A high-precision strain mode frequency domain digital image displacement field measurement method and system

Abstract

The present invention discloses a high-precision strain mode frequency domain digital image displacement field measurement method and system, which belongs to the field of engineering measurement. It includes obtaining two images of the same object to be measured at the same position before and after deformation, and randomly selecting an analysis area in the two images; performing fast Fourier transform on the grayscale values ​​of the pixels in the two analysis areas to obtain the first and second transformation results representing the object to be measured before and after deformation; applying an incremental shape function to the first transformation result, subtracting it from the second transformation result and multiplying it with its own conjugate, and then summing them to obtain the first function; performing a first-order Taylor expansion on the spatial domain image corresponding to the modified first transformation result and bringing it into the first function to obtain an incremental deformation vector; repeating the process multiple times until the difference between all quantities in the incremental deformation vectors obtained by the two calculations is less than the allowable threshold. The technical solution proposed by the present invention has more accurate calculation results and a wider measurement range in the calculation of displacement fields under the influence of strain.

Description

Technical Field

[0001] The present invention belongs to the field of engineering measurement, and more specifically, relates to a high-precision strain mode frequency domain digital image displacement field measurement method and system. Background Art

[0002] Measuring structural deformation to determine the mechanical properties of materials has long been a crucial topic of interest to engineers and mechanics. In mechanical behavior experiments, standard specimens are typically prepared and extensometers are used to measure the specimen deformation, thereby calculating the material's mechanical properties. Early mechanical lever extensometers were used, but strain gauge extensometers are now commonly used. The sensitive deformation element is a cantilever beam made of elastic material. The free end of the beam is indented and tightly bonded to the test piece. Strain gauges for measuring deformation are attached to the beam. Strain gauges come in two types: metallic resistance strain gauges and semiconductor strain gauges. The former has a low sensitivity coefficient, while the latter suffers from nonlinearity and significant temperature dependence. Furthermore, because both employ contact measurement, repeated use can introduce various errors, significantly limiting their applicability. Based on this, digital image correlation (spatial domain) has been developed to measure displacement and strain on material surfaces. Due to its non-destructive, non-contact nature and strong environmental adaptability, this method has found widespread application in fields such as aerospace, electronic packaging, and biomechanics.

[0003] However, existing spatial-domain digital image correlation methods have certain limitations in measurement accuracy and range. When deformation exceeds the range, a segmented measurement strategy is required, which results in an increase in cumulative error and a significant decrease in accuracy as deformation increases. The introduction of the frequency-domain digital image correlation method has greatly improved this situation. Compared with the spatial-domain digital image correlation method, the frequency-domain digital image correlation method improves measurement accuracy under small deformation by nearly an order of magnitude and increases the measurement range by nearly 10 times. For measurements of large deformations, the number of segmented measurements can be effectively reduced, and there is no significant deterioration in accuracy as deformation increases. Summary of the Invention

[0004] In response to the shortcomings of the existing technology, the purpose of the present invention is to provide a high-precision strain mode frequency domain digital image displacement field measurement method and system, aiming to use image processing technology to analyze the deformation of the object and obtain a more accurate object deformation value without contacting the component and causing damage to the component.

[0005] To achieve the above objectives, the present invention analyzes the properties of digital images in the frequency domain and proposes a matching criterion for evaluating the matching of two images before and after deformation in the frequency domain. Based on this matching criterion, an iterative function suitable for iteration is constructed, thereby providing a high-precision analytical method for obtaining the amount of deformation of an object, which is used to obtain the amount of deformation caused by the object itself or by external forces. The specific technical solution adopted includes the following steps:

[0006] S1. Using a camera to capture two images of the same object before and after deformation at the same location, wherein the two images include at least one identical portion of the object;

[0007] A rectangular analysis region is randomly selected from the same part of the same object in the two images. The two analysis regions have the same shape and number of pixels, and the starting and ending pixel coordinates of the two regions in the images are also the same. The relationship between the analysis regions in the two images before and after deformation is expressed in the following form:

