CN110033435A - A kind of high-sensitivity digital picture displacement frequency-domain analysis method - Google Patents
A kind of high-sensitivity digital picture displacement frequency-domain analysis method Download PDFInfo
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- CN110033435A CN110033435A CN201910166269.XA CN201910166269A CN110033435A CN 110033435 A CN110033435 A CN 110033435A CN 201910166269 A CN201910166269 A CN 201910166269A CN 110033435 A CN110033435 A CN 110033435A
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- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/0002—Inspection of images, e.g. flaw detection
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
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- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/20—Special algorithmic details
- G06T2207/20048—Transform domain processing
- G06T2207/20056—Discrete and fast Fourier transform, [DFT, FFT]
Abstract
The invention belongs to engineering measurement fields, and specifically disclose a kind of high-sensitivity digital picture displacement frequency-domain analysis method.This method includes obtaining the analyzed area of deformation front and back image, the gray value of its pixel is converted, obtain the first transformation results and the second transformation results, first function spectral matrix W (ξ corresponding with its is obtained by calculation, η), the coordinate that spectral matrix W (ξ, η) obtains maximum value is whole pixel displacement, centered on obtaining the total displacement of the above an iteration in conjunction with broad sense increasing sampling technique, using preset step-length as the spectral matrix W of m × m size at interval1(ξ ', η '), then to spectral matrix W1(ξ ', η ') into surface fitting is carried out, which is the Displacement of current iteration at a distance from matrix center point coordinate, is computed repeatedly until the difference of total displacement is less than acceptable threshold.The present invention increases sampling technique by broad sense and analyzes the spectral matrix of certain a part, computational efficiency not only can be improved, and the sensitivity calculated can be made to have obtained greatly being promoted.
Description
Technical field
The invention belongs to engineering measurement fields, more particularly, to a kind of high-sensitivity digital picture displacement frequency-domain analysis
Method.
Background technique
Measurement structure deformation is always that vast engineering and mechanics worker are of concern heavy to obtain material mechanical performance
Want project.In the mechanical behavior experiment of material, material is usually made into standard sample, then sample is obtained by extensometer and becomes
Shape, to calculate the mechanical property of material.
Early stage is mainly tested using mechanical lever-type extensometer, now commonly used Strain Extensometer.Strain-type
The sensitive deformation element of extensometer is the cantilever beam made of elastic material, and the foil gauge of measurement deformation, foil gauge are stained on beam
It is divided into metal resistance strain gauge and two kinds of semiconductor gauge, wherein the former sensitivity coefficient is lower, the sensitivity system of the latter
Number haves the shortcomings that non-linear and is affected by temperature big.And what it is due to their uses is all contact type measurement mode, multiple
Various errors can be introduced when Reusability, and are extremely limited in terms of the scope of application.
Therefore, contactless digital picture measurement method is come into being, but current digital image measurement is only applicable to
Measure the larger situation of moving distance.Because the error in spatial domain method and frequency domain method causes the accuracy and sensitivity of measurement to reach
One bottleneck, cannot achieve the measurement of miniature deformation.
Summary of the invention
For the disadvantages mentioned above and/or Improvement requirement of the prior art, the present invention provides a kind of high-sensitivity digital images
It is displaced frequency-domain analysis method, wherein sampling technique and make improvements using increasing, accordingly can be improved computational efficiency and sensitive
Degree is therefore particularly suitable for the application of miniature deformation measurement etc.
