CN104657955B - The displacement field iteration smoothing method of Digital Image Correlation Method based on kernel function - Google Patents
The displacement field iteration smoothing method of Digital Image Correlation Method based on kernel function Download PDFInfo
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Abstract
The invention discloses a kind of displacement field iteration smoothing methods of Digital Image Correlation Method based on kernel function, using the correlation function ρ based on kernel function*,And it is handled using the displacement field that iteration smoothing method obtains the Digital Image Correlation Method based on kernel function.The displacement field iteration smoothing method of Digital Image Correlation Method based on kernel function of the invention can be efficiently modified the measurement accuracy of displacement field, define a kind of new correlation function ρ based on kernel function*, the influence of picture noise is considered, so that there is better measurement accuracy for the present invention is compared with conventional method.Displacement field iteration smoothing method is on the basis of former least square method, add coarse penalty term, make to reach a balance between the roughening of the accuracy reconciliation of solution, wherein, smoothing parameter α can be solved adaptively, without facilitating, being practical with the parameter is artificially selected, the smooth displacement field of output is calculated, it is as a result relatively accurate.
Description
Technical field
The invention belongs to digital image processing fields, and in particular to a kind of Digital Image Correlation Method based on kernel function
Displacement field iteration smoothing method.
Background technique
Digital picture is related, is proposed earliest by Sutton et al., is a kind of natural line by body surface random distribution
Reason or artificial carrier of the speckle field as deformation information obtain body structure surface under external load function by machine vision technique
The measuring method of the whole audience displacement and strain information.Since DIC has many advantages, such as, such as measurement process is simple, measurement knot
Fruit accuracy is high, it is non-contact, can get full field data etc., be applied widely in recent years in Experimental Mechanics field.
As a kind of effective measuring method, DIC technology obtains rapid development in recent two decades, and is trying
Mechanics is tested, material and its related fields obtain a large amount of successful applications.These are all attributed to all the advantages of DIC method itself,
Such as contactless, pilot system builds convenient, available full field data and relatively high measurement accuracy, etc..For
This, a large amount of methods are proposed for improving the measurement accuracy and processing speed of DIC, and this method is pushed to obtain more in a wider context
It must be applied successfully.Unfortunately, although the measure theory based on DIC obtains sufficient research in recent years, conventional method is still
There are great number of issues, when facing practical application.Speckle pattern, image subsection size, correlation function, iterated conditional etc. it is many because
Element can be to measurement result influence of noise.For problems, has some scholars and carried out more careful point to DIC performance
Analysis, and propose some bulking property principles for instructing practical application.
It must be noted that picture noise is inevitable in practical application.And the measurement process of tradition DIC method is serious
Luminance information dependent on image.In the presence of noise, Luminance Distribution of the deformation front and back in matched image subsection also can
It changes with the distribution of noise, to drastically influence the accuracy of measurement result.To reduce picture noise to measurement
As a result influence, some methods that measured deviation is eliminated based on pre-treatment or post-processing technology are suggested.Although obtaining one
Fixed effect, but when being used for actual measurement, these methods still face the problem of how smoothing parameter is chosen lacked.
The basic principle of DIC is very simple, interrecord structure deformation sequence image, and before being deformed after image subsection in
Search maximizes certain correlation criterion, such as: zero-mean normalizes crosscorrelation criterion, to obtain the displacement number of measurement point
According to.In order to improve the computational accuracy of displacement field, research focuses mainly on exporting high-precision sub-pix by improving DIC algorithm
Displacement.Higher-order gradients are introduced shape function to realize the description to complex deformation by Lu et al., are become so as to improve DIC to complexity
The measurement effect of shape field.DIC is corrected in Cofaru et al. proposition with irregular speckle pattern, and is come in conjunction with regularization method
Increase the output accuracy of displacement field.Pan's research shows that: using size is the gauss low frequency filter of 5*5 pixel to speckle pattern
As being pre-processed, the displacement field error of DIC output can be effectively reduced.
In Experimental Mechanics field, for simple displacement field data, strain field distribution information seems more valuable.To the greatest extent
Pipe DIC technology experienced the development of many years, and since current conditions limit, the displacement field of DIC output can still have various deviations, have
The analysis for closing DIC system deviation is detailed in document.All information due to calculating strain field are included in displacement data, if directly
It connects using these include the displacement data of noise and calculates strain, error will be amplified, so that effective strain field distribution
Rule is difficult to obtain.Just because of this, the post-processing technology based on data smoothing or surface fitting be used to eliminate making an uproar for displacement field
Sound.However, the defect of these methods is to need to manually adjust the parameter of algorithm.During actual measurement, due to not enough
Priori knowledge carry out guide parameters adjustment, thus hinder its practical application.
Therefore, it is necessary to a kind of new Digital Image Correlation Method displacement field smoothing methods to solve the above problems.
Summary of the invention
The purpose of the present invention is being directed to Digital Image Correlation Method and its deficiency of displacement field smoothing method in the prior art,
A kind of displacement field iteration smoothing method of Digital Image Correlation Method based on kernel function is provided.
