CN104616271B - A kind of displacement field adaptive smooth method related suitable for digital picture - Google Patents

A kind of displacement field adaptive smooth method related suitable for digital picture Download PDF

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CN104616271B
CN104616271B CN201510100472.9A CN201510100472A CN104616271B CN 104616271 B CN104616271 B CN 104616271B CN 201510100472 A CN201510100472 A CN 201510100472A CN 104616271 B CN104616271 B CN 104616271B
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CN104616271A (en
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沈峘
张佩泽
沈翔
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a kind of displacement field adaptive smooth method related suitable for digital picture, based on penalized least-squares regression technique, the roughening on noise displacement field surface is punished, realizes the purpose of the noise effectively eliminated in displacement field.In addition, Generalized Cross Validation（GCV）Method and discrete cosine transform are respectively used to estimate penalty factor and real displacement field from noise displacement field.This method, which has, realizes that simple, amount of calculation is small, full automatic advantage.Simulation analysis and result of the test demonstrate the validity of context of methods, while amount of calculation is not dramatically increased, can effectively improve the regularity of distribution of strain field.

Description

A kind of displacement field adaptive smooth method related suitable for digital picture
Technical field
The invention belongs to digital image processing field, and in particular to a kind of displacement field related suitable for digital picture is adaptive Answer smoothing method.
Background technology
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, body structure surface is obtained under external load function by machine vision technique Whole audience displacement and the measuring method of strain information.Because DIC has many advantages, such as, such as measurement process is simple, measurement knot Fruit accuracy is high, it is non-contact, full field data etc. can be obtained, be applied widely in recent years in Experimental Mechanics field.
DIC general principle 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 algorithms Displacement.Higher-order gradients are introduced shape function to realize the description to complex deformation by Lu et al., and complexity is become so as to improve DIC The measurement effect of shape field.Cofaru et al. propose to correct DIC with irregular speckle pattern, and combine regularization method Increase the output accuracy of displacement field.Pan research shows：It is the gauss low frequency filter of 5*5 pixels to speckle pattern to use size As being pre-processed, the displacement field error of DIC outputs can be effectively reduced.
In Experimental Mechanics field, for simple displacement field data displacement field, strain field distribution information, which seems more, to be had Value.Although DIC technologies experienced development for many years, because current conditions limit, the displacement field that DIC is exported can still exist various Deviation, the analysis about DIC system deviations refer to document.All information due to calculating strain field are included in displacement data and worked as In, if the displacement data for directly including noise using these strains to calculate, error will be exaggerated, 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 displacement The noise of field.However, the defects of these methods is to need to manually adjust the parameter of algorithm.In actual measurement process, due to not having There are enough prioris to carry out guide parameters adjustment, thus hinder its practical application.
Therefore, it is necessary to which a kind of new be applied to the related displacement field adaptive smooth method of digital picture to solve above-mentioned ask Topic.
The content of the invention
The purpose of the present invention is the deficiency for being applied to the related displacement field smoothing method of digital picture in the prior art, A kind of displacement field adaptive smooth method related suitable for digital picture is provided.
For achieving the above object, the present invention, which is applied to the related displacement field adaptive smooth method of digital picture, to adopt With following technical scheme：
A kind of displacement field adaptive smooth method related suitable for digital picture, comprises the following steps：
1) the displacement field U after deformation, is measured, wherein displacement field U is expressed from the next：
Wherein,Displacement field after representing smooth, ξ represent the random error that measurement process introduces；
2), quadratic function of the construction with penalty term eliminates random error：
Wherein, | | | | it is European norm,Represent data approximation degree, C is high-order differential operators, α ∈ [0.1] penalty factor is represented；
To quadratic function derivation, and its another derivative is zero, is obtainedWherein, InFor unit pair Angular moment battle array, β=α/(α+1), C=V Λ V-1, wherein, V is unitary matrice, meets VT=V-1, Λ forms diagonal for C characteristic value Matrix,
Λ=diag (λ1,λ2... λi…,λn), wherein λi=-2+cos [(i-1) π/n],
Wherein, VTRepresent discrete cosine transformation matrix and inverse cosine transformation matrix respectively with V；
3), penalty factor β is calculated using Generalized Cross Validation method；Wherein, Generalized Cross Validation method passes through minimum Following formula obtains penalty factor β
Wherein, the mark of Tr () representing matrix；Wherein,
4), the penalty factor β obtained according to step 3), the displacement field after being calculated smoothly according to following formula
Wherein, DCT and IDCT represents discrete cosine transform and inverse cosine conversion respectively.
Further, C is second order granny rag Laplacian operater in step 2).
Beneficial effect：It is minimum that the displacement field adaptive smooth method for being applied to digital picture correlation of the present invention is based on punishment Two multiply regression technique, and the roughening on noise displacement field surface is punished, realization effectively eliminates the noise in displacement field Purpose.In addition, GCV methods and discrete cosine transform are respectively used to estimate penalty factor and real displacement from noise displacement field .This method, which has, realizes that simple, amount of calculation is small, full automatic advantage.