To achieve the above object, the invention proposes a kind of high-sensitivity digital picture displacement frequency-domain analysis methods, special
Sign is that this method comprises the following steps:
(a) two images using photographing device before and after same position shoots same object deformation, then above-mentioned two
Choose an analyzed area in width image in same section respectively；
(b) according in the two of selection analyzed areas pixel gray value obtain object deformation before the first transformation results and
Deformed second transformation results of object, and be obtained by calculation first function spectral matrix W corresponding with the first function (ξ,
η), it is the whole pixel displacement (U because of caused by object deformation that the spectral matrix W (ξ, η), which obtains the coordinate of maximum value,1,V1)；
(c) total displacement (U of the above an iteration is obtained by the first function3 n-1,V3 n-1) centered on, with default step
The spectral matrix W of m × m size at a length of interval1(ξ ', η '), to the spectral matrix W1(ξ ', η ') carries out surface fitting and obtains
Fit equation, the extreme point by solving the fit equation determine the maximum value coordinate of the curved surface, the maximum value coordinate and square
The distance of battle array center point coordinate is the Displacement (U of the current iteration because of caused by object deformation2 n,V2 n)；
(d) Displacement (U of the current iteration obtained according to step (c)2 n,V2 n) and step (b) obtain whole pixel
It is displaced (U1,V1) obtain the total displacement (U of current iteration3 n,V3 n), and with the total displacement (U of current iteration3 n,V3 n) centered on carry out
Iteration obtains the Displacement (U of next iteration2 n+1,V2 n+1), to obtain the total displacement (U of next iteration3 n+1,V3 n +1)；
(e) compare the total displacement (U of current iteration3 n,V3 n) with the total displacement (U of next iteration3 n+1,V3 n+1) difference whether
Less than acceptable threshold, if so, the total displacement because of caused by object deformation is exported, if it is not, then according to total position of next iteration
Move (U3 n+1,V3 n+1) continue iteration.
As it is further preferred that the step (a) in choose analyzed area shape be rectangle, and further preferably
It is square.
As it is further preferred that the step (b) includes following sub-step:
(i) Fast Fourier Transform (FFT) is carried out to the gray value of pixel in the analyzed area of deformation front and back, obtains object deformation
The first preceding transformation results F1(u, v) are as follows:
The deformed second transformation results F of object2(u, v) are as follows:
In formula, u and v are the coordinate after Fourier transformation respectively, and M is pixel of the analyzed area in the direction x or the direction y
Value, f1(x, y) is the gray matrix of analyzed area before deforming, and j is imaginary unit, and dx and dy are because deforming in the direction x or y respectively
The whole pixel displacement that direction generates；
(ii) by the first transformation results F1(u, v) and the second transformation results F2The conjugate function of (u, v) is multiplied, then
It is converted to obtain first function I (u, v) are as follows:
(iii) Fast Fourier Transform (FFT) is carried out to first function I (u, v) and zero-frequency is moved to matrix center, obtained
The corresponding spectral matrix W (ξ, η) of the first function are as follows:
W (ξ, η)=δ (ξ-dx, η-dy) (4)
In formula, ξ, η are the coordinate of spectral matrix W, and value range isδ is Dirac function.
As it is further preferred that spectral matrix W in the step (c)1(ξ ', η ') are as follows:
In formula, ξ ' and η ' are desirableAmong arbitrary value.
As it is further preferred that the value of m is preferably m >=3 in the step (c).
As it is further preferred that the value of m is more preferably m=3 in the step (c).
As it is further preferred that acceptable threshold is less than the 1% of measurement sensitivity in the step (e).
In general, through the invention it is contemplated above technical scheme is compared with the prior art, mainly have below
Technological merit:
1. the present invention, which increases sampling technique by broad sense, carries out discrete Fourier transform to first function, and obtains with the last time
The spectral matrix W of m × m size centered on the total displacement of iteration1(ξ ', η ') then carries out it to calculate acquisition sub-pix position
It moves, the present invention need to only analyze the spectral matrix of a certain interesting part, increase sampling technique so as to avoid tradition and need
Large-scale zero padding is carried out the problem of calculating, not only to improve computational efficiency in this way to whole picture figure, but also is reduced a large amount of superfluous
Remaining calculating, and broken " fence effect ", make the sensitivity calculated obtain greatly being promoted；
2. especially, the present invention is preferably m >=3 by the way that the value of m is repeatedly calculated, and improves m to precision and spirit
The promotion of sensitivity is almost nil, but computational efficiency is deteriorated, therefore can not only guarantee computational accuracy and sensitivity when m=3, also
Computational efficiency can be improved；
3. the tiny characteristic point of body surface can be with surface position simultaneously, when object since deformation causes surface displacement
It moves and moves, the present invention obtains object because deformation generates by calculating whole pixel displacement and Displacement using this feature
Displacement, can accurately obtain object displacement caused by deformation.
