CN103729849A - Method for calculating digital image morphing initial value - Google Patents

Abstract

The invention discloses a method for calculating a digital image morphing initial value and provides an automatic morphing initial value estimation method to solve the problem that a common morphing initial value estimation method fails when large rigid rotation or great morphing happens to the surface of a to-be-tested object. According to the method, by means of SIFI algorithm matching, corresponding points of image calculation sub regions before and after morphing are obtained, and morphing initial value estimation is obtained by means of a least square method and serves as an iteration initial value of a Newton-Rapshon method. Simulation calculation is carried out on simulation speckle patterns under great morphing, and the result indicates that the method can still effectively measure displacement at a large rotation angle of 30 degrees.

Description

A kind of computing method of digital picture distortion initial value

Technical field

The invention belongs to optical measurement mechanics technical field, be specifically related to a kind of computing method of digital picture distortion initial value.

Background technology

Digital picture (the Digital Image Correlation that is correlated with, DIC) appear at the earliest the beginning of the eighties in last century, Peters and Ranson by South Carolina, United States university propose the earliest, the method reaches its maturity, and has become a kind of noncontact full-filled optical measurements method that is widely known by the people and has numerous application.

For calculating the displacement of certain point in the front image of distortion, conventionally select a square subarea centered by this point.Due to reference picture square subarea after distortion in image shape can change, therefore can carry out with shape function the shape of image subsection after approximate description distortion.Now, the related function of distortion front and back image subsection similarity degree can be expressed as the nonlinear equation of deformation parameter.This equation can with after Newton-Rapshon(referred to as N-R) method or other method solve.Though other method can, for asking for deformation parameter, be compared N-R method very consuming time as genetic algorithm, differential evolution algorithm, shows with rare in application.Over nearly 30 years, the research of N-R method is related generally to following key issue: 1. related function is selected problem; 2. be out of shape initial estimate problem; 3. the selection problem of shape function; 4. the optimization problem of Hessian matrix.Due to N-R method convergence range (Knauss think restrain) in several pixels, therefore just require to provide initial estimate more accurately in 7 pixel coverages.When distortion hour, simple whole pixel relevant search can obtain being out of shape more accurately initial value (now strain parameter is made as 0).And when distortion is when larger, the method receive rope to result facies relationship numerical value little and become unreliable, be even wrong.Distortion initial estimate method based on man-machine interaction can be any deformation state and provides rapidly and be out of shape accurately and reliably initial estimate, avoids the search procedure that calculated amount is larger, and shortcoming is to realize the full automation of computation process.

Prior art list of references is as follows:

[1] Pan Bing, the Xie Hui people, continuous uncle admires etc. the Displacement location algorithm progress [J] during digital picture is relevant. Proceedings of Mechanics, 2005,35 (3): 345～351.

Pan?Bing,Xie?Huimin,Xu?Boqin?et?al..Development?of?sub-pixel?displacements?registration?algorithms?in?digital?image?correlation[J].Advances?in?Mechanics,2005,34(3):345～351.

[2]Peters?W?H,Ranson?WF.Digital?Imaging?Techniques?in?Experimental?Stress?Analysis[J].Optical?Engineering,1981,21(3):427～431.

[3]Pan?B,Xie?H?M,Guo?Z?Q?et?al..Full-field?strain?measurement?usingtwo-dimensional?Savitzky-Golay?digital?differentiator?in?digital?image?correlation[J].Optical?Engineering,2007,46(3):033601-033601-10.

[4] Pan Bing, Xie Hui is bright. the whole audience strain measurement [J] based on the matching of displacement field local least square method during digital picture is relevant. and Acta Optica, 2007,27 (11): 1980～1986.

Pan?Bing,Xie?Huiming.Full-field?strain?measurement?based?on?local?least-square?fitting?for?digital?image?correlation?method[J].Acta?Optica?Sinica,2007,27(11):1980～1986.

