is transformed into a homogeneous linear form about x:

[0045] Cx=0 (12)

[0046] where C is a 6x6 matrix composed of the elements of H k,k＝1,2 ; according to equation (11), 6 constraint equations are constructed by corresponding two groups of points, so that the 6 unknowns of x are linearly solved; ω * and ω are further calculated and obtained; the specific expression of ω after expansion is as follows:

[0047]

[0048] According to equation (13), the initial estimated values of the main parameters a x , a y , u0 and v0 of the camera intrinsic parameters are obtained.

[0049] Further, the step c includes: after the camera intrinsic parameter matrix K is solved, the rotation matrix R between the camera coordinate system and the turntable coordinate system is linearly solved.

[0050] A k X=XB k , k=1, 2 (14)

[0051] where,

[0052]

[0053] where A k matrix is first transformed into an orthogonal matrix by SVD decomposition; let:

[0054] α1= logA1, α2= logA2, β1= logB1, β2= logB2 (16)

[0055] In the above equation, α1, α2, β1 and β2 are all in the form of rotation vectors, then has a linear solution:

[0056]

[0057] Wherein, M=(α1α2α1×α2), N=(β1β2β1×β2).

[0058] Further, the step d comprises: based on the minimum residual error of the point correspondence before and after the pure rotation motion, establishing an optimization target equation for solving; determining the minimized target function as follows:

[0059]

[0060] Wherein, And are the undistorted image points before and after the pure rotation respectively, k is the serial number of the pure rotation motion, and n is the group number of the rotation angle values of the middle frame and the outer frame; the initial estimated values of the main internal parameters a x ,a y ,u0,v0 and are used as the initial values, the initial values of the distortion coefficients k1, k2, p1 and p2 are all 0, and the Levenberg-Marquardt method (L-M method) is used for optimization solving to obtain the final calibration result.

[0061] Compared with the existing calibration method of integrated modeling of internal and external parameters based on a three-axis turntable and the calibration method of separated internal and external parameters, the present application has the following advantages:

[0062] (1) The traditional calibration method of integrated modeling of internal and external parameters based on a three-axis turntable can only obtain high-precision measurement results when all parameters are used together, and the precision may be reduced when only part of the parameters or the parameters are used alone. The internal and external parameter separation method of the present application separates the coupled parameters, thereby improving the precision of a single parameter;

[0063] (2) The traditional calibration method of separated internal and external parameters based on a three-axis turntable needs to be repeatedly fine-tuned in the process of solving the relative turntable zero position vector direction R v0 of the calibration point, which requires more manual participation, so that the efficiency of the method is not high. The internal and external parameter separation method of the present application eliminates the relative turntable zero position vector R v0 of the calibration point from the principle derivation process through the internal and external parameter separation calibration model of the long-distance imaging camera, so that the calibration process does not need manual tuning and only needs to be calculated theoretically. The calibration efficiency is greatly improved while maintaining high precision. BRIEF DESCRIPTION OF DRAWINGS

[0064] Figure 1 is a schematic diagram of a precision three-axis turntable calibration system adopted by the present application;

[0065] Figure 2 is a principle diagram of the same point correspondence constructed by the first group of pure rotation motions of the present application;

[0066] Figure 3The same point correspondence principle diagram is constructed for the second group of pure rotation motion of the application. DETAILED DESCRIPTION

[0067] The advantages and features of the application will be more easily understood by those skilled in the art, and the protection scope of the application will be more clearly defined, by describing the embodiments of the application in detail below with reference to the drawings.

