CN110033435B - High-sensitivity digital image displacement frequency domain analysis method - Google Patents

High-sensitivity digital image displacement frequency domain analysis method Download PDF

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CN110033435B
CN110033435B CN201910166269.XA CN201910166269A CN110033435B CN 110033435 B CN110033435 B CN 110033435B CN 201910166269 A CN201910166269 A CN 201910166269A CN 110033435 B CN110033435 B CN 110033435B
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何玉明
韩世豪
杨凯
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Huazhong University of Science and Technology
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Abstract

The invention belongs to the field of engineering measurement, and particularly discloses a high-sensitivity digital image displacement frequency domain analysis method. The method comprises obtaining analysis regions of the image before and after deformation, and transforming the gray value of its pixel to obtain a first transformation result and a second transformation resultAnd obtaining a transformation result by calculating a first function and a corresponding frequency spectrum matrix W (xi, eta), wherein the coordinate of the maximum value of the frequency spectrum matrix W (xi, eta) is integer pixel displacement, and combining a generalized upsampling technology to obtain the frequency spectrum matrix W with the size of m multiplied by m with a preset step length as an interval and with the total displacement of the previous iteration as a center1(xi ', η') then for the spectral matrix W1(xi ', eta') performing surface fitting, wherein the distance between the maximum value coordinate of the surface and the central point coordinate of the matrix is the sub-pixel displacement of the current iteration, and repeating the calculation until the difference of the total displacement is smaller than an allowable threshold. According to the method, a spectrum matrix of a certain part is analyzed through a generalized upsampling technology, so that the calculation efficiency can be improved, and the calculation sensitivity can be greatly improved.

Description

High-sensitivity digital image displacement frequency domain analysis method
Technical Field
The invention belongs to the field of engineering measurement, and particularly relates to a high-sensitivity digital image displacement frequency domain analysis method.
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, and then the deformation of the sample is obtained by means of an extensometer, so that the mechanical property of the material is calculated.
Early tests were conducted primarily using mechanical lever extensometers, and strain extensometers are now commonly used. The strain extensometer has a sensitive deformation element which is a cantilever beam made of elastic material, a strain gauge for measuring deformation is adhered on the beam, and the strain gauge is divided into a metal resistance strain gauge and a semiconductor strain gauge, wherein the sensitivity coefficient of the former is lower, and the sensitivity coefficient of the latter has the defects of nonlinearity and large influence of temperature. And because they all adopt the contact measurement mode, will introduce many-sided error when using repeatedly many times, and receive very big restriction in the aspect of the application scope.
Therefore, a non-contact digital image measuring method is available, but at present, digital image measurement is only suitable for measuring a large moving distance. Due to errors in the space domain method and the frequency domain method, the measurement precision and sensitivity reach a bottleneck, and the measurement of micro deformation cannot be realized.
Disclosure of Invention
In view of the above-mentioned shortcomings and/or needs of the prior art, the present invention provides a high-sensitivity digital image displacement frequency domain analysis method, in which an upsampling technique is adopted and improved, and accordingly, the calculation efficiency and sensitivity can be improved, and thus, the method is particularly suitable for applications such as micro-deformation measurement.
In order to achieve the above object, the present invention provides a high-sensitivity digital image displacement frequency domain analysis method, which is characterized in that the method comprises the following steps:
(a) shooting two images of the same object before and after deformation at the same position by utilizing shooting equipment, and then respectively selecting an analysis area in the same part of the two images;
(b) obtaining a first transformation result before object deformation and a second transformation result after object deformation according to the gray values of pixels in the two selected analysis areas, and obtaining a first function and a frequency spectrum matrix W (xi, eta) corresponding to the first function through calculation, wherein the coordinate of the maximum value of the frequency spectrum matrix W (xi, eta) is the integral pixel displacement (U) caused by object deformation1,V1)；
(c) Obtaining the total displacement (U) of the above iteration through the first function3 n-1,V3 n-1) Centered on a m × m-sized spectrum matrix W with a predetermined step size as an interval1(xi ', η') for the spectral matrix W1(xi ', eta') fitting the curved surface to obtain a fitting equation, determining the maximum value coordinate of the curved surface by solving the extreme point of the fitting equation, wherein the distance between the maximum value coordinate and the coordinate of the central point of the matrix is the sub-pixel displacement (U) of the current iteration caused by the deformation of the object2 n,V2 n)；
(d) Obtaining a sub-pixel displacement (U) for the current iteration based on step (c)2 n,V2 n) And the integer pixel displacement (U) obtained in step (b)1,V1) Obtain the total displacement (U) of the current iteration3 n,V3 n) And with the total displacement (U) of the current iteration3 n,V3 n) Iterating as a center to obtain the sub-pixel displacement (U) of the next iteration2 n+1,V2 n+1) To obtain the total displacement (U) of the next iteration3 n+1,V3 n +1)；
(e) Comparing the total displacement (U) of the current iteration3 n,V3 n) Total displacement (U) from next iteration3 n+1,V3 n+1) Whether the difference is less than an allowable threshold, if so, outputting a total displacement caused by the deformation of the object, and if not, outputting a total displacement (U) according to the next iteration3 n+1,V3 n+1) The iteration continues.