[5]Schreier?H?M,Sutton?M?A.Systematic?errors?in?digital?image?correlation?due?to?undermatched?subset?shape?functions[J].Experimental?Mechanics,1989,29(3):303～310.

[6]Ma?S?P,Jin?G?C.Digital?speckle?correlation?method?improved?by?genetic?algorithm[J].Acta?Mechanica?Solida?Sinica,2003,16(4):366～373.

[7]Pan?B,Xie?H?M.Digital?image?correlation?method?with?differential?evolution[J].Optoelectronics?&?Laser,2007,18(1):100～103.

[8] Pan Bing, Xie Hui is bright, Xia Yong etc. the large-deformation measuring [J] based on reliable distortion initial estimate during digital picture is relevant. and Acta Optica, 2009,2 (29): 400～406.

Pan?Bing,Xie?Huimin,Xia?Yong?et?al..Large-Deformation?Measurement?Based?on?Reliable?Initial?Guess?in?Digital?Image?Correlation?Method[J].Acta?Optica?Sinica,2009,2(29):400～406.

[9]G.Vendroux,W.G.Knauss.Submicron?deformation?field?measurements:Part2.Improved?digital?image?correlation[J].Experimental?Mechanics,1998,38(2):86～92.

[10]Bruck?H?A,McNeil?S?R,Sutton?M?A?et?al..Digital?image?correlation?using?newton-rapshon?method?of?partial?differential?correlation[J].Experimental?Mechanics,1989,29(3):261～267.

[11]LOWE?D?G.Object?Recognition?from?local?scale-invariant?features[C].The?International?Conference?on?Computer?Vision,1999(2):1150-1157.

[12]Peng?Zhou,Kenneth?E,Goodson.Subpixel?displacement?and?deformation?gradient?measurement?using?digital?image/speckle?correlation[J].Optical?Engineering,2001,40(8):1613～1620.

[13]Hung?PC,Voloshin?PS.In-plain?Strain?Measurement?by?Digital?Image?Correlation[J].Journal?of?the?Brazilian?Society?of?Mechanical?Sciences?and?Engineering,2003,25(3):215-221.

Summary of the invention

Technical matters to be solved by this invention is: the computing method of a kind of digital picture distortion initial value are provided, have solved digital picture distortion initial value carculation method in prior art and can not realize full automation and the low problem of computational accuracy of computation process.

The present invention is for solving the problems of the technologies described above by the following technical solutions:

Computing method for digital picture distortion initial value, comprise the steps:

(1) obtain the digital picture after digital picture and the surface deformation before testee surface deformation, using the digital picture before surface deformation as " reference picture ", the image after surface deformation is as " target image ", first, with reference to image and target image, be all placed in same plane coordinate system, on reference picture, choose arbitrarily a pixel as grid node, and centered by this grid node point, take 2M+1 as the length of side, divide square area, as with reference to image subsection, wherein M is pixel number, secondly, by feature point extraction and matching algorithm, from target image, automatically extract the pixel corresponding with reference picture subarea, with this, obtain many group pixels one to one, transformation relation between arbitrary corresponding pixel represents with " shape function " in described reference picture and in target image,

(2) according to corresponding pixel points and reference picture subarea center point coordinate calculative determination intermediate computations amount one by one, described intermediate computations measurer body comprises: in reference picture subarea with target image subarea under the same coordinate system in the coordinate figure of all pixels and reference picture subarea the coordinate of all pixels with respect to the variable quantity at center;

(3) according to the many group pixels one to one that obtain in the intermediate computations amount obtaining in step (2) and step (1), utilize least square method to solve the parameter value of described " shape function ", the distortion initial value using the parameter value of " shape function " that obtain as described digital picture.

