CN104200474A - Digital image analysis method for obtaining object deformation quantity - Google Patents

Abstract

The invention discloses a digital image analysis method for obtaining object deformation quantity. The digital image analysis method for obtaining the object deformation quantity includes steps: S1, obtaining object images before and after deformation; S2, respectively selecting analysis areas of the same coordinate from the same portion of the same object in two images; S3, respectively performing fast Fourier transformation and mathematical treatment on gray values of pixel dots in the two analysis areas so as to obtain functions related to the gray values and the deformation quantity of the pixel dots in the two analysis areas and related to a variable in the mathematical treatment; S4, respectively calculating four different functions obtained when four different fixed values are respectively assigned to the variable in the mathematical treatment; S5, performing the mathematical treatment on the four different functions obtained in the step S4 so as to obtain a fifth function; S6, performing the Fourier transformation on the fifth function so as to obtain an impulse function including the object deformation quantity, and performing calculation so as to obtain the position of the highest impulse point in the impulse function, wherein the coordinate of the position of the highest impulse point in the impulse function is the deformation quantity caused by object deformation in the X axis direction and the Y axis direction.

Description

A kind of method of digital image analysis of obtaining deformation of body amount

Technical field

The invention belongs to engineering survey field, more specifically, relate to a kind of method of digital image analysis of obtaining deformation of body amount.

Background technology

It is the important topic that vast mechanics worker is concerned about that thereby the malformation of measuring material obtains its mechanical property always.In the mechanical behavior experiment of material, conventionally material is made to standard sample, relend and help extensometer to obtain sample deformation, can calculate the mechanical property of material according to material deformation.Early application mechanical lever-type extensometer, conventionally by Strain Extensometer, the responsive deformation element in Strain Extensometer is the semi-girder of being made up of resilient material now, and the free end of this semi-girder is an edge of a knife, when work, itself and measured piece are closely fixing, are stained with the foil gauge of measuring distortion on beam.

There are the following problems more than to adopt the contact measurement method of foil gauge: at some fabrics, cannot adopt the metering system of extensometer on the flexible materials such as plastics; Under the rugged surroundings such as High Temperature High Pressure, conventional foil gauge cannot adapt to severe environment for use at all, and high temperature can make member generation creep, even if adopt the high temperature resistance strainometer also can Measurement accuracy because being subject to temperatures involved; The semi-girder edge of a knife on extensometer can use rust because of permanent, thereby causes contact force decline and cause test error; In this class large deformation material of testing rubber or metal fracture torture test, the extensometer semi-girder edge of a knife can be because vibrations and impact and badly damaged when Materials Fracture; During for some small test specimens, there is no the extensometer of suitable gauge length and cannot record distortion.

Summary of the invention

For above defect or the Improvement requirement of prior art, the invention provides a kind of method of digital image analysis of obtaining deformation of body amount, its object is to obtain the displacement that object causes due to self-deformation, without contact member, member is not damaged, adopt the distortion of image processing techniques object analysis, can quick obtaining result, solve thus and in current method, need contactant surface or the treatment step long technical matters that expends time in.

For achieving the above object, the invention provides a kind of method of digital image analysis of obtaining deformation of body amount, for obtaining the displacement that object causes due to self-deformation, surface displacement amount is object due to the relative movement distance between distortion or the mobile particle causing, it is characterized in that, comprise following steps:

S1: utilize the two width images of photographing device before and after same position is taken same deformation of body, and this two width image at least comprises at least one same section of this object;

S2: choose at random respectively an analyzed area in the region of same object same section in described two width images, the shape of these two analyzed areas is all identical with the pixel quantity comprising, and these two regions origin coordinates of pixel in image is also identical respectively with the terminal point coordinate of pixel;