[0008]

[0009]

[0010] Among them, x and y are the global image coordinates, f is the grayscale matrix of the analysis area in the image before deformation, which can be recorded as the reference image, and g is the grayscale matrix of the analysis area in the image after deformation, which can be recorded as the target image; is the deformation function, Δx and Δy are the local coordinates of the analysis area, and p is the deformation vector, which can be written as p=[u c u x u y v c v x v y ], where u c and v c To calculate the displacement of the sub-region center, u x ,u y ,v x ,v y is the first-order derivative of the displacement with respect to the direction, namely the strain, specifically

[0011] S2. Perform fast Fourier transform on the grayscale values ​​of the pixels in the two regions in step S1, respectively, to obtain a first transformation result representing the object before deformation and a second transformation result representing the object after deformation, specifically expressed as follows:

[0012]

[0013]

[0014] Wherein, F and G are the first transformation result and the second transformation result, respectively, u and v are the coordinates after Fourier transformation, and M is the pixel value of the selected square analysis area. For the convenience of calculation and explanation, the same pixel length M is used in both the x and y directions, and M is used and explained as an odd number.

[0015] To improve the efficiency of iterative calculation, the first transformation result is changed as follows:

[0016]

[0017] S3. Subtract the modified first transformation result from the second transformation result, multiply the result by its own conjugate, and then sum to obtain the first function W, which is specifically expressed as follows:

[0018]

[0019] With the matching criteria for evaluating the image analysis area before and after deformation and the iterative function that can be used for iteration, the frequency domain correlation algorithm can be combined with the iterative method. Here, the most widely used in the correlation algorithm is the inverse synthetic Gauss-Newton iteration method (IC-GN). The spatial domain image corresponding to the modified first transformation result is converted into Performing a first-order Taylor expansion yields:

[0020]

[0021]

[0022] in,

[0023]

[0024]

[0025] Substituting the above three equations into the first function and taking the derivative of Δp, we can obtain:

[0026] By simplifying we can get:

[0027]

[0028] Where Δp is the incremental deformation vector obtained in the i-th iteration, p i-1 is the total deformation vector after the i-1th iteration, and there exists p i =p i-1 -Δp. It should be noted that, since p i-1is a known quantity, so the second transformation result of the target image does not change during each iteration, while the first transformation result of the reference image changes. However, the initial value of each iteration is 0, and the calculated incremental deformation vector Δp ​​will act on the second transformation result of the target image before the next iteration. Therefore, during the entire iteration process, although the first transformation result of the reference image is allowed to change, in fact, the first transformation result of the reference image does not change because the initial value of each iteration is 0.

[0029] Here we explain in detail the gradient and Hessian matrix of the first transformation result:

[0030] The Hessian matrix is ​​obtained through the gradient of the first transformation result. The specific expression is as follows:

[0031]

[0032] It should be noted that in step S3, since the initial value of the IC-GN iteration is zero at the beginning of each iteration, the following relationship exists in the actual calculation:

[0033]

[0034] That is, when the first transformation result does not change during the entire iterative process, the Δp obtained by iterative calculation is reversely applied to the second transformation result, and the effect is as follows:

[0035]

[0036] Where G(u,v) is the second transformation result at the integer pixel position corresponding to the grayscale matrix at the integer pixel position of the deformed image g. After obtaining the grayscale matrix of the deformed image corresponding to the pre-deformed image through the second transformation result at the integer pixel position, the second transformation result used for iterative calculation in step S3 can be obtained through fast Fourier transform:

[0037]

[0038] S4. Repeat step S3 multiple times until the difference between all the quantities in the incremental deformation vector Δp ​​calculated twice is less than the allowable threshold.

