CN110288564B - Binarization speckle quality evaluation method based on power spectrum analysis - Google Patents

Abstract

The invention discloses a method for evaluating the quality of binarized speckle based on power spectrum analysis. The method includes the following steps: collecting a binarized speckle pattern by a camera; extracting the gray value of the collected pattern and performing noise reduction processing ; Set the size of the sub-region and frame the target sub-region; obtain the image power spectrum, speckle duty cycle, and noise variance in the selected sub-region; perform inverse Fourier transform on the power spectrum, and then solve the two adjacent points of the speckle is the probability density function of the same speckle primitive; set the error solving precision, solve the speckle error value and the corresponding probability of each value, and find the error mean and variance, and solve the average mean and variance of all target sub-regions, so as to achieve the purpose of evaluating speckle. The present invention uses the power spectrum analysis method to evaluate the quality of the binarized speckle, the method can freely select the error precision according to the experimenter's requirement for the precision of the experiment, and has the advantages of simple equipment, convenience and practicality, and the like.

Description

A Binarized Speckle Quality Evaluation Method Based on Power Spectrum Analysis

technical field

The invention relates to the field of solid mechanics of optical measurement experiments, in particular to a binarized speckle quality evaluation method based on power spectrum analysis.

Background technique

Binarized speckle is widely used in the measurement of digital image coherence (DIC), which has the advantages of large gray gradient and small measurement error.

Nowadays, the quality evaluation of binarized speckle mostly starts from the angle of speckle duty ratio and speckle radius, and lacks the consideration of speckle power spectrum. In addition, the existing speckle quality evaluation mostly adopts the method of numerical simulation. For example, Pan Bing, Wu Dafang et al. used five distinctly different speckle images for precise translation in the paper "Research on the Quality Evaluation of Speckle Images in Digital Image Correlation Methods", and compared the measured values with the predicted values. The analysis of mean error and standard deviation lacks generality and lacks specific experimental implementations.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a binarized speckle quality evaluation method based on power spectrum analysis. Based on the power spectrum analysis, from an experimental point of view, the quality of the power spectrum can be evaluated concisely and intuitively, with simple operation and easy implementation.

The technical solution to achieve the purpose of the present invention is: a method for evaluating the quality of binarized speckle based on power spectrum analysis, the experimental device of the method includes a camera, a speckle pattern fixing plate, a binarized speckle to be measured, a white light source, Optical platform, electronic computer; the method includes the following steps:

Step 1. The camera collects the binarized speckle pattern;

Step 2, extracting the gray value of the collected pattern and saving it in the form of a matrix, extracting and removing noise components from the matrix, and obtaining the expression of speckle duty ratio and camera noise;

Step 3. Set the size of the sub-area, and frame several target sub-areas;

Step 4, select the target sub-region, obtain the corresponding sub-region power spectrum of the picture: utilize the image sub-region autocorrelation Fourier transform or other methods to obtain the picture sub-region power spectrum, and store the result in the matrix S _xx ;

Step 5. Set the size of the sub-region, subtract the product of the fixed value component determined by the size of the sub-region and the square of the speckle duty cycle from the power spectrum, and then solve the probability density function that two adjacent points of the speckle are the same speckle primitive ;

Step 6. Set the error solving precision, solve the speckle error value and the probability corresponding to each value, and obtain the error mean and variance;

Step 7: Re-select the target sub-area, repeat steps 4 to 6 until the target sub-area is selected, and use the error mean and variance of each sub-area to obtain the total error mean and variance.

Compared with the prior art, the present invention has the following significant advantages: (1) the method of the present invention innovatively adopts the power spectrum analysis method to evaluate the quality of the binarized speckle, and realizes this function from an experimental point of view; (2) The method can freely choose the error accuracy according to the experimenter's requirements for the accuracy of the experiment, and the accuracy value can be less than 0.001 pixel; (3) The required equipment is simple, convenient and practical, and the results are intuitive and obvious.

Description of drawings

FIG. 1 is a schematic diagram of the measuring device of the present invention.

FIG. 2 is a flow chart of a method for evaluating the quality of binarized speckle based on power spectrum analysis according to the present invention.

FIG. 3 is a schematic diagram of a quality analysis result of speckle in an embodiment of the present invention.

Detailed ways

As shown in Figures 1 and 2, the experimental device of the binarized speckle quality evaluation method includes: an industrial camera 1, a high-resolution lens 2, a speckle pattern fixing plate and its clamping device 3, a second to be measured Valued speckle 4, white light source 5, optical table 6, electronic computer 7; the method includes the following steps:

Step 1. The camera collects the binarized speckle pattern: under the illumination of a white light source, an industrial camera with a high-resolution lens is used to collect the binarized speckle.

Step 2: Extracting image features and noise features: extracting grayscale values of the collected patterns and saving them in the form of a matrix. Furthermore, the grayscale matrix is divided into two sub-matrices, and the data between the two sub-matrices have obvious numerical differences. Then, average the two sub-matrices respectively, and record the difference between the actual value of each pixel and the average, and record the difference as the noise value of each pixel. Finally, the noise expression is regarded as a Gaussian probability distribution expression with a mean value of zero, and the variance of the pixel noise value is the variance of the expression, then the noise probability density distribution expression f(I) is:

Among them, I is the noise gray value, σ is the noise variance;

The ratio of the number of elements of the sub-matrix with a larger value to the number of elements of the entire grayscale matrix is regarded as the speckle duty ratio, denoted as δ.

Step 3. Set the size of the sub-area, which is a L*L rectangular area, and the user sets N target sub-areas.

Step 4: Select the target sub-region, and obtain the power spectrum of the corresponding sub-region of the picture: obtain the power spectrum of the picture sub-region by using the autocorrelation Fourier transform of the image sub-region or other methods, and then store the result in the matrix S _xx .

结果如下：Step 5. First solve the fixed value component determined by the size of the sub-region, which is expressed as

The result is as follows:

Among them, u and v are power spectrum variables, and L is the sub-region size parameter.

结果为：Next, multiply the speckle duty cycle by the fixed value component determined by the size of the sub-area, and calculate the difference between the speckle power spectrum and the speckle power spectrum and store it in the form of a matrix. The obtained difference is expressed as

The result is:

与(δ-δ²)的商的傅里叶逆变换F_same(x,y)，以矩阵形式保存：Solve again

The inverse Fourier transform of the quotient with (δ-δ ² ), F _same (x,y), is stored as a matrix:

Finally, solve the probability density function f _same (x, y) that two adjacent points of the speckle are the same speckle primitive:

Step 6. Set the error solving precision in pixels.

The steps for solving the speckle error value and the probability corresponding to each value are as follows:

First, the 3σ region is defined as the possible error range, and the region is divided by the set error solution accuracy ε, and the coordinates of each sampling point are obtained:

i=-N _i ,-N _i +1...0...N _i -1,N _i ,

j=-N _j ,-N _j +1...0...N _j -1,N _j

in,

Then confirm the coherence value Ri _,j between the two grayscales:

Among them, I～N(1,2σ ² ).

Then solve the probability that each sampling point achieves the maximum value:

Among them, erf(x) is the error function, f(R _i,j ) is the probability density distribution function satisfied by R _i,j , and its expression is:

in,

The above maximum value is obtained by numerical solution.

After solving the speckle error value and the corresponding probability of each