S3: respectively the gray-scale value of the described pixel in two regions in described step S2 is carried out to Fast Fourier Transform (FFT), obtain respectively representing the first transformation results before deformation of body and represent the second transformation results after deformation of body, because image after deformation of body is out of shape with respect to being out of shape front image modification the displacement causing, so the second transformation results is exactly the function of the first result of variations and displacement; The second transformation results is multiplied by an angle variables, further obtain the 3rd transformation results, described the first transformation results and described the 3rd transformation results are added, to obtain the result that converts, described conversion result is matrix, this matrix is carried out to conjugate multiplication processing, obtain about the gray-scale value of pixel in the described analyzed area of image before distortion, displacement that distortion causes and the function of described angle variables;

S4: calculate respectively the 4th function obtaining when the 3rd function that obtains when the second function, the angle variables that obtain when the first function, the angle variables that obtain when described angle variables is got the first definite value are got the second definite value are got the 3rd definite value and angle variables are got the 4th definite value;

S5: to the first function in described step S4, the second function, the 3rd function and the 4th function carry out mathematics manipulation, to balance out the caused coefficient of gray-scale value conjugate multiplication in frequency domain of image before deformation of body, thereby obtain the 5th function;

S6: described the 5th function is carried out to Fourier transform, obtain comprising the impulse function of the displacement that distortion causes, calculate the position that obtains in this impulse function high impulse point, the coordinate of this position is the displacement that deformation of body causes.

Further, in described step S4 the first definite value, the second definite value, the 3rd definite value and the 4th definite value be respectively 0, pi/2, π and 3 pi/2s.

Further, the 5th function I obtaining in described step S5 ₅as follows:

$\begin{array}{c}{I}_5(u,v)=\frac{I_1-I_3}{\sqrt{{(I_1-I_3)}^2+{(I_4-I_2)}^2}}\\ =\cos 2\mathrm{\π}(\frac{\mathrm{dxu}}{M}+\frac{\mathrm{dyv}}{N})\end{array}$

Wherein, I ₁, I ₂, I ₃and I ₄be respectively the first function, the second function, the 3rd function and the 4th function, u, v is respectively the coordinate unit after its Fourier transform, M, N is respectively the x of the described analyzed area chosen, the picture number quantity of y direction, and dx and dy are respectively the displacement that distortion causes, π is angle in mathematics, equals 180 °.

Further, in described step S6, described impulse function and conversion process thereof are:

$\begin{array}{c}W(x,y)=\frac{1}{\mathrm{MN}}\underset{u=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{v=0}{\overset{N-1}{\mathrm{\Σ}}}{I}_5(u,v)e^{-j2\mathrm{\π}(\frac{\mathrm{ux}}{M}+\frac{\mathrm{vy}}{N})}\\ =\frac{1}{\mathrm{MN}}\underset{u=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{v=0}{\overset{N-1}{\mathrm{\Σ}}}\cos \left[2\mathrm{\π}(\frac{\mathrm{udx}}{M}+\frac{\mathrm{vdy}}{N})\right]e^{-j2\mathrm{\π}(\frac{\mathrm{ux}}{M}+\frac{\mathrm{vy}}{N})}\\ =\frac{1}{2}[\mathrm{\δ}(x+\mathrm{dx},y+\mathrm{dy})+\mathrm{\δ}(x-\mathrm{dx},y-\mathrm{dy})]\end{array}$

In formula, M, N are respectively the x of the described analyzed area chosen, the picture number quantity of y direction, x and y are respectively the time coordinate unit in dummy section being made up of the gray-scale value of plane of delineation displacement and pixel, and dx and dy are out of shape respectively the x causing, the surface displacement amount of y direction, u, v is respectively the coordinate unit after Fourier transform, j is imaginary unit, δ (x) is Dirac function, the truth of a matter that e is natural logarithm.

The inventive method thinks that object is because distortion has caused surface displacement, and this surface displacement amount is only because deformation of body causes, and therefore this displacement is less.At the image of same position shot object distortion front and rear surfaces, there is variation because of deformation of body in this surface image, also there is movement in its corresponding pixel, identical according to gray-scale value, the displacement that solves the pixel generation with same grayscale value, is the surface displacement causing due to deformation of body.

