CN102221341A - Quick digital image correlation measurement method based on stochastic parallel gradient descent optimization technology - Google Patents

Abstract

The invention provides a quick digital image correlation measurement method based on stochastic parallel gradient descent optimization technology, comprising the following steps of comprehensively considering related parameters such as displacement, differential coefficient and the like of any one point in a speckle field of an object to be measured; and utilizing the stochastic parallel optimization technology to realize quick digital image correlation measurement. In the method, by adopting stochastic parallel disturbance on a deformation parameter, the correlation coefficient is convergent to a global unique extremum, thus obtaining the deformation parameter. The method has a simple principle, can be realized easily, is a DIC (digital image correlation) measurement method with totally new concept, can realize the aim of quickly measuring DIC with high precision and high reliability, and is expected to realize the real-time online measurement on the DIC.

Description

Fast digital image relevant measurement method based on random paralleling gradient decline optimisation technique

Technical field

The present invention relates to a kind of fast digital image relevant measurement method, especially a kind of method of utilizing random paralleling gradient decline optimisation technique to realize fast digital image measurement of correlation, this method can be used for online quick Measuring Object deformation field parameter.

Technical background

Digital Image Correlation Method (Digital Image Correlation Measurement, DICM) or claim Digital Speckle Correlation Method (Digital Speckle Correlation Measurement, DSCM) in early 1980s by the I.Yamaguchi of Japan (Yamaguchi I.A laser-speckle strain gauge[J] .Journal of Physics E:Scientific Instruments, 1981,14:1270～1273) and the W.H.Peter of American South card Lehner university and W.F.Ranson (Peter W H, Ranson W F.Digital imaging technique in experimental stress analysis[J] .Optical Engineering, 1982,21 (3): 427～431) etc. independent the proposition.It carries out relevant treatment by two width of cloth images (speckle field) to the body surface of collection before and after the distortion, to realize the measurement of deformation of body field.

DIC (Digital Image Correlation Chinese full name: digital picture is relevant) compares with the conventional interference measuring method to have that test condition requires low, test area and the range variation range is big, precision is high, can use advantage such as white-light illuminating.At present, it has become the popular research field in the optical measurement, and had at aspects such as material properties test, structure detection, electronic component detection, nanometer mechanics, biomechanics widely and use, be the most widely used displacement, strain measurement technique at present.

In actual applications, how to improve precision and speed and be core and difficult point problem in the DIC measuring method, present DIC implementation method has two-parameter process of iteration, Newton-Raphson process of iteration, cross search procedure, climbing method, least square method etc., these method principle complexity, relatively poor to complexity or large deformation situation precision and robustness, even may draw error result sometimes.In addition, said method can not guarantee that related coefficient reaches global optimum, and therefore the accuracy and confidence of measurement also is affected.

Summary of the invention

In order to overcome the deficiencies in the prior art, the present invention proposes and utilize random paralleling gradient decline (Stochastic Parallel Gradient Descent, SPGD) optimisation technique realizes the method that DIC measures, this method is by adopting the random paralleling disturbance to deformation parameter, make related coefficient converge on overall unique extreme value, obtain deformation parameter thus, this method principle is simple, be easy to realize, it is a kind of DIC measuring method of novel concept, can realize DIC fast, the measurement of high precision, high reliability, use this technology also to be expected to realize the real-time online measuring of DIC.

A kind of fast digital image relevant measurement method that the invention provides based on parallel gradient decline optimisation technique, utilize the principle of random paralleling gradient decline technology, by deformation parameter K is carried out disturbance, make performance evaluation function J (K) converge to global extremum, finally obtain the optimum deformation parameter of this point.

