CN105469398B - A kind of deformation speckle generation method based on back mapping method - Google Patents
A kind of deformation speckle generation method based on back mapping method Download PDFInfo
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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
- G06T7/0004—Industrial image inspection
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- G06T2210/00—Indexing scheme for image generation or computer graphics
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Abstract
The invention discloses a kind of deformation speckle generation method based on back mapping method, first, generates reference picture using the speckle particle superposition generated at random, then in speckle pattern known to the gray scale of each pixel position.Shape function describes the position of deformation correspondence pixel, and inverse transformation, i.e. (x, y)=F (x', y') are now done to shape function, then (x', y') after deformation, can try to achieve before deformation (x, y).And the gray value of the deformation front position point of whole location of pixels has been superimposed by speckle particle gray scale and produced; by deform front position gray value extract be filled into deformation after corresponding position; speckle pattern after an amplitude variation shape can be then generated, the speckle pattern generating process is simple, meets the deformation requirements of actual experiment.
Description
Technical field：
The present invention relates to a kind of deformation speckle generation method based on back mapping method, it belongs to the related neck of digital picture
Domain.
Background technology：
Loading by means of digital image correlation method (DIC), characterized by surface of test piece natural texture or artificial speckle, by material problem on deformation
It is converted into the matching search problem of characteristic point in image before and after material surface deforms.This method have high certainty of measurement, it is non-contact,
Full field deformation measure, experimental stand are built the features such as easy, thus are widely used in Experimental Mechanics with analysis of material
Deformation characteristic.
, need to be to the factor of influence algorithm, such as sub-district size, shape letter in order to improve the measurement accuracy of Digital Image Correlation Method
Number order, sub-pixel interpolation method, condition of convergence etc. are analyzed.During due to actual experiment, camera lens is inevitably introduced
Distortion, camera noise, light source fluctuation equal error, and the true strain of actual experiment is unknowable, therefore true strain is controllable, nothing
The emulation speckle pattern of noise jamming is widely applied.The method of generation emulation speckle pattern is very much, and Schreier etc. utilizes FFT
Conversion, is calculated, so as to be deformed image in a frequency domain；Orteu etc. is according to the coherent noise function of Perlin, generation symbol
Close the emulation speckle pattern of true experiment deformation state；Peng Zhou, Pan Bing etc. utilize the superposition generation reference of gaussian random speckle field
Image, after further according to shape function movement gaussian random speckle center, and be superimposed deformed after image.First two mode generates
Speckle pattern error it is small, and more meet actual deformed state, but realize more difficult；Later approach generates the formula of speckle pattern
Clearly, programming is simple, but introduces error in itself during generation deformation pattern, and when emulation obtains moderate finite deformation, calculation error is particularly bright
It is aobvious.
The controllable simulation speckle pattern of deformation parameter provides means to analyze influence of all kinds of factors to DIC computational accuracies.And
The existing method for preparing simulation speckle pattern comes with some shortcomings, as systematic error is larger, generation side during speckle pattern after generation deformation
Method is complicated, hardly possible programs realization etc..
Therefore, it is necessary to a kind of new deformation speckle generation method to solve the above problems.
The content of the invention：
The present invention is directed to problem of the prior art, there is provided a kind of deformation speckle generation method based on back mapping method.
The present invention adopts the following technical scheme that：A kind of deformation speckle generation method based on back mapping method, it include with
Lower step：
1) K speckle particle, is generated at random, wherein, the coordinate of the center of i-th of speckle particle and brightness are respectively
(xi,yi) and fi, wherein, fiScope be [0,255], wherein, 1≤i≤K；
2), the inverse function of shape function (x', y')=F (x, y) is：(x, y)=F-1(x', y'), (x, y) are speckle before deformation
Point coordinates in image, (x', y') are the correspondence point coordinates in (x, y) after deformation speckle image, that is, utilize speckle after deformation
Point coordinates (x', y') in image tries to achieve the point coordinates (x, y) in speckle image before deformation；
3) speckle image and the brightness value of corresponding points in deformed speckle image before, deforming meet：
G (x', y')=f (x, y)
Wherein, g (x', y') represents the brightness value at point (x', y') place in speckle image after deforming, and utilizes what is generated at random
Speckle particle obtains the brightness of each point in speckle image before deforming：
Wherein, K represents the number of speckle particle, and (x, y) is the point coordinates in speckle image, (x before deformingi,yi) it is i-th
The coordinate of a speckle particle center, fiFor the brightness of i-th of speckle particle center, R is the radius of speckle particle,
Speckle image corresponding points (x', y') place after being deformed using the brightness f (x, y) at speckle image midpoint (x, y) place before deformation
Brightness；
4), the speckle image before output skew and deformed speckle image.