For achieving the above object, the present invention is based on the displacement field iteration of the Digital Image Correlation Method of kernel function is smooth
Following technical solution can be used in method:
A kind of displacement field iteration smoothing method of the Digital Image Correlation Method based on kernel function, it is characterised in that: be based on
The Digital Image Correlation Method of kernel function uses the correlation function ρ based on kernel function*,
Wherein, c is normaliztion constant, and k () is kernel function, and h is the bandwidth control parameter of kernel function, spTo deform preceding figure
As region S0In pixel, f (sp) it is to deform pixel s in preceding imagepThe brightness of image at place, g (sp, P) and it is image after deformation
In with pixel spBrightness of image at corresponding pixel, P are shape function parameter；
Wherein, iteration smoothing method the following steps are included:
(1), deformed displacement field data d is measured using the Digital Image Correlation Method based on kernel functionn,
Middle displacement field data dnIt is expressed from the next: dn=d+n；
Wherein, d is smoothed out displacement field, and n is displacement field noise；
(2), quadratic function is constructed
Wherein, dnFor deformed displacement field data, d is smoothed out displacement field data, and n is displacement field noise, and α is flat
Sliding parameter, C are high-order operator；
The first-order partial derivative for solving quadratic function, obtains
Wherein, C is high-order operator,
D and α are become into column vector and enable Q=[d1,d2,d3...dm, α], wherein m is points；It can then obtain
(3), according to step (2)Solve the second-order partial differential coefficient of quadratic function
Above-mentioned matrix is combined, is obtained
(4), it is obtained using step (2) and (3)WithCalculating is iterated to following formula:
Wherein, the initial value of Q is [dn,α]T, wherein dnFor deformed displacement field data, the d obtained after above formula convergence
As ideal real displacement value, PkAnd Pk+1Respectively+1 element of k-th of element of vector P and kth.
Further, the range of the α is (0,1).
Further, the condition of convergence of step 4) isWherein, ε≤0.1.
Further, the Digital Image Correlation Method based on kernel function the following steps are included:
One) shape function, is defined: the arbitrary point (x in setting reference picture0,y0) and surrounding neighborhood S0, (x, y) is ginseng
The coordinate of any pixel in image in neighborhood S is examined,For in target image with pixel (x, y) corresponding pixel
The coordinate of point, there are one group of mapping relations χ, and following formula is set up:
Wherein, f (x, y) indicates the brightness of image at pixel (x, y),Indicate pixelThe image at place
Brightness, mapping relations χ are shape function；Wherein, shape function χ is expressed from the next:
Wherein, u and v is respectively the displacement in the direction x and y caused by deforming, (x0,y0) be neighborhood S center position coordinates,To deform the single order displacement gradient generated in the x and y direction；
Two), by step 1) shape function parametrization, and indicated with vector P,
Define correlation function ρ*,
Wherein, c is normaliztion constant, and k () is kernel function, and h is the bandwidth control parameter of kernel function, spFor neighborhood S0In
One pixel, f (sp) it is to deform pixel s in preceding imagepThe brightness of image at place, g (sp, P) be after deformation in image with pixel
Point spBrightness of image at corresponding pixel；
Three) it, is calculated and enables correlation function ρ*Shape function parameter P when minimum.
Further, step 3) in be calculate by the following formula correlation function ρ*Minimum value, construct iterative equations:
In formula, P0For deformation parameter initial value,WithIt is correlation function ρ*First-order Gradient and Hessian matrix,
InWithFormula it is as follows:
Utilize iterative equationsIt is calculated and enables correlation function ρ*Minimum when solution, in formula, PiAs
I-th of element, P in vector PjJ-th of element in as vector P.
Further, the Digital Image Correlation Method based on kernel function the following steps are included:
1), the preceding and deformed image of acquisition object deformation, the image before deformation is reference picture, and deformed image is
Target image；
2) interest region S, is chosen on a reference1, interest region S1For reference picture sub-district；
3) region of search S, is established on target image2, region of search S2For target image sub-district, target image sub-district packet
Containing deformed reference picture sub-district；
4) gray value of target image sub-district and the point in reference picture sub-district, is obtained；
5) shape function, is constructed, determines the positional relationship of corresponding points in reference picture sub-district and target image sub-district, wherein
(x1,y1) be any pixel in reference picture sub-district coordinate, (x2,y2) be target image sub-district in pixel (x1,y1)
The coordinate of corresponding pixel, there are one group of mapping relations χ, and following formula is set up:
χ(x1,y1)→(x2,y2)
f(x1,y1)=g (x2,y2)
Wherein, f (x1,y1) indicate pixel (x1,y1) at brightness of image, g (x2,y2) indicate pixel (x2,y2) at
Brightness of image, mapping relations χ are shape function；Wherein, shape function χ is expressed from the next:
Wherein, x caused by u' and v' is deformed respectively1And y1The displacement in direction, (x', y') are the center of reference picture sub-district
Position coordinates,To deform in x1And y1The single order displacement gradient generated on direction；
6), the shape function of step 5) is parameterized, and is indicated with vector P',
Define correlation function ρ*',
Wherein, c is normaliztion constant, and k () is kernel function, and h is the bandwidth control parameter of kernel function, sp' it is reference picture
A pixel in sub-district, f (sp') it is to deform pixel s in preceding imagep' place brightness of image, g (sp', P') it is after deforming
In image with pixel sp' brightness of image at corresponding pixel；
7) vector, is setInitial value P0', and set maximum number of iterations n '；
8), by P0' bring iterative equations into:
In formula, P0' it is deformation parameter initial value,WithIt is correlation function ρ*First-order Gradient and Hessian matrix,
WhereinWithFormula it is as follows:
In formula, Pi' and Pj' be respectively vector P' i-th of element and j-th of element；
P is calculated according to iterative equations1'；
9), judge whether iterative equations restrain according to the following formula,If convergence, saves
Interest region S1Shift value u' and v'；If do not restrained, P is enabled0'=P1', and repeat step 8) and 9)；If the number of iterations
Reach maximum number of iterations n ', then terminates iteration；
10) shift value in interest region, is exported.
