CN115631237A - High-precision strain mode frequency domain digital image displacement field measurement method and system - Google Patents

High-precision strain mode frequency domain digital image displacement field measurement method and system Download PDF

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CN115631237A
CN115631237A CN202211267909.4A CN202211267909A CN115631237A CN 115631237 A CN115631237 A CN 115631237A CN 202211267909 A CN202211267909 A CN 202211267909A CN 115631237 A CN115631237 A CN 115631237A
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何玉明
韩世豪
雷剑
胡轶宇
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Huazhong University of Science and Technology
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Abstract

The invention discloses a high-precision strain mode frequency domain digital image displacement field measurement method and system, and belongs to the field of engineering measurement. Acquiring two images of the same object to be detected at the same position before and after deformation, and randomly selecting an analysis area from the two images; performing fast Fourier transform on gray values of pixel points in the two analysis regions to obtain a first transform result and a second transform result which represent the deformation of the object to be detected before and after; applying an incremental form shape function to the first transformation result, subtracting the second transformation result, carrying out conjugate multiplication with the second transformation result, summing to obtain a first function, carrying out first-order Taylor expansion on the airspace image corresponding to the modified first transformation result, and then carrying out first-order Taylor expansion on the airspace image to obtain an incremental deformation vector; and repeating for multiple times until the difference of all the quantities in the incremental deformation vectors obtained by two times of calculation is smaller than an allowable threshold value. According to the technical scheme provided by the invention, in the displacement field calculation result under the influence of strain, the calculation result is more accurate, and the measurement range is wider.