Further, the shape function is single order shape function,
Wherein, the in-plane displacement in u and v x and y directions respectively caused by deformation, (x0,y0) it is speckle image before deformation
Center position coordinates, (x, y) are the point coordinates in speckle image before deforming, and (x', y') is in (x, y) after deformation speckle image
Correspondence point coordinates.
Further, the shape function is second order shape function,
In formula, deformation parameter vector P=(u, v, ux, vx, uy, vy, uxx, vxx, uxy, vxy, uyy, vyy)T, Δ x=
x-x0, Δ y=y-y0, u and v are the in-plane displacement in x and y directions, (ux,vx,uy,vy) it is displacement gradient, uxx,vxx,uxy,vxy,
uyy,vyyFor the second-order partial differential coefficient of displacement.
Further, in step 3), the brightness value of sub-pixel location is obtained into row interpolation to speckle image before deformation, numeral
Interpolation method in image procossing has arest neighbors interpolation either bilinear interpolation or bicubic spline interpolation.
The present invention has the advantages that：Deformation speckle generation method thought letter of the present invention based on back mapping method
It is single, realization is easily programmed, and the error calculated is smaller, and deformation rule more meets the deformation state of actual test specimen.By imitative
True experiment is analyzed, and demonstrates the validity of this patent generation deformation speckle drawing method and high-precision characteristic.
Brief description of the drawings：
Fig. 1 is DIC schematic diagram calculations.
Fig. 2 is that former method generates speckle pattern.
Fig. 3 generates speckle pattern for back mapping method.
Fig. 4 is back mapping method schematic diagram.
Fig. 5 is the x directions translation calculation Error Graph of the rigid translation of embodiment 1.
Fig. 6 is the x directions translation calculation standard deviation figure of the rigid translation of embodiment 1.
Fig. 7 is the x directions translation calculation Error Graph of the homogeneous deformation of embodiment 2.
Fig. 8 is the x directions translation calculation standard deviation figure of the homogeneous deformation of embodiment 2.
Fig. 9 is the y directions translation calculation Error Graph of the homogeneous deformation of embodiment 2.
Figure 10 is the y directions translation calculation standard deviation figure of the homogeneous deformation of embodiment 2.
Figure 11 is that the sin deformations of the heterogeneous deformation of embodiment 3 calculate Error Graph.
Figure 12 is that the sin deformations of the heterogeneous deformation of embodiment 3 calculate standard deviation figure.
Figure 13 is the flow diagram of the deformation speckle generation method based on back mapping method.
Embodiment：
As shown in figure 13, the deformation speckle generation method of the invention based on back mapping method, comprises the following steps：
1) K speckle particle, is generated at random, wherein, the coordinate of the center of i-th of speckle particle and brightness are respectively
(xi,yi) and fi, wherein, fiScope be [0,255], wherein, 1≤i≤K；
2), the inverse function of shape function (x', y')=F (x, y) is：(x, y)=F-1(x', y'), (x, y) are speckle before deformation
Point coordinates in image, (x', y') are the correspondence point coordinates in (x, y) after deformation speckle image, that is, utilize speckle after deformation
Point coordinates (x', y') in image tries to achieve the point coordinates (x, y) in speckle image before deformation, wherein, shape function can be single order
Shape function：
Wherein, the in-plane displacement in u and v x and y directions respectively caused by deformation, (x0,y0) for deformation before image center
Position coordinates, (x, y) are that the point coordinates in image, (x', y') sit for the corresponding points in (x, y) after deformation image before deforming
Mark；
Wherein shape function can also be second order shape function：
In formula, deformation parameter vector P=(u, v, ux,vx,uy,vy,uxx,vxx,uxy,vxy,uyy,vyy)T, Δ x=x-x0, Δ
Y=y-y0, u and v are the in-plane displacement in x and y directions, (ux,vx,uy,vy) it is displacement gradient, uxx,vxx,uxy,vxy,uyy,vyyFor
The second-order partial differential coefficient of displacement；The present invention can realize using single order or second order shape function, but second order accuracy is higher than single order, one
The computational efficiency of rank is better than second order, therefore, in the not high occasion of required precision, recommends single order shape function, otherwise just uses two