Brief description of the drawings
Fig. 1 is the flow chart for being applied to the related displacement field adaptive smooth method of digital picture of the present invention；
Fig. 2 is that the result of conventional method processing DIC output datas is utilized in the case of homogeneous deformation；
Fig. 3 is to be applied to the related displacement field adaptive smooth side of digital picture using the present invention in the case of homogeneous deformation The result that method processing DIC output datas obtain；
Fig. 4 is that the result of conventional method processing DIC output datas is utilized in the case of heterogeneous deformation；
Fig. 5 is to be applied to the related displacement field adaptive smooth of digital picture using the present invention in the case of heterogeneous deformation The result that method processing DIC output datas obtain；
Fig. 6 is simulated speckle pattern；
Fig. 7 is speckle pattern；
Fig. 8 is speckle schematic diagram；
Fig. 9 is the elongation strain field deformation measurement result that Multiple-Hole Specimen handles to obtain using conventional DIC methods；
Figure 10 is the shear strain field deformation measurement that Multiple-Hole Specimen handles to obtain using conventional DIC methods；
Figure 11 is that Multiple-Hole Specimen handles obtained elongation strain field deformation measurement result using the method for the present invention；
Figure 12 is that Multiple-Hole Specimen handles obtained shear strain field deformation measurement using the method for the present invention.
Embodiment
Below in conjunction with the accompanying drawings and specific embodiment, the present invention is furture elucidated, it should be understood that these embodiments are merely to illustrate The present invention rather than limitation the scope of the present invention, after the present invention has been read, those skilled in the art are each to the present invention's The modification of the kind equivalent form of value falls within the application appended claims limited range.
Refer to shown in Fig. 1, 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 from noise data by means of GCV methods to punish because Son punishes the roughening of solution, so as to realizing effective smoothing processing of displacement field.This method have realize simple, amount of calculation 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 steps.First, construction is suitable Deformation of the shape function description scheme under external load function；Then, certain correlation metric is established, is tested for quantitative assessment The degree of similarity of image brightness distribution before and after malformation；Finally, solved by Multi-variables optimum design method and make similitude The maximized shape function parameter of criterion, so as to measure the displacement field data after deformation indirectly.
The arbitrfary point (x, y) in not deformed image and its a small neighborhood S of surrounding are given, one group of mapping relations be present χ meetsAndF (x, y) represents the brightness of image at point (x, y) place,Represent the brightness of image at corresponding coordinate after deforming.If neighborhood S is sufficiently small, mapping relations χ can be retouched by formula (1) State,
Wherein, u and v is respectively the in-plane displacement in x and y directions, (x0,y0) be region S center.
Make parameter vectorAnd define coefficient correlation
As can be seen from the above equation, when correlation function minimalization, the similitude of image subsection reaches maximum before and after deformation Value, now, 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.
For minimize ρ, can by solving the solution that formula (2) First-order Gradient is zero,
There are many methods to can be used to solve formula (3), herein using Newton-Raphson method iterative, have
In formula, P0For deformation parameter initial value,It is correlation function ρ Hessian matrixes, meets
From above procedure as can be seen that many factors can impact to the accuracy of displacement field measurement result, such as son Area's size, interpretational criteria, iteration convergence condition etc..Although DIC methods have obtained substantial amounts of research, instruct to eliminate various systems The effective ways of measured deviation also lack very much.Such as wish to obtain valuable strain field distribution data, it is necessary to containing with chance error The displacement field data of difference is handled meticulously.
Displacement field is smoothed using GCV methods (GCV methods i.e. Generalized Cross Validation method)：
Assuming that U represents the displacement field of DIC outputs, being said from mathematical meaning, U can be described by such as drag,
Wherein,Real displacement field is represented, ξ represents the random error that measurement process introduces, and generally assumes that it to meet The Gaussian Profile of zero-mean.
To eliminate random error, the quadratic function of penalty term can be carried as follows by minimizing
Wherein, | | | | it is European norm,Data approximation degree is represented, C is high-order differential operators, for retouching The rough type of solution is stated, is taken as second order granny rag Laplacian operater herein, α ∈ [0.1] represent penalty factor, the representative pair of value size The degree of roughening punishment.
To above formula derivation, arrange
Wherein, InFor unit diagonal matrix, β=α/(α+1).
It is very time-consuming although above formula can be solved by numerical computation method.If displacement field is equally spaced, one kind can be used Effective method realizes rapid solving.In practical application, view data is assumed to be at equal intervals generally in units of pixel Vertical.If between assuming displacement measurement point at intervals of 1, and be directed to a data, C is represented by following square formation,
Eigenvalues Decomposition is carried out to C, had
C=V Λ V-1 (9)