Described " shape function " is:

x′=x+u+u _xΔx+u _yΔy

y′=y+v+v _xΔx+v _yΔy

Wherein, x ', y ' be in target image subarea except central point the coordinate of arbitrary pixel, x, y be in reference picture subarea with x ', the coordinate of the pixel of y ' correspondence, Δ x, Δ y is respectively as the pixel x in reference picture subarea, y is the distance at transverse and longitudinal change in coordinate axis direction to center, reference picture subarea, u, v is the displacement at transverse and longitudinal change in coordinate axis direction to center, target image subarea of center, reference picture subarea, u _x, u _y, v _x, v _ybe respectively in reference picture subarea the displacement gradient of corresponding point in target image subarea.

Described M is more than or equal to 20 and be less than or equal to 50 integer.

The parameter value of described " shape function " is by obtaining intermediate computations amount substitution single order or second order " shape function ".

Compared with prior art, the present invention has following beneficial effect:

1, the present invention is simple to operate, and automaticity is high.

2, be not subject to body structure surface to be out of shape big or small restriction, in the situation that there is larger in-plane displacement or torsional deflection, can use.

Accompanying drawing explanation

Fig. 1 is image subsection schematic diagram before and after digital picture distortion of the present invention.

Fig. 2 is small deformation whole audience distribution of correlation coefficient of the present invention.

Fig. 3 is large deformation whole audience distribution of correlation coefficient of the present invention.

Fig. 4 is SIFT Feature Points Matching of the present invention.

Fig. 5 is that the present invention is out of shape front image.

Fig. 6 is that the present invention is out of shape rear image.

Embodiment

Below in conjunction with accompanying drawing, structure of the present invention and the course of work are described further.

1, Digital Image Correlation Method

Digital Image Correlation Method is to obtain testee surface deformation front and back digital picture by shooting, matches the appointment corresponding point of two width images, calculates the measuring method of whole audience displacement and strain.Before distortion, image becomes " reference picture ", and after distortion, image is called " target image ", and its schematic diagram as shown in Figure 1.Digital Image Correlation Method is divided a virtual grid for asking for discrete whole audience displacement at reference picture first in advance.In figure, p point is a grid node, and centered by it, the square area of (2M+1) × (2M+1) pixel size is as reference picture subarea (dotted line frame), and wherein M is pixel number, and preferably value is the integer in 20 to 50.After distortion in image by certain searching method, by the related function defining, carry out correlation computations, find the related function of sening as an envoy to and get the target image subarea (solid box) of extreme value.Combining target image subsection center point P ' (x ₀', y ' ₀) coordinate can calculate a P (x ₀, y ₀) at x, the displacement u of y direction, v.

All there is before variation in the shape in the target image subarea after distortion compared with position.In the situation that adopting single order shape function, there is following linear relationship with the G (x, y) in reference picture in the G ' in target image subarea (x ', y ') now:

x′=x+u+u _xΔx+u _yΔy

⑴

y′=y+v+v _xΔx+v _yΔy

In (1) formula, Δ x, Δ y is that point (x, y) is to reference picture subarea center (x ₀, y ₀) distance, u, v be center, reference picture subarea at x, the displacement of y direction, u _x, u _y, v _x, v _yfor the displacement gradient of image subsection.

According to the research of document 0, adopt following related function to pass judgment on the similarity degree of distortion front and back image subsection herein:

$C\left(P\right)=\frac{\underset{G_s\∈S}{\mathrm{\Σ}}{\{f\left(G_s\right)-[g\left({\mathrm{\χ}}_1\left(G_s\right)\right)-w_0\left]\right\}}^2}{\underset{G_s\∈S}{\mathrm{\Σ}}{f}^2\left(G_s\right)}\left(2\right)$

P=in formula (u, u _x, u _y, v, v _x, v _y, w ₀) ^tdeformation parameter vector, w ₀it is luminance compensation parameter.S is the point set in reference picture subarea, G _srepresentative point wherein.χ ₁for the (1) linear mapping of representative of formula.F and g represent respectively the image before and after distortion.