Stepped function；
3) speckle image and the brightness value of corresponding points in deformed speckle image before, deforming meet：
G (x', y')=f (x, y),
Wherein, g (x', y') represents the brightness value at point (x', y') place in speckle image after deforming, before f (x, y) is deformation
The brightness at speckle image midpoint (x, y) place, before obtaining deforming using the speckle particle generated at random in speckle image each point it is bright
Degree：
Wherein, K represents the number of speckle particle, and (x, y) is the point coordinates in speckle image, (x before deformingi,yi) it is i-th
The coordinate of a speckle particle center, fiFor the brightness of i-th of speckle particle center, R is the radius of speckle particle,
Wherein, since the point coordinates (x, y) in image before the deformation that is obtained using the inverse function of shape function is probably sub-pixel values,
Bicubic spline interpolation is carried out to speckle image before deformation and reads f (x, y), that is, utilizes speckle image midpoint (x, y) before deformation
The brightness at speckle image corresponding points (x', y') place after the brightness f (x, y) at place is deformed；Interpolation side in Digital Image Processing
Method further includes arest neighbors interpolation or bilinear interpolation, wherein bicubic spline interpolation precision in addition to bicubic spline interpolation
It is higher, it is more commonly used in high-acruracy survey.
4), the speckle image before output skew and deformed speckle image.
DIC Method And Principle introductions：
Refering to Figure 1, the basic principle of DIC methods is very simple, i.e., the measurement problem of malformation is converted into
(reference picture), the relevant matches problem of rear (image after deformation) image are solved before test piece deformation.Therefore, tied for description
The deformation on structure surface, it is necessary first to define shape function.It is assumed that arbitrary point (x, y) in reference picture and one surrounding
Small neighborhood S, there are one group of mapping relations χ to meet
χ (x, y) → (x', y'), f (x, y)=g (x', y')
Wherein, f (x, y) represents the brightness of image at point (x, y) place, and g (x', y') represents the figure at point (x', y') place after deformation
Image brightness, (x, y) are the point in reference picture, and (x', y') is the corresponding points in (x, y) after deformation image.
Mapping χ is referred to as so-called shape function.If neighborhood S and deflection are sufficiently small, shape function χ can be described by formula (1),
Wherein, the in-plane displacement in u and v x and y directions respectively caused by deformation, (x0,y0) sat for the center of region S
Mark.
Write shape function as vector form,
And related coefficient is defined,
The optimal solution for making formula (2) minimize is obtained followed by nonlinear optimization method, problem just achieves a solution.
During from formula (2) as can be seen that when correlation function minimalization, the similitude of image subsection reaches maximum before and after deformation
Value.At this time, the displacement parameter u and v that parameter vector P is included represent the best estimate to displacement after deformation, right in the same way
All measurement points are calculated, you can obtain whole audience displacement.
Minimizing ρ has a variety of method for solving, according to the inventors knowledge, Newton-Raphson method because computational accuracy is higher and
Used by numerous documents, that is, construct following iterative equations
In formula, P0For deformation parameter initial value,WithIt is the First-order Gradient and Hessian matrixes of correlation function ρ, meets
With
It can see from above analytical derivation, the matching that test piece deformation is converted into corresponding points in image before and after test piece deformation is asked
Topic, and the process of matching search is the similitude based on corresponding points gray feature, therefore after the reference and deformation of emulation generation
The intensity profile of speckle pattern needs to correspond, and just can guarantee that the matched correctness of search.
2nd, former theoretical method error analysis
Formed with reference to speckle pattern by random Gaussian Bright folding, generation formula is as follows：
In formula, k represents the number of speckle particle；(xi,yi) be speckle particle center, randomly generate；R is speckle
The radius of particle；fiBrightness for the speckle center generated at random, scope 0-255.Image size is M × N.
