An improved method for calibrating interior orientation elements of a planar array camera by precise angle measurement

Abstract

The present application relates to a kind of improved precision angle measurement method of face array camera interior orientation element calibration method, steps are as follows: according to the arrangement of precision angle measurement method, record the angle of each measuring line and camera image coordinate axis, the coordinates of each measuring point and corresponding two-dimensional turntable angle of measurement equipment;Measuring point coordinates normalization calculation, constructs distortion model;All interior orientation parameters and measurement data are uniformly constructed distortion correction residual model;With distortion residual minimum as objective function, solve interior orientation element using nonlinear optimization algorithm.The present application method is applied to face array camera, without limiting the angle of parallel light rotation respectively and the accurate parallelism of camera image coordinate axis in experimental measurement, reduce the cost and difficulty of calibration, and construct the interior orientation element unified solution framework covering camera principal point, camera principal distance, distortion parameter, improve the precision of interior orientation element.

Description

Technical Field

[0001] This invention relates to the field of aerial photogrammetry and remote sensing, and in particular to an improved method for calibrating the orientation elements within an area array camera using a precision angle measurement method. Background Technology

[0002] Area array cameras are widely used in aerospace remote sensing missions, and the accuracy of their internal orientation element calibration directly affects the performance of spatial geometry-related applications such as direct positioning, photogrammetry, and 3D reconstruction.

[0003] The calibration methods for the interior orientation elements of area array cameras can be mainly divided into two technical routes: calibration based on calibration fields and calibration based on laboratory precision angle measurement methods. The calibration field calibration algorithm establishes the relationship between the world coordinate system of the calibration field and the camera's interior orientation elements by constructing a three-dimensional calibration field or a virtual calibration field using markers such as a checkerboard pattern, and then solves the problem. The calibration field-based algorithm involves not only the camera's interior orientation elements but also its exterior orientation elements. In the calculation, the interior and exterior orientation elements have a certain degree of coupling, which brings difficulties to solving for the interior orientation elements. Furthermore, this type of method is generally not applicable to infrared cameras because the calibration field target is difficult to maintain strong contrast in the infrared spectral band.

[0004] The laboratory precision angle measurement method based on parallel light does not involve the camera's exterior orientation elements and has been widely used in measuring the interior orientation elements of linear scan cameras. When applied to area scan cameras, it requires that the angle of rotation of the parallel light be parallel to the coordinate axes of the camera image, thus decomposing the area scan camera into two one-dimensional linear scan cameras, and then solving for the principal point, principal distance, and distortion parameters step by step. This algorithm requires precise adjustment of the two-dimensional turntable and camera on the collimator in two degrees of freedom before calibration, which places high demands on laboratory field measurement work. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of existing precision angle measurement methods and provide a method for calibrating the orientation elements of an area array camera that no longer restricts the measurement line to be parallel to the camera image coordinate axis.

[0006] The technical solution of this invention is: an improved precision angle measurement method for calibrating the interior orientation elements of an area array camera, wherein the interior orientation elements include the abscissa X0 of the camera principal point, the ordinate Y0 of the camera principal point, the principal distance f of the camera, radial distortion model parameters, and eccentric distortion model parameters. The steps of this method are as follows:

[0007] The target is imaged using a precise angle measurement method. m measurement lines are obtained on the image from the area array camera, with n measurement points on each line. Measurement data is recorded, including the angle λ between measurement line i and the x-axis of the camera image. i Measuring point T ij Coordinates in the camera image coordinate system (X)ij ,Y ij ), and the formation of measuring point T ij The rotation angle α of the two-dimensional turntable relative to the zero position ij , i∈[1,m], j∈[1,n]; the total number of survey lines m≥2, the number of survey points n on each survey line is greater than the number of parameters in the interior orientation element, and the angles between the m survey lines i and the x-axis of the camera image are not the same.