From formula (2), related function C (P) is the function about deformation parameter P.When matching corresponding image subsection in target image, related function C (P) minimalization, C (P) single order inverse is 0, that is has:

$\▿C={\left(\frac{\∂C}{{\∂P}_i}\right)}_{i=1..7}=\frac{-2}{\underset{G_s\∈S}{\mathrm{\Σ}}{f}^2\left(G_s\right)}{\left\{\underset{G_s\∈S}{\mathrm{\Σ}}\right\{f\left(G_s\right)-\stackrel{\‾}{g}(G_s,P)\left\}\frac{\∂\tilde{g}(G_s,P)}{{\∂P}_i}\right\}}_{i=1..7}=0---\left(3\right)$

In formula

above formula can be used N-R solution by iterative method, and its equation is:

$\▿\▿C\left(P_0\right)(P-P_0)=-\▿C\left(P_0\right)---\left(4\right)$

Therefore:

$P=P_0-\frac{\▿C\left(P_0\right)}{\▿\▿C\left(P_0\right)}---\left(5\right)$

Here P ₀for distortion initial estimate, P is the approximate value after iteration, for the gradient vector of related function, be the secondary local derviation of related function, be also known as Hessian matrix.The visible document 0 of approximate processing to Hessian matrix and detailed process.From numerical analysis knowledge, for Nonlinear System of Equations, only have the initial estimate of the true value of approaching under specified criteria, to restrain.Therefore be out of shape reliably initial estimate particularly important for N-R method.

2, the distortion initial estimate based on SIFT

Under normal circumstances, can obtain distortion initial value by simple search.The whole pixel search of paper below and weak point thereof, the distortion initial estimate of subsequent introduction based on SIFT algorithm.

2.1 whole pixel displacement search

The shape invariance of based target image subsection, there is the hypothesis changing in its position only, can be after distortion in the region of search in image pointwise move image subsection and calculate related coefficient, the point of standard covariance correlation function value maximum is source location.Whole pixel displacement relevant search is carried out take whole pixel as unit, and the displacement that therefore obtained is the integral multiple of pixel.The iteration initial value of N-R method just can be write as P like this ₀=(u, v, 0,0,0,0,0) ^t.

In situation, the distortion in reference picture subarea is all less mostly, and therefore the relevant search take pixel as unit can provide Pixel-level Displacement Estimation accurately.As shown in Figure 2, in figure, the maximal value of related coefficient approaches 1, shows that search is reliable.Problem is that in some situation, after distortion, image may have larger Rigid Body in Rotation With or large deformation occurs with respect to reference picture.Fig. 3 has shown that reference picture subarea, at the whole audience distribution of correlation coefficient having occurred after 30 ° of Rigid Body in Rotation With, can find out that now neither one is as the relevant peak occurring in Fig. 2.In the situation that related coefficient maximal value is 0.3829, although found related coefficient maximal value, such target location is obviously wrong.Therefore in whole pixel, search in inoperative large deformation situation, with regard to the method that needs other, obtain distortion initial estimate.

2.2 distortion initial estimates based on SIFT algorithm

SIFT(Scale Invariant Feature Transform) algorithm proposes in 1999 by Lowe0, and improved and summed up in 2004.SIFT algorithm is realized and is mainly comprised 4 steps: 1. set up metric space, detect yardstick spatial extrema; 2. remove unsettled unique point; 3. the descriptor of calculated characteristics point, determines the direction of unique point; 4. generate local feature descriptor, proper vector is set up in combination.The visible document 0 of specific implementation of SIFT algorithm.