Detailed description of the invention
Fig. 1 is the flow chart of high-sensitivity digital picture displacement frequency-domain analysis method provided by the invention；
Fig. 2 a is same position before the deformation obtained in the preferred embodiment of the present invention using MATLAB software programming program
Speckle pattern；
Same position dissipates after the deformation obtained in Fig. 2 b preferred embodiment of the present invention using MATLAB software programming program
Spot figure
Fig. 3 is the spectrogram of first function obtained in step (b) in the preferred embodiment of the present invention；
Fig. 4 is curved surface maximum of points obtained in step (e) in the preferred embodiment of the present invention.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as in addition, technical characteristic involved in the various embodiments of the present invention described below
Not constituting a conflict with each other can be combined with each other.
As shown in Figure 1, the invention proposes a kind of high-sensitivity digital picture displacement frequency-domain analysis method, this method includes
Following steps:
(a) two images using photographing device before and after same position shoots same object deformation, above-mentioned two images
Including at least a same section of the object, then distinguish in the region of same object same section in above-mentioned two images
Randomly select an analyzed area, the shape of two analyzed areas and comprising pixel quantity it is all the same, and two analysis areas
Origin coordinates, the terminal point coordinate difference of domain pixel in respective image are identical, and to improve computational efficiency, the shape of analyzed area is excellent
It is selected as rectangle, and is further preferably square；
(b) Fast Fourier Transform (FFT) is carried out to the gray value of pixel in two analyzed areas of selection respectively, obtains object
Deformed second transformation results of the first transformation results and object before deformation, wherein the first transformation results F1(u, v) are as follows:
Second transformation results F2(u, v) are as follows:
In formula, u and v are the coordinate after Fourier transformation respectively, and M is pixel of the analyzed area in the direction x or the direction y
Value, in order to which convenience of calculation M is used and is illustrated according to odd number, f1(x, y) is the gray matrix of analyzed area before deforming, f2(x,
It y) is the gray matrix for deforming post analysis region, dx and dy are the displacement generated by object deformation in the direction x and the direction y, j respectively
It is imaginary unit；
Displacement caused by being produced relative to the image before deformation because of deformation due to the deformed image of object, so the
Two transformation results are the functions of the first transformation results and displacement；
By the first transformation results F1(u, v) and the second transformation results F2The conjugate function of (u, v) is multiplied, and then carries out to it
Transformation obtains first function I (u, v) are as follows:
Due to the second transformation results F2(u, v) is the first transformation results F1The function of (u, v) and displacement, therefore the first letter
Number is also the function about the first transformation results and displacement；
Fast Fourier Transform (FFT) is carried out to first function I (u, v) and zero-frequency is moved to matrix center, obtains first function
Corresponding spectral matrix W (ξ, η):
In formula, ξ, η are the coordinate of spectral matrix W, and value range isδ is Dirac function, W (ξ,
It is η) that impulse function about dx and dy can just obtain the maximum of frequency spectrum in the region only at point (ξ, η)=(dx, dy)
Value, therefore it is the whole pixel displacement (U because of caused by object deformation that the spectral matrix, which obtains the coordinate of maximum value,1,V1), pass through
The above process handles the size of not only available ohject displacement as dx and dy, while the symbol in the direction of ohject displacement and dx and dy
It is number consistent；
(c) sampling technique is increased by broad sense, first function is subjected to discrete Fourier transform, obtains the above an iteration
Total displacementCentered on, using preset step-length as the spectral matrix W of m × m size at interval1(ξ ', η ') are as follows:
At this point, m × m is spectral matrix W1The length and width of (ξ ', η '), m is preferably odd number and its value is preferably m >=3,
Higher computational efficiency is obtained while capable of guaranteeing accuracy and sensitivity as m=3, ξ ' and η ' are desirable
Among arbitrary value；
But the computational accuracy of the method and the quantisation depth of picture are closely related, such as the picture of 16 quantisation depths,
To point (- 0.001,0.0005), point calculated when K=10000 in calculated result and traditional increasing sampling technique at this time (-
10,5) value is identical, but is calculated due to not needing to carry out the Fourier after a large amount of zero paddings, and computational efficiency substantially mentions
Height, and broken " fence effect ", with this technology, it can be calculated and be calculated with whole pixel displacement acquired in step (c)
