CN105469398A - Deformation speckle generation method based on reverse mapping method - Google Patents

Abstract

The invention discloses a deformation speckle generation method based on a reverse mapping method. The method is characterized in that speckle particles which are generated randomly are used to superpose and generate a reference image and each pixel point position gray level in a speckle picture is known; a shape function describes corresponding pixel point positions before and after deformation, and inverse transformation is performed on the shape function, which satisfies the following equation: (x, y)=F(x', y'), the position (x', y') after the deformation is known so that the position (x, y) before the deformation can be obtained. A gray level value of the position point before the deformation of a whole pixel position is generated through speckle particle gray level superposition. A gray level of the position before the deformation is extracted and fills into a corresponding position after the deformation so that a speckle picture after the deformation can be generated. A speckle picture generation process is simple and accords with a deformation requirement of an actual experiment.

Description

Deformation speckle generation method based on reverse mapping method

The technical field is as follows:

the invention relates to a deformed speckle generation method based on a reverse mapping method, and belongs to the field of digital image correlation.

Background art:

a Digital Image Correlation (DIC) method is characterized by natural texture or artificial speckle on the surface of a test piece, and converts the problem of material deformation into the problem of matching search of characteristic points in images before and after the material surface is deformed. The method has the characteristics of high measurement precision, non-contact, full-field deformation measurement, easy establishment of an experiment bench and the like, and is widely applied to experimental mechanics to analyze the deformation characteristic of the material.

In order to improve the measurement accuracy of the digital image correlation method, factors influencing the algorithm, such as the size of a sub-area, the order of a shape function, a sub-pixel interpolation method, convergence conditions and the like, need to be analyzed. In the actual experiment, errors such as lens distortion, camera noise, light source fluctuation and the like are inevitably introduced, and the real deformation of the actual experiment is unknown, so that the simulated speckle pattern with controllable real deformation and no noise interference is widely applied. The method for generating the simulated speckle pattern is many, Schreier and the like utilize FFT transformation to calculate in a frequency domain, so as to generate a deformation image; orteu et al generate a simulated speckle pattern conforming to a true experimental deformation state according to a coherent noise function of Perlin; PengZhou, Pan and the like generate a reference image by superposition of Gaussian random speckle fields, then move the center of the Gaussian random speckles according to a shape function, and obtain a deformed image by superposition. The speckle pattern generated by the first two modes has small error and is more consistent with the actual deformation state, but the realization is more difficult; the latter method has clear formula for generating the speckle pattern and simple programming, but introduces errors when generating the deformation image, and the calculation errors are particularly obvious when large deformation is obtained through simulation.

The simulated speckle pattern with controllable deformation parameters provides a means for analyzing the influence of various factors on DIC calculation precision. The existing method for preparing the simulated speckle pattern has some defects, such as large system error, complex generation method, difficult programming realization and the like when the deformed speckle pattern is generated.

Therefore, a new deformed speckle generation method is required to solve the above problems.

The invention content is as follows:

aiming at the problems in the prior art, the invention provides a deformed speckle generation method based on a reverse mapping method.

The invention adopts the following technical scheme: a deformed speckle generation method based on an inverse mapping method comprises the following steps:

1) and randomly generating K speckle particles, wherein the coordinate and the brightness of the center position of the ith speckle particle are respectively (x)_i,y_i) And f_iWherein f is_iIn the range of [0,255]Wherein i is more than or equal to 1 and less than or equal to K;

2) the inverse function of (x ', y') F (x, y) is: (x, y) ═ F^-1(x ', y'), (x, y) are point coordinates in the speckle image before deformation, and (x ', y') are corresponding point coordinates in the speckle image after deformation, namely, the point coordinates (x, y) in the speckle image before deformation are obtained by using the point coordinates (x ', y') in the speckle image after deformation;

3) the brightness values of corresponding points in the speckle images before and after deformation meet the following requirements:

g(x',y')＝f(x,y)

wherein g (x ', y') represents the brightness value at the point (x ', y') in the speckle image after deformation, and the brightness of each point in the speckle image before deformation is obtained by using the randomly generated speckle particles:

$f(x,y)=\underset{i}{\overset{K}{\Σ}}{f}_i*\exp (-({\left(x-x_i\right)}^2+{\left(y-y_i\right)}^2)/R^2)$

where K represents the number of speckle particles, (x, y) is the coordinates of the points in the speckle image before deformation, (x)_i,y_i) Is the coordinate of the center position of the ith speckle particle, f_iObtaining the brightness of the deformed speckle image at the corresponding point (x ', y') by using the brightness f (x, y) at the point (x, y) in the speckle image before deformation;

4) and outputting the speckle images before deformation and the speckle images after deformation.