[0068] As Figure 1 shown, the long-distance imaging camera internal and external parameter separation calibration method based on the precision three-axis turntable of the application adopts the precision three-axis turntable to realize high precision of calibration; adopts the long-distance imaging camera internal and external parameter separation calibration model to realize high efficiency of calibration, involves automatic acquisition of two groups of light point sub-pixel coordinates by the precision three-axis turntable, long-distance imaging camera perspective projection model and distortion model, and mainly includes initial estimation values of internal parameters (a x ,a y ,u0,v0) and external parameters and all internal and external parameter joint optimization with the minimum point correspondence error as the target based on the Levenberg-Marquardt method (L-M method), including all internal parameters (a x ,a y ,u0,v0,k1,k2,p1,p2) and external parameters

[0069] The precision three-axis turntable includes a fixed base 1, an outer frame 2, a middle frame 3, an inner frame 4, an outer frame rotating shaft 5, a middle frame rotating shaft 6, an inner frame rotating shaft 7, and a calibration point 8. The precision three-axis turntable takes the base 1 as a carrier, the outer frame 2 is located above the base 1 and is fixedly connected through the outer frame rotating shaft 5, the middle frame 3 is located in the outer frame 2 and is fixedly connected through the middle frame rotating shaft 6, the inner frame 4 is located in the middle frame 3 and is fixedly connected through the inner frame rotating shaft 7, and the camera is fixed on the inner frame 4 through screws. The base 1 is placed on the ground to provide support and stability; the outer frame 2 rotates around the outer frame rotating shaft 5 to change the azimuth angle of the camera, the middle frame 3 rotates around the middle frame rotating shaft 6 to change the pitch angle ψ of the camera, and the inner frame 4 rotates around the inner frame rotating shaft 7 to change the roll angle of the camera, which is 0° and 90° in the application; the calibration point 8 is a single light point simulated by a parallel light pipe, i.e., a single calibration point. As Figure 1 shown, X R Y R Z R is a turntable coordinate system, the X axis points to the right and coincides with the middle frame rotating shaft 6, the Y axis points downward and coincides with the outer frame rotating shaft 5, and the Z axis points forward and coincides with the inner frame rotating shaft 7, and the turntable coordinate system changes with the rotation of the three-axis turntable; X c Y c Z cA camera coordinate system is defined in the same way as the turntable coordinate system, but due to the installation error of the camera, the camera coordinate system and the turntable coordinate system do not completely coincide, and there is an external parameter Conversion relationship; during the rotation of the three-axis turntable, a single calibration point 8 is imaged on the camera image plane, and a series of light point sub-pixel coordinates are projected.

[0070] The specific implementation steps of the camera internal and external parameter separation calibration method based on the precise three-axis turntable of the present application are as follows:

[0071] Step 1: A camera calibration system is formed based on the rotation of the precise three-axis turntable and a single light point (calibration point) of the collimator, under the condition that the inner frame is rotated at different angles, the camera automatically collects the light point sub-pixel coordinates of two groups of calibration point images through a series of rotations of the middle frame and the outer frame;

[0072] Specifically, the long-distance imaging camera is placed at the center of the precise three-axis turntable, and the collimator is placed in front of the turntable to simulate a single calibration point at a long distance. Under the condition that the inner frame of the turntable is rotated by 0° and 90°, the middle frame and the outer frame are rotated by a series of fixed rotation angle values, and the camera automatically collects two groups of light point images of the calibration point images, and the light point sub-pixel coordinates are obtained according to the light point centroid, and the collection process does not require human intervention, wherein the rotation angle range of the middle frame and the outer frame is-10° to 10°, and the rotation angle interval is 2°; However, due to the limitation of the field of view of the camera, when the rotation angles of the middle frame and the outer frame are (±10°±10°), (±10°±8°) and (±8°±10°), the camera cannot collect light point images, therefore, the 12 groups of rotation angle values are excluded, and there are a total of 109 groups of rotation angle values.

[0073] Step 2: According to the light point sub-pixel coordinates of the two groups of calibration point images in step 1, the correspondence relationship of the same points under the pure rotation motion of the two groups is established, and the initial estimated value of the main internal parameter (a x , a y , u0, v0) of the long-distance imaging camera is linearly solved;

[0074] Specifically, during the rotation of the turntable, for each rotation of the middle frame relative to the outer frame, the next rotation position relative to the previous position also always maintains a fixed rotation angle, and since the calibration point is at a long distance, the next position of the middle frame rotation direction relative to the current position is a fixed pure rotation motion, therefore, the correspondence relationship of the same points under the pure rotation motion of the two groups is established through the collected light point sub-pixel coordinates of the two groups of calibration point images, and the initial estimated value of the main internal parameter of the long-distance imaging camera is linearly solved.