As a result the spectrum value of surrounding's a certain range data centered on (dx, dy) (is said by taking 3 × 3 sizes as an example herein and later
It is bright)；
To the spectral matrix W1(ξ ', η ') carries out surface fitting and obtains fit equation, by solving the fit equation
Extreme point determines the maximum value coordinate of the curved surface, which is because object becomes at a distance from matrix center point coordinate
The Displacement of current iteration caused by shape
More specifically, the total displacement of the last time iterationFor the Displacement of last iterationWhole pixel displacement (the U obtained with step (b)1,V1) summation, total displacement when first iterationAs
Whole pixel displacement (U1,V1)；
(d) Displacement of the current iteration obtained according to step (c)The whole pixel obtained with step (b)
It is displaced (U1,V1) obtain the total displacement of current iterationAnd with the total displacement of current iterationCentered on carry out
Iteration obtains the Displacement of next iterationTo obtain the total displacement of next iteration
(e) compare the total displacement of current iterationWith the total displacement of next iterationDifference it is whether small
In acceptable threshold, if so, the total displacement because of caused by object deformation is exported, if it is not, then according to the total displacement of next iterationContinue iteration；
Specific iterative process are as follows: to spectral matrix W1The total displacement of (ξ ', η ') in next iterationPosition
Surface fitting is carried out, the Displacement of next iteration is obtainedTo update the total displacement of lower next iterationCompare the total displacement of next iterationWith the total displacement of next iterationDifference
Whether acceptable threshold is less than, if so, output total displacement because of caused by object deformation, if it is not, then according to next iteration
Total displacementContinue iteration.
Further, the acceptable threshold is preferably smaller than the 1% of measurement sensitivity.
Below according to a preferred embodiment of the present invention, invention is further explained.
(a) simulated speckle pattern of object deformation front and back is obtained using MATLAB software programming program, wherein Fig. 2 a is to become
The photo of speckle part before shape, Fig. 2 b are the photos of speckle part after deformation, and two images include same section i.e. speckle part,
Analyzed area is randomly selected respectively in the region near speckle part in two images, the shape of two analyzed areas is identical,
It is square, and the pixel quantity that two analyzed areas include is also identical, size is 61 × 61, the origin coordinates of pixel
It is (200,200) that terminal point coordinate is (260,260), given displacement is 0, the direction x pixel, 0.0005, the direction y pixel
Displacement；
(b) Fast Fourier Transform (FFT) is carried out to the gray value of pixel in two analyzed areas respectively, obtains the first transformation knot
Fruit F1(u, v) are as follows:
Second transformation results F2(u, v) are as follows:
First transformation results are multiplied with the conjugate function of the second transformation results, then it is converted to obtain the first letter
Number I (u, v):
Fast Fourier Transform (FFT) is carried out to first function and zero-frequency is moved to matrix center, it is corresponding to obtain first function
Spectral matrix W (ξ, η):
W (ξ, η)=δ (ξ-dx, η-dy) (4)
The coordinate of W (ξ, η) maximum value is (0,0), and whole pixel displacement is 0, the direction x pixel, 0, the direction y pixel, frequency
Spectrogram is as shown in Figure 3；
(c) combine broad sense increase sampling technique, first function is subjected to discrete Fourier transform, obtain with (u, v)=(dx,
Dy the spectral matrix W in 3 × 3 ranges centered on) putting1(ξ ', η ') are as follows:
Wherein, step-length is chosen in ξ '=(- 0.001,0,0.001), η '=(- 0.001,0,0.001)
To the spectral matrix W1(ξ ', η ') carries out surface fitting and obtains fit equation, by solving the fit equation
Extreme point determines the maximum value coordinate of the curved surface, which is because object becomes at a distance from matrix center point coordinate
The Displacement of current iteration caused by shape
(d) Displacement of the current iteration obtained according to step (c)The whole pixel obtained with step (b)
It is displaced (U1,V1) obtain the total displacement of current iterationTo spectral matrix W1The total displacement of (ξ ', η ') in current iterationPosition be iterated to obtain the Displacement of next iterationTo obtain next iteration
Total displacement
(e) compare the total displacement of current iterationWith the total displacement of next iterationDifference it is whether small
In acceptable threshold 0.0000001, if so, the total displacement because of caused by object deformation is exported, if it is not, then according to next iteration
Total displacementContinue iteration, as shown in figure 4, finally obtaining Displacement is 0, the direction x pixel, the side y
To 0.00049584 pixel, relative error is -0.832%.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all include
Within protection scope of the present invention.