A kind of fast digital image relevant measurement method that the invention provides based on parallel gradient decline optimisation technique, at first utilize speckle image F before the charge coupled cell camera obtains deformation of body (x, y) with distortion after speckle image G (x ^*, y ^*), realize according to following concrete steps then:

1) (x, y) middle any point P is that correlate template T is got at the center with P, the some Q distortion corresponding G (x in back among the T for F ^*, y ^*) in some Q ', its deformation parameter is made as K=[k ₀, k ₁, K, k ₅];

2) initialization deformation parameter vector is K ⁰=[0,0,0,0,0,0];

3) rule that satisfies according to the random paralleling disturbance produces random perturbation

4) according to the speckle image G ' (x after formula (1) the calculating disturbance ^*, y ^*), and to G ' (x ^*, y ^*) carry out interpolation processing, with further raising measuring accuracy, its Chinese style (1) is: the single order deformation formula

$\left.\begin{array}{c}{x}^{*}=x+u+\frac{\mathrm{du}}{\mathrm{dx}}\mathrm{\Δx}+\frac{\mathrm{du}}{\mathrm{dy}}\mathrm{\Δy}\\ y^{*}=y+v+\frac{\mathrm{dv}}{\mathrm{dx}}\mathrm{\Δx}+\frac{\mathrm{dv}}{\mathrm{dy}}\mathrm{\Δy}\end{array}\right\}$

Or high-order deformation formula

$\left.\begin{array}{c}{x}^{*}=x+u+\frac{\mathrm{du}}{\mathrm{dx}}\mathrm{\Δx}+\frac{\mathrm{du}}{\mathrm{dy}}\mathrm{\Δy}+\frac{1}{2}\frac{{\∂}^{2}u}{{\∂x}^2}{\left(\mathrm{\Δx}\right)}^2+\frac{1}{2}\frac{{\∂}^{2}u}{{\∂y}^2}{\left(\mathrm{\Δy}\right)}^2\frac{1}{2}\frac{{\∂}^{2}u}{\∂\mathrm{xdy}}\left(\mathrm{\Δx\Δy}\right)+...\\ y^{*}=y+v+\frac{\mathrm{dv}}{\mathrm{dx}}\mathrm{\Δx}+\frac{\mathrm{dv}}{\mathrm{dy}}\mathrm{\Δy}+\frac{1}{2}\frac{{\∂}^{2}v}{{\∂x}^2}{\left(\mathrm{\Δx}\right)}^2+\frac{1}{2}\frac{{\∂}^{2}v}{{\∂y}^2}{\left(\mathrm{\Δy}\right)}^2\frac{1}{2}\frac{{\∂}^{2}v}{\∂\mathrm{xdy}}\left(\mathrm{\Δx\Δy}\right)+...\end{array}\right\},$

Wherein, u and v are respectively center point P displacement in the x and y direction, and Δ x and Δ y are respectively distance in the x and y direction the component of a Q to a P;

5) from G (x ^*, y ^*) and G ' (x ^*, y ^*) take out matching template and calculate disturbance front and back performance evaluation function J (K) respectively with correlate template T, and calculate its change amount δ J ⁿ=J (K ⁿ+ δ K ⁿ)-J (K ⁿ); Wherein n represents the number of times or the iteration step number of optimizing process;

6) deformation parameter K satisfies random paralleling gradient decline (SPGD) replacement criteria:

N represents the number of times or the iteration step number of optimizing process;

7) judge whether to satisfy the measurement end condition, then withdraw from as satisfied, two width of cloth speckle images obtain the final deformation parameter K of a P to relevant fully at this moment, then return step 4) continuation execution if do not satisfy; The measurement end condition is: δ J ⁿLess than certain threshold value, and J satisfies certain threshold condition; Perhaps calculate step number and reach preset value;

8) to F (x, y) the every bit repeating step 2)～8) promptly obtain the deformation parameter of the whole audience.

Above-mentioned steps 2) the described correlate template rectangle template that is m * n size, wherein m is the length of correlation module, n is the wide of correlation module, perhaps according to other modules of the different any Reasonable Shape of getting of Measuring Object deformation type.

Above-mentioned steps 5) described performance evaluation function J (K) is: definition J (K)=J (k ₀, k ₁..., k ₅), K=[k ₀, k ₁, K, k ₅] for treating the changes persuing shape parameter, this performance evaluation function comprises standardization covariance related function, every function that meets the following conditions is the performance evaluation function: when speckle image to F (x, y), G (x ^*, y ^*) when being correlated with fully, J gets overall unique extreme value.

Explanation about part word among the present invention:

CCD (Charge-coupled Device) Chinese: charge coupled cell can be called ccd image sensor.CCD is a kind of semiconductor devices, can be converted into digital signal to optical image.