[0008] The image coordinates of the measurement points are normalized to obtain normalized coordinates (x, y). ij ,y ij ), will (x ij ,y ij Substituting the x-coordinate (X0) and y-coordinate (Y0) of the camera principal point, and the camera principal distance (f) into the distortion model formula containing radial distortion model parameters and eccentric distortion model parameters, we obtain the distortion projection coordinates (xd). ij ,yd ij The theoretical calculation formula;

[0009] Construct a distortion correction residual model and convert the distortion projection coordinates (xd) ij ,yd ij The measurement data, along with the camera principal point x0, camera principal point y0, and camera principal distance f, are substituted into the distortion correction residual model to obtain the distortion correction residual v. ij The calculation formula;

[0010] The distortion correction residuals of all measuring points are used to construct the error matrix V, with J = V T V is the objective function to be minimized, and the interior orientation elements are solved using a nonlinear optimization algorithm.

[0011] Preferably, the specific steps for imaging the target using the precision angle measurement method are as follows:

[0012] S1-1. Place the camera on a two-dimensional turntable, with the camera's image plane perpendicular to the optical axis of the collimator, and aim the collimator at the target.

[0013] S1-2. Rotate the two-dimensional turntable so that the imaging points of the target on the camera image are on a straight line. This straight line is denoted as the survey line, and the angle λ between the survey line i and the x-axis of the camera image is recorded. i Each imaging point is recorded as a measurement point, and the measurement point T is recorded. ij Coordinates in the camera image coordinate system (X) ij ,Y ij ), and the formation of measuring point T ij The rotation angle α of the two-dimensional turntable relative to the zero position ij ;

[0014] S1-3. After measuring one survey line, rotate the camera around the optical axis of the collimator and repeat step S1-2 to form m different survey lines.

[0015] Preferably, the maximum included angle between the m measuring lines is greater than 60°.

[0016] Preferably, all m measuring lines pass through the center of the phase plane.

[0017] Preferably, the normalization calculation formula is:

[0018] x ij =(X ij -X0) / f

[0019] y ij =(Y ij -Y0) / f.

[0020] Preferably, the distorted projection coordinates (xd) ij ,yd ij The theoretical calculation formula for ) is:

[0021] xd ij =xk ij +xp ij

[0022] yd ij =yk ij +yp ij

[0023] Among them, xk ij yk ij For measuring point T ij The radial distortion is projected onto the x-axis and y-axis; xp ij yp ij For measuring point T ij The eccentric distortion projected onto the x-axis and y-axis, xk ij yk ij XP ij yp ij The calculation formulas are as follows:

[0024] xk ij =x ij ×(k1×r 2 +k2×r 4 +k3×r 6 )

[0025] yk ij =y ij ×(k1×r 2 +k2×r 4 +k3×r 6 )

[0026] xp ij =p2(r 2 +2x ij 2 )+2p1x ij y ij

[0027] yp ij =p1(r 2 +2y ij 2 )+2p2x ij y ij

[0028]

[0029] Wherein, k1 represents the first radial distortion model parameter, k2 represents the second radial distortion model parameter, k3 represents the third radial distortion model parameter, p1 represents the first eccentric distortion model parameter, and p2 represents the second eccentric distortion model parameter. The radial distortion model parameters include the first radial distortion model parameter k1, the second radial distortion model parameter k2, and the third radial distortion model parameter k3. The eccentric distortion model parameters include the first eccentric distortion model parameter p1 and the second eccentric distortion model parameter p2.

[0030] Preferably, the distortion correction residual v ij The formula for calculation is:

[0031] v ij =p ij -p i0 -Ht ij

[0032] p ij =((x) ij +xd ij )*f+X0)*cos(λ i )-((y ij +yd ij )*f+Y0)*sin(λ i )

[0033] p i0 =X0*cos(λ) i )-Y0*sin(λ i )

[0034]

[0035] Preferably, the error matrix is:

[0036]

[0037] Preferably, the nonlinear optimization solution algorithm is the LM nonlinear least squares method.