Further, the shape function is a first shape function,

$x^{\′}=x+u(x_0,y_0)+\frac{\∂u}{\∂x}{|}_{x_0,y_0}(x-x_0)+\frac{\∂u}{\∂y}{|}_{x_0,y_0}(y-y_0)$

$y^{\′}=x+v(x_0,y_0)+\frac{\∂v}{\∂x}{|}_{x_0,y_0}(x-x_0)+\frac{\∂v}{\∂y}{|}_{x_0,y_0}(y-y_0)$

wherein u and v are in-plane displacements in x and y directions caused by deformation, respectively, (x)₀,y₀) The coordinates of the center position of the speckle image before deformation, (x, y) the coordinates of a point in the speckle image before deformation, and (x ', y') the coordinates of a corresponding point in the speckle image after deformation.

Further, the shape function is a second order shape function,

$\left\{\begin{array}{c}{x}^{\′}=x+P_1+P_3\mathrm{\Δ}x+P_5\mathrm{\Δ}y+P_7{\mathrm{\Δx}}^2+P_9\mathrm{\Δ}x\mathrm{\Δ}y+P_{11}{\mathrm{\Δy}}^2\\ y^{\′}=y+P_2+P_4\mathrm{\Δ}x+P_6\mathrm{\Δ}y+P_8{\mathrm{\Δx}}^2+P_{10}\mathrm{\Δ}x\mathrm{\Δ}y+P_{12}{\mathrm{\Δy}}^2\end{array}\right.$

wherein the distortion parameter vector P is (u, v, u)_x,v_x,u_y,v_y,u_xx,v_xx,u_xy,v_xy,uy_y,vy_y)^T，Δx＝x-x₀，Δy＝y-y₀In-plane displacement in the u and vx and y directions, (u)_x,v_x,u_y,v_y) To shift the gradient, u_xx,v_xx,u_xy,v_xy,u_yy,vy_yThe second partial derivative of the displacement.

Further, in step 3), the speckle image before deformation is interpolated to obtain the brightness value of the sub-pixel position, and the interpolation method in the digital image processing includes nearest neighbor interpolation, bilinear interpolation or bicubic spline interpolation.

The invention has the following beneficial effects: the deformation speckle generation method based on the reverse mapping method is simple in idea, easy to program and achieve, small in calculation error, and more consistent with the deformation state of an actual test piece. The effectiveness and high-precision characteristic of the method for generating the deformed speckle pattern are verified through simulation experiment analysis.

Description of the drawings:

FIG. 1 is a schematic diagram of DIC calculation.

FIG. 2 is a speckle pattern generated by the original method.

FIG. 3 is a speckle pattern generated by the inverse mapping method.

Fig. 4 is a schematic diagram of the inverse mapping method.

Fig. 5 is a graph of the x-direction translation calculation error for the rigid translation of example 1.

FIG. 6 is a plot of the x-direction translational calculation standard deviation of the rigid translations of example 1.

Fig. 7 is a graph of the x-direction translational calculation error for uniform deformation of example 2.

Fig. 8 is a plot of the x-direction translation calculated standard deviation for uniform deformation of example 2.

Fig. 9 is a y-direction translation calculation error map of uniform deformation of example 2.

Fig. 10 is a plot of the calculated standard deviation for the y-direction translation for uniform deformation of example 2.

Fig. 11 is a sin deformation calculation error map of the non-uniform deformation of example 3.

Fig. 12 is a calculated standard deviation plot of sin deformation for non-uniform deformation of example 3.

Fig. 13 is a schematic flow chart of a deformed speckle generation method based on the inverse mapping method.