" correlate template ": before distortion, be that a zone that certain area is arranged and comprise some pixels is got at the center with certain point in the image promptly, generally can be taken as the rectangular area that the length of side is an odd number of pixels, rectangle as 21 * 21.

" matching template ": be that a zone that certain area is arranged and comprise some pixels is got at the center with certain point in the image after distortion promptly, this region shape and size are consistent with correlate template.

" end condition ": be the condition that need satisfy when finishing of measuring.

" certain threshold value " is according to the actual measurement situation and require satisfied precision to determine its size, and " certain threshold condition " generally is made as J and is greater than or less than certain threshold value, and this threshold size also is to determine according to actual measurement situation and the precision that requires to satisfy.

A kind of fast digital image relevant measurement method of the present invention based on parallel gradient decline optimisation technique, concrete technical scheme designs according to following thinking:

If F (x, y), G (x ^*, y ^*) be respectively two width of cloth speckle images that utilize before and after the deformation of body that CCD obtains, as accompanying drawing 1 as show, according to the basic distorted pattern of DIC as can be known, (x moves to G (x after the arbitrfary point Q distortion in y) to F ^*, y ^*) in Q ' point, the coordinate of this point can be expressed as:

$\left.\begin{array}{c}{x}^{*}=x+u+\frac{\mathrm{du}}{\mathrm{dx}}\mathrm{\Δx}+\frac{\mathrm{du}}{\mathrm{dy}}\mathrm{\Δy}\\ y^{*}=y+v+\frac{\mathrm{dv}}{\mathrm{dx}}\mathrm{\Δx}+\frac{\mathrm{dv}}{\mathrm{dy}}\mathrm{\Δy}\end{array}\right\},---\left(1\right)$

This season

For treating the changes persuing shape parameter.

At first define an overall performance evaluation function J (K)=J (k ₀, k ₁..., k ₅), K=[k ₀, k ₁, K, k ₅] for treating the changes persuing shape parameter.Every function that meets the following conditions all can be used as the performance evaluation function: when speckle image to F (x, y), G (x ^*, y ^*) when being correlated with fully, J gets overall unique extreme value.Performance evaluation function J in the technical program can be taken as standardization covariance related function C.

The principle of utilizing the SPGD technology to realize that quick DIC measures is to utilize the SPGD technology to make performance evaluation function J converge on unique extreme value of the overall situation fast, what this moment was corresponding is the relevant fully situations of two width of cloth images, so just obtained final deformation parameter, realized measurement of correlation fast and accurately object.According to the SPGD know-why, the present technique principle is: for the n time random paralleling perturbation process, at first to deformation parameter K ⁿApply a random perturbation

(j=0 wherein, 1, K, 5),

Be the stochastic variable of obeying statistical law, satisfy

σ wherein _JiBe perturbation amplitude, the perturbation amplitude size is decided δ by the practical operation situation that DIC measures _JiBe the Kronecker symbol,＜L〉for getting average.

According to the speckle image G (x after the n time random paralleling disturbance of formula (1) calculating ^*, y ^*), calculate the variable quantity of the performance evaluation function J that brings because of the random paralleling disturbance then:

$\begin{array}{c}{\mathrm{\δJ}}^n=J(k_0^n+{\mathrm{\δk}}_0^n,...k_j^n+{\mathrm{\δk}}_j^n,...k_5^n+{\mathrm{\δk}}_5^n)\\ -J(k_0^n,...k_j^n,...k_5^n)\end{array}---\left(2\right)$

According to the parameter update principle of SPGD, upgrade the n+1 deformation parameter K=[k in step ₀, k ₁, K, k ₅], its replacement criteria is:

$k_j^{n+1}=k_j^n+{\mathrm{\γ}}_j\mathrm{\δ}{J}^n\mathrm{\δ}{k}_j^n---\left(3\right)$

γ in the following formula _jBe system gain factor, decide γ according to the practical operation situation of DIC measurement _j＞0 corresponding J maximization, γ _j＜0 corresponding J minimizes; J=0,1, K, 5 expression different distortion parameters.

Like this, by deformation parameter K is carried out repeatedly random paralleling disturbance, the SPGD technology can converge to global extremum by guaranteed performance evaluation function J on statistical significance, realizes that the DIC of deformation of body parameter measures.