[0038] Preferably, the nonlinear optimization solution algorithm is a genetic algorithm.

[0039] The advantages of this invention compared to the prior art are:

[0040] (1) A typical method for calibrating the interior orientation elements of an area array camera based on the precision angle measurement method is proposed. The camera principal point, camera principal distance and distortion parameters are solved step by step. When solving the camera principal point and principal distance, the distortion parameters are not considered, which restricts the accuracy of the interior orientation element solution. A method is proposed to construct a unified solution framework for the interior orientation elements covering the principal point, principal distance and distortion parameters, which improves the accuracy of the interior orientation element solution.

[0041] (2) The typical method for calibrating the orientation elements of an area array camera based on the precision angle measurement method requires that the axis of rotation of the camera light and the coordinate axis of the camera image be precisely parallel during the test, which puts high demands on the construction of the test system and the laboratory measurement process, and increases the cost and difficulty of calibration. The proposed method for calibrating the orientation elements of an area array camera supports the calculation of at least two measurement lines in any direction, which reduces the cost of the laboratory measurement process.

[0042] (3) Compared with the typical precision angle measurement method, the use of nonlinear optimization method avoids the theoretical error caused by model linearization.

[0043] (4) Compared with commonly used area array camera calibration methods such as the checkerboard method, the method proposed in this invention does not involve the external orientation elements of the camera, is easy to calculate, and is compatible with the internal orientation element calibration applications of different types of cameras such as visible light and infrared cameras. Attached Figure Description

[0044] Figure 1 This is a flowchart of the method for calibrating the orientation elements of an area array camera using the improved precision angle measurement method of the present invention.

[0045] Figure 2 This is a measurement schematic diagram of the method for calibrating the orientation elements of an area array camera using the improved precision angle measurement method of this invention. Detailed Implementation

[0046] like Figure 1 As shown, the steps of the improved precision angle measurement method for calibrating the internal orientation elements of an area array camera according to the present invention are as follows:

[0047] Step 1: Laboratory measurement and pretreatment.

[0048] The laboratory measurement equipment is arranged in the same way as the conventional precision angle measurement method. The area array camera is placed on a two-dimensional turntable, and the collimator is aimed at the target. The collimator is then leveled so that the optical axis of the collimator is perpendicular to the camera image plane.

[0049] During measurement, adjust the high-precision turntable angle scanning camera and record the angle λ between the i-th measurement line and the x-axis. i , λ i Clockwise is positive; the j-th measurement point on the i-th measurement line is denoted as measurement point T. ij Record the formation of measurement point T ij The rotation angle α of the two-dimensional turntable relative to the zero position ij and measuring point T ij Coordinates (X) in the image captured by the camera ij ,Y ij Measurement diagram as follows Figure 2 As shown.

[0050] After scanning one survey line is completed, the camera is rotated a certain angle around the optical axis of the collimator, and the 2D turntable is adjusted to repeat the scanning of new survey lines until data acquisition of m survey lines and each measuring point on each line is completed. The number of survey lines m is greater than or equal to 2, and the number of measuring points n on each survey line must be greater than the number of parameters in the interior orientation elements, generally twice the number of parameters in the interior orientation elements. The included angle between survey lines is greater than 60°, and the survey lines pass through the center of the phase plane.

[0051] Step 2: Unified optimization model construction of in-camera orientation elements.

[0052] The initial normalization calculation is performed on the survey data, and the calculation formula is as follows:

[0053] x ij =(X ij -X0) / f

[0054] y ij =(Y ij -Y0) / f

[0055] Where X0 is the x-coordinate of the camera principal point, Y0 is the y-coordinate of the camera principal point, and f is the camera focal length. ij For measuring point T ij The normalized projected coordinates of the x-axis, y ij For measuring point T ij The y-axis normalized projected coordinates.