[0039] The method of the present invention considers that deformation of an object causes nonlinear surface displacement, and that the object's surface has many tiny feature points that move with the surface displacement. Current analysis methods in the frequency domain are unable to accurately calculate the displacement field in the presence of strain and are often used for initial value calculations. The present invention improves the digital image frequency domain correlation method, thereby remedying the inaccurate displacement field calculations in the presence of strain, significantly improving the computational accuracy of the digital image frequency domain correlation method.

[0040] The above technical solution conceived by the present invention, compared with the existing technology, aims to analyze the frequency domain of digital images before and after deformation. In contrast to the current algorithm that performs calculations in the spatial domain, the Fourier transform is used to calculate the gradient of the image and the displacement and strain in the frequency domain by utilizing the properties of the Fourier transform. The Fourier transform is used to avoid interpolation errors caused by interpolation, thereby improving the accuracy of displacement and strain analysis and expanding the strain measurement range of digital image visual deformation measurement technology. The technical solution proposed by the present invention has more accurate calculation results and a wider measurement range in the calculation of displacement fields under the influence of strain. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a flow chart of the high-precision strain pattern frequency domain digital image displacement field measurement method provided by the present invention;

[0042] FIG. 2( a ) and FIG. 2( b ) are speckle patterns at the same position before and after deformation obtained by programming using MATLAB software in an example of the present invention.

[0043] Figure 3 It is the spectrum peak map between the image before deformation and the original deformed image.

[0044] Figure 4 A spectrum peak diagram between an image obtained by correcting a deformed image using the method of the present invention and the image before deformation. DETAILED DESCRIPTION

[0045] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0046] like Figure 1 As shown, the specific implementation process of this method is as follows:

[0047] 1) A simulation experiment was conducted using a series of 2D-Challenge 1.0 sample 6 images provided by the International DIC Challenge Committee. Figure 2(a) shows a photograph of the speckle portion before deformation, and Figure 2(b) shows a photograph of the speckle portion after deformation. Both images include the same portion, i.e., the speckle portion.

[0048] 2) Randomly select analysis regions within the area near the speckle in both images. The two analysis regions are identical in shape, both being squares, and contain the same number of pixels. In this embodiment, the starting pixel coordinates for both the pre- and post-deformation images are (20, 20), the ending pixel coordinates are (60, 60), and the analysis region size is 41×41.

[0049] 3) Perform fast Fourier transform on the grayscale values ​​of the pixels in the two regions, respectively, to obtain a first transform result representing the object before deformation and a second transform result representing the object after deformation. The first transform result is the exponential function F(u,v), and the second transform result is the exponential function G(u,v;p). The two exponential functions are shown as follows:

[0050]

[0051]

[0052] Among them, f(x,y) represents the gray value of the corresponding point (x,y) before deformation, and g(x,y;p) represents the gray value of the corresponding point after deformation. M is the number of pixels in the x and y directions of the selected square analysis area, and x and y are the spatial coordinates of the image grayscale value. and where x and y are the displacements of the pixel point due to deformation, respectively. u and v are the coordinates after Fourier transformation. The result of subtracting the result from the second transformation is then multiplied by its own conjugate and summed to obtain the first function W. The specific expression of the first function after applying the IC-GN iterative method to correct it is as follows:

[0053]

[0054] 4) The spatial domain image corresponding to the first transformation result Performing a first-order Taylor expansion yields:

[0055]

[0056] Substituting it into W(Δp) and taking the derivative with respect to Δp, we can obtain:

[0057]

[0058] By simplifying we can get:

[0059]

[0060] It should be noted that since the initial value of IC-GN iteration is zero at the beginning of each iteration, the following relationship exists when actually calculating the selected points:

[0061]

[0062] The expression of the second transformation result is:

[0063]

[0064] Where G(u,v) is the second transformation result of the integer pixel position corresponding to the grayscale matrix of the integer pixel position of the deformed image g. After obtaining the grayscale matrix of the deformed image corresponding to the undeformed image through the second transformation result of the integer pixel position, the second transformation result for iterative calculation can be obtained through fast Fourier transform:

[0065]

[0066] 5) Repeat step 4) multiple times until the calculated value of Δp is less than the allowable threshold, and add up the Δp obtained from multiple iterations to obtain the final result.