The specific implementation mode is as follows:

as shown in fig. 13, the method for generating deformed speckles based on the inverse mapping method of the present invention includes the following steps:

1) and randomly generating K speckle particles, wherein the coordinate and the brightness of the center position of the ith speckle particle are respectively (x)_i,y_i) And f_iWherein f is_iIn the range of [0,255]Wherein i is more than or equal to 1 and less than or equal to K;

2) the inverse function of (x ', y') F (x, y) is: (x, y) ═ F^-1(x ', y'), (x, y) are point coordinates in the speckle image before deformation, (x ', y') are corresponding point coordinates in the speckle image after deformation, that is, the point coordinates (x, y) in the speckle image before deformation are obtained by using the point coordinates (x ', y') in the speckle image after deformation, wherein the shape function can be a first order shape function:

$x^{\′}=x+u(x_0,y_0)+\frac{\∂u}{\∂x}{|}_{x_0,y_0}(x-x_0)+\frac{\∂u}{\∂y}{|}_{x_0,y_0}(y-y_0)$

$y^{\′}=x+v(x_0,y_0)+\frac{\∂v}{\∂x}{|}_{x_0,y_0}(x-x_0)+\frac{\∂v}{\∂y}{|}_{x_0,y_0}(y-y_0)$

wherein u and v are in-plane displacements in x and y directions caused by deformation, respectively, (x)₀,y₀) The coordinate of the central position of the image before deformation, (x, y) the coordinate of a point in the image before deformation, and (x ', y') the coordinate of a corresponding point in the image after deformation;

wherein the shape function can also be a second order shape function:

$\left\{\begin{array}{c}{x}^{\′}=x+P_1+P_3\mathrm{\Δ}x+P_5\mathrm{\Δ}y+P_7{\mathrm{\Δx}}^2+P_9\mathrm{\Δ}x\mathrm{\Δ}y+P_{\mathrm{11}}{\mathrm{\Δy}}^2\\ y^{\′}=y+P_2+P_4\mathrm{\Δ}x+P_6\mathrm{\Δ}y+P_8{\mathrm{\Δx}}^2+P_{10}\mathrm{\Δ}x\mathrm{\Δ}y+P_{12}{\mathrm{\Δy}}^2\end{array}\right.$

wherein the distortion parameter vector P is (u, v, u)_x,v_x,u_y,v_y,u_xx,v_xx,u_xy,v_xy,u_yy,v_yy)^T，Δx＝x-x₀，Δy＝y-y₀In-plane displacement in the u and vx and y directions, (u)_x,v_x,u_y,v_y) To shift the gradient, u_xx,v_xx,u_xy,v_xy,u_yy,v_yyIs the second partial derivative of the displacement; the method can be realized by adopting a first-order or second-order shape function, but the second-order precision is higher than the first order, and the first-order calculation efficiency is better than the second order, so that the first-order shape function is recommended in the occasion with low precision requirement, otherwise, the second-order shape function is adopted;

3) the brightness values of corresponding points in the speckle images before and after deformation meet the following requirements:

g(x',y')＝f(x,y)，

wherein g (x ', y') represents the brightness value at the point (x ', y') in the speckle image after deformation, f (x, y) is the brightness at the point (x, y) in the speckle image before deformation, and the brightness of each point in the speckle image before deformation is obtained by using the randomly generated speckle particles:

$f(x,y)=\underset{i}{\overset{K}{\Σ}}{f}_i*\exp (-({\left(x-x_i\right)}^2+{\left(y-y_i\right)}^2)/R^2)$

where K represents the number of speckle particles, (x, y) is the coordinates of the points in the speckle image before deformation, (x)_i,y_i) Is the coordinate of the center position of the ith speckle particle, f_iThe brightness of the ith speckle particle center position is shown, and R is the radius of the speckle particle, wherein, because the point coordinates (x, y) in the image before deformation obtained by using the inverse function of the shape function can be sub-pixel values, the speckle image before deformation is subjected to bicubic spline interpolation and f (x, y) is read, namely, the brightness f (x, y) at the point (x, y) in the speckle image before deformation is used for obtaining the brightness at the corresponding point (x ', y') in the speckle image after deformation; the interpolation method in digital image processing includes nearest neighbor interpolation or bilinear interpolation besides bi-cubic spline interpolation, wherein the bi-cubic spline interpolation has higher precision and is more commonly used in high-precision measurement.

4) And outputting the speckle images before deformation and the speckle images after deformation.