Further, obtain in step 4) gray value of the point in target image sub-district by target image sub-district into
Row bicubic spline interpolation obtains the gray value of sub-pixel location in target image sub-district.
Further, obtain in step 4) gray value of the point in reference picture sub-district by reference picture sub-district into
Row bicubic spline interpolation obtains the gray value of sub-pixel location in reference picture sub-district.
Further, interest region S is chosen in step 2) on a reference1, interest region S1For reference picture sub-district
It is obtained by following steps: the first grid being respectively divided on a reference, the number of the first grid is M row × N column, is being referred to
Spacing on the length and width direction of image between the first grid is respectively l and w, is established on a reference with a-th
Interest region S centered on one grid1, interest region S1Length and width for reference picture sub-district, reference picture sub-district is distinguished
For L and W, wherein a=1,2,3 ..., M × N.By interest region is chosen in the way of grid division on a reference, letter
Folk prescription is just, easy to accomplish.
Further, region of search S is established in step 3) on target image2, region of search S2For target image
Area, target image sub-district include that deformed reference picture sub-district is obtained by following steps: second is divided on target image
Grid, the number of the second grid are M row × N column, the spacing on the length and width direction of target image between the second grid
Respectively l and w；The region of search S centered on b-th of second grids is established on target image2, region of search S2For target
Image subsection, the length and width of target image sub-district are respectively k ' * L and k ' * W, wherein k ' > 1, b=a.Using in target figure
Region of search is chosen by way of grid division as on, it is simple and convenient, it is easy to accomplish.
The utility model has the advantages that the displacement field iteration smoothing method of the Digital Image Correlation Method of the invention based on kernel function can be with
It is efficiently modified the measurement accuracy of displacement field.A kind of new likeness coefficient based on kernel function is defined, considers picture noise
It influences, so that there is better measurement accuracy for the present invention is compared with conventional method.Displacement field iteration smoothing method is former minimum
On the basis of square law, coarse penalty term is added, makes to reach a balance between the roughening of the accuracy reconciliation of solution, wherein
Smoothing parameter α can be solved adaptively, without facilitating, being practical, calculating the smooth displacement of output with the parameter is artificially selected
, it is as a result relatively accurate.
Detailed description of the invention
Fig. 1, be the Digital Image Correlation Method of the invention based on kernel function displacement field iteration smoothing method process
Figure；
Reference picture before Fig. 2, deformation；
Image (4% noise of addition) after Fig. 3, deformation；
Four groups of displacement error comparison diagrams that Fig. 4, NR method are calculated；
Four groups of shift standards difference comparison diagrams that Fig. 5, NR method are calculated；
Four groups of positions being calculated of displacement field iteration smoothing method of Fig. 6, Digital Image Correlation Method based on kernel function
Shift error comparison diagram；
Four groups of positions being calculated of displacement field iteration smoothing method of Fig. 7, Digital Image Correlation Method based on kernel function
Move standard deviation comparison diagram；
It Fig. 8, is test specimen figure；
Fig. 9, for the Digital Image Correlation Method based on kernel function displacement field iteration smoothing method treatment effect figure；
It Figure 10, is test specimen handling principle figure；
Figure 11 is the flow chart of displacement field iteration smoothing method of the invention；
Figure 12 is α iteration situation of change under different α initial conditions；
The comparison diagram of shift value and real displacement value after Figure 13 is N-R iterative calculation shift value, is smooth；
Figure 14 is that the processing result of conventional method processing DIC output data is utilized in the case of heterogeneous deformation；
Figure 15 is the knot obtained in the case of heterogeneous deformation using displacement field iteration smoothing method processing DIC output data
Fruit；
Figure 16 is simulated speckle pattern；
Figure 17 is speckle pattern；
Figure 18 is speckle schematic diagram；
Figure 19 is the elongation strain field deformation measurement result that Multiple-Hole Specimen is handled using conventional DIC method；
Figure 20 is the shear strain field deformation measurement that Multiple-Hole Specimen is handled using conventional DIC method；
Figure 21 is the elongation strain field deformation measurement result that Multiple-Hole Specimen is handled using method of the invention；
Figure 22 is the shear strain field deformation measurement that Multiple-Hole Specimen is handled using method of the invention.
Specific embodiment
In the following with reference to the drawings and specific embodiments, the present invention is furture elucidated, it should be understood that these embodiments are merely to illustrate
It the present invention rather than limits the scope of the invention, after the present invention has been read, those skilled in the art are to of the invention each
The modification of kind equivalent form falls within the application range as defined in the appended claims.
Traditional DIC method
The basic principle of DIC method is very simple, i.e., (refers to before converting test piece deformation for the measurement problem of malformation
Image), the relevant matches problem of rear (target image) image solved.It therefore, is the deformation on description scheme surface,
Firstly the need of definition shape function.It is assumed that arbitrary point (x, y) and a surrounding small neighborhood S in reference picture, there are one
Group mapping relations χ meets
Wherein, f (x, y) indicates the brightness of image at point (x, y),Indicate point after deformingThe image at place is bright
Degree.
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, u and v is respectively the in-plane displacement in the direction x and y caused by deforming, (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 enabling formula (2) to minimize is obtained followed by nonlinear optimization method, problem just achieves a solution.
From formula (2) as can be seen that when correlation function minimalization, the similitude of deformation front and back image subsection reaches maximum
Value.At this point, displacement parameter u and v that parameter vector P includes represent the best estimate to being displaced after deformation, it is right in the same way
All measurement points are calculated, and whole audience displacement can be obtained.