Description

High-precision strain mode frequency domain digital image displacement field measurement method and system
Technical Field
The invention belongs to the field of engineering measurement, and particularly relates to a high-precision strain mode frequency domain digital image displacement field measurement method and system.
Background
Measuring structural deformation to obtain mechanical properties of materials has been an important issue of concern for a large number of engineering and mechanical workers. In the mechanical behavior experiment of the material, the material is usually made into a standard sample, the deformation of the sample can be obtained by means of an extensometer, so that the mechanical property of the material can be calculated, a mechanical lever-type extensometer is used in the early stage, a strain-type extensometer is usually used at present, a sensitive deformation element is a cantilever beam made of an elastic material, the free end of the beam is a knife edge and is tightly fixed with a measured piece, a strain gauge for measuring the deformation is adhered to the beam, and the strain gauge comprises a metal resistance strain gauge and a semiconductor strain gauge. The former has a low sensitivity coefficient, and the latter has the disadvantages of non-linearity and large influence by temperature. And because they all adopt the contact measurement mode, will introduce many-sided error when using repeatedly many times, and application scope receives very big restriction. On the basis, a digital image correlation measurement method (airspace) is developed to measure the displacement and the strain of the surface of the material, and the method is widely applied to the fields of aerospace, electronic packaging, biomechanics and the like due to the characteristics of no damage, non-contact, strong environment adaptability and the like.
However, the current spatial domain digital image correlation method has certain limitations on measurement accuracy and measurement range, and when the deformation exceeds the measurement range, a strategy of segmented measurement is required, which causes an increase of accumulated errors and can cause a significant decrease of accuracy with the increase of the deformation. Compared with the spatial domain digital image correlation method, the frequency domain digital image correlation method has the advantages that the measurement precision under small deformation is improved by nearly one order of magnitude, the measurement range is improved by nearly 10 times, the segmented measurement times can be effectively reduced for large deformation measurement, and the precision is not obviously deteriorated along with the increase of deformation.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a high-precision strain mode frequency domain digital image displacement field measurement method and system, aiming at analyzing the deformation of an object by adopting an image processing technology to obtain the deformation of the object with higher precision on the premise of not contacting a component and not damaging the component.
In order to achieve the purpose, the invention provides a matching criterion for evaluating whether two images before and after deformation are matched in the frequency domain by analyzing the properties of the digital image in the frequency domain, and constructs an iterative function suitable for iteration according to the matching criterion, thereby providing an analysis method for obtaining the deformation of the object with high precision, which is used for obtaining the deformation of the object caused by self or external force. The adopted specific technical scheme comprises the following steps:
s1, shooting two images of the same object before and after deformation at the same position by using shooting equipment, wherein the two images at least comprise at least one same part of the object;
randomly selecting a rectangular analysis area in the same area of the same object in the two images respectively, wherein the shapes and the contained pixel numbers of the two analysis areas are the same, the initial coordinates of the pixels in the images and the terminal coordinates of the pixels in the two areas are also the same respectively, and expressing the relationship of the analysis areas in the two images before and after deformation in the following forms:
Figure BDA0003893810930000021
Figure BDA0003893810930000022
wherein, x and y are respectively global image coordinates, f is a gray matrix of an analysis area in the image before deformation and can be recorded as a reference image, and g is a gray matrix of the analysis area in the image after deformation and can be recorded as a target image;
Figure BDA0003893810930000023
for the deformation function, Δ x and Δ y are the local coordinates of the analysis area, p is the deformation vector, which can be written as p = [ u ] c u x u y v c v x v y ]Wherein u is c And v c For calculating the displacement of the center of the sub-region, u x ,u y ,v x ,v y For obtaining the first derivative of the displacement with respect to direction, i.e. strain, in particular
Figure BDA0003893810930000031
Figure BDA0003893810930000032
S2, performing fast Fourier transform on the gray values of the pixel points in the two areas in the step S1 respectively to obtain a first transform result before representing the deformation of the object and a second transform result after representing the deformation of the object, wherein the specific expression forms are as follows:
Figure BDA0003893810930000033
Figure BDA0003893810930000034
wherein F and G are the first and second transform results, respectively, u and v are the fourier transformed coordinates thereof, respectively, M is the pixel value of the selected square analysis area, for convenience of calculation and explanation, the same pixel length M is used and explained for x and y directions hereafter, and M is odd.
To improve the efficiency of the iterative computation, the first transformation result is changed as follows:
Figure BDA0003893810930000035
s3, subtracting the modified first transformation result from the second transformation result, multiplying the result by the conjugate of the function, and summing to obtain a first function W, wherein the specific expression form is as follows:
Figure BDA0003893810930000036
after the matching criterion of the image analysis area before and after the evaluation of the deformation and the iterative function which can be used for iteration are obtained, the frequency domain correlation algorithm and the iterative method can be combined, and the inverse synthetic Gaussian-Newton iterative method (IC-GN) which is most widely used in the correlation algorithm is adopted. The modified first transformation result corresponds to a spatial domain image
Figure BDA0003893810930000037
Performing a first order Taylor expansion to obtain:
Figure BDA0003893810930000041
Figure BDA0003893810930000042
wherein,
Figure BDA0003893810930000043
Figure BDA0003893810930000044
substituting the above three equations into the first function and deriving Δ p yields:
Figure BDA0003893810930000045
the method can be simplified to obtain:
Figure BDA0003893810930000046
where Δ p is the incremental deformation vector obtained in the ith iteration, p i-1 Is the total deformation vector after the i-1 th iteration and existsp i ＝p i-1 - Δ p. Note that p is the number of i iterations i-1 The second transformation result of the target image is not changed and the first transformation result of the reference image is changed in each iteration, but the initial value of each iteration is 0, and the calculated incremental deformation vector Δ p is used as the second transformation result of the target image before the next iteration, so that the first transformation result of the reference image is not changed actually because the initial value of each iteration is 0 although the first transformation result of the reference image is allowed to be changed in the whole iteration.
The gradient and Hessian matrix of the first transformation result are explained in detail here:
the Hessian matrix is obtained by gradient of the first transformation result, and the specific expression is as follows:
Figure BDA0003893810930000051
it should be noted in step S3 that since the initial value of IC-GN iteration is zero at the beginning of each iteration, the following relationship exists in the actual calculation:
Figure BDA0003893810930000052
that is, when the first transformation result is not changed in the whole iteration process, the iteratively calculated Δ p is inversely applied to the second transformation result, and the action form is as follows:
Figure BDA0003893810930000053
wherein, G (u, v) is a second transformation result of the integer pixel position corresponding to the gray matrix of the integer pixel position of the image G after deformation. After the gray matrix of the deformed image corresponding to the image before deformation is obtained through the second transformation result of the integer pixel position, the second transformation result for iterative computation in the step S3 can be obtained through fast fourier transformation:
Figure BDA0003893810930000054
and S4, repeating the step S3 for multiple times until the difference of all the quantities in the incremental deformation vector delta p obtained by two times of calculation is smaller than an allowable threshold value.
The method of the invention considers that the object causes nonlinear displacement of the surface due to deformation, and the surface of the object has a plurality of tiny characteristic points which move along with the displacement of the surface. At present, an analysis method in a frequency domain cannot accurately calculate a displacement field with strain, and is often used for initial value calculation. By improving the digital image frequency domain correlation method, the problem of inaccurate calculation of the displacement field under the influence of strain can be solved, so that the calculation accuracy of the digital image frequency domain correlation method is greatly improved.
Through the technical scheme, compared with the prior art, the method aims to analyze the frequency domain of the digital image before and after deformation, and is contrary to the existing algorithm for calculating in a space domain, the method utilizes the property of Fourier transform to calculate the gradient of the image and calculate the displacement and the strain in the frequency domain, avoids interpolation errors caused by interpolation by adopting the Fourier transform, improves the precision of displacement and strain analysis, and expands the strain measurement range of the digital image visual deformation measurement technology. According to the technical scheme provided by the invention, in the displacement field calculation result under the influence of strain, the calculation result is more accurate, and the measurement range is wider.
Drawings
FIG. 1 is a flow chart of a high-precision strain mode frequency domain digital image displacement field measurement method provided by the invention;
fig. 2 (a) and 2 (b) are speckle patterns of the same positions before and after deformation, respectively, obtained by using a MATLAB software program in the example of the present invention.
Fig. 3 is a graph of spectral peaks between a pre-warped image and an original warped image.
FIG. 4 is a graph of the peak of the spectrum between the image obtained by correcting the deformed image by the method of the present invention and the image before deformation.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, the method is implemented as follows:
1) The simulation experiment was performed using 2D-Challenge 1.0sample 6 series images provided by the international DIC Challenge committee, fig. 2 (a) being a photograph of a speckle part before deformation and fig. 2 (b) being a photograph of a speckle part after deformation, the two images including the same part, i.e., the speckle part.
2) And respectively and randomly selecting analysis areas in the areas near the speckles in the two images, wherein the two analysis areas are the same in shape and are both square, and the number of pixels contained in the two areas is also the same. In this embodiment, the initial coordinates of the selected pixel points in the image before and after deformation are both (20, 20), the coordinates of the selected pixel points are both (60, 60), and the size of the analysis area is both 41 × 41.
3) Fast Fourier transform is respectively carried out on gray values of pixel points in the two regions to respectively obtain a first transform result before object deformation and a second transform result after object deformation, wherein the first transform result is an exponential function F (u, v), and the second transform result is an exponential function G (u, v; p), two exponential functions are respectively as follows:
Figure BDA0003893810930000071
Figure BDA0003893810930000072
wherein f (x, y) represents the gray value at the corresponding point (x, y) before deformation, and g (x, y; p) represents the corresponding point after deformation
Figure BDA0003893810930000073
The gray value of (b). M is the number of pixels in the x and y directions of the selected square analysis region, x and y are the spatial coordinates of the gray values of the image,
Figure BDA0003893810930000074
and
Figure BDA0003893810930000075
the displacement of the pixel point in the x direction and the y direction is caused by deformation, and u and v are coordinates after Fourier transformation. And then subtracting the second transformation result, multiplying the result by self conjugate, and summing to obtain a first function W, wherein the first function is modified by applying an IC-GN iterative method to obtain a specific expression form as follows:
Figure BDA0003893810930000081
4) The spatial domain image corresponding to the first transformation result
Figure BDA0003893810930000082
Performing a first order Taylor expansion to obtain:
Figure BDA0003893810930000083
bringing it into W (Δ p) and taking the derivative of Δ p yields:
Figure BDA0003893810930000084
the method is characterized by comprising the following steps:
Figure BDA0003893810930000085
it should be noted that 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 of the setpoint:
Figure BDA0003893810930000091
and the expression of the second transformation result is:
Figure BDA0003893810930000092
and G (u, v) is a second transformation result of the integer pixel position corresponding to the gray matrix of the integer pixel position of the image G after deformation. After the gray matrix of the deformed image corresponding to the image before deformation is obtained through the second transformation result of the integral pixel position, the second transformation result for iterative computation can be obtained through fast Fourier transformation:
Figure BDA0003893810930000093
5) Repeating the step 4) for multiple times until the calculated value of the delta p is smaller than the allowable threshold value, and adding the delta p obtained by multiple iterations to obtain a final result.
6) And reserving the displacement and strain results obtained by the iterative calculation as initial values of the iteration when the seeds are used for the calculation of the next point. So far we have obtained the displacement and strain due to the deformation of the object.
In this example, the simulated speckle pattern is given by a 10% positive strain magnitude in the x-direction, no strain in the y-direction, and no shear strain. The spectrograms of the pre-distorted image and the original distorted image are shown in fig. 3. The frequency spectrum of the image after the modification of the deformed image and the frequency spectrum of the image before the deformation are shown in fig. 4. The results obtained in step 5) and step 6) were (2, 9.98e-04,0.1, -2.38e-05, -1.12e-04, -4.06 e-05) with an error of (1.55 e-05,9.98e-04,3.15e-05, -2.38e-05, -1.12e-04, -4.06 e-05).
It will be understood by those skilled in the art that the foregoing is only an exemplary embodiment of the present invention, and is not intended to limit the invention to the particular forms disclosed, since various modifications, substitutions and improvements within the spirit and scope of the invention are possible and within the scope of the appended claims.