[0056] The calculation is performed using radial distortion and eccentric distortion models, and the calculation formula is as follows:

[0057] xd ij =xk ij +xp ij

[0058] yd ij =yk ij +yp ij

[0059] Among them, xkij yk ij For measuring point T ij The radial distortion is projected onto the x-axis and y-axis; xp ij yp ij For measuring point T ij The eccentric distortion is projected onto the x-axis and y-axis.

[0060] The radial distortion model is:

[0061] xk ij =x ij ×(k1×r 2 +k2×r 4 +k3×r 6 )

[0062] yk ij =y ij ×(k1×r 2 +k2×r 4 +k3×r 6 )

[0063] The eccentric distortion model is as follows:

[0064] xp ij =p2(r 2 +2x ij 2 )+2p1x ij y ij

[0065] yp ij =p1(r 2 +2y ij 2 )+2p2x ij y ij

[0066]

[0067] Wherein, k1 is the parameter of the first radial distortion model, k2 is the parameter of the second radial distortion model, k3 is the parameter of the third radial distortion model, p1 is the parameter of the first eccentric distortion model, and p2 is the parameter of the second eccentric distortion model.

[0068] Step 3: Establish a distortion correction residual model based on the principle of minimizing the distortion residual at the observation point:

[0069] p ij =((x) ij +xd ij )*f+X0)*cos(λ i )-((y ij +yd ij )*f+Y0)*sin(λi )

[0070] p i0 =X0*cos(λ) i )-Y0*sin(λ i )

[0071]

[0072] Where, p ij For measuring point T ij The correction image is high; xd ij yd ij They are measuring points T ij Theoretical calculations are performed to project the distortion onto the x-axis and y-axis; p i0 Ht is the projection of the principal point onto the i-th survey line; i Let be the theoretical image height on measurement line i.

[0073] Measuring point T ij The corresponding distortion correction residual v ij The formula for calculation is:

[0074] v ij =p ij -p i0 -Ht ij

[0075] Thus, there are a total of eight interior orientation parameters: X0, Y0, k1, k2, k3, p1, p2, and f. For each sampling observation point, a corresponding error equation can be derived. All error equations are combined into a matrix V as follows:

[0076]

[0077] Step 4: Solve for the interior orientation elements using a nonlinear optimization algorithm:

[0078] Minimize the objective function J = V T V can be solved using the LM nonlinear least squares method or optimization algorithms such as genetic algorithms to obtain accurate results for the interior orientation elements.

[0079] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. An improved method for calibrating interior orientation elements of a planar array camera in precise angle measurement, the interior orientation elements comprising a camera principal point horizontal coordinate X0, a camera principal point vertical coordinate Y0, a camera principal distance f, a radial distortion model parameter, an eccentric distortion model parameter, characterized in that The steps are as follows: The target is imaged by using a precision angle measuring method, m lines of measurement are measured on a surface array camera image, n measurement points are on each line of measurement, measurement data is recorded, and the measurement data includes: an included angle λ of a line of measurement i and an x axis of the camera image i , a coordinate (X ij , Y ij ) of a measurement point T ij in a camera image coordinate system, and a rotation angle α ij of a two-dimensional rotary table relative to a zero position when the measurement point T ij is formed i , i∈[1,m], j∈[1,n]; the total number of lines of measurement m is greater than or equal to 2, the number of measurement points on each line of measurement n is greater than the number of parameters in interior orientation elements, and the included angles of the m lines of measurement i and the x axis of the camera image are different. The image coordinates of the measuring point are normalized to obtain normalized coordinates (x ij ,y ij ), and the (x ij ,y ij ), camera principal point horizontal coordinate X0, camera principal point vertical coordinate Y0, and camera principal distance f are substituted into a distortion model formula containing radial distortion model parameters and eccentric distortion model parameters to obtain a theoretical calculation formula of the distortion projection coordinates (xd ij ,yd ij ); The distortion correction residual model is constructed, the distortion projection coordinates (xd ij ,yd ij ), the measurement data, and the camera principal point horizontal coordinate X0, the camera principal point vertical coordinate Y0 and the camera principal distance f are substituted into the distortion correction residual model to obtain the calculation formula of the distortion correction residual v ij . The distortion correction residual of all measuring points is constituted as error matrix V, and J = V T V is the minimum objective function, and the inner orientation elements are solved by using a nonlinear optimization algorithm.