The estimation of distortion initial value is exactly to ask for 6 parameters of formula in (1).Undetermined parameter can by solution below two system of equations directly obtain:

$\mathrm{XU}=D_x\&DoubleRightArrow;\left[\begin{array}{ccc}1& {\mathrm{\&Delta;x}}_1& {\mathrm{\&Delta;<figure-callout\; id="1"\; label="y"\; filenames="HDA0000450802250000012.png,HDA0000450802250000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1\\ 1& {\mathrm{\&Delta;x}}_2& {\mathrm{\&Delta;<figure-callout\; id="1"\; label="y"\; filenames="HDA0000450802250000012.png,HDA0000450802250000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1\\ & \&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;& \\ 1& {\mathrm{\&Delta;x}}_n& {\mathrm{\&Delta;y}}_n\end{array}\right]\left(\begin{array}{c}u\\ u_x\\ u_y\end{array}\right)=\left(\begin{array}{c}{x}_1^{\&prime;}-x_1\\ x_2^{\&prime;}-x_2\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ x_n^{\&prime;}-x_n\end{array}\right)---\left(6\right)$

$\mathrm{XV}=D_y\&DoubleRightArrow;\left[\begin{array}{ccc}1& {\mathrm{\&Delta;x}}_1& {\mathrm{\&Delta;<figure-callout\; id="1"\; label="y"\; filenames="HDA0000450802250000012.png,HDA0000450802250000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1\\ 1& {\mathrm{\&Delta;x}}_2& {\mathrm{\&Delta;<figure-callout\; id="1"\; label="y"\; filenames="HDA0000450802250000012.png,HDA0000450802250000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1\\ & \&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;& \\ 1& {\mathrm{\&Delta;x}}_n& {\mathrm{\&Delta;y}}_n\end{array}\right]\left(\begin{array}{c}v\\ v_x\\ v_y\end{array}\right)=\left(\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA0000450802250000012.png,HDA0000450802250000021.png"\; state="\{\{state\}\}">y</figure-callout>}}_1^{\&prime;}-y_1\\ y_2^{\&prime;}-y_2\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ y_n^{\&prime;}-y_n\end{array}\right)---\left(\text{7}\right)$

Δ x=x-x in above formula ₀, Δ y=y-y ₀, x ₀, y ₀for the centre coordinate in reference picture subarea.(6) formula can solve by least square method:

$\left(\begin{array}{c}u\\ u_x\\ u_y\end{array}\right)={\left(X^{T}X\right)}^{-1}{X}^T{D}_x---\left(8\right)$

Here (X ^tx) ^-1x ^tfor the pseudo inverse matrix of X, for formula, (7) can obtain by same method $\left(\begin{array}{c}v\\ v_x\\ v_y\end{array}\right)={\left(X^{T}X\right)}^{-1}{X}^T{D}_y.$ Like this, problem has just become and has asked for 3 pairs or more multipair reference picture and the corresponding point of target image.

The problem of asking for corresponding point is the problem of an image characteristics extraction and coupling.Due to SIFT operator to image scaling, rotate even affined transformation and maintain the invariance, therefore can utilize SIFT algorithm to find many group corresponding point.Generally, SIFT algorithm can find the corresponding point (as shown in Figure 4,19 groups of corresponding point connect with straight line) that are greater than 3 groups, and this up-to-date style (6), (7) just can solve iteration initial value by least square method, and has P ₀=(u, v, u _x, v _x, u _y, v _y, 0) ^t(luminance compensation parameter w ₀be made as 0).

3, experiment

For the validity of checking this paper method, by experiment of rotation of rigid, carry out the accuracy of verification method.First by 0 speckle analogy methods proposing such as Peng Zhou, generate a speckle pattern as the front image of distortion.As shown in Figure 5, concrete parameter is simulation speckle pattern: image size is 256pixel × 256pixel, and speckle particle size is 4pixel, and speckle particle number is 4000.The image that Jiang Tu5Rao center turns clockwise after 30 ° is as the rear image of distortion, as shown in Figure 6.Now owing to there being larger Rigid Body in Rotation With angle, image subsection after rotation and original reference picture subarea similarity degree are lower, the method of searching for the rear image subsection of distortion position by whole pixel relevant search lost efficacy, and document 0 thinks when corner is greater than 7 ° that whole pixel relevant search is with regard to complete failure.