Claims (10)

1. A high-precision strain mode frequency domain digital image displacement field measurement method is characterized by comprising the following steps:
s1, obtaining two images of the same object to be detected at the same position before and after deformation, and respectively and randomly selecting an analysis area in the areas of the same part of the object to be detected in the two images;
s2, performing fast Fourier transform on the gray values of the pixel points in the two analysis areas to obtain a first transform result before representing the deformation of the object to be detected and a second transform result after representing the deformation of the object;
s3, applying an incremental form shape function to the first transformation result, subtracting the modified first transformation result from the second transformation result, conjugate multiplying the modified first transformation result by the modified first transformation result, summing to obtain a first function W, performing first-order Taylor expansion on the airspace image corresponding to the modified first transformation result, and then bringing the airspace image into the first function W to obtain an incremental deformation vector;
and S4, repeating the step S3 for multiple times until the difference of all the quantities in the incremental deformation vectors obtained by two times of calculation is smaller than an allowable threshold value.
2. The measurement method according to claim 1, wherein the shape and the number of pixels included in the two analysis regions in S1 are the same, and the start coordinates and the end coordinates of the two analysis regions in the two images are also the same, respectively, and the relationship between the analysis regions in the two images before and after the deformation is expressed as follows:
Figure FDA0003893810920000011
Figure FDA0003893810920000012
wherein x and y are respectively global image coordinates, f (x, y) is a gray matrix of an analysis area in the image before deformation and is recorded as a reference image, and g (x, y) is a gray matrix of the analysis area in the image after deformation and is recorded as a target image;
Figure FDA0003893810920000013
for the deformation function, Δ x and Δ y are the local coordinates of the analysis area, p is the deformation vector, which can be written as p = [ u ] c u x u y v c v x v y ]Wherein u is c And v c For analyzing the amount of displacement of the center of the region, u x ,u y ,v x ,v y For the first derivative of the displacement with respect to direction, i.e. strain, to be determined, in particular
Figure FDA0003893810920000021
Figure FDA0003893810920000022
3. The measurement method according to claim 2, wherein the first transformation result F and the second transformation result G in S2 are expressed in the following forms:
Figure FDA0003893810920000023
Figure FDA0003893810920000024
where u and v are the fourier transformed coordinates thereof, respectively, and M is the pixel value of the selected analysis region.
4. The measurement method according to claim 3, wherein the modified first transformation result is embodied in the form:
Figure FDA0003893810920000025
5. the measurement method according to claim 4, wherein the first function W is expressed as follows:
Figure FDA0003893810920000026
6. the measurement method according to claim 4, wherein the incremental deformation vector is expressed in the following form:
Figure FDA0003893810920000027
Figure FDA0003893810920000031
where Δ p is the incremental deformation vector obtained in the ith iteration, p i-1 Is the total deformation vector after the i-1 th iteration and p is present i ＝p i-1 - Δ p.
7. The measurement method according to claim 6, wherein the iteratively calculated Δ p is applied back to the second transformation result in the form:
Figure FDA0003893810920000032
wherein G (u, v) is a second transformation result of the integer pixel position corresponding to the gray matrix of the integer pixel position of the image G after the deformation.
8. The measurement method according to claim 1, wherein the shape of the selected analysis area in S1 is rectangular, and further preferably square.
9. A method of measurement according to claim 3, wherein M is an odd number.
10. A high-precision strain mode frequency domain digital image displacement field measurement system is characterized by comprising: a computer-readable storage medium and a processor;
the computer-readable storage medium is used for storing executable instructions;
the processor is used for reading executable instructions stored in the computer readable storage medium and executing the high-precision strain mode frequency domain digital image displacement field measurement method of any one of claims 1 to 9.
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