2D-DIC full-field deformation measurement method based on calibration plate thickness compensation

Abstract

The present invention relates to the field of non-contact image measurement technology. Specifically, it relates to a 2D-DIC full-field deformation measurement method based on calibration plate thickness compensation. Compared with the existing technology, the present invention more accurately describes the homography relationship between the measured surface and the pixel plane, thereby improving the measurement accuracy of 2D-DIC. At the same time, the present invention adopts a PnP algorithm that allows for non-ideal coplanarity of the calibration plate to solve the spatial posture of the calibration plate, which has better applicability than the existing method of solving extrinsic parameters through H matrix decomposition.

Description

Technical Field

[0001] The present invention relates to the technical field of non-contact image measurement, in particular to a 2D-DIC full-field deformation measurement method based on calibration plate thickness compensation. Background Art

[0002] Traditional 2D-DIC methods require the optical axis to be perpendicular to the surface being measured, or the optical axis tilt cannot exceed 5°. However, this is not always possible in actual measurements. Oblique optical axis measurement is the most widely used form of 2D-DIC. In this case, to achieve full-field deformation measurement, the homography relationship (H matrix) between the measured surface and the camera target surface must be solved. Zhang Zhengyou's calibration method is generally used. However, the presence of the calibration plate thickness means that the H matrix does not express the homography relationship between the measured surface and the image plane, but rather the relationship between the surface on which the calibration plate is located and the image plane. This introduces measurement errors, which can be ignored in long-distance measurements. However, in close-range experiments, this measurement error may be far greater than the sub-pixel matching error level, reducing the inherent full-field and high-precision measurement advantages of 2D-DIC, necessitating correction. However, this problem has not been addressed in current research. Summary of the Invention

[0003] The purpose of this paper is to propose a 2D-DIC full-field deformation measurement method based on calibration plate thickness compensation. The method corrects the homography matrix calibration error caused by the thickness of the calibration plate, making the final 2D-DIC-based full-field displacement conversion result more accurate. At the same time, since the spatial posture of the calibration plate is solved by the PnP technology, it has better tolerance for the non-ideal coplanarity of the calibration plate itself.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0005] A 2D-DIC full-field deformation measurement method based on calibration plate thickness compensation includes the following steps:

[0006] S1: Use Zhang Zhengyou’s method to calibrate the single camera intrinsic parameters and lens distortion parameters;

[0007] S2: Collect speckle calculation images before and after deformation. Using the initial calculation image as the reference image, set the calculation area ROI. Use the 2D-DIC method to match the deformed image sub-area with the reference image sub-image, thereby obtaining the pixel coordinates of each calculation point within the ROI range before and after deformation.

[0008] The corresponding position of the (2M+1)×(2M+1) rectangular image subregion centered at the query pixel point in the deformed image is confirmed in the reference image, and a widely used correlation function, the zero-normalized sum of squared differences, is used to evaluate the similarity between the reference subregion and the target subregion (Formula (1)); wherein f and g represent the grayscale values at the pixel point (x, y) of the reference subregion and the target subregion, respectively; M is the half-width of the subregion; ξ(x, y; p) is a shape function that describes the position and shape of the target subregion relative to the reference subregion, and the present invention uses a second-order shape function; in order to achieve fast and robust subregion matching, the present invention uses an inverse Gauss-Newton algorithm for optimization.

[0009]

[0010] Where:

[0011]

[0012]

[0013]

[0014] S3: Dedistort the pixel coordinates before and after deformation based on the distortion parameters calibrated in S1;

[0015] S4: Place the calibration plate close to the measured surface, ensuring that the length and width of the calibration plate are as consistent as possible with the horizontal and vertical displacement directions of the measured surface. Collect an image and use the PnP (Perspective-n-Point) method to calculate the spatial pose parameters [RT] of the calibration plate in the camera coordinate system based on the image.

[0016] S5: Correct the external parameter of the calibration plate to [R'T'] according to the thickness D of the calibration plate. The specific process is as follows;

[0017] Establish the world coordinates Xm-Ym-Zm on the measured surface, assuming that the world coordinates P of point P on the plane m (X m ,Y m ,0), establish the world coordinates XM-YM-ZM on the side, and the rotation and translation matrix R1T1 of point P from the XM-YM-ZM coordinate system to the Xw-Yw-Zw coordinate system is expressed as:

[0018]