Introduction of the principle of the DIC method:

referring to fig. 1, the basic principle of the DIC method is very simple, that is, the measurement problem of structural deformation is converted into the correlation matching problem of the images before (reference image) and after (image after) deformation of the test piece, and the correlation matching problem is solved. Therefore, to describe the deformation of the structured surface, a shape function needs to be defined first. Assuming an arbitrary point (x, y) in the reference image and a small neighborhood S around it, there is a set of mapping relations χ that satisfy

χ(x,y)→(x',y'),f(x,y)＝g(x',y')

Where f (x, y) represents the image intensity at point (x, y), g (x ', y') represents the image intensity at point (x ', y') after deformation, (x, y) is a point in the reference image, and (x ', y') is the corresponding point of (x, y) in the deformed image.

The mapping χ is called a so-called shape function. If the neighborhood S and the deformation are sufficiently small, the shape function χ may be described by equation (1),

$\begin{array}{c}{x}^{\′}=x+u(x_0,y_0)+\frac{\∂u}{\∂x}{|}_{x_0,y_0}(x-x_0)+\frac{\∂u}{\∂y}{|}_{x_0,y_0}(y-y_0)\\ y^{\′}=y+v(x_0,y_0)+\frac{\∂v}{\∂x}{|}_{x_0,y_0}(x-x_0)+\frac{\∂v}{\∂y}{|}_{x_0,y_0}(y-y_0)\end{array}---\left(1\right)$

wherein u and v are in-plane displacements in x and y directions caused by deformation, respectively, (x)₀,y₀) Is the center position coordinates of the area S.

The shape function is written in the form of a vector,

$P=(u,v,\frac{\∂u}{\∂x},\frac{\∂v}{\∂x},\frac{\∂u}{\∂y},\frac{\∂v}{\∂y}),$

and a correlation coefficient is defined, and,

$\mathrm{\ρ}=\frac{\underset{s_p\∈S}{\Σ}{\[f\left(s_p\right)-g(s_p,P)\]}^2}{\underset{s_p\∈S}{\Σ}{f}^2\left(s_p\right)}---\left(2\right)$

the problem is then solved by obtaining an optimal solution that minimizes equation (2) by means of a non-linear optimization method.

As can be seen from equation (2), when the correlation function takes a minimum value, the similarity of the image sub-regions before and after the deformation reaches a maximum value. At this time, the displacement parameters u and v contained in the parameter vector P represent the best estimation of the displacement after deformation, and the full-field displacement can be obtained by calculating all the measurement points in the same way.

There are several solutions for minimizing ρ, and as far as the inventors know, the Newton-Raphson method is adopted by many documents because of its high calculation accuracy, i.e. the following iterative equation is constructed

$P=P_0-\frac{\▿\mathrm{\ρ}\left(P_0\right)}{\▿\▿\mathrm{\ρ}\left(P_0\right)}---\left(3\right)$

In the formula, P₀For the initial values of the deformation parameters, ▽ rho and ▽▽ rho are the first-order gradient of the correlation function rho and a Hessian matrix, and satisfy the condition that

$\begin{array}{c}\▿\mathrm{\ρ}={\left(\frac{\∂\mathrm{\ρ}}{\∂P_i}\right)}_{i=1,...,6}\\ =\frac{-2}{\underset{s_p\∈S}{\Σ}{f}^2\left(s_p\right)}{\{\underset{s_p\∈S}{\Σ}\[f\left(s_p\right)-g(s_p,P)\]\frac{\∂g(s_p,P)}{\∂P_i}\}}_{i=1,...,6}\end{array}---\left(4\right)$

And

$\begin{array}{c}\▿\▿\mathrm{\ρ}={\left(\frac{{\∂}^2\mathrm{\ρ}}{\∂P_i\∂P_j}\right)}_{\underset{j=1,...,6}{i=1,...,6}}\\ \≈\frac{2}{\underset{s_p\∈S}{\Σ}{f}^2\left(s_p\right)}{\left\{\underset{s_p\∈S}{\Σ}\frac{\∂g(s_p,P)}{\∂P_i}\frac{\∂g(s_p,P)}{\∂P_j}\right\}}_{\underset{j=1,...,6}{i=1,...,6}}\end{array}---\left(5\right)$

from the analysis and derivation, it can be seen that the deformation of the test piece is converted into the matching problem of the corresponding points in the image before and after the deformation of the test piece, and the matching search process is based on the similarity of the gray features of the corresponding points, so that the reference generated by simulation and the gray distribution of the speckle pattern after the deformation need to be in one-to-one correspondence to ensure the accuracy of the search matching.