In general, the above technical scheme of conceiving by the present invention compared with prior art, can obtain following beneficial effect:

1, the method that the present invention gathers raw data takes the photo before and after deformable object, and mode is simple, and all can take various test environments, and tested person environmental impact, not applied widely, and take pictures without contact member, has advantages of and do not destroy member.

2, the inventive method is out of shape based on image processing techniques object analysis, adopt common Fourier transform or speed change Fourier transform in mathematics to process, do not need to carry out search process, can directly obtain the displacement that deformation of body causes, can quick obtaining result, save time.

Brief description of the drawings

Fig. 1 (a) and Fig. 1 (b) are respectively the pictures before surface is sprayed with the distortion of speckle object same section in the embodiment of the present invention and after distortion;

Fig. 2 is the bar graph that adopts the 5th function that in the embodiment of the present invention, method obtains;

Fig. 3 is the spectrogram that adopts the impulse function in the step S6 that embodiment of the present invention method obtains.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearer, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein, only in order to explain the present invention, is not intended to limit the present invention.In addition,, in each embodiment of described the present invention, involved technical characterictic just can combine mutually as long as do not form each other conflict.

Embodiment comprises following steps:

S1: utilize the image of camera before and after same position is taken the surperficial deformation of body with speckle, as shown in Figure 1, Fig. 1 (a) is the photo of speckle part before distortion, Fig. 1 (b) is the photo of speckle part after distortion, this two width image comprises this same section, i.e. speckle part.

S2: near the region in two width images speckle difference random Analysis on Selecting region, the shape of these two analyzed areas is identical, be square, and the pixel quantity of two district inclusions is also identical, in the present embodiment, before distortion and after distortion image in the pixel origin coordinates chosen be (350,150), end pixel point coordinate is (450,250), and analyzed area is size 101 × 101.

S3: respectively the gray-scale value of the pixel in two regions is carried out to Fast Fourier Transform (FFT), obtain respectively representing the first transformation results before deformation of body and representing the second transformation results after deformation of body, the first transformation results is exponential function F ₀(u, v), the second transformation results is exponential function F ₁(u, v), two exponential functions are as follows respectively:

$F_0(u,v)=\frac{1}{\mathrm{MN}}\underset{x=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{y=0}{\overset{N-1}{\mathrm{\Σ}}}{f}_0(x,y)e^{-j2\mathrm{\π}(\frac{\mathrm{xu}}{M}+\frac{\mathrm{yv}}{N})}$

$\begin{array}{c}{F}_1(u,v)=\frac{1}{\mathrm{MN}}\underset{x=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{y=0}{\overset{N-1}{\mathrm{\Σ}}}{f}_0(x+\mathrm{dx},y+\mathrm{dy})e^{-2\mathrm{\πj}(\frac{\mathrm{xu}}{M}+\frac{\mathrm{yv}}{N})}\\ =F_0(u,v)e^{2\mathrm{\πj}(\frac{\mathrm{udx}}{M}+\frac{\mathrm{vdy}}{N})}\end{array}$

In formula, M, N are respectively the x of the analyzed area chosen, the picture number quantity of y direction, x and y are respectively the time coordinate in dummy section being made up of the gray-scale value of plane of delineation displacement and pixel, dx and dy be respectively due to distortion cause pixel its at x, the displacement of y direction, u, v is respectively the coordinate unit after Fourier transform, j is imaginary unit, the truth of a matter that e is natural logarithm, and π is angle in mathematics, equal 180 °, f ₀(x, y) represents the function of relation between the front gradation of image value of distortion and coordinate, f ₀(x+dx, y+dy) represents the relation function between gray-scale value and the coordinate of image after distortion.Being translation relation owing to can thinking that distortion moves forward and backward, so before and after distortion, the gray-scale value of image pixel exists the shift value of directions X and Y-direction, is respectively dx and dy, is also the surface displacement amount producing before and after deformation of body.