ρ is minimized there are many method for solving, according to known to author, Newton-Raphson method due to computational accuracy is higher by
Numerous documents are used, that is, construct following iterative equations
In formula, P0For deformation parameter initial value,WithIt is the First-order Gradient and Hessian matrix of correlation function ρ, meets
With
Carefully analyzing formula (3-5) can be seen that tradition DIC during minimizing ρ, f (sp)-g(sp, P) andIt is two very big on iteration result influence, or even will affect whether iteration restrains.It (does not make an uproar ideally
Sound), every iteration is primary, and the parameter of shape function can all become further along gradient direction to true strain parameter.When iteration meets eventually
Only when condition, Ying YouIt is intended to zero.However, in the presence of the picture noise, not only f
(sp)-g(sp, P) item be not equal to zero,As noise influence and magnification distortion.Therefore, traditional DIC exists
When practical application can because noise there are due to reduce measurement effect.
DIC method of the invention
To improve tradition DIC to the adaptability of noise, kernel function is introduced into the definition of similarity function herein.Kernel function
It is normally defined certain radially symmetrical scalar function.For example, gaussian kernel function, i.e., so-called radial basis function (Radial
Basis Function, RBF), it is defined as any point x to a certain center x in spacecBetween Euclidean distance monotonic function, can
Be denoted as k (| | x-xc| |), form is
Wherein, xcFor kernel function center, σ is the width parameter of function, and the radial effect range of control function, acting on is
Part, when x is far from xcWhen function value very little.
Pass through the figure before and after deforming in given neighborhood S for the control ability using kernel function in radial extension
The similarity measurement of deformation front and back image subsection is transformed to the feature space centered on zero by the mode that image brightness makes the difference, and
It is indicated in the form of error of sum square, constructs the related coefficient based on kernel function
Wherein, c is normaliztion constant, and k () is kernel function, and h is the bandwidth control parameter of kernel function.
To simplify expression, enable
r(sp, p) and=f (sp)-g(sp,p)
Formula (4) is reduced to,
The First-order Gradient and Hessian matrix of ρ be,
Similarly, formula (8) and formula (9) can be brought into formula (3), and obtains the numerical solution of minimum formula (7) by iterative process.
The comparison of two methods
The First-order Gradient and Hessian matrix for comparing two methods similarity function can be seen that formal KDIC and be
The weighted version of TDIC, and weight function is equivalent to the first derivative of kernel function.Therefore, the type of different kernel functions will correspond to not
Same weighted version.Intuitively to analyze, discuss by taking most common two kinds of kernel functions as an example.One is Epanechnikov
Core, another kind are Gaussian kernels.
Case1:Epanechnikov core
That is,
If Epanechnikov nucleus band is entered formula (8) and (9), from expression-form, KDIC and TDIC are equivalents
's.That is, TDIC is a special case of KDIC when using Epanechnikov core.
Case2: Gaussian kernel
And
Due to the derivative and original function profile having the same of Gaussian function, the mathematics that we can use Gaussian function is special
Property and its relationship between actual physical meaning realize weighting, to obtain to the immunity of picture noise.Assuming that figure
Noise as in is the white noise of random distribution, and variance is σ.When accordingly, we can be by the bandwidth parameter (formula in kernel function
(6) h in) it is set as the multiple of σ.Show to change the time when deviation is more than the multiple place pixel it is very tight by noise pollution
Weight, one almost nil weight of distribution, which can directly eliminate larger noise spot, to be influenced.On the contrary, when deviation falls in the multiple range
When interior, it is weighted in such a way that Gauss weights according to deviation of the noise pollution degree to difference, as zoning
In each pixel distribution contribution intensity, to obtain more accurate measurement result.
Embodiment 1:
The displacement field iteration smoothing method of Digital Image Correlation Method based on kernel function, comprising the following steps:
1), the preceding and deformed image of acquisition object deformation, the image before deformation is reference picture, and deformed image is
Target image；
2) interest region S, is chosen on a reference1, interest region S1For reference picture sub-district；It is obtained by following steps
To: the first grid is respectively divided on a reference, the number of the first grid is M row × N column, in the length and width of reference picture
The spacing spent on direction between the first grid is respectively l and w, is established centered on i-th of first grids on a reference
Interest region S1, interest region S1For reference picture sub-district, the length and width of reference picture sub-district is respectively L and W, wherein a
=1,2,3 ..., M × N.It is simple and convenient by choosing interest region in the way of grid division on a reference, it is easy real
It is existing.
3) region of search S, is established on target image2, region of search S2For target image sub-district, target image sub-district packet
Containing deformed reference picture sub-district；It is obtained by following steps: dividing the second grid, of the second grid on target image
Number is M row × N column, and the spacing on the length and width direction of target image between the second grid is respectively l and w；In target
The region of search S centered on b-th of second grids is established on image2, region of search S2For target image sub-district, target image
The length and width of sub-district is respectively k*L and k*W, wherein k > 1, b=a.Utilize the side on target image through grid division
Formula chooses region of search, simple and convenient, easy to accomplish.Wherein, l and w is 3-5 pixel.
4) gray value of target image sub-district and the point in reference picture sub-district, is obtained.It obtains in target image sub-district
The gray value of point obtains sub-pixel location in target image sub-district by carrying out bicubic spline interpolation to target image sub-district
Gray value.The gray value for obtaining the point in reference picture sub-district carries out bicubic spline interpolation also by reference picture sub-district,
Obtain the gray value of sub-pixel location in reference picture sub-district.