When emulation generates deformation pattern, former method is that the central point of speckle particle shifts, and meets shape in formula (1)
The description of function, (x', y') is tried to achieve by (x, y), and the intensity profile of deformation speckle pattern can be obtained by bringing formula (6) into.
Assuming that one Gauss speckle of generation among image, and there is 0.2 strain in x directions, then, it can be seen that Gauss light
Spot is simply translated, as shown in Figure 2.And in fact, due to the effect of stretching, which should be changed into similar ellipse
Round shape, as shown in Figure 3.The irrationality of former method is theoretically analyzed below.
Assuming that there are three points in figure before deformation, wherein B is speckle central point, and A and C are R respectively with a distance from central point
2 points, 3 points have identical y values.It is deformed according to former method, then three in reference picture point are changed into A ', B ', C ', from
It can be seen that, the curve of three mappings is parallel in figure, that is, the displacement for thinking 3 points before and after deforming is the same.
Assuming that the abscissa of B points is S, according to the definition of strain, the strain for obtaining x directions is
Wherein, uBImplication be B point x directions strain, xB'And xBPosition after referring to B points respectively before being deformed in speckle pattern,
ΔxBFor the alternate position spike in B points before being deformed rear speckle pattern.
It can be obtained according to figure (2)：ΔxA=Δ xB=Δ xC
Then
Formula (7) is substituted into formula (8), is obtained
Since speckle particle radius R can not possibly be equal to 0, so the strain of 3 points of A, B, C is different.It is and actual whole
Uniform stretcher strain, i.e. u occur in the x-direction for speckle patternA=uB=uC, it is seen that the method for original generation speckle pattern causes speckle
Figure can see in itself there are error from formula (7), the size of error and the radius R of speckle, the position S for calculating point
And the size of the strain u of deformation is related.When being superimposed by multiple Gauss speckles, generating the quality of speckle pattern can also influence to tie
Fruit, therefore cannot directly carry out error size judgement with the relevant parameter R and S of speckle.The present invention only studies different distortion to drawing
Enter the influence of speckle pattern itself error.
3rd, back mapping method
Refer to shown in Fig. 4, the deformation speckle generation method proposed by the present invention based on back mapping method is as shown in Figure 4.
First, reference picture is generated using the speckle particle superposition generated at random, then in speckle pattern known to the gray scale of each pixel position.It is real
Image after the border of deformation on to(for) M × N sizes, the position of each pixel is known.Formula (1) shape function describes to become
The position of shape correspondence pixel, now does shape function inverse transformation, i.e. (x, y)=F (x', y'), then after deformation (x',
Y'), can try to achieve before deforming (x, y), and the value is probably sub-pixel location.And the deformation front position point of whole location of pixels
Gray value is superimposed by speckle particle gray scale and produced, sub-pixel location value can be obtained by bicubic spline interpolation, before deformation
The gray value of position extract be filled into deformation after corresponding position, then can generate speckle pattern after an amplitude variation shape, the speckle pattern
Generating process is simple, meets the deformation requirements of actual experiment.
Simulation analysis
According to theory analysis, initial deformation can make to introduce error in speckle pattern after deformation, and this section will study different changes
The influence of shape and the size of deformation to former generation method, and prove that the validity of back mapping method of the present invention and high accuracy are special
Property.
Embodiment 1：Translation of rigid body
Reference picture is the speckle image generated at random, and resolution ratio is 256 × 256pixels, and speckle particle number is 2000,
Speckle particle radius is 4.Using former method and back mapping method, the translation figure at intervals of 0.05pixel is generated in the x-direction respectively
As totally 20, i.e., the displacement of image sequence is in 0-1pixel.The parametric variable chosen during DIC is calculated is consistent, analyzes two groups of speckles
Figure, and the error and standard deviation of displacement field are calculated, it is expressed as follows：
Wherein,Represent all average values for calculating point displacement in same width figure, i.e.,vtrueRepresentation theory becomes
Shape parameter；N represents all and calculates points.
From fig. 5, it is seen that the worst error for the displacement field that two methods are calculated is in 0.001pixel, still
The error calculated based on back mapping method generation speckle pattern meets sin back propagation nets, the rule and the knot analyzed in document
Fruit coincide.In terms of the result of calculation of Fig. 6 Plays difference, the standard deviation calculated based on back mapping method speckle pattern is smaller and small
In 0.001pixel, meet the requirement of high-acruracy survey.