[0067] 6) The displacement and strain results obtained from this iteration are saved as seeds for the initial values ​​of the next iteration. At this point, we have obtained the displacement and strain caused by the deformation of the object.

[0068] In this embodiment, the simulated speckle pattern is given a 10% normal strain in the x-direction, no strain in the y-direction, and no shear strain. The spectrum of the image before deformation and the original image after deformation is shown in the figure. Figure 3 As shown. The spectrum of the image after the deformation is corrected and the spectrum of the image before the deformation are as follows Figure 4 The calculation results obtained by steps 5) and 6) are (2, 9.98e-04, 0.1, -2.38e-05, -1.12e-04, -4.06e-05), and the errors are (1.55e-05, 9.98e-04, 3.15e-05, -2.38e-05, -1.12e-04, -4.06e-05).

[0069] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A high-precision strain pattern frequency domain digital image displacement field measurement method, characterized in that: The following steps are involved: S1. Obtain two images of the same object to be measured at the same position before and after deformation, and randomly select an analysis area within the same portion of the object to be measured in the two images; S2. Performing a fast Fourier transform on the grayscale values ​​of the pixels in the two analysis areas to obtain a first transformation result representing the object to be measured before deformation and a second transformation result representing the object after deformation; a first transformation result F and the second transformation result G The specific expressions are as follows: in, x and y are the global image coordinates, is the grayscale matrix of the analysis area in the image before deformation, recorded as the reference image, is the grayscale matrix of the analysis area in the deformed image, recorded as the target image, is the deformation function, and are the local coordinates of the analysis area, is the deformation vector, u and v are their Fourier transformed coordinates, M is the pixel value of the selected analysis area; S3. Applying an incremental shape function to the first transformation result, subtracting the modified first transformation result from the second transformation result and multiplying it by its own conjugate to obtain a first function W , perform first-order Taylor expansion on the spatial domain image corresponding to the modified first transformation result and bring it into the first function W , get the incremental deformation vector; S4. Repeat step S3 multiple times until the difference between all quantities in the incremental deformation vectors calculated twice is less than the allowable threshold.

2. The measuring method according to claim 1, wherein The two analysis regions in S1 have the same shape and the same number of pixels. The starting and ending coordinates of the two analysis regions in the two images are also the same. The relationship between the analysis regions in the two images before and after deformation is expressed as follows: in, , and To analyze the displacement of the center of the region, is the first-order derivative of the displacement with respect to the direction, namely the strain, specifically , , , .

3. The measuring method according to claim 2, characterized in that The modified first transformation result is specifically expressed as follows: 。 4. The measuring method according to claim 3, characterized in that First function W The specific expression is as follows: 。 5. The measuring method according to claim 3, characterized in that The specific expression of the incremental deformation vector is as follows: in, It is i The incremental deformation vector obtained by the iteration, For the i -The total deformation vector after 1 iteration, and there is relationship.

6. The measuring method according to claim 5, characterized in that The iterative calculation The reverse action is applied to the second transformation result, as shown below: in, The deformed image The second transformation result of the integer pixel position corresponding to the grayscale matrix of the integer pixel position.

7. The measuring method according to claim 1, wherein: The shape of the analysis area selected in S1 is a rectangle.

8. The measuring method according to claim 1, wherein: M An odd number.

9. A high-precision strain mode frequency domain digital image displacement field measurement system, characterized in that: include: Computer-readable storage medium and processor; The computer-readable storage medium is used to store executable instructions; The processor is configured to read the executable instructions stored in the computer-readable storage medium and execute the high-precision strain pattern frequency domain digital image displacement field measurement method according to any one of claims 1 to 8.

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