As a further preference, the shape of the analysis region selected in the step (a) is a rectangle, and further preference is given to a square.
As a further preference, said step (b) comprises the sub-steps of:
(i) carrying out fast Fourier transform on the gray values of the pixels in the analysis area before and after deformation to obtain a first transform result F before deformation of the object1(u, v) are:
Figure BDA0001986388640000031
second transformation result F after deformation of the object2(u, v) are:
Figure BDA0001986388640000032
wherein u and v are the Fourier transformed coordinates, M is the pixel value of the analysis region in the x-direction or y-direction, and f1(x, y) is the gray matrix of the analysis area before deformation, j is the imaginary unit, dx and dy are the integer pixel displacements in the x-direction or y-direction respectively due to deformation;
(ii) converting the first conversion result F1(u, v) and the second transformation result F2(u, v) are multiplied and then transformed to obtain a first function I (u, v) as:
Figure BDA0001986388640000033
(iii) performing fast Fourier transform on the first function I (u, v) and moving a zero frequency to the center of a matrix to obtain a frequency spectrum matrix W (xi, eta) corresponding to the first function, wherein the frequency spectrum matrix W (xi, eta) is as follows:
W(ξ,η)＝δ(ξ-dx,η-dy) (4)
in the formula, xi and eta are coordinates of the frequency spectrum matrix W, and the value range is
Figure BDA0001986388640000034
δ is the dirac function.
As a further preference, the spectral matrix W in said step (c)1(ξ ', η') are:
Figure BDA0001986388640000035
where ξ 'and η' are preferred
Figure BDA0001986388640000036
To any value of (a).
More preferably, m in the step (c) is preferably greater than or equal to 3.
More preferably, m in the step (c) is set to 3.
As a further preference, the allowable threshold in said step (e) is less than 1% of the measurement sensitivity.
Generally, compared with the prior art, the above technical solution conceived by the present invention mainly has the following technical advantages:
1. the invention carries out discrete Fourier transform on the first function by the generalized upsampling technology and obtainsM × m spectrum matrix W centered on the total displacement of the previous iteration1(xi ', eta') and then calculating to obtain sub-pixel displacement, the invention only needs to analyze the frequency spectrum matrix of a certain interested part, thereby avoiding the problem that the traditional upsampling technology needs to carry out large-scale zero padding on the whole image for calculation, improving the calculation efficiency, reducing a large amount of redundant calculation, breaking the fence effect and greatly improving the calculation sensitivity;
2. particularly, the value of m obtained by multiple calculations is preferably m is more than or equal to 3, and the improvement of the precision and the sensitivity by improving m is almost zero, but the calculation efficiency is poor, so that the calculation precision and the sensitivity can be ensured and the calculation efficiency can be improved when m is 3;
3. meanwhile, when the surface displacement is caused by the deformation of the object, the tiny characteristic points on the surface of the object can move along with the surface displacement, and the displacement of the object caused by the deformation can be obtained by calculating the whole pixel displacement and the sub-pixel displacement by utilizing the characteristic, so that the displacement of the object caused by the deformation can be accurately obtained.
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FIG. 1 is a flow chart of a high sensitivity digital image displacement frequency domain analysis method provided by the present invention;
FIG. 2a is a speckle pattern of the same location before deformation obtained by using MATLAB software programming in the preferred embodiment of the present invention;
FIG. 2b is a schematic diagram of the deformed speckle pattern at the same position obtained by using MATLAB software program in the preferred embodiment of the present invention
FIG. 3 is a graph of the spectrum of the first function obtained in step (b) in the preferred embodiment of the present invention;
FIG. 4 is the maximum point of the curved surface obtained in step (e) in the preferred embodiment of the present invention.