Embodiment 2：Homogeneous deformation
It is constant with reference to speckle pattern, using former method and back mapping method, generate Uniform Tension figure in the y-direction respectively, it is micro- to answer
Becoming from 1000-20000, the parametric variable that Poisson's ratio is maximized during 0.5. selections DIC is calculated is consistent, analyzes two groups of speckle patterns,
Regard the v in formula (10) as strains, the error and standard deviation of strain field are calculated, as a result as shown in Fig. 7, Fig. 8, Fig. 9 and Figure 10.
For x Direction distortions, when microstrain is less than 10000, the speckle pattern calculation error of two methods generation is close, and
When microstrain is more than 10000, the almost linear increase of the error based on former method, and based on the calculation error of back mapping method
Without significant change, maximum strain error is no more than 50 microstrains.Found from Fig. 8, the standard deviation of the calculating strain based on former method
It is larger always, and almost as the increase of strain, standard deviation are also increasing.
For y Direction distortions, y is principal strain directions, either calculation error, or standard deviation, is generated based on former method
Speckle pattern calculate larger, and almost linearly increase with the increase of strain, be consistent with the linear relationship that theory deduction obtains.
On the other hand the validity of back mapping speckle drawing generating method proposed by the present invention and high-precision characteristic are also demonstrated.
Embodiment 3：Heterogeneous deformation
Reference picture is the speckle image generated at random, and resolution ratio is 500 × 500pixels, and speckle particle number is 4000,
Speckle particle radius is 4, using former method and back mapping method, generates heterogeneous deformation figure, the position in y directions in the y-direction respectively
Move field and meet sin distributions, i.e. v=Asin (2 π y/T), A=1, T=200.
It will be seen from figure 11 that the error on the whole based on the generation speckle pattern calculating of former method is bigger, maximum deviation
It can reach 2000 microstrains.And the back propagation net of the latter more meets reality, i.e., error is maximum at strain peak value.Contrast
Figure 12 understands that the standard deviation being calculated based on two kinds of speckles is not much different, and maximum is less than 300 microstrains.On the whole, it is based on
The speckle pattern calculation error of back mapping method generation is relatively low, and more meets actual deformation rule.
Due to emulation experiment deformation it is known that and can preferably exclude lens distortion, light source fluctuation, non-ideal loading bar
The influence that part etc. calculates DIC, emulation speckle pattern are widely applied among DIC emulation experiments.In view of primary into speckle
Drawing method itself introduces the problem of large error, and this patent uses back mapping method, generation deformation speckle pattern, the letter of this method thought
It is single, realization is easily programmed, and the error calculated is smaller, and deformation rule more meets the deformation state of actual test specimen.By imitative
True experiment is analyzed, and demonstrates the validity of this patent generation deformation speckle drawing method and high-precision characteristic.
The above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, some improvement can also be made without departing from the principle of the present invention, these improvement also should be regarded as the present invention's
Protection domain.
Claims (4)
- A kind of 1. deformation speckle generation method based on back mapping method, it is characterised in that：Comprise the following steps1) K speckle particle, is generated at random, wherein, the coordinate of the center of i-th of speckle particle and brightness are respectively (xi, yi) and fi, wherein, fiScope be [0,255], wherein, 1≤i≤K；2), the inverse function of shape function (x', y')=F (x, y) is：(x, y)=F-1(x', y'), (x, y) are speckle image before deformation In point coordinates, (x', y') is the correspondence point coordinates of (x, y) after deformation in speckle image, that is, utilizes speckle image after deformation In point coordinates (x', y') try to achieve point coordinates (x, y) before deformation in speckle image；3) speckle image and the brightness value of corresponding points in deformed speckle image before, deforming meet：G (x', y')=f (x, y)Wherein, g (x', y') represents the brightness value at point (x', y') place in speckle image after deforming, and utilizes the speckle generated at random Particle obtains the brightness of each point in speckle image before deforming：<mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mi>i</mi> <mi>K</mi> </munderover> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>*</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mo>(</mo> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>-</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow> <mi>y</mi> <mo>-</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <mo>)</mo> <mo>/</mo> <msup> <mi>R</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow>Wherein, K represents the number of speckle particle, and (x, y) is the point coordinates in speckle image, (x before deformingi,yi) dissipated for i-th The coordinate of spot granular center position, fiFor the brightness of i-th of speckle particle center, R is the radius of speckle particle, i.e., sharp Speckle image corresponding points (x', y') place is bright after being deformed with the brightness f (x, y) at speckle image midpoint (x, y) place before deformation Degree；4), the speckle image before output skew and deformed speckle image.