Theoretical error analysis of original method

The reference speckle pattern is formed by superposing random Gaussian spots, and the generation formula is as follows:

$f(x,y)=\underset{i=1}{\overset{K}{\Σ}}{f}_i*\exp (-({\left(x-x_i\right)}^2+{\left(y-y_i\right)}^2)/R^2)---\left(6\right)$

wherein k represents the number of speckle particles; (x)_i,y_i) The central position of speckle particles is randomly generated; r is the radius of speckle particles; f. of_iThe brightness of the randomly generated speckle center is in the range of 0-255. the image size is M × N.

When a deformation image is generated through simulation, the original method is that the central point of the speckle grains is shifted to meet the description of the shape function in the formula (1), and the gray level distribution of the deformation speckle pattern can be obtained by substituting (x ', y') into the formula (6) and solving the problem of (x ', y').

Assuming a gaussian speckle is generated in the middle of the image and a strain of 0.2 in the x-direction, it is found that the gaussian spot is only translated, as shown in fig. 2. In fact, the circular spot should become oval-like due to the stretching, as shown in fig. 3. The irrationality of the original method is analyzed below theoretically.

Assuming that three points exist in the graph before deformation, wherein B is a speckle central point, A and C are two points with a distance R from the central point respectively, and the three points have the same y value. When the deformation is generated according to the original method, the three points in the reference image are changed into A ', B ' and C ', and as can be seen from the figure, the three mapped curves are parallel, that is, the displacement of the three points before and after the deformation is considered to be the same.

Assuming that the abscissa of the point B is S, the strain in the x direction is obtained as

Δx_B＝x_B'-x_B(7)

Wherein u is_BMeans strain in x-direction of point B, x_B'And x_BRespectively, the position of point B in the speckle pattern before and after deformation, Deltax_BThe position difference of the point B in the speckle pattern before and after deformation.

From FIG. 2, it can be seen that: Δ x_A＝Δx_B＝Δx_C

Then

$u_A=\frac{{\mathrm{\Δx}}_A}{S-R}=\frac{{\mathrm{\Δx}}_B}{S-R}$

(8)

$u_C=\frac{{\mathrm{\Δx}}_C}{S+R}=\frac{{\mathrm{\Δx}}_C}{S+R}$

Substituting the formula (7) into the formula (8) to obtain

$u_A=\frac{{\mathrm{\Δx}}_A}{S-R}=\frac{S}{S-R}{u}_B$

(9)

$u_C=\frac{{\mathrm{\Δx}}_C}{S+R}=\frac{S}{S+R}{u}_B$

Since the speckle particle radius R cannot be exactly equal to 0, the strain at point A, B, C is not the same. While practically the entire speckle pattern is subjected to a uniform tensile deformation in the x-direction, i.e. u_A＝u_B＝u_CIt can be seen that the original method for generating the speckle pattern makes the speckle pattern itself have an error, and as can be seen from equation (7), the magnitude of the error is related to the radius R of the speckle pattern, the position S of the calculated point, and the magnitude of the deformed strain u. When a plurality of gaussian speckles are superposed, the quality of the generated speckle pattern also affects the result, so that the parameters R and S related to the speckles cannot be directly used for error size judgment. The invention only studies the influence of different deformations on the introduced speckle pattern self error.

Three, reverse mapping method

Referring to fig. 4, a deformed speckle generating method based on the inverse mapping method according to the present invention is shown in fig. 4. Firstly, a reference image is generated by overlapping speckle grains which are generated randomly, and the gray level of the position of each pixel point in the speckle image is known. In fact, for a deformed image of size M × N, the position of each pixel point is known. The shape function in formula (1) describes the positions of corresponding pixels before and after deformation, and the inverse transformation is performed on the shape function, that is, (x, y) ═ F (x ', y '), then (x, y ') before deformation can be obtained by knowing (x ', y ') after deformation, and the value can be the sub-pixel position. The gray value of the position point before deformation of the whole pixel position is generated by speckle particle gray level superposition, the sub-pixel position value can be obtained through bicubic spline interpolation, the gray value of the position before deformation is extracted and filled into the corresponding position after deformation, a speckle pattern after deformation can be generated, the speckle pattern generation process is simple, and the deformation requirement of an actual experiment is met.