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 present invention provides a high-sensitivity digital image displacement frequency domain analysis method, which includes the following steps:
(a) shooting two images of the same object before and after deformation at the same position by utilizing a shooting device, wherein the two images at least comprise one same part of the object, then randomly selecting an analysis area in the area of the same part of the same object in the two images respectively, the shapes and the contained pixel numbers of the two analysis areas are the same, and the initial coordinates and the terminal coordinates of the pixels of the two analysis areas in the respective images are the same respectively, so that the shape of the analysis area is preferably rectangular and is further preferably square for improving the calculation efficiency;
(b) respectively carrying out fast Fourier transform on the gray values of the pixels in the two selected analysis areas to obtain a first transform result before the deformation of the object and a second transform result after the deformation of the object, wherein the first transform result F is1(u, v) are:
Figure BDA0001986388640000051
second transformation result F2(u, v) are:
Figure BDA0001986388640000052
wherein u and v are the Fourier transformed coordinates, respectively, M is the pixel value of the analysis region in the x-direction or the y-direction, and M is used and explained as an odd number for the convenience of calculation, f1(x, y) is the gray matrix of the analysis area before deformation, f2(x, y) is the gray matrix of the analysis area after deformation, dx and dy are the displacements in the x direction and y direction respectively due to the deformation of the object, j is the unit of imaginary number;
the second transformation result is a function of the first transformation result and the displacement amount, since the image of the object after the deformation has a displacement amount caused by the deformation relative to the image before the deformation;
the first transformation result F1(u, v) and the second transformation result F2(u, v) are multiplied and then transformed to obtain a first function I (u, v) as:
Figure BDA0001986388640000061
due to the second transformation result F2(u, v) is the first transformation result F1(u, v) as a function of the amount of displacement, whereby the first function is also a function of the first transformation result and the amount of displacement;
and (3) carrying out fast Fourier transform on the first function I (u, v) and moving the zero frequency to the center of the matrix to obtain a frequency spectrum matrix W (xi, eta) corresponding to the first function:
Figure BDA0001986388640000062
in the formula, xi and eta are coordinates of the frequency spectrum matrix W, and the value range is
Figure BDA0001986388640000071
δ is a dirac function, W (ξ, η) is an impulse function about dx and dy, and the maximum value of the spectrum in the region can be obtained only at the point (ξ, η) ═ dx, dy, so the coordinate where the maximum value is obtained by the spectrum matrix is the integer pixel displacement (U) caused by the deformation of the object1,V1) Through the above processing, the magnitude of the object displacement is dx and dy, and the direction of the object displacement is consistent with the signs of dx and dy;
(c) through a generalized upsampling technology, discrete Fourier transform is carried out on the first function to obtain the total displacement of the iteration of the previous time
Figure BDA0001986388640000072
Is used as the center of the device,m × m spectrum matrix W with preset step length as interval1(ξ ', η') are:
Figure BDA0001986388640000073
at this time, m × m is a spectrum matrix W1The length and width of (xi ', eta'), m is preferably odd number and the value is preferably m ≧ 3, when m ═ 3, the precision and sensitivity can be ensured and simultaneously higher calculation efficiency can be obtained, xi 'and eta' are preferably selected
Figure BDA0001986388640000074
Any value of;
however, the calculation accuracy of this method is closely related to the quantization depth of the picture, for example, for a picture with 16 bits of quantization depth, the value of the point (-0.001, 0.0005) is the same as the value of the point (-10, 5) calculated when K is 10000 in the conventional upsampling technique, but since it is not necessary to perform a large amount of fourier calculation after zero padding, the calculation efficiency is greatly improved, and the "fence effect" is broken, and by using this technique, the spectral value of a certain range of data around the whole pixel displacement calculation result (dx, dy) obtained in step (c) can be calculated (here and after, the size of 3 × 3 is taken as an example);
for the spectrum matrix W1(xi ', eta') fitting the curved surface to obtain a fitting equation, determining the maximum value coordinate of the curved surface by solving the extreme point of the fitting equation, wherein the distance between the maximum value coordinate and the coordinate of the central point of the matrix is the sub-pixel displacement of the current iteration caused by the deformation of the object
Figure BDA0001986388640000081
More specifically, the total displacement of the last iteration
Figure BDA0001986388640000082
Sub-pixel shift for last iteration
Figure BDA0001986388640000083
And the integer pixel displacement (U) obtained in step (b)1,V1) Sum of (1), total displacement at first iteration
Figure BDA0001986388640000084
I.e. integer pixel shift (U)1,V1)；
(d) Sub-pixel displacement of the current iteration obtained according to step (c)
Figure BDA0001986388640000085
And the integer pixel displacement (U) obtained in step (b)1,V1) Obtaining the total displacement of the current iteration
Figure BDA0001986388640000086
And by the total displacement of the current iteration
Figure BDA0001986388640000087
Iteration is carried out as the center to obtain the sub-pixel displacement of the next iteration
Figure BDA0001986388640000088
Thereby obtaining the total displacement of the next iteration
Figure BDA0001986388640000089
(e) Comparing the total displacement of the current iteration
Figure BDA00019863886400000810
Total displacement from next iteration
Figure BDA00019863886400000811
If the difference is smaller than the allowable threshold, outputting the total displacement caused by the deformation of the object if the difference is smaller than the allowable threshold, and if the difference is not smaller than the allowable threshold, outputting the total displacement according to the next iteration
Figure BDA00019863886400000812
Continuing iteration;
the specific iterative process is as follows: for the frequency spectrum matrix W1(xi ', eta') Total Displacement at the next iteration
Figure BDA00019863886400000813
The position of the sub-pixel is subjected to surface fitting to obtain the sub-pixel displacement of the next iteration
Figure BDA00019863886400000814
Thereby updating the total displacement for the next iteration
Figure BDA00019863886400000815
Comparing the total displacement of the next iteration
Figure BDA00019863886400000816
Total displacement from next iteration
Figure BDA00019863886400000817
If the difference is smaller than the allowable threshold, outputting the total displacement caused by the deformation of the object if the difference is smaller than the allowable threshold, and if the difference is not smaller than the allowable threshold, outputting the total displacement according to the next iteration
Figure BDA00019863886400000818
The iteration continues.