Wherein, V is unitary matrice, meets VT=V-1, the diagonal matrix of Λ expressions C characteristic value composition, have
Λ=diag (λ1,λ2... λi…,λn), with λi=-2+cos [(i-1) π/n]
VTRepresent discrete cosine transformation matrix and inverse cosine transformation matrix respectively with V, accordingly, formula (9) substituted into formula (8), And combine VTWith the matrixing relation of V descriptions, have
Wherein, DCT and IDCT represents discrete cosine transform and inverse cosine conversion respectively.
From formula (10) as can be seen that penalty factor β values (α in formula (7)) it is most important for accurately estimating, it is excessive or Person is too small all to face excessive or deficient smooth risk.Present invention selection Generalized Cross Validation (GCV) method come realize to β from Dynamic estimation.
GCV methods obtain preferable penalty factor β by minimizing formula (11).
Wherein, the mark of Tr () representing matrix.
For Tr (In+βCTC) for item, have
And forFor, have
To sum up, we can first estimate penalty factor β by formula (11) from the displacement field U for cry out noise, then substitute into formula (10) displacement field after calculating smoothly estimates that whole calculating process is all very succinct, efficient.
Experiment proves：
The validity of the above method is assessed with reference to simulation analysis and verification experimental verification.First, in simulation analysis of computer, Using digital speckle image come the deformation of analogue measurement object.Due to deformation parameter, it is known that processing effect can be evaluated objectively The quality of fruit.
Two groups of deformation parameters are selected, simulate uniform heterogeneous deformation respectively.Digital speckle image size be 500 × 500pixels, speckle particle number are 4000, and speckle particle radius is 4, and speckle signal to noise ratio is 40db.Simulated speckle pattern referring to Fig. 6.
Embodiment 1：Homogeneous deformation
Deformation parameter takes P=(0,0.3,0.001,0,0,0)T, this represents the Uniform Tension for having 1000 μ ε in x directions, and Vanishing is answered on other directions, the speckle image after stretching is as shown in Figure 7.The Newton-Raphson provided using formula (4) Method (traditional DIC methods) first calculates displacement field, then the strain field data obtained by calculus of differences is as shown in Fig. 2 to pass through The result crossed after this paper smoothing processings provides in Fig. 3.
Objectively to evaluate, the calculated value of traditional DIC and smooth DIC result and deformation parameter is entered respectively Row compares, using root-mean-square error formula,
Wherein, σ is theoretical value,For estimate, n represents data count.
Result of calculation is listed in table 1, it can be seen that no matter the strain for x, y direction, or shear strain, context of methods In RMS evaluation indexes, improve 39%, 48% and 52% than traditional DIC methods respectively, show context of methods for uniform Deformation is effective.
The root-mean-square error contrast of the homogeneous deformation of table 1
Embodiment 2：Heterogeneous deformation
Practical distortion is often heterogeneous, to assess the effect under heterogeneous deformation operating mode, select SIN function u (x, Y)=Asin (2 π x/p) carrys out the deformation of description scheme, and wherein amplitude A takes 0.1, and cycle parameter p takes 200, and remaining becomes parameter Number is the same as embodiment 1.As shown in Figure 4 and Figure 5, the left side is that the displacement field data difference of traditional DIC outputs calculates to result of calculation Strain field, the right are the strain field datas that smooth DIC is calculated.It can be seen that the strain field that is calculated of traditional DIC methods compared with It is more serious by displacement field influence of noise to be coarse.And after being smoothed using context of methods to displacement field, what is obtained should Variable field data smoothing, is closer to theoretical value.The RMS index correction datas of heterogeneous deformation operating mode refer to table 2, it can be seen that Context of methods is in the case of heterogeneous deformation and effective.
The root-mean-square error contrast of the heterogeneous deformation of table 2
Embodiment 3：Hole is tested:
Refer to shown in Fig. 6,7 and 8, in order to further verify the practicality of context of methods, herein by the test specimen of reality Deformation is handled.Test test specimen be one band hole test specimen, its schematic diagram as shown in figure 8, test specimen numbering be BD1W2L3, Wherein B represents steel, and D=1 is hole diameter, and W=2 is horizontal hole interval, and L=3 is longitudinal bore interval, test specimen overall length 200mm, a width of 20mm.During test, using industrial AVT cameras, model F-125B/C, image before and after collection deformation.
The strain cloud atlas of traditional DIC and smooth DIC outputs provides in Fig. 9,10,11 and 12 respectively.Understand by contrast, two Kind method result of calculation totality rule is consistent, that is, the position that stress concentration occurs matches.But what traditional DIC methods calculated As a result due to larger distortion situation by the strain distributing disciplinarian of noise jamming, data representation be present, contour presentation is shown as Go out zigzag or discontinuous, the actual loading situation of this and test specimen is not inconsistent.And the strain field distribution that context of methods is calculated is more Meet practical distortion rule, contour is continuous and smooth, and strain gradient and symmetry distribution rule are more nearly with theoretical value.
Conclusion：
In summary, the displacement field data directly exported for traditional DIC, it is proposed that a kind of adaptive displacement field is smooth Method, this method are based on GCV technologies, can automatically be fallen into a trap from noise field data and calculate penalty factor, and estimate smooth position Field data is moved, so as to provide more believable displacement field data for the calculating of strain field.Simulation analysis and analysis of experiments result table Bright, this method can realize full automatic smoothing process, and more rational strain cloud atlas can be provided compared with conventional method.