Claims (7)
1. a kind of high-sensitivity digital picture displacement frequency-domain analysis method, which is characterized in that this method comprises the following steps:
(a) two images using photographing device before and after same position shoots same object deformation, then in above-mentioned two width figure
An analyzed area is chosen respectively in same section as in；
(b) the first transformation results and object before object deformation are obtained according to the gray value of pixel in the two of selection analyzed areas
Deformed second transformation results, and first function spectral matrix W (ξ, η) corresponding with the first function is obtained by calculation,
The coordinate that the spectral matrix W (ξ, η) obtains maximum value is the whole pixel displacement (U because of caused by object deformation1,V1)；
(c) total displacement of the above an iteration is obtained by the first functionCentered on, between being with preset step-length
Every m × m size spectral matrix W1(ξ ', η '), to the spectral matrix W1(ξ ', η ') carries out surface fitting and obtains fitting side
Journey, the extreme point by solving the fit equation determine the maximum value coordinate of the curved surface, the maximum value coordinate and matrix center
The distance of point coordinate is the Displacement of the current iteration because of caused by object deformation
(d) Displacement of the current iteration obtained according to step (c)The whole pixel displacement obtained with step (b)
(U1,V1) obtain the total displacement of current iterationAnd with the total displacement of current iterationCentered on be iterated
Obtain the Displacement of next iterationTo obtain the total displacement of next iteration
(e) compare the total displacement of current iterationWith the total displacement of next iterationDifference whether be less than appearance
Perhaps threshold value, if so, output total displacement because of caused by object deformation, if it is not, then according to the total displacement of next iterationContinue iteration.
2. high-sensitivity digital picture displacement frequency-domain analysis method as described in claim 1, which is characterized in that the step
(a) shape for the analyzed area chosen in is rectangle, and is further preferably square.
3. high-sensitivity digital picture displacement frequency-domain analysis method as claimed in claim 1 or 2, which is characterized in that the step
Suddenly (b) includes following sub-step:
(i) Fast Fourier Transform (FFT) is carried out to the gray value of pixel in the analyzed area of deformation front and back, before obtaining object deformation
First transformation results F1(u, v) are as follows:
The deformed second transformation results F of object2(u, v) are as follows:
In formula, u and v are the coordinate after Fourier transformation respectively, and M is pixel value of the analyzed area in the direction x or the direction y, f1
(x, y) is the gray matrix of analyzed area before deforming, and j is imaginary unit, and dx and dy are because deforming in the direction x or the direction y respectively
The whole pixel displacement generated；
(ii) by the first transformation results F1(u, v) and the second transformation results F2The conjugate function of (u, v) is multiplied, then to it
It is converted to obtain first function I (u, v) are as follows:
(iii) Fast Fourier Transform (FFT) is carried out to first function I (u, v) and zero-frequency is moved to matrix center, obtained described
The corresponding spectral matrix W (ξ, η) of first function are as follows:
W (ξ, η)=δ (ξ-dx, η-dy) (4)
In formula, ξ, η are the coordinate of spectral matrix W, and value range isδ is Dirac function.
4. high-sensitivity digital picture displacement frequency-domain analysis method as claimed in any one of claims 1 to 3, which is characterized in that
Spectral matrix W in the step (c)1(ξ ', η ') are as follows:
In formula, ξ ' and η ' are desirableAmong arbitrary value.
5. such as the described in any item high-sensitivity digital picture displacement frequency-domain analysis methods of Claims 1 to 4, which is characterized in that
The value of m is preferably m >=3 in the step (c).
6. high-sensitivity digital picture displacement frequency-domain analysis method as claimed in any one of claims 1 to 5, which is characterized in that
The value of m is more preferably m=3 in the step (c).
7. high-sensitivity digital picture displacement frequency-domain analysis method as described in any one of claims 1 to 6, which is characterized in that
Acceptable threshold is less than the 1% of measurement sensitivity in the step (e).
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