Further, the allowable threshold is preferably less than 1% of the measurement sensitivity.
The invention will be further illustrated below with reference to a preferred embodiment of the invention.
(a) Obtaining simulated speckle images of an object before and after deformation by using a MATLAB software programming program, wherein FIG. 2a is a photograph of a speckle part before deformation, FIG. 2b is a photograph of the speckle part after deformation, the two images comprise the same part, namely the speckle part, analysis areas are respectively and randomly selected in areas near the speckle part in the two images, the two analysis areas are the same in shape and are both squares, the two analysis areas also have the same number of pixels, the size is 61 x 61, the initial coordinates of the pixels are both (200 ), the end coordinates are both (260 ), the given displacement is the displacement of 0 pixel in the x direction, and the y direction is 0.0005 pixel;
(b) respectively to twoCarrying out fast Fourier transform on the gray value of the pixels in the analysis area to obtain a first transform result F1(u, v) are:
Figure BDA0001986388640000091
second transformation result F2(u, v) are:
Figure BDA0001986388640000092
multiplying the first transform result by the conjugate function of the second transform result, and then transforming it to obtain a first function I (u, v):
Figure BDA0001986388640000093
and carrying out fast Fourier transform on the first function and moving the zero frequency to the center of the matrix to obtain a frequency spectrum matrix W (xi, eta) corresponding to the first function:
W(ξ,η)＝δ(ξ-dx,η-dy) (4)
the coordinate of the maximum value of W (ξ, η) is (0,0), the integer pixel displacement is 0 pixels in the x direction and 0 pixels in the y direction, and the spectrogram is shown in fig. 3;
(c) combining with the generalized upsampling technology, performing discrete Fourier transform on the first function to obtain a frequency spectrum matrix W in a 3 × 3 range with (u, v) ═ dx, dy) points as centers1(ξ ', η') are:
Figure BDA0001986388640000094
wherein xi '(-0.001, 0,0.001), η' (-0.001,0,0.001), and the step length is selected
Figure BDA0001986388640000095
For the spectrum matrix W1(xi ', eta') is subjected to surface fitting to obtainDetermining the maximum value coordinate of the curved surface by solving the extreme point of the fitting equation, wherein the distance between the maximum value coordinate and the matrix center point coordinate is the sub-pixel displacement of the current iteration caused by the deformation of the object
Figure BDA0001986388640000101
(d) Sub-pixel displacement of the current iteration obtained according to step (c)
Figure BDA0001986388640000102
And the integer pixel displacement (U) obtained in step (b)1,V1) Obtaining the total displacement of the current iteration
Figure BDA0001986388640000103
For the frequency spectrum matrix W1(ξ ', η') the total displacement at the current iteration
Figure BDA0001986388640000104
The position of the sub-pixel is iterated to obtain the sub-pixel displacement of the next iteration
Figure BDA0001986388640000105
Thereby obtaining the total displacement of the next iteration
Figure BDA0001986388640000106
(e) Comparing the total displacement of the current iteration
Figure BDA0001986388640000107
Total displacement from next iteration
Figure BDA0001986388640000108
Whether the difference is less than the allowable threshold value of 0.0000001, if so, outputting the total displacement caused by the deformation of the object, and if not, outputting the total displacement according to the next iteration
Figure BDA0001986388640000109
The iteration continues, as shown in FIG. 4, resulting in sub-pixel bitsShifting to 0 pixels in the x-direction and 0.00049584 pixels in the y-direction, the relative error is-0.832%.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. A high-sensitivity digital image displacement frequency domain analysis method is characterized by comprising the following steps:
(a) shooting two images of the same object before and after deformation at the same position by utilizing shooting equipment, and then respectively selecting an analysis area in the same part of the two images;
(b) obtaining a first transformation result before object deformation and a second transformation result after object deformation according to the gray values of pixels in the two selected analysis areas, and obtaining a first function and a frequency spectrum matrix W (xi, eta) corresponding to the first function through calculation, wherein the coordinate of the maximum value of the frequency spectrum matrix W (xi, eta) is the integral pixel displacement (U) caused by object deformation1,V1) The method specifically comprises the following substeps:
(i) carrying out fast Fourier transform on the gray values of the pixels in the analysis area before and after deformation to obtain a first transform result F before deformation of the object1(u, v) are:
Figure FDA0002810913870000011
second transformation result F after deformation of the object2(u, v) are:
Figure FDA0002810913870000012
wherein u and v are the Fourier transformed coordinates, M is the pixel value of the analysis region in the x direction, and f1(x, y) is before deformationAnalyzing a gray matrix of the area, wherein j is an imaginary unit, and dx and dy are integer pixel displacements generated in the x direction and the y direction respectively due to deformation;
(ii) converting the first conversion result F1(u, v) and the second transformation result F2(u, v) are multiplied and then transformed to obtain a first function I (u, v) as:
Figure FDA0002810913870000013
(iii) performing fast Fourier transform on the first function I (u, v) and moving a zero frequency to the center of a matrix to obtain a frequency spectrum matrix W (xi, eta) corresponding to the first function, wherein the frequency spectrum matrix W (xi, eta) is as follows:
W(ξ,η)＝δ(ξ-dx,η-dy) (4)
in the formula, xi and eta are coordinates of the frequency spectrum matrix W, and the value range is
Figure FDA0002810913870000021
Delta is a dirac function;
(c) obtaining the total displacement of the previous iteration through the first function
Figure FDA0002810913870000022
Centered on a m × m-sized spectrum matrix W with a predetermined step size as an interval1(xi ', η') for the spectral matrix W1(xi ', eta') fitting the curved surface to obtain a fitting equation, determining the maximum value coordinate of the curved surface by solving the extreme point of the fitting equation, wherein the distance between the maximum value coordinate and the coordinate of the central point of the matrix is the sub-pixel displacement of the current iteration caused by the deformation of the object
Figure FDA0002810913870000023
(d) Sub-pixel displacement of the current iteration obtained according to step (c)
Figure FDA0002810913870000024
And the integer pixel displacement (U) obtained in step (b)1,V1) Adding to obtain the total displacement of the current iteration
Figure FDA0002810913870000025
And by the total displacement of the current iteration
Figure FDA0002810913870000026
Iteration is carried out as the center to obtain the sub-pixel displacement of the next iteration
Figure FDA0002810913870000027
Sub-pixel shift of next iteration
Figure FDA0002810913870000028
And the total displacement of the current iteration
Figure FDA0002810913870000029
Adding to obtain the total displacement of the next iteration
Figure FDA00028109138700000210
(e) Comparing the total displacement of the current iteration
Figure FDA00028109138700000211
Total displacement from next iteration
Figure FDA00028109138700000212
If the difference is smaller than the allowable threshold, outputting the total displacement caused by the deformation of the object if the difference is smaller than the allowable threshold, and if the difference is not smaller than the allowable threshold, outputting the total displacement according to the next iteration
Figure FDA00028109138700000213
The iteration continues.
2. The method of claim 1, wherein the analysis region selected in step (a) has a rectangular shape,
3. the method for frequency domain analysis of displacements of a high sensitivity digital image according to claim 1, wherein the shape of the analysis area selected in said step (a) is a square.
4. The method for frequency domain analysis of the displacements of a high sensitivity digital image according to claim 1, wherein in said step (c) the spectral matrix W is defined by1(ξ ', η') are:
Figure FDA0002810913870000031
where ξ 'and η' are preferred
Figure FDA0002810913870000032
To any value of (a).
5. The frequency domain analysis method of high sensitivity digital image displacement according to claim 4, wherein m in the step (c) is equal to or greater than 3.
6. The method for frequency domain analysis of displacement of high sensitivity digital image according to any one of claims 1 to 5, wherein the allowable threshold in the step (e) is less than 1% of the measurement sensitivity.
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