Claims (2)

  1. A kind of 1. displacement field adaptive smooth method related suitable for digital picture, it is characterised in that：Comprise the following steps：
    1) the displacement field U after deformation, is measured, wherein displacement field U is expressed from the next：
    Wherein,Displacement field after representing smooth, ξ represent the random error that measurement process introduces；
    2), quadratic function of the construction with penalty term eliminates random error：
    <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> <mi>U</mi> <mo>-</mo> <mover> <mi>U</mi> <mo>^</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>+</mo> <mfrac> <mi>&amp;alpha;</mi> <mn>2</mn> </mfrac> <mo>|</mo> <mo>|</mo> <mi>C</mi> <mover> <mi>U</mi> <mo>^</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow>
    Wherein, | | | | it is European norm,Data approximation degree is represented, C is high-order differential operators, and α ∈ [0.1] are represented Penalty factor；
    To quadratic function derivation, and it is zero to make its derivative, is obtainedWherein, InIt is unit to angular moment Battle array, β=α/(α+1), C=V Λ V-1, wherein, V is unitary matrice, meets VT=V-1, the diagonal matrix for the characteristic value composition that Λ is C,
    Λ=diag (λ1,λ2... λi...,λn), wherein λi=-2+cos [(i-1) π/n],
    Wherein, VTRepresent discrete cosine transformation matrix and inverse cosine transformation matrix respectively with V；
    3), penalty factor β is calculated using Generalized Cross Validation method；Wherein, Generalized Cross Validation method is by minimizing following formula Obtain penalty factor β
    <mrow> <mi>G</mi> <mi>C</mi> <mi>V</mi> <mrow> <mo>(</mo> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <mo>|</mo> <mi>U</mi> <mo>-</mo> <mover> <mi>U</mi> <mo>^</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <mi>n</mi> <mo>-</mo> <mi>T</mi> <mi>r</mi> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>n</mi> </msub> <mo>+</mo> <msup> <mi>&amp;beta;C</mi> <mi>T</mi> </msup> <mi>C</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mfrac> </mrow>
    Wherein, the mark of Tr () representing matrix；Wherein,
    <mrow> <mi>T</mi> <mi>r</mi> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>n</mi> </msub> <mo>+</mo> <msup> <mi>&amp;beta;C</mi> <mi>T</mi> </msup> <mi>C</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msubsup> <mi>&amp;beta;&amp;lambda;</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>,</mo> <mo>|</mo> <mo>|</mo> <mi>U</mi> <mo>-</mo> <mover> <mi>U</mi> <mo>^</mo> </mover> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msubsup> <mi>&amp;beta;&amp;lambda;</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mn>2</mn> </msup> <msubsup> <mi>DCT</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mrow> <mo>(</mo> <mi>U</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    4), the penalty factor β obtained according to step 3), the displacement field after being calculated smoothly according to following formula
    <mrow> <mover> <mi>U</mi> <mo>^</mo> </mover> <mo>=</mo> <mi>I</mi> <mi>D</mi> <mi>C</mi> <mi>T</mi> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mi>n</mi> </msub> <mo>+</mo> <msup> <mi>&amp;beta;&amp;Lambda;</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> <mi>D</mi> <mi>C</mi> <mi>T</mi> <mrow> <mo>(</mo> <mi>U</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow>
    Wherein, DCT and IDCT represents discrete cosine transform and inverse cosine conversion respectively.
  2. 2. as claimed in claim 1 suitable for the related displacement field adaptive smooth method of digital picture, it is characterised in that：Step It is rapid 2) in C be second order granny rag Laplacian operater.
CN201510100472.9A 2015-03-06 2015-03-06 A kind of displacement field adaptive smooth method related suitable for digital picture Expired - Fee Related CN104616271B (en)

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