[0019] Through the camera intrinsic parameter A and lens distortion parameter K (k1, k2, k3, k4, k5, k6, p1, p2), with the help of the PnP method, the rotation and translation matrix from the coordinate system Xw-Yw-Zw to the image optical center coordinate system is obtained as [R0T0]. Then the coordinates of point P in the optical center coordinate system can be expressed as:

[0020]

[0021] The intrinsic parameters and distortion parameters are solved by the calibration function provided by OpenCV. The distortion is applied in the normalized optical center coordinate system. The normalized coordinates of point P are:

[0022]

[0023] The coordinates taking into account lens distortion are:

[0024]

[0025] The corresponding pixel coordinates are:

[0026]

[0027] Obtaining (x', y') from (u, v) is a linear process, whereas obtaining (x', y') from (x', y') is a nonlinear iterative process. Here we directly use the undistortPoints function in OpenCV to solve it.

[0028] (x',y')=undistortPoints(u,v,A,K) (7)

[0029]

[0030] S6: Based on [R' T'], calculate the homography relationship matrix H' considering the thickness of the calibration plate. Through formula (3), formula (4) and formula (8), the regularized optical center coordinate system and the surface coordinate system of the measured structure can be represented by a homography matrix H':

[0031]

[0032] S7: Using H', the pixel coordinates of each calculation point in the ROI range before and after deformation are converted to world coordinates, and the displacement field is obtained by subtraction;

[0033] S8: Based on the displacement field obtained in S6, the strain field is fitted using the local least squares method.

[0034] Beneficial effects of the present invention: Compared with existing methods, the present invention can solve the measurement error caused by the thickness of the calibration plate during 2D-DIC full-field deformation measurement, so that the 2D-DIC measurement method has higher accuracy and a wider range of application. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Flowchart of the 2D-DIC full-field deformation measurement method of the present invention;

[0036] Figure 2 Schematic diagram of experimental details: (a) Equipment layout; (b) Schematic diagram of the dot-shaped calibration plate used; (c) Test surface pre-sprayed with random speckles; (d) Schematic diagram of the calibration plate thickness;

[0037] Figure 3 Test results: (a) Horizontal displacement measurement error caused by calibration plate thickness; (b) measurement error comparison. DETAILED DESCRIPTION

[0038] In order to deepen the understanding of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. The embodiments are only used to explain the present invention and do not limit the scope of protection of the present invention.

[0039] Example: Figure 1 As shown, a 2D-DIC full-field deformation measurement method based on calibration plate thickness compensation includes the following steps:

[0040] S1: The camera is set up in front of the structure to be measured, such as Figure 2 As shown in (a), the angle between the optical axis of the T camera and the measured surface is α≈28°, and the pitch angle is ignored. The distance between the measured surface and the camera is 60 cm. The industrial camera model used is IDSUI-3370CP-M-GL, with a resolution of 2048×2048 pixels and a pixel size of l ps =5.5μm, the focal length of the Kowa lens used is f=25mm. Figure 2 As shown in (b), the calibration plate used is a dot-shaped calibration plate with a spacing of 1 cm. Figure 2 As shown in (c), the surface being measured is pre-sprayed with random speckles to obtain better correlation matching using the digital image correlation method. The surface being measured is moved horizontally under the control of a translation stage with an accuracy of 0.01mm. The thickness of the calibration plate used is relatively thick, approximately 12mm.

[0041] S2: Use Zhang Zhengyou’s method to calibrate the single camera intrinsic parameters and lens distortion parameters;

[0042] S3: First, the speckle calculation images of the measured surface before and after the horizontal translation of 5mm are collected. The 2D-DIC method is used for image correlation matching to obtain the pixel coordinates before and after the deformation. The pixel coordinates are then dedistorted based on the distortion parameters calibrated in S2.

[0043] S4: Place the calibration plate close to the measured surface, ensuring that the length and width of the calibration plate are as consistent as possible with the horizontal and vertical displacement directions of the measured surface. Collect an image and use the Harris algorithm to detect the checkerboard corners. First, calculate the homography matrix H that ignores the effect of the calibration plate thickness.

[0044] S5: Then, the PnP (Perspective-n-Point) method is used to calculate the spatial attitude parameter [RT] of the calibration plate in the camera coordinate system, and the extrinsic parameter of the calibration plate is corrected to [R' T'] according to the thickness D of the calibration plate; based on [R' T'], the homography relationship matrix H' considering the thickness of the calibration plate is calculated;

[0045] S6: Use H' to convert the pixel coordinates of each calculation point in the ROI range before and after deformation into world coordinates, perform subtraction to obtain the displacement field as the displacement measurement value, and calculate the measurement error with the stage step as the true value. This will give the displacement measurement error when the calibration plate thickness is 12 mm.