2. The method for calibrating interior orientation elements of a planar array camera for improved precise angle measurement method according to claim 1, characterized in that, The specific steps of imaging the target by using the precise angle measurement method are as follows: S1-1, place the camera on a two-dimensional turntable, the image plane of the camera is perpendicular to the optical axis of the collimator, and the collimator aims at the target; S1-2, rotate the two-dimensional rotary table so that the imaging points of the targets on the camera image are on a straight line, which is recorded as a measuring line, and record the angle λ between the measuring line i and the x-axis of the camera image i , each imaging point is recorded as a measuring point, and record the measuring point T ij In the camera image coordinate system, the coordinates (X ij ,Y ij ), and the rotation angle α of the two-dimensional rotary table relative to the zero position when the measuring point T ij is formed ij ; S1-3, after measuring a measuring line, rotate the camera around the optical axis of the collimator, repeat step S1-2, and form m different measuring lines.

3. The method of claim 1, wherein the method is characterized by: The maximum included angle between the m measuring lines is greater than 60°.

4. The method of claim 1, wherein: The m measuring lines all pass through the center of the image plane.

5. The method for calibrating the interior orientation elements of a planar array camera for improved precise angle measurement method according to claim 1, characterized in that The normalization processing calculation formula is: x ij = (X ij - X0) / f y ij = (Y ij - Y0) / f.

6. The method for calibrating the interior orientation elements of a planar array camera for improved precise angle measurement method according to claim 1, characterized in that The theoretical calculation formula of the distorted projection coordinates (xd ij ,yd ij ) is: xd ij = xk ij + xp ij yd ij = yk ij + yp ij wherein xk ij , yk ij are the projections of the radial distortion of the measuring point T ij on the x-axis and y-axis; xp ij , yp ij are the projections of the decentration distortion of the measuring point T ij on the x-axis and y-axis, and the calculation formulas of xk ij , yk ij , xp ij , yp ij are respectively: xk ij = x ij × (k1 x r 2 + k2 x r 4 + k3 x r 6 ) yk ij = y ij x (k1 x r 2 + k2 x r 4 + k3 x r 6 ) xp ij = p2(r 2 + 2x ij 2 ) + 2p1x ij y ij yp ij = p1(r 2 + 2y ij 2 ) + 2p2x ij y ij Wherein, k1 is the first radial distortion model parameter, k2 is the second radial distortion model parameter, k3 is the third radial distortion model parameter, p1 is the first eccentric distortion model parameter, and p2 is the second eccentric distortion model parameter.

7. The method for calibrating the interior orientation elements of a planar array camera for improved precise angle measurement method according to claim 1, characterized in that The distortion correction residual v ij The calculation formula is: v ij = p ij - p i0 - Ht ij p ij = ((x ij + xd ij ) * f + X0) * cos(λ i - ((y ij + yd ij ) * f + Y0) * sin(λ i ) p i0 = X0*cos(λ i ) - Y0*sin(λ i ) 8. The method for calibrating the interior orientation elements of a planar array camera for improved precise angle measurement method according to claim 1, characterized in that: The error matrix is:

9. The method for calibrating the interior orientation elements of a planar array camera for improved precise angle measurement method according to any one of claims 1 or 2, characterized in that The nonlinear optimization solving algorithm is the LM nonlinear least square method.

10. The method for calibrating the interior orientation elements of a planar array camera for improved precise angle measurement according to any one of claims 1 or 2, characterized in that The nonlinear optimization solving algorithm is a genetic algorithm.

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