Owing to being experiment of rotation, for ease of observation experiment result, in Fig. 5, only choosing 5 points (the red point in Fig. 5) and calculate.Image calculation subarea size is 61pixel × 61pixel, and SIFT algorithm threshold value is 0.6.For first calculation level, the distortion actual value of the distortion initial estimate based on SIFT algorithm and final convergence is as shown in table 1 respectively, and table 1 shows that both are very approaching.The distortion initial estimate that utilizes SIFT algorithm to provide, N-R method can restrain rapidly through iteration several times (5 points of experiment use have all been used iteration 4 times).Fig. 6 Green spider is put position for distortion is front, red spider is position after distortion, from the variation of position, can find out, tests measured result and expects and coincide, and has shown the validity of this paper method.

Distortion initial value and the true value of first calculation level of table 1

Table?1?Initial?guess?and?actual?value?of?deformation?for?the?first?calculation?point

4, conclusion

(1) utilize SIFT operator to image scaling, rotate the characteristic that even affined transformation remains unchanged, by SIFT algorithmic match, obtain the corresponding point in image calculation subarea, distortion front and back, and utilize least square method can obtain the iterative initial value of distortion initial estimate as N-R method.

(2) the method still can be carried out deformation measurement accurately and reliably when larger Rigid Body in Rotation With or large deformation appear comprising in tested object plane.

(3) the method compares to previous existing method and possesses the effect of automatically asking for iterative initial value.

Claims (4)

1. computing method for digital picture distortion initial value, is characterized in that: comprise the steps:

(1) obtain the digital picture after digital picture and the surface deformation before testee surface deformation, using the digital picture before surface deformation as " reference picture ", the image after surface deformation is as " target image ", first, with reference to image and target image, be all placed in same plane coordinate system, on reference picture, choose arbitrarily a pixel as grid node, and centered by this grid node point, take 2M+1 as the length of side, divide square area, as with reference to image subsection, wherein M is pixel number, secondly, by feature point extraction and matching algorithm, from target image, automatically extract the pixel corresponding with reference picture subarea, with this, obtain many group pixels one to one, transformation relation between arbitrary corresponding pixel represents with " shape function " in described reference picture and in target image,

(2) according to corresponding pixel points and reference picture subarea center point coordinate calculative determination intermediate computations amount one by one, described intermediate computations measurer body comprises: in reference picture subarea with target image subarea under the same coordinate system in the coordinate figure of all pixels and reference picture subarea the coordinate of all pixels with respect to the variable quantity at center;

(3) according to the many group pixels one to one that obtain in the intermediate computations amount obtaining in step (2) and step (1), utilize least square method to solve the parameter value of described " shape function ", the distortion initial value using the parameter value of " shape function " that obtain as described digital picture.

2. the computing method of digital picture distortion initial value according to claim 1, is characterized in that: described " shape function " is:

x′=x+u+u _xΔx+u _yΔy

y′=y+v+v _xΔx+v _yΔy

Wherein, x ', y ' be in target image subarea except central point the coordinate of arbitrary pixel, x, y be in reference picture subarea with x ', the coordinate of the pixel of y ' correspondence, Δ x, Δ y is respectively as the pixel x in reference picture subarea, y is the distance at transverse and longitudinal change in coordinate axis direction to center, reference picture subarea, u, v is the displacement at transverse and longitudinal change in coordinate axis direction to center, target image subarea of center, reference picture subarea, u _x, u _y, v _x, v _ybe respectively in reference picture subarea the displacement gradient of corresponding point in target image subarea.

3. the computing method of digital picture according to claim 1 distortion initial value, is characterized in that: described M is more than or equal to 20 and be less than or equal to 50 integer.

4. the computing method of digital picture distortion initial value according to claim 1, is characterized in that: the parameter value of described " shape function " is by obtaining intermediate computations amount substitution single order or second order " shape function ".

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