[0046] S7: By manually adjusting the initial position of the measured surface, construct the effect of different calibration plate thicknesses, repeat S4 to S6, and continue to use the calculation diagram in S3. The displacement measurement error under different calibration thickness conditions is thus obtained and statistically analyzed. Figure 3 In (a), it can be seen that the greater the thickness of the calibration plate, the higher the error level;

[0047] S8: Further, the measured surface is translated horizontally, with each step being 1mm. The calibration diagram is collected when the thickness of the calibration plate is 12mm, and S4 to S5 are repeated.

[0048] S9: Use H and H' to transform the pixel coordinates of each calculation point in the ROI range before and after deformation into world coordinates, and perform the difference to obtain the displacement field. And calculate the measurement error of the displacement obtained by different homography matrices, such as Figure 3 As shown in (b), it can be seen that considering the influence of the thickness of the calibration plate can significantly reduce the displacement measurement error.

[0049] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A 2D-DIC full-field deformation measurement method based on calibration plate thickness compensation, characterized in that: The following steps are involved: S1: Use Zhang Zhengyou’s method to calibrate the single camera intrinsic parameters and lens distortion parameters; S2: Using the initial calculation image as the reference image, set the calculation area ROI, and use the 2D-DIC method to match the deformed image sub-area with the reference image sub-image, thereby obtaining the pixel coordinates of each calculation point within the ROI range before and after deformation; S3: Dedistort the pixel coordinates before and after deformation of the calculation point based on the distortion parameters calibrated in S1; S4: Place the calibration plate close to the measured surface, ensuring that the length and width of the calibration plate are consistent with the horizontal and vertical displacement directions of the measured surface. Collect an image and use the PnP method to calculate the spatial attitude parameters [RT] of the calibration plate in the camera coordinate system based on the image. S5: Correct the external parameter of the calibration plate to [R' T '] according to the thickness D of the calibration plate; S6: Calculate the homography relationship matrix H' considering the thickness of the calibration plate based on [R' T']; S7: Using H', the pixel coordinates of each calculation point before and after deformation in the ROI range after the dedistortion obtained in S3 are converted to world coordinates, and the displacement field is obtained by subtraction. S8: Based on the displacement field obtained in S6, the strain field is fitted by the local least squares method; In S5, the calibration plate external parameter is corrected to [R' T '] according to the calibration plate thickness D. The specific process is as follows: Establish the world coordinates Xm-Ym-Zm on the measured surface and set the world coordinates P of point P on the plane m (X m ,Y m ,0), establish the world coordinates XM-YM-ZM on the side, and the rotation and translation matrix R1T1 of point P from the XM-YM-ZM coordinate system to the Xw-Yw-Zw coordinate system is expressed as: Through the camera internal parameter A and lens distortion parameter K (k1, k2, k3, k4, k5, k6, p1, p2), with the help of PnP method, we can get the coordinate system X w -Y w -Z w The rotation and translation matrices to the optical center coordinate system are [R0T0], and the coordinates of point P in the optical center coordinate system are expressed as: The intrinsic parameters and distortion parameters are solved by the calibration function provided by OpenCV. The distortion is applied in the normalized optical center coordinate system. The normalized coordinates of point P are: The coordinates taking into account lens distortion are: The corresponding pixel coordinates are: Obtaining (x", y") from (u, v) is a linear change, while obtaining (x', y') from (x", y") is a nonlinear iterative process. We can directly use the undistortPoints function in OpenCV to solve it: (x',y')=undistortPoints(u,v,A,K) (7) Said S6, based on [R'T'], calculates the homography relationship matrix H' taking into account the thickness of the calibration plate. Through formula (3), formula (4) and formula (8), the regularized optical center coordinate system and the measured structure surface coordinate system can be represented by a homography matrix H':

2. The 2D-DIC full-field deformation measurement method based on calibration plate thickness compensation according to claim 1 is characterized in that: In S2, the corresponding position of the (2M+1)×(2M+1) rectangular image sub-region centered at the query pixel in the reference image is confirmed in the deformed image, and the zero-normalized sum of squared differences is used to evaluate the similarity between the reference sub-region and the target sub-region, as shown in the following formula: Where: Where f and g represent the grayscale values at the pixel point (x, y) of the reference subregion and the target subregion, respectively; M is the half-width of the subregion; (x, y; p) is the shape function that describes the position and shape of the target subregion relative to the reference subregion, which is optimized using the inverse Gauss-Newton algorithm.

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