[0075] Step 3: For the correspondence relationship of the same points under the pure rotation motion of the two groups constructed in step 2, a constraint equation about the external parameter is constructed, and the camera external parameter initial estimated values of the main intrinsic parameters (a

[0076] Step 4, according to the initial estimated values of the main intrinsic parameters (a x ,a y ,u0,v0) and the initial estimated values of the camera extrinsic parameters , iteratively optimize all the camera intrinsic and extrinsic parameters to obtain the optimal estimated values of all the camera intrinsic and extrinsic parameters .

[0077] Further, the step 1 comprises:

[0078] Step 101, a single calibration point forms two groups of sub-pixel coordinates of light points under a series of rotations of the turntable, and a long-distance imaging camera perspective projection model is as follows:

[0079]

[0080] wherein:

[0081]

[0082] wherein, ρ is a proportional coefficient, m = [u (i,j) v (i,j) 1] T is the pixel coordinates of the calibration point under the camera image, R v0is the vector of the calibration point when the turntable is at zero position in the turntable coordinate system, C v (i,j) is the vector of the calibration point in the camera coordinate system after the rotation of the turntable, and K is the camera intrinsic parameter matrix, which is determined by the main intrinsic parameters a x , a y , u0, v0, a x , a y are the normalized focal lengths on the x-axis and y-axis respectively, and u0, v0are the pixel coordinates of the image principal point. R R (i,j) is the rotation matrix of the outer frame rotation angle of the middle frame rotation angle ψ (j) , is the conversion matrix from the turntable coordinate system to the camera coordinate system, i.e. the camera extrinsic parameter.

[0083] The distortion model of the long-distance imaging camera is as follows:

[0084]

[0085] wherein, (x u ,y u ) and (x d ,y d) are the undistorted pixel coordinates, r is the physical distance from (x u ,y u ) to the principal point (u0, v0), k1, k2 are the first two radial distortion coefficients of the camera, p1, p2 are the first two tangential distortion coefficients of the camera

[0086] Further, the step 2 comprises:

[0087] Step 201, obtaining an initial estimation of the main intrinsic parameters according to a long-distance imaging camera intrinsic-extrinsic parameter separation calibration model.

[0088] The turntable forms a series of imaging points by rotating the single calibration point in front, which can be equivalent to a cluster of virtual calibration point arrays once imaged on the image plane. For the first group of rotations, the middle frame and the outer frame are rotated n times, which can be equivalent to n point arrays. For each rotation of the middle frame relative to the outer frame, the next rotation position always maintains a fixed rotation angle Δ relative to the previous position. According to the long-distance imaging camera perspective projection model, we have:

[0089]

[0090] wherein, R v (i,j) is R v0vector after the outer frame of the turntable is rotated by an angle middle frame rotation angle ψ (j) calibration point vector in the turntable coordinate system after the middle frame is rotated by an angle R v (i,j+1) is R v0vector after the outer frame of the turntable is rotated by an angle middle frame rotation angle ψ (j) calibration point vector in the turntable coordinate system after the middle frame is rotated by an angle Δ

[0091]

[0092] Equation (4) shows that the next position of the middle frame rotation direction relative to the current position is a fixed pure rotation. Let m1 and m2 be the projection points of the calibration point at the previous position and the next position of the middle frame rotation, respectively. According to equations (1) and (4), we have:

[0093]

[0094] wherein ρ1 and ρ2 are homogeneous coefficients, R v (i,j) is the calibration point vector in the turntable coordinate system after the turntable is rotated. Equation (6) shows that m1 and m2 are corresponding homonymous points under pure rotation. In this way, all point arrays can be divided into two groups of homonymous points in the direction of the middle frame rotation, such as​Figure 2 As shown, this process can be equivalent to all points in the upper octagonal region are fixedly rotated by an angle Δ by the outer frame once, and the points in the lower octagonal region are obtained.