5) shape function, is constructed, determines the positional relationship of corresponding points in reference picture sub-district and target image sub-district, wherein
(x1,y1) be any pixel in reference picture sub-district coordinate, (x2,y2) be target image sub-district in pixel (x1,y1)
The coordinate of corresponding pixel, there are one group of mapping relations χ, and following formula is set up:
χ(x1,y1)→(x2,y2)
f(x1,y1)=g (x2,y2)
Wherein, f (x1,y1) indicate pixel (x1,y1) at brightness of image, g (x2,y2) indicate pixel (x2,y2) at
Brightness of image, mapping relations χ are shape function；Wherein, shape function χ is expressed from the next:
Wherein, u and v is respectively the displacement in the direction x and y caused by deforming, and (x', y') is the centre bit of reference picture sub-district
Coordinate is set,To deform in x1And y1The single order displacement gradient generated on direction；
6), the shape function of step 5) is parameterized, and is indicated with vector P',
Define correlation function ρ*,
Wherein, c is normaliztion constant, and k () is kernel function, and h is the bandwidth control parameter of kernel function, sp' it is reference picture
A pixel in sub-district, f (sp') it is to deform pixel s in preceding imagep' place brightness of image, g (sp', P') it is after deforming
In image with pixel sp' brightness of image at corresponding pixel；
7) vector, is setInitial value P0', and maximum number of iterations n is set,
8), by P0' bring iterative equations into:
In formula, P0' it is deformation parameter initial value,WithIt is correlation function ρ*First-order Gradient and Hessian matrix,
WhereinWithFormula it is as follows:
In formula, Pi' and Pj' be respectively vector P' i-th of element and j-th of element；
P is calculated according to iterative equations1'；
9), judge whether iterative equations restrain according to the following formula,If convergence, saves
Interest region S1Shift value u' and v'；If do not restrained, P is enabled0'=P1', and repeat step 8) and 9)；If the number of iterations
Reach maximum number of iterations n, then terminates iteration；
10) shift value in interest region, is exported.
What this algorithm inputted is the speckle pattern before and after the test piece deformation acquired, utilizes the gray feature of image, final output
Be test piece deformation displacement field；When calculating, the area-of-interest grid division point of test specimen before being deformed, purpose is exactly to seek this
The position of a little mesh points image after deformation finds out displacement at these mesh points so as to make difference.
Reference picture sub-district is divided, centered on the mesh point of division to divide in same central point after deformation image
Target image sub-district, size are k times of reference picture sub-district, k > 1.It, will in order to find the position after deformation where mesh point
Reference picture sub-district carries out point by point search in target image sub-district, finds most like sub-district, then the central point of the sub-district
Position is position of the mesh point after deformation in image.
Utilize image grayscale feature construction similarity function, such as minimum squared distance function.To improve the similitude letter
Several noise immunities adds weighted value items for the function,In formula, k be may be selected
Gaussian function.
In formula, f is the gray value of each point in reference picture sub-district, and g is the gray value of each point after deforming in image subsection.
The position (x', y') of point after deformation in image subsection is described by shape function, and (x', y') is sub-pixel location value, therefore
Interpolation, such as bicubic spline interpolation, to obtain the gray value of sub-pixel location need to be carried out to target sub-district.P=[U, V, Ux, Vx,
Uy,Vy]TThe function is minimized in fact, the similar function is the function of P for the unknown quantity in shape function, can solve P's
Value.
Similar functionIt is the function of a multivariable, it can be by nonlinear optimization side
Method, such as Newton-Raphson method are iterated solution.
The iteration convergence condition of iterative equations: desirableε < 0.1, it is convergent in guarantee
Under the premise of, ε is smaller, and output displacement field is more accurate.Or setting convergence number, such as 50 times, under the premise of guaranteeing convergent, which is got over
Greatly, output displacement field is more accurate.
Sunykatuib analysis: for the validity for assessing the above method, the method quilt of digital speckle image analogue measurement test piece deformation
Using.Due to deformation parameter it is known that the superiority and inferiority for the treatment of effect can be evaluated objectively.Reference picture is the digital speckle generated at random
Image, resolution ratio are 256 × 256pixels, and speckle particle number is 2000, and speckle particle radius is 4, as shown in Figure 2.By pre-
The deformation parameter first set generates an amplitude variation shape speckle pattern every 0.5pixel, symbiosis is at 20 in the y-direction.To this group displacement
1%, 2% and 4% noise is added respectively for the image of 0-1pixel, in addition muting one group of speckle pattern, obtains 4 groups altogether and dissipate
Spot figure.Wherein, the speckle pattern for adding 4% noise level is as shown in Figure 3.
For the influence for investigating different stage noise, four groups of speckle patterns are handled first with traditional DIC method, position is calculated
Shifting value will be evaluated using two methods, i.e., displacement mean error and standard deviation, expression formula are as follows:
Wherein,Indicate all average values for calculating point displacement in same width figure, i.e.,vtrueRepresentation theory
Deformation parameter；N indicates all calculating points.
Figure 4 and 5, which are shown respectively, calculates the error and standard deviation that displacement field post analysis obtains by NR method.It can be with from Fig. 4
See, random noise influences displacement field computation significant.With the increase of noise grade, displacement error is integrally in rising trend,
From the point of view of worst error value, increase to 0.0994pixel from 0.0077pixel.
Equally, it is seen from fig 5 that the standard deviation of gained displacement field is also the increase with noise grade and increases, most
Big standard deviation increases to 0.0133pixel from 0.0029pixel.