Simulation analysis

According to theoretical analysis, errors can be introduced into the speckle pattern after deformation due to initial deformation, the influence of different deformations and deformation sizes on the original generation method is researched, and the effectiveness and high-precision characteristics of the reverse mapping method are proved.

Example 1: rigid body translation

The reference image is a randomly generated speckle image with a resolution of 256 × 256pixels, a speckle particle count of 2000, and a speckle particle radius of 4. By using the original method and the inverse mapping method, 20 pieces of translation images with the interval of 0.05pixel are generated along the x direction respectively, namely the displacement of the image sequence is 0-1 pixel. Selecting parameter variables in DIC calculation to be consistent, analyzing two groups of speckle patterns, and calculating the error and standard deviation of a displacement field, wherein the expression is as follows:

$e_v=\stackrel{\‾}{v}-v_{true}$

(10)

${\mathrm{\σ}}_v=\sqrt{\frac{1}{N-1}\underset{i=1}{\overset{N}{\Σ}}{(v_i-\stackrel{\‾}{v})}^2}$

wherein,representing the mean of the displacements of all calculated points in the same graph, i.e.v_trueRepresents a theoretical deformation parameter; n represents all the calculation points.

It can be seen from fig. 5 that the maximum error of the displacement field calculated by the two methods is 0.001pixel, but the error calculated by generating the speckle pattern based on the inverse mapping method conforms to the sin error distribution rule, which is consistent with the analysis result in the literature. From the calculation result of the standard deviation in fig. 6, the standard deviations calculated based on the speckle pattern of the inverse mapping method are small and are all less than 0.001pixel, and the requirement of high-precision measurement is met.

Example 2: uniform deformation

And (3) generating a uniform stretching graph along the y direction respectively by using an original method and a reverse mapping method with the reference of the invariant speckle graphs, wherein the micro strain is 1000-.

For the deformation in the x direction, when the micro strain is less than 10000, the calculated errors of the speckle patterns generated by the two methods are similar, when the micro strain is more than 10000, the error based on the original method is almost linearly increased, the calculated error based on the inverse mapping method has no obvious change, and the maximum strain error is not more than 50 micro strain. It is found from fig. 8 that the standard deviation of the calculated strain based on the original method is always large, and almost as the strain increases, the standard deviation also increases.

For the deformation in the y direction, y is the main strain direction, and no matter the calculation error or the standard deviation, the speckle pattern generated based on the original method is larger in calculation and almost linearly increases along with the increase of strain, so that the linear relation is consistent with the linear relation obtained by theoretical derivation. On the other hand, the effectiveness and high-precision characteristic of the reverse mapping speckle pattern generation method provided by the invention are also proved.

Example 3: non-uniform deformation

The reference image is a randomly generated speckle image, the resolution is 500 × 500pixels, the number of speckle particles is 4000, the radius of the speckle particles is 4, the original method and the inverse mapping method are utilized to respectively generate a non-uniform deformation image along the y direction, the displacement field in the y direction conforms to sin distribution, namely v equals Asin (2 π y/T), A equals 1, and T equals 200.

As can be seen from fig. 11, the calculated errors of the speckle patterns generated based on the original method are relatively large, and the maximum deviation can reach 2000 microstrain. And the error distribution rule of the latter is more practical, namely the error is maximum at the strain peak. Comparing fig. 12, it can be seen that the standard deviation calculated based on the two speckles is not much different, and the maximum is less than 300 microstrain. In general, the speckle pattern generated based on the inverse mapping method has lower calculation error and better conforms to the actual deformation rule.

Because the deformation of the simulation experiment is known, and the influence of lens distortion, light source fluctuation, non-ideal loading conditions and the like on DIC calculation can be well eliminated, the simulated speckle pattern is widely applied to the DIC simulation experiment. In consideration of the problem that a large error is introduced into a primary speckle pattern generation method, the method adopts a reverse mapping method to generate the deformed speckle pattern, the method is simple in idea and easy to program, the calculated error is small, and the deformation rule is more in line with the deformation state of an actual test piece. The effectiveness and high-precision characteristic of the method for generating the deformed speckle pattern are verified through simulation experiment analysis.