By the Fast Fourier Transform (FFT) result of gradation of image value function after distortion, be also the second transformation results F ₁(u, v) is multiplied by an angle variables obtain the 3rd transformation results F ₃(u, v), is shown below:

In formula, M, N are respectively the x of the described analyzed area chosen, the picture number quantity of y direction, x and y are respectively the time coordinate in dummy section due to the gray-scale value composition of plane of delineation displacement and pixel, and dx and dy are respectively at x, the displacement of y direction, u, v is respectively the coordinate unit after Fourier transform, and j is imaginary unit for the offset variable of needs increase.

The displacement causing due to distortion is a result that relative motion causes, and it depends on the gray-scale value of the image before distortion, why increases exactly for the displacement that utilizes the displacement of this increase that distortion is caused is independent of the gray-scale value of image before distortion, thereby provide possibility for solving the displacement that distortion causes in the processing in later stage.

F ₃(u, v) is one and F ₀(u, v), surface displacement amount dx and dy and angle variables relevant function, then the Fast Fourier Transform (FFT) result F with the front image of distortion by this function ₀(u, v) is added, and obtains a function A _i(u, v), this function result that converts exactly, detailed process is shown below:

In formula, M, N are respectively the x of the described analyzed area chosen, the picture number quantity of y direction, x and y are respectively the time coordinate in dummy section due to the gray-scale value composition of plane of delineation displacement and pixel, and dx and dy are respectively at x, the displacement of y direction, u, v is respectively the coordinate unit after Fourier transform, and j is imaginary unit for the offset variable of needs increase.

The function A of this conversion result will be represented _i(u, v) conjugate multiplication, obtains about the gray-scale value of pixel in the analyzed area of image before distortion, displacement that distortion causes and the function I of angle variables _i(u, v), specifically obtain one and F ₀(u, v), in surface displacement amount dx and dy and variable relevant function, is shown below:

Wherein, B ₀(u, v)=2F ₀(u, v) F ₀ ^*(u, v),, in formula, M, N are respectively the x of the described analyzed area chosen, the picture number quantity of y direction, x and y are respectively the time coordinate in dummy section due to the gray-scale value composition of plane of delineation displacement and pixel, and dx and dy are respectively at x, the displacement of y direction, u, v is respectively the coordinate unit after Fourier transform, and j is imaginary unit for the offset variable that needs increase, * represent its be shown in the transposition of function.

S4: calculate respectively the 4th function obtaining when the 3rd function that obtains when the second function, the variable that obtain when the first function, the variable that obtain when described variable is got the first definite value are got the second definite value are got the 3rd definite value and variable are got the 4th definite value, in the present embodiment, the first definite value, the second definite value, the 3rd definite value and the 4th definite value are respectively pi/2, π and 3 pi/2s, obtain the first function, the second function, the 3rd function and the 4th function, corresponds to respectively I ₁, I ₂, I ₃and I ₄, specific as follows:

$I_1(u,v)=B_0(u,v)(1+\cos 2\mathrm{\π}(\frac{\mathrm{dxu}}{M}+\frac{\mathrm{dyv}}{N}))$

$I_2(u,v)=B_0(u,v)(1-\sin 2\mathrm{\π}(\frac{\mathrm{dxu}}{M}+\frac{\mathrm{dyv}}{N}))$

$I_3(u,v)=B_0(u,v)(1-\cos 2\mathrm{\π}(\frac{\mathrm{dxu}}{M}+\frac{\mathrm{dyv}}{N}))$

$I_4(u,v)=B_0(u,v)(1+\sin 2\mathrm{\π}(\frac{\mathrm{dxu}}{M}+\frac{\mathrm{dyv}}{N}))$

In formula, in formula, M, N are respectively the x of the described analyzed area chosen, the picture number quantity of y direction, and x and y are respectively the time coordinate in dummy section due to the gray-scale value composition of plane of delineation displacement and pixel, dx and dy are respectively at x, the displacement of y direction, u, v is respectively the coordinate unit after Fourier transform, j is imaginary unit, B ₀(u, v)=2F ₀(u, v) F ₀ ^*(u, v).