[0095] The second group of rotations rotates the inner frame by 90° on the basis of the rotation of the middle frame and the outer frame, and essentially rotates the two groups of homonymous points in the first group of rotations by 90° as a whole. The two groups of homonymous points under the second group of rotations correspond to as shown in the figure. Figure 3 As shown, the homonymous points under the second group of rotations correspond to the following equations:

[0096]

[0097] wherein R 90o is the rotation angle of the inner frame, and the expression is as follows:

[0098]

[0099] According to equations (6) and (7), the homonymous point correspondence equation is further derived. Eliminating R v (i,j) , we have:

[0100] ρm2=H k ·m1,k=1,2 (9)

[0101] wherein ρ=ρ2 / ρ1 is the homogeneous coefficient, H k,k＝1,2 is the homography matrix corresponding to the two groups of pure rotations, and the homography matrix corresponding to the two groups of pure rotations is:

[0102]

[0103] wherein the upper index -1 on the right side of the formula represents the inverse operation of the matrix. H1 and H2 represent the point correspondence homography matrices of the first group of pure rotation motions and the second group of pure rotation motions, respectively, which can be solved by the homonymous point correspondence in Figure 2 and Figure 3 , and then the known homography matrix H k,k＝1,2 is used to solve the camera intrinsic matrix K. Let ω=(KK T ) -1 be the image of the absolute conic, and ω * =KK T be the dual of the image ω of the absolute conic. According to equation (10), the irrelevant rotation matrix can be eliminated, and the constraint relationship between ω * and H k,k＝1,2 is established:

[0104]

[0105] Note that the above formula needs to be normalized in determinant before H k,k＝1,2 . ω *is a 3x3 symmetric matrix, which contains only 6 elements, then equation (11) constitutes 6 linear constraint equations about 6 unknowns. Let the 6 unknown elements of ω * be denoted as x, then equation (11) can be transformed into a homogeneous linear form about x:

[0106] Cx=0 (12)

[0107] where C is a 6x6 matrix composed of the elements of H k,k＝1,2 . Equation (12) essentially has only 3 constraint equations, and 6 constraint equations can be constructed by corresponding to two groups of points, so that the 6 unknowns of x can be linearly solved. Further, ω * and ω can be calculated and obtained. The specific expression of ω after expansion is as follows:

[0108]

[0109] According to equation (13), the initial values of the main parameters a x , a y , u0 and v0 of the camera intrinsic parameters can be easily obtained.

[0110] Further, the step 3 comprises:

[0111] Step 301, solving the initial estimated value of the extrinsic parameters ω according to the long-distance imaging camera intrinsic and extrinsic parameter separation calibration model.

[0112] After the camera intrinsic parameter matrix K is solved, the rotation matrix R between the camera coordinate system and the turntable coordinate system can be linearly calculated. Equation (9) can be converted into:

[0113] A k X=XB k , k=1, 2 (14)

[0114] where,

[0115]

[0116] Note that the A k matrix needs to be first transformed into an orthogonal matrix by SVD decomposition. Let:

[0117] α1= logA1, α2= logA2, β1= logB1, β2= logB2 (16)

[0118] In the above equation, α1, α2, β1 and β2 are all in the form of rotation vectors. Then has a linear solution:

[0119]

[0120] Wherein, M=(a1a2a1xa2), N=(b1b2b1xb2).

[0121] Further, the step 4 comprises:

[0122] Step 401, based on L-M method iterative optimization of all camera internal and external parameters

[0123] Based on the minimum residual error of the point correspondence before and after the pure rotation motion, the optimal objective equation is established to solve. After removing the distortion, the pixel coordinates of the calibration points before pure rotation are transformed by the homography matrix corresponding to pure rotation, and the pixel coordinates of the calibration points after removing the distortion are equal in ideal case. Therefore, the minimum objective function is determined as follows:

[0124]

[0125] Wherein, and are the distortion-removed image points before and after pure rotation respectively, k is the serial number of pure rotation motion, and n is the group number of the rotation angle values of the middle frame and the outer frame. The initial estimated values of the main internal parameters a x ,a y ,u0,v0 and the external parameters are used as the initial values, the initial values of k1, k2, p1 and p2 are all 0, and the Levenberg-Marquardt method is used for optimal solution to obtain the final calibration result.