- 2. the deformation speckle generation method based on back mapping method as claimed in claim 1, it is characterised in that：The shape function is Single order shape function,<mrow> <msup> <mi>x</mi> <mo>&prime;</mo> </msup> <mo>=</mo> <mi>x</mi> <mo>+</mo> <mi>u</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>u</mi> </mrow> <mrow> <mo>&part;</mo> <mi>x</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>u</mi> </mrow> <mrow> <mo>&part;</mo> <mi>y</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mi>y</mi> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow><mrow> <msup> <mi>y</mi> <mo>&prime;</mo> </msup> <mo>=</mo> <mi>x</mi> <mo>+</mo> <mi>v</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>v</mi> </mrow> <mrow> <mo>&part;</mo> <mi>x</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <mo>&part;</mo> <mi>v</mi> </mrow> <mrow> <mo>&part;</mo> <mi>y</mi> </mrow> </mfrac> <msub> <mo>|</mo> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mi>y</mi> <mo>-</mo> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow>Wherein, the in-plane displacement in u and v x and y directions respectively caused by deformation, (x0,y0) for deformation before speckle image center Position coordinates, (x, y) are the point coordinates in speckle image before deforming, and (x', y') is pair in (x, y) after deformation speckle image Answer point coordinates.
- 3. the deformation speckle generation method based on back mapping method as claimed in claim 1, it is characterised in that：The shape function is Second order shape function,<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msup> <mi>x</mi> <mo>&prime;</mo> </msup> <mo>=</mo> <mi>x</mi> <mo>+</mo> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>P</mi> <mn>3</mn> </msub> <mi>&Delta;</mi> <mi>x</mi> <mo>+</mo> <msub> <mi>P</mi> <mn>5</mn> </msub> <mi>&Delta;</mi> <mi>y</mi> <mo>+</mo> <msub> <mi>P</mi> <mn>7</mn> </msub> <msup> <mi>&Delta;x</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>P</mi> <mn>9</mn> </msub> <mi>&Delta;</mi> <mi>x</mi> <mi>&Delta;</mi> <mi>y</mi> <mo>+</mo> <msub> <mi>P</mi> <mn>11</mn> </msub> <msup> <mi>&Delta;y</mi> <mn>2</mn> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>y</mi> <mo>&prime;</mo> </msup> <mo>=</mo> <mi>y</mi> <mo>+</mo> <msub> <mi>P</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>P</mi> <mn>4</mn> </msub> <mi>&Delta;</mi> <mi>x</mi> <mo>+</mo> <msub> <mi>P</mi> <mn>6</mn> </msub> <mi>&Delta;</mi> <mi>y</mi> <mo>+</mo> <msub> <mi>P</mi> <mn>8</mn> </msub> <msup> <mi>&Delta;x</mi> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>P</mi> <mn>10</mn> </msub> <mi>&Delta;</mi> <mi>x</mi> <mi>&Delta;</mi> <mi>y</mi> <mo>+</mo> <msub> <mi>P</mi> <mn>12</mn> </msub> <msup> <mi>&Delta;y</mi> <mn>2</mn> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced>In formula, deformation parameter vector P=(u, v, ux,vx,uy,vy,uxx,vxx,uxy,vxy,uyy,vyy)T, Δ x=x-x0, Δ y= y-y0, u and v are the in-plane displacement in x and y directions, (ux,vx,uy,vy) it is displacement gradient vuxx, vxx, uxy, vxy,uyy,vyyFor displacement Second-order partial differential coefficient.
- 4. the deformation speckle generation method based on back mapping method as claimed in claim 1, it is characterised in that：It is right in step 3) Speckle image obtains the brightness value of sub-pixel location into row interpolation before deformation, and the interpolation method in Digital Image Processing has arest neighbors Interpolation either bilinear interpolation or bicubic spline interpolation.
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