Adopt the fast digital image relevant measurement method based on parallel gradient decline optimisation technique of the present invention, can reach following technique effect:

1, the present invention proposes a kind of fast digital image relevant measurement method, it has utilized random paralleling gradient decline optimisation technique, by deformation parameter is adopted the random paralleling disturbance, make related coefficient converge on overall unique extreme value, obtain deformation parameter thus, can realize DIC fast, the measurement of high precision, high reliability, use this technology also to be expected to realize the real-time online measuring of DIC.

2, the present invention can converge on overall unique extreme value by the guaranteed performance evaluation function concurrently on statistical significance, corresponding deformation parameter is a global optimum, avoided some method can only obtain the shortcoming of local optimum parameter, and after the suitable parameter design, this technology also can obtain high-precision result fast for the situation that has moderate finite deformation.

3, the fast digital image relevant measurement method principle that proposes of the present invention simple, be easy to realize, be a kind of DIC measuring method of novel concept, be suitable for promoting the use of on a large scale.

4, the present invention not only is suitable for the single order distortion that object produces, and also is applicable to the high-order distortion that second order is above, and can't significantly increases system complexity.

Description of drawings

Fig. 1 is out of shape the speckle image synoptic diagram of front and back for the present invention;

Wherein (x y) is the preceding scattered-spot drawing picture of distortion to F; P (x ₀, y ₀) be the coordinate of central point; (x y) is any coordinate of any to Q; G (x ⁺, y ⁺) be the speckle image after the distortion.

Fig. 2 is an analog D IC speckle pattern: size is 256 * 256, and the speckle number is 500, and speckle size is 4 pixels.

Embodiment

For a better understanding of the present invention, below in conjunction with embodiment the present invention is done detailed description further, but the scope of protection of present invention is not limited to the scope that embodiment represents.

We utilize (Zhou such as Zhou Peng, P.and K.E.Goodson, Subpixel displacement and deformation gradient measurement using digital image/speckle correlation (DISC) .Opt.Eng., 2001.40 (8): p.1613-1620.) the speckle analogy model that is used for DIC of Ti Chuing carries out following two case study on implementation.Simulation drawing is as shown in Figure 2: size is 256 * 256, and the speckle number is 500, and speckle size is 4 pixels; The correlate template size is 41 * 41, perturbation amplitude δ u0=δ u1=0.1, δ u2=δ u3=δ u4=δ u5=0.01, and system-gain γ=100, fixedly the iteration step number is 200, uses bilinear interpolation to calculate sub-pixel displacement.

Embodiment 1: the displacement measurement of rigid body

Rigid body displacement is respectively u ₀=0.01,0.05,0.1,0.5,1,3 pixels, use SPGD DIC and the result that the external Newton-Raphson measuring method that generally adopts obtains to contrast as shown in table 1:

Table 1 measuring method of the present invention and the contrast of Newton-Raphson methods and results

Embodiment 2: the wheel measuring of rigid body

The anglec of rotation is respectively θ=0.01 °, 0.05 °, 0.1 °, 0.5 °, 1 °, 3 °, uses the result who obtains based on measuring method and the Newton-Raphson method of SPGD DIC of the present invention to contrast as shown in table 2:

Table 2 measuring method of the present invention and the contrast of Newton-Raphson methods and results

By above two cases as can be seen, the DIC measuring method based on SPGD of the present invention can significantly improve measuring accuracy, because this method need not to calculate deformation matrix parameter secondary local derviation, can save Measuring Time greatly in addition, is used for operating mode and measures in real time.

Claims (4)

1. fast digital image relevant measurement method based on parallel gradient decline optimisation technique, it is characterized in that, utilize the principle of random paralleling gradient decline technology, by deformation parameter K is carried out disturbance, make performance evaluation function J (K) converge to global extremum, finally obtain the optimum deformation parameter of this point.