To verify the validity for improving DIC method herein, KDIC method is used to calculate four groups of emulation speckle patterns.Equally,
Displacement two kinds of evaluation indexes of mean error and standard deviation are used to the validity of appraisal procedure.Calculated result such as Fig. 6 and Fig. 7 institute
Show.
As can see from Figure 7, the displacement field error containing 4% noise level that comparison tradition DIC is calculated, by KDIC
The error for all noise levels that method is calculated is smaller, wherein analyzed so that 4% noise level calculates error as an example, it is maximum
Error drops to 0.0271 from 0.0094pixel, new method significant effect.
For convenient for comparing, the worst error of 4 groups of displacement calculated result and average standard deviation are listed in table 1.The results show that
DIC method based on kernel function can effectively reduce the calculating error of displacement field, also, the bigger effect of noise level is more significant.
But from the point of view of the calculated result of standard deviation, treatment effect is not apparent.For 1% noise level, i.e. image noise
Than for 40dB, the calculating error of displacement field is 6 ‰, and the industrial camera for being actually used in acquisition image can achieve 40dB's substantially
Signal-to-noise ratio is even higher, thus this method be used for handle actual acquisition image when, the precision of thousand quartiles can satisfy completely to be wanted
It asks.
Table 1TDIC and KDIC method calculated result worst error and average standard deviation comparison
The above simulation analysis demonstrates the validity for improving DIC method reduction displacement field computation error herein.To prove to be somebody's turn to do
Method can effectively deal with the image of actual acquisition, will carry out calculating analysis below in KDIC method.Actual picture as shown in figure 8,
Test specimen is aluminum material, carries out the stretching of the direction y.Treatment effect is as shown in Figure 9.
From processing result, it can be seen that, the displacement field being calculated through KDIC method is more smooth, can effectively reduce the later period
By the error for the strain field computation that displacement field difference obtains, which demonstrates improves DIC method for actual experiment point herein
The feasibility and validity of analysis.
It please refers to shown in Figure 11, the displacement field adaptive smooth method suitable for DIC of the invention.According to body surface
Slickness is true, establishes penalized least-squares regressive object function, and estimate by means of GCV method to punish from noise data because
Son punishes the roughening of solution, to realize effective smoothing processing of displacement field.This method have realize simple, calculation amount it is small and
Full automatic advantage.
The deformation field measurement of body structure surface is carried out using DIC:
DIC is used for the deformation field measurement problem of body structure surface, mainly includes three important links.Firstly, construction is suitable
Deformation of the shape function description scheme under external load function；Then, certain correlation metric is established, it is tested for quantitative assessment
The degree of similarity of image brightness distribution before and after malformation；Similitude is enabled finally, solving by Multi-variables optimum design method
The maximized shape function parameter of criterion, to measure deformed displacement field data indirectly.
The arbitrary point (x, y) in undeformed image and a surrounding small neighborhood S are given, there are one group of mapping relations
χ meetsAndF (x, y) indicates the brightness of image at point (x, y),It indicates
Brightness of image after deformation at corresponding coordinate.If neighborhood S is sufficiently small, mapping relations χ can be described by formula (1),
Wherein, u and v is respectively the in-plane displacement in the direction x and y, (x0,y0) be region S center.
Enable parameter vectorAnd define related coefficient
As can be seen from the above equation, when correlation function minimalization, the similitude of deformation front and back image subsection reaches maximum
Value, at this point, displacement parameter u and v that parameter vector P includes represent the best estimate to being displaced after deformation, it is right in the same way
All measurement points are calculated, and whole audience displacement can be obtained.
For minimize ρ, the solution that can be zero by solution formula (10) First-order Gradient,
There are many methods to can be used to solve formula (12), is iteratively solved, had using Newton-Raphson method herein
In formula, P0For deformation parameter initial value,It is the Hessian matrix of correlation function ρ, meets
From above procedure as can be seen that many factors can impact the accuracy of displacement field measurement result, such as son
Area's size, interpretational criteria, iteration convergence condition etc..Although DIC method has obtained a large amount of research, various systems are eliminated in guidance
The effective ways of measured deviation also lack very much.Such as wish to obtain valuable strain field distribution data, need to containing with chance error
The displacement field data of difference is handled meticulously.
Displacement field is smoothed using N-R alternative manner:
It solves and enables the smallest shape function parameter of correlation coefficient ρ, it is deformed out according to obtained shape function parameter measurement
It is displaced field data dn, wherein displacement field data dnIt is expressed from the next: dn=d+n；
Wherein, d is ideal real displacement value, and n is displacement field noise；
The random error for eliminating deformed displacement field data U eliminates random error by minimizing following formula
Wherein, dnFor deformed displacement field data, d is ideal real displacement value, and n is displacement field noise, and α is smooth ginseng
Number；To above formula derivation, obtain
Wherein, C is Laplace operator,
D and α are become into column vector and enable Q=[d1, d2, d3...dm, α], wherein m is the number of element in d；It can then obtain
According toAcquire second-order partial differential coefficient
Above-mentioned matrix is combined, is obtained
Utilize what is obtainedWithCalculating is iterated to following formula:
Wherein, the initial value of Q is [dn,α]T, the condition of convergence isIt is obtained after above formula convergence
D be ideal real displacement value.