The foregoing is only a preferred embodiment of this invention and it should be noted that modifications can be made by those skilled in the art without departing from the principle of the invention and these modifications should also be considered as the protection scope of the invention.

Claims (4)

1. A deformation speckle generation method based on a reverse mapping method is characterized in that: comprises the following steps

1) And randomly generating K speckle particles, wherein the coordinate and the brightness of the center position of the ith speckle particle are respectively (x)_i,y_i) And f_iWherein f is_iIn the range of [0,255]Wherein i is more than or equal to 1 and less than or equal to K;

2) the inverse function of (x ', y') F (x, y) is: (x, y) ═ F^-1(x ', y'), (x, y) are the coordinates of points in the speckle image before deformation, and (x ', y') are the speckle pattern after deformationObtaining the coordinates (x, y) of the points in the speckle images before deformation by using the coordinates (x ', y') of the points in the speckle images after deformation;

3) the brightness values of corresponding points in the speckle images before and after deformation meet the following requirements:

g(x',y')＝f(x,y)

wherein g (x ', y') represents the brightness value at the point (x ', y') in the speckle image after deformation, and the brightness of each point in the speckle image before deformation is obtained by using the randomly generated speckle particles:

$f(x,y)=\underset{i}{\overset{K}{\Σ}}{f}_i*\exp (-({\left(x-x_i\right)}^2+{\left(y-y_i\right)}^2)/R^2)$

where K represents the number of speckle particles, (x, y) is the coordinates of the points in the speckle image before deformation, (x)_i,y_i) Is the coordinate of the center position of the ith speckle particle, f_iBrightness of the ith speckle particle center positionThe degree R is the radius of the speckle particles, namely the brightness f (x, y) at the point (x, y) in the speckle image before deformation is used for obtaining the brightness at the corresponding point (x ', y') in the speckle image after deformation;

4) and outputting the speckle images before deformation and the speckle images after deformation.

2. The deformed speckle generation method based on the inverse mapping method as claimed in claim 1, wherein: the shape function is a first order shape function,

$x^{\′}=x+u(x_0,y_0)+\frac{\∂u}{\∂x}{|}_{x_0,y_0}(x-x_0)+\frac{\∂u}{\∂y}{|}_{x_0,y_0}(y-y_0)$

$y^{\′}=x+v(x_0,y_0)+\frac{\∂v}{\∂x}{|}_{x_0,y_0}(x-x_0)+\frac{\∂v}{\∂y}{|}_{x_0,y_0}(y-y_0)$

wherein u and v are in-plane displacements in x and y directions caused by deformation, respectively, (x)₀,y₀) The coordinates of the center position of the speckle image before deformation, (x, y) the coordinates of a point in the speckle image before deformation, and (x ', y') the coordinates of a corresponding point in the speckle image after deformation.

3. The deformed speckle generation method based on the inverse mapping method as claimed in claim 1, wherein: the shape function is a second order shape function,

$\left\{\begin{array}{c}{x}^{\′}=x+P_1+P_3\mathrm{\Δ}x+P_5\mathrm{\Δ}y+P_7{\mathrm{\Δx}}^2+P_9\mathrm{\Δ}x\mathrm{\Δ}y+P_{11}{\mathrm{\Δy}}^2\\ y^{\′}=y+P_2+P_4\mathrm{\Δ}x+P_6\mathrm{\Δ}y+P_8{\mathrm{\Δx}}^2+P_{10}\mathrm{\Δ}x\mathrm{\Δ}y+P_{12}{\mathrm{\Δy}}^2\end{array}\right.$

wherein the distortion parameter vector P is (u, v, u)_x,v_x,u_y,v_y,u_xx,v_xx,u_xy,v_xy,u_yy,v_yy)^T，Δx＝x-x₀，Δy＝y-y₀In-plane displacement in the u and vx and y directions, (u)_x,v_x,u_y,v_y) To shift the gradient, u_xx,v_xx,u_xy,v_xy,u_yy,v_yyThe second partial derivative of the displacement.

4. The deformed speckle generation method based on the inverse mapping method as claimed in claim 1, wherein: in the step 3), the speckle image before deformation is interpolated to obtain the brightness value of the sub-pixel position, and the interpolation method in the digital image processing comprises nearest neighbor interpolation, bilinear interpolation or bicubic spline interpolation.