2. according to the described fast digital image relevant measurement method of claim 1, it is characterized in that based on parallel gradient decline optimisation technique, at first utilize speckle image F before the charge coupled cell camera obtains deformation of body (x, y) with distortion after speckle image G (x ^*, y ^*), realize according to following concrete steps then:

1) (x, y) middle any point P is that correlate template T is got at the center with P, the some Q distortion corresponding G (x in back among the T for F ^*, y ^*) in some Q ', its deformation parameter is made as K=[k ₀, k ₁, K, k ₅];

2) initialization deformation parameter vector is K ⁰=[0,0,0,0,0,0];

3) rule that satisfies according to the random paralleling disturbance produces random perturbation

4) according to the speckle image G ' (x after formula (1) the calculating disturbance ^*, y ^*), and to G ' (x ^*, y ^*) carry out interpolation processing, its Chinese style (1) is: the single order deformation formula

$\left.\begin{array}{c}{x}^{*}=x+u+\frac{\mathrm{du}}{\mathrm{dx}}\mathrm{\Δx}+\frac{\mathrm{du}}{\mathrm{dy}}\mathrm{\Δy}\\ y^{*}=y+v+\frac{\mathrm{dv}}{\mathrm{dx}}\mathrm{\Δx}+\frac{\mathrm{dv}}{\mathrm{dy}}\mathrm{\Δy}\end{array}\right\}$

Or high-order deformation formula

$\left.\begin{array}{c}{x}^{*}=x+u+\frac{\mathrm{du}}{\mathrm{dx}}\mathrm{\Δx}+\frac{\mathrm{du}}{\mathrm{dy}}\mathrm{\Δy}+\frac{1}{2}\frac{{\∂}^{2}u}{{\∂x}^2}{\left(\mathrm{\Δx}\right)}^2+\frac{1}{2}\frac{{\∂}^{2}u}{{\∂y}^2}{\left(\mathrm{\Δy}\right)}^2\frac{1}{2}\frac{{\∂}^{2}u}{\∂\mathrm{xdy}}\left(\mathrm{\Δx\Δy}\right)+...\\ y^{*}=y+v+\frac{\mathrm{dv}}{\mathrm{dx}}\mathrm{\Δx}+\frac{\mathrm{dv}}{\mathrm{dy}}\mathrm{\Δy}+\frac{1}{2}\frac{{\∂}^{2}v}{{\∂x}^2}{\left(\mathrm{\Δx}\right)}^2+\frac{1}{2}\frac{{\∂}^{2}v}{{\∂y}^2}{\left(\mathrm{\Δy}\right)}^2\frac{1}{2}\frac{{\∂}^{2}v}{\∂\mathrm{xdy}}\left(\mathrm{\Δx\Δy}\right)+...\end{array}\right\},$

Wherein, u and v are respectively center point P displacement in the x and y direction, and Δ x and Δ y are respectively distance in the x and y direction the component of a Q to a P;

5) from G (x ^*, y ^*) and G ' (x ^*, y ^*) take out matching template and calculate disturbance front and back performance evaluation function J (K) respectively with correlate template T, and calculate its change amount δ J ⁿ=J (K ⁿ+ δ K ⁿ)-J (K ⁿ); Wherein n represents the number of times or the iteration step number of optimizing process;

6) deformation parameter K satisfies random paralleling gradient decline replacement criteria:

N represents the number of times or the iteration step number of optimizing process;

7) judge whether to satisfy the measurement end condition, then withdraw from as satisfied, two width of cloth speckle images obtain the final deformation parameter K of a P to relevant fully at this moment, then return step 4) continuation execution if do not satisfy; The measurement end condition is: δ J ⁿLess than certain threshold value, and J satisfies certain threshold condition; Perhaps calculate step number and reach preset value;

8) to F (x, y) the every bit repeating step 2)～8) promptly obtain the deformation parameter of the whole audience.

3. fast digital image relevant measurement method according to claim 2, it is characterized in that, step 2) the described correlate template rectangle template that is m * n size, wherein m is the length of correlation module, n is the wide of correlation module, perhaps according to other modules of the different any Reasonable Shape of getting of Measuring Object deformation type.

4. fast digital image relevant measurement method according to claim 2 is characterized in that, the described performance evaluation function of step 5) J (K) is: definition J (K)=J (k ₀, k ₁..., k ₅), K=[k ₀, k ₁, K, k ₅] for treating the changes persuing shape parameter, this performance evaluation function comprises standardization covariance related function, every function that meets the following conditions is the performance evaluation function: when speckle image to F (x, y), G (x ^*, y ^*) when being correlated with fully, J gets overall unique extreme value.

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