S5: the first function in step S4, the second function, the 3rd function and the 4th function are carried out to mathematics manipulation to balance out the gray-scale value of the pixel in described four functions, just can obtain the 5th function about surface displacement amount dx and dy, the 5th function is following trigonometric function:

$\begin{array}{c}{I}_5(u,v)=\frac{I_1-I_3}{\sqrt{{(I_1-I_3)}^2+{(I_4-I_2)}^2}}\\ =\cos 2\mathrm{\π}(\frac{\mathrm{dxu}}{M}+\frac{\mathrm{dyv}}{N})\end{array}$

Wherein, I ₁, I ₂, I ₃and I ₄be respectively the first function, the second function, the 3rd function and the 4th function, u, v is respectively the coordinate unit after its Fourier transform, M, N is respectively the x of the described analyzed area chosen, the picture number quantity of y direction, and dx and dy are respectively the displacement that distortion causes, π is angle in mathematics, equals 180 °.

With software matlab to trigonometric function I ₅(u, v) draws, and obtains the bar graph about surface displacement amount dx and dy, as shown in Figure 2.

S6: last, then to I ₅(u, v) carries out Fourier transform, can obtain removing the impulse function W (x, y) of zero-frequency component, and the position of the point that its high impulse is corresponding is exactly required surface displacement amount dx and dy, specific as follows shown in:

$\begin{array}{c}W(x,y)\\ =\frac{1}{\mathrm{MN}}\underset{u=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{v=0}{\overset{N-1}{\mathrm{\Σ}}}{I}_5(u,v)e^{-j2\mathrm{\π}(\frac{\mathrm{ux}}{M}+\frac{\mathrm{vy}}{N})}\\ =\frac{1}{\mathrm{MN}}\underset{u=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{v=0}{\overset{N-1}{\mathrm{\Σ}}}\cos \left[2\mathrm{\π}(\frac{\mathrm{udx}}{M}+\frac{\mathrm{vdy}}{N})\right]e^{-j2\mathrm{\π}(\frac{\mathrm{ux}}{M}+\frac{\mathrm{vy}}{N})}\\ =\frac{1}{2}[\mathrm{\δ}(x+\mathrm{dx},y+\mathrm{dy})+\mathrm{\δ}(x-\mathrm{dx},y-\mathrm{dy})]\end{array}$

In formula, M, N are respectively the x of the described analyzed area chosen, the picture number quantity of y direction, x and y are respectively the time coordinate unit in dummy section being made up of the gray-scale value of plane of delineation displacement and pixel, and dx and dy are out of shape respectively the x causing, the surface displacement amount of y direction, u, v is respectively the coordinate unit after Fourier transform, j is imaginary unit, δ (x) is Dirac function, the truth of a matter that e is natural logarithm.

Utilizing MAYLAB or other software programming programs, calculate coordinate points position corresponding to peak value, is exactly required surface displacement amount dx and the concrete numerical value of dy.In the present embodiment for dx and dy are respectively 9 pixels, and 7 pixels, use Software on Drawing to go out this impulse function, as shown in Figure 3.

Those skilled in the art will readily understand; the foregoing is only preferred embodiment of the present invention; not in order to limit the present invention, all any amendments of doing within the spirit and principles in the present invention, be equal to and replace and improvement etc., within all should being included in protection scope of the present invention.

Claims (4)

1. one kind is obtained the method for digital image analysis of deformation of body amount, for obtaining the displacement that object causes due to self-deformation, surface displacement amount is object due to the relative movement distance between distortion or the mobile surperficial particle causing, and it is characterized in that, comprises following steps:

S1: utilize the two width images of photographing device before and after same position is taken same deformation of body;

S2: choose at random respectively an analyzed area in the region of same object same section in described two width images, the shape of these two analyzed areas is all identical with the pixel quantity comprising, and these two regions origin coordinates of pixel in image is also identical respectively with the terminal point coordinate of pixel;