Simulation analysis: emulation speckle graph parameter, 500pixel × 500pixel, speckle particle radius 4, speckle particle number
4000
(1) homogeneous deformation, 1000 microstrain of the direction x, the direction y are displaced in 0.3 image and add noise.In two kinds of situation:
The first situation: signal-to-noise ratio 40db
The displacement of table 1, strain by N-R are compared with this paper error calculated
The first situation: signal-to-noise ratio 35db
The displacement of table 2, strain by N-R are compared with this paper error calculated
The initial value for changing α, is iterated calculating, and shown in α variation diagram 12, Figure 12 is under different α initial conditions, and α iteration becomes
Change situation
(2) heterogeneous deformation: emulation speckle graph parameter, 500pixel × 500pixel, speckle particle radius 4, speckle
Grain number 4000
Deformation: u (x, y)=0.1sin (2*pi*x/200) in two kinds of situation: first, signal-to-noise ratio 30；Second, noise
Than 35
The first situation: signal-to-noise ratio 30db
It please refers to shown in Figure 13, Figure 14 and Figure 15,
Under the conditions of table 1, signal-to-noise ratio 30db, two methods output resultant error compares
| Method | Std_v/pixel | Std_vy/με |
| N-R alternative manner | 0.02488 | 1227.8411 |
| Distinguish smooth displacement t | 0.02299 | 770.0738 |
Second situation, signal-to-noise ratio 35db
Figure 16, Figure 17 and Figure 18 are please referred to,
Under the conditions of table 2, signal-to-noise ratio 35db, two methods output resultant error compares
Experimental analysis: rivet plate test specimen strain calculation
When experiment, rivet plate lower end is fixed, and upper end stretches, and theory analysis should be that rivet lower end stress is maximum.Figure 19 and
What Figure 20 was provided is the experiment of rivet peripheral region linear deformation situation (can be supplemented other Direction distortion situations) (2) Multiple-Hole Specimen
It please refers to shown in Figure 21 and Figure 22,
Conclusion
Through analysis it is found that obtain accurate strain field, two conditions need to be met:
(1) it is more accurate to calculate the displacement field exported by N-R.If the displacement field deviation of N-R output is too big, that strain calculated
It as a result must inaccuracy.Displacement field deviation is very big, and smoothed out data peaks will not drop very much, because of data accuracy and smooth
There are a balances between property；If be displaced, field data is less than normal, that smoothed out value can be smaller, and error is also big.Therefore, N-R compared with
The output of exact shift field is necessary.
(2) suitably it is displaced noise-reduction method.Because strain is got by displacement difference, the fluctuation of displacement can be to strain gauge
Calculation brings large error.
Claims (10)
1. a kind of displacement field iteration smoothing method of Digital Image Correlation Method based on kernel function, it is characterised in that: be based on core
The Digital Image Correlation Method of function uses the correlation function ρ based on kernel function*,
Wherein, c is normaliztion constant, and k () is kernel function, and h is the bandwidth control parameter of kernel function, spTo deform preceding image-region
S0In pixel, f (sp) it is to deform pixel s in preceding imagepThe brightness of image at place, g (sp, P) be after deformation in image with picture
Vegetarian refreshments spBrightness of image at corresponding pixel, P are shape function parameter；
Wherein, iteration smoothing method the following steps are included:
(1), deformed displacement field data d is measured using the Digital Image Correlation Method based on kernel functionn, wherein position
Move field data dnIt is expressed from the next: dn=d+n；
Wherein, d is smoothed out displacement field, and n is displacement field noise；
(2), quadratic function is constructed
Wherein, dnFor deformed displacement field data, d is smoothed out displacement field data, and n is displacement field noise, and α is smooth ginseng
Number, C are high-order operator；
The first-order partial derivative for solving quadratic function, obtains
Wherein, C is high-order operator,
D and α are become into column vector and enable Q=[d1,d2,d3...dm,α]T, wherein m is points；It can then obtain
(3), according to step (2)Solve the second-order partial differential coefficient of quadratic function
Above-mentioned matrix is combined, is obtained
(4), it is obtained using step (2) and (3)WithCalculating is iterated to following formula:
Wherein, the initial value of Q is [dn,α]T, wherein dnFor deformed displacement field data, the d obtained after above formula convergence is
Ideal real displacement value, PkAnd Pk+1The respectively kth of vector P time+1 iteration result of iteration result and kth.
2. the displacement field iteration smoothing method of the Digital Image Correlation Method based on kernel function as described in claim 1, special
Sign is: the range of the α is (0,1).
3. the displacement field iteration smoothing method of the Digital Image Correlation Method based on kernel function as described in claim 1, special
Sign is: the condition of convergence of step (4) isWherein, ε≤0.1.
4. the displacement field iteration smoothing method of the Digital Image Correlation Method based on kernel function as described in claim 1, special
Sign is: the Digital Image Correlation Method based on kernel function the following steps are included:
One) shape function, is defined: the arbitrary point (x in setting reference picture0,y0) and surrounding neighborhood S0, (x, y) is with reference to figure
The neighborhood S as in0In any pixel coordinate,For in target image with pixel (x, y) corresponding pixel
Coordinate, there are one group of mapping relations χ, and following formula is set up:
Wherein, f (x, y) indicates the brightness of image at pixel (x, y),Indicate pixelThe brightness of image at place,
Mapping relations χ is shape function；Wherein, shape function χ is expressed from the next:
Wherein, u and v is respectively the displacement in the direction x and y caused by deforming, (x0,y0) it is neighborhood S0Center position coordinates,To deform the single order displacement gradient generated in the x and y direction；
Two), by step 1) shape function parametrization, and indicated with vector P,
Define correlation function ρ*,
Wherein, c is normaliztion constant, and k () is kernel function, and h is the bandwidth control parameter of kernel function, spFor neighborhood S0In one
Pixel, f (sp) it is to deform pixel s in preceding imagepThe brightness of image at place, g (sp, P) be after deformation in image with pixel sp
Brightness of image at corresponding pixel；
Three) it, is calculated and enables correlation function ρ*Shape function parameter P when minimum.