[0126] Those skilled in the art can easily understand that the above description is only the preferred embodiment of the present application, and is not intended to limit the present application. Any modification, equivalent replacement and improvement within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for separating the internal and external parameters of a long-range imaging camera based on a precision three-axis turntable, characterized in that, The method comprises the following steps: Step a, a camera calibration system is composed of rotation of a precision three-axis turntable and a single calibration point formed by an adjustable collimator, under the condition that the inner frame rotates at different angles, a series of rotations of the middle frame and the outer frame are performed, and sub-pixel coordinates of imaging points of two groups of calibration points are measured by the camera; the single point of the collimator is the calibration point, the focusing position of the collimator is the same as the measurement position of the measurement camera; the measurement camera is a long-distance imaging camera; for each rotation of the middle frame relative to the outer frame, the next rotation position is also always kept at a fixed rotation angle relative to the previous position, and since the calibration point is at a long distance, the next position of the middle frame rotation direction is a fixed pure rotation relative to the current position; Step b, according to the light spot sub-pixel coordinates of the two sets of calibration points imaged in step a, establishing the corresponding relationship of homonymic points under the pure rotation motion, thereby linearly solving the initial estimated value of the main intrinsic parameters of the long-distance imaging camera, including the normalized focal length on the x-axis and y-axis , and the pixel coordinates of the image principal point , ; Step c, constructing constraint equations about camera extrinsic parameters based on the corresponding relation of the same name points constructed in step b, so as to linearly solve the initial estimated value of the camera extrinsic parameters, which are i.e. the conversion matrix from the turntable coordinate system to the camera coordinate system; Step d, according to the initial estimated value of the main internal parameter and the initial estimated value of the camera external parameter solved linearly in step b and step c, iteratively optimize all camera internal and external parameters with the minimum correspondence error of the same point as the optimization goal, to obtain the optimal estimated value of the camera internal and external parameters , , is the radial distortion coefficient of the camera, , is the tangential distortion coefficient of the camera.

2. The method according to claim 1, wherein, In the step a, the measurement camera is placed at the center of the precision three-axis turntable, and the collimator is placed in front of the precision three-axis turntable to simulate a single calibration point at a long distance; under the condition that the inner frame of the precision three-axis turntable rotates at 0° and 90°, the middle frame and the outer frame of the precision three-axis turntable are rotated by setting a series of fixed rotation angle values, while the measurement camera automatically collects images of the light points of two groups of calibration points, and sub-pixel coordinates of the light points are obtained according to the light point centroids, wherein the series of fixed rotation angle values are set between -10° and 10°, and the rotation angle interval is 2°.

3. The method of claim 2, wherein, The step a comprises: The single calibration point is imaged to form two groups of sub-pixel coordinates under a series of rotations of the turntable, and a perspective projection model of the long-distance imaging camera is as follows: （1） Wherein: （2） where ρ is a proportionality coefficient, is the pixel coordinate of the calibration point under the camera image, is the vector of the calibration point when the turntable is at zero position under the turntable coordinate system, is the vector of the calibration point under the camera coordinate system after the turntable rotates, and K is the camera intrinsic matrix, which is composed of the main intrinsic parameters , , , , , are the normalized focal lengths in the x-axis and y-axis respectively, , is the pixel coordinate of the image principal point; is the rotation matrix of the outer frame rotation angle of the middle frame rotation angle , is the conversion matrix from the turntable coordinate system to the camera coordinate system, i.e., the camera extrinsic parameters; A camera distortion model is as follows: （3） wherein, and are the de-distorted pixel point coordinates and the pixel point coordinates without de-distortion, is the physical distance from the principal point , , is the radial distortion coefficient of the camera, , is the tangential distortion coefficient of the camera.