S3: respectively the gray-scale value of the described pixel in two regions in described step S2 is carried out to Fast Fourier Transform (FFT), obtain respectively representing the first transformation results before deformation of body and represent the second transformation results after deformation of body, described the second transformation results is the function of the first transformation results and surface displacement amount, the second transformation results is multiplied by an angle variables, further obtain the 3rd transformation results, described the first transformation results and described the 3rd transformation results are added, to obtain the result that converts, described conversion result is matrix, this matrix is carried out to conjugate multiplication processing, obtain the gray-scale value about pixel in the described analyzed area of image before distortion, the function of surface displacement amount and described angle variables,

S4: calculate respectively the 4th function obtaining when the 3rd function that obtains when the second function, the angle variables that obtain when the first function, the angle variables that obtain when described angle variables is got the first definite value are got the second definite value are got the 3rd definite value and angle variables are got the 4th definite value;

S5: to the first function in described step S4, the second function, the 3rd function and the 4th function carry out mathematics manipulation, to balance out the caused coefficient of gray-scale value conjugate multiplication in frequency domain of image before deformation of body, to obtain the 5th function;

S6: described the 5th function is carried out to Fourier transform, obtain comprising the impulse function of the displacement that distortion causes, calculate the position that obtains in this impulse function high impulse point, the coordinate of this position is the displacement that deformation of body causes.

2. a kind of method of digital image analysis of obtaining deformation of body amount as claimed in claim 1, is characterized in that, in described step S4 the first definite value, the second definite value, the 3rd definite value and the 4th definite value be respectively 0, pi/2, π and 3 pi/2s.

3. a kind of method of obtaining deformation of body amount as claimed in claim 1 or 2, is characterized in that, the 5th function I obtaining in described step S5 ₅as follows:

$\begin{array}{c}{I}_5(u,v)=\frac{I_1-I_3}{\sqrt{{(I_1-I_3)}^2+{(I_4-I_2)}^2}}\\ =\cos 2\mathrm{\π}(\frac{\mathrm{dxu}}{M}+\frac{\mathrm{dyv}}{N})\end{array}$

Wherein, I ₁, I ₂, I ₃and I ₄be respectively the first function, the second function, the 3rd function and the 4th function, u, v is respectively the coordinate unit after its Fourier transform, M, N is respectively the x of the described analyzed area chosen, the picture number quantity of y direction, dx and dy are respectively the x axle that distortion causes, the axial displacement of y.

4. a kind of method of obtaining deformation of body amount as claimed in claim 1 or 2, is characterized in that, in described step S6, described impulse function and conversion process thereof are:

$\begin{array}{c}W(x,y)=\frac{1}{\mathrm{MN}}\underset{u=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{v=0}{\overset{N-1}{\mathrm{\Σ}}}{I}_5(u,v)e^{-j2\mathrm{\π}(\frac{\mathrm{ux}}{M}+\frac{\mathrm{vy}}{N})}\\ =\frac{1}{\mathrm{MN}}\underset{u=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{v=0}{\overset{N-1}{\mathrm{\Σ}}}\cos \left[2\mathrm{\π}(\frac{\mathrm{udx}}{M}+\frac{\mathrm{vdy}}{N})\right]e^{-j2\mathrm{\π}(\frac{\mathrm{ux}}{M}+\frac{\mathrm{vy}}{N})}\\ =\frac{1}{2}[\mathrm{\δ}(x+\mathrm{dx},y+\mathrm{dy})+\mathrm{\δ}(x-\mathrm{dx},y-\mathrm{dy})]\end{array}$

In formula, M, N are respectively the x axles of the described analyzed area chosen, the axial picture quantity of y, x and y are respectively the time coordinate unit in dummy section being made up of the gray-scale value of plane of delineation displacement and pixel, and dx and dy are out of shape respectively the x axle causing, the axial surface displacement amount of y, u, v is respectively the coordinate unit after Fourier transform, j is imaginary unit, δ (x) is Dirac function, the truth of a matter that e is natural logarithm.