5. the displacement field iteration smoothing method of the Digital Image Correlation Method based on kernel function as claimed in claim 4, special
Sign is: step 3) in be calculate by the following formula correlation function ρ*Minimum value, construct iterative equations:
In formula, P0For deformation parameter initial value,WithIt is correlation function ρ*First-order Gradient and Hessian matrix, whereinWithFormula it is as follows:
Utilize iterative equationsIt is calculated and enables correlation function ρ*Minimum when solution, in formula, PiAs vector
I-th of element in P, PjJ-th of element in as vector P.
6. the displacement field iteration smoothing method of the Digital Image Correlation Method based on kernel function as claimed in claim 1,
Be characterized in that: the Digital Image Correlation Method based on kernel function the following steps are included:
1), the preceding and deformed image of acquisition object deformation, the image before deformation are reference picture, and deformed image is target
Image；
2) interest region S, is chosen on a reference1, interest region S1For reference picture sub-district；
3) region of search S, is established on target image2, region of search S2For target image sub-district, target image sub-district includes to become
Reference picture sub-district after shape；
4) gray value of target image sub-district and the point in reference picture sub-district, is obtained；
5) shape function, is constructed, determines the positional relationship of corresponding points in reference picture sub-district and target image sub-district, wherein (x1,
y1) be any pixel in reference picture sub-district coordinate, (x2,y2) be target image sub-district in pixel (x1,y1) opposite
The coordinate for the pixel answered, there are one group of mapping relations χ, and following formula is set up:
χ(x1,y1)→(x2,y2)
f(x1,y1)=g (x2,y2)
Wherein, f (x1,y1) indicate pixel (x1,y1) at brightness of image, g (x2,y2) indicate pixel (x2,y2) at image
Brightness, mapping relations χ are shape function；Wherein, shape function χ is expressed from the next:
Wherein, x caused by u' and v' is deformed respectively1And y1The displacement in direction, (x', y') are the center of reference picture sub-district
Coordinate,To deform in x1And y1The single order displacement gradient generated on direction；
6), the shape function of step 5) is parameterized, and is indicated with vector P',
Define correlation function ρ*',
Wherein, c is normaliztion constant, and k () is kernel function, and h is the bandwidth control parameter of kernel function, sp' it is reference picture sub-district
In a pixel, f (sp') it is to deform pixel s in preceding imagep' place brightness of image, g (sp', P') it is image after deformation
In with pixel sp' brightness of image at corresponding pixel；
7) vector, is setInitial value P0', and set maximum number of iterations n '；
8), by P0' bring iterative equations into:
In formula, P0' it is deformation parameter initial value,WithIt is correlation function ρ respectively*' First-order Gradient and Hessian square
Battle array, whereinWithFormula it is as follows:
In formula, Pi' and Pj' be respectively vector P' i-th of element and j-th of element；
P is calculated according to iterative equations1'；
9), judge whether iterative equations restrain according to the following formula,If convergence, saves emerging
Interesting region S1Shift value u' and v'；If do not restrained, P is enabled0'=P1', and repeat step 8) and 9)；If the number of iterations reaches
To maximum number of iterations n ', then terminate iteration；
10) shift value in interest region, is exported.
7. the displacement field iteration smoothing method of the Digital Image Correlation Method based on kernel function as claimed in claim 6, special
Sign is: the gray value of the point in target image sub-district is obtained in step 4) by carrying out bicubic spline to target image sub-district
Interpolation obtains the gray value of sub-pixel location in target image sub-district.
8. the displacement field iteration smoothing method of the Digital Image Correlation Method based on kernel function as claimed in claim 6, special
Sign is: the gray value of the point in reference picture sub-district is obtained in step 4) by carrying out bicubic spline to reference picture sub-district
Interpolation obtains the gray value of sub-pixel location in reference picture sub-district.
9. the displacement field iteration smoothing method of the Digital Image Correlation Method based on kernel function as claimed in claim 6, special
Sign is: choosing interest region S in step 2) on a reference1, interest region S1Pass through following steps for reference picture sub-district
Obtain: being respectively divided the first grid on a reference, the number of the first grid is M row × N column, reference picture length and
Spacing in width direction between the first grid is respectively l and w, is established centered on a-th of first grids on a reference
Interest region S1, interest region S1For reference picture sub-district, the length and width of reference picture sub-district is respectively L and W, wherein
A=1,2,3 ..., M × N.
10. the displacement field iteration smoothing method of the Digital Image Correlation Method based on kernel function as claimed in claim 6, special
Sign is: establishing region of search S in step 3) on target image2, region of search S2For target image sub-district, target image
Area includes that deformed reference picture sub-district is obtained by following steps: the second grid, the second grid are divided on target image
Number be M row × N column, the spacing on the length and width direction of target image between the second grid is respectively l and w；?
The region of search S centered on b-th of second grids is established on target image2, region of search S2For target image sub-district, target
The length and width of image subsection is respectively k ' * L and k ' * W, wherein k ' > 1, b=a.
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Denomination of invention: Displacement field iteration smoothing method of kernel function based digital image correlation method Effective date of registration: 20191217 Granted publication date: 20190719 Pledgee: Nanjing Bank Co., Ltd. Chengnan Branch Pledgor: Nanjing Dashu Intelligence Technology Co., Ltd. Registration number: Y2019320000367 |