4. The method of claim 3, wherein, The step b comprises: a precision three-axis turntable forms a series of imaging points by rotating a single calibration point in front, which is equivalent to a cluster of virtual calibration point arrays in a single imaging on the image plane; for the first group of rotations, the middle frame and the outer frame rotate n times, which is equivalent to n point arrays; for each rotation of the middle frame relative to the outer frame, the next rotation position always maintains a fixed rotation angle relative to the previous position According to the perspective projection model of the long-distance imaging camera, there is: （4） wherein, is vector in the outer frame of the turntable rotation angle , middle frame rotation angle after the calibration point vector in the turntable coordinate system, is vector in the outer frame of the turntable rotation angle , middle frame rotation angle after the calibration point vector in the turntable coordinate system, is: （5） Formula (4) shows that the next position of the middle frame rotation direction is a fixed pure rotation relative to the current position at any calibration position; Let and be the projection points of the calibration points on the camera image in the previous and next positions of the middle frame rotation, respectively, according to equations (1) and (4): （6） wherein, and are homogeneous coefficients, is the vector of the calibration points in the coordinate system of the turntable after the rotation of the turntable; equation (6) shows and are the corresponding homonymous points under pure rotation, so all point arrays are divided into two groups of homonymous points in the direction of the middle frame rotation. The second group of rotations rotates the inner frame by 90° on the basis of the rotation of the middle frame and the outer frame, rotates the two groups of homonymous points in the first group of rotations by 90° as a whole, and the homonymous points under the second group of rotations correspond to the following equation: （7） wherein is the inner frame rotation angle, and the expression is as follows: （8） According to the formula (6) and (7), the homonymy point correspondence equation is further derived; eliminating , we get: （9） wherein, are homogeneous coefficients, are homographies corresponding to the two sets of pure rotations, the homographies corresponding to the two sets of pure rotations: （10） Wherein, the formula right side superscript -1 represents the matrix inverse operation; and By the same name point correspondence relationship solution, next use the known homography matrix To solve the camera intrinsic matrix ; Let be the image of the absolute conic, be the dual of the absolute conic image , then eliminate the irrelevant rotation matrix according to formula (10), and perform determinant normalization on to establish the constraint relationship between and : （11） where is a 3x3 symmetric matrix, containing only 6 elements, then equation (11) constitutes 6 linear constraint equations on 6 unknowns; let be the 6 unknown elements of , then equation (11) transforms into the homogeneous linear form: ​ （12） wherein, is composed of the elements of matrix; according to formula (11) by two sets of point correspondence, i.e. constructing 6 constraint equations, so as to linearly solve 6 unknowns of ; further calculation is obtained and ; The specific expression after expansion is as follows: （13） According to equation (13), the initial estimated values of the main intrinsic parameters of the camera are obtained , , and .

5. The method of claim 4, wherein, The step c comprises: obtaining the camera intrinsic matrix After the solving, the rotation matrix between the camera coordinate system and the turntable coordinate system is linearly solved Equation (10) is converted into: （14） Wherein, （15） wherein, The matrix is first transformed into an orthogonal matrix by SVD decomposition; let: （16） In the above equation , , and are in the form of a rotation vector, then has a linear solution: （17） wherein , .

6. The method of claim 5, wherein, The step d comprises: establishing an optimal objective equation based on the minimum residual error of the points before and after the pure rotation to solve; and determining the minimum objective function as follows: （18） wherein, and are pure rotation before and pure rotation after distortion image points respectively, is the sequence number of pure rotation movement, is the number of groups of the middle frame and the outer frame rotation angle values; the initial estimated values of the main intrinsic parameters and the camera extrinsic parameters are used as initial values, the initial values of all are 0, and the final calibration result is obtained by using the Levenberg-Marquardt method for optimal solution. The joint optimization solves all the intrinsic parameters and extrinsic parameters in one process. In the process, the in equation (1) is eliminated without solving, and the is the calibration point vector when the turntable is at zero position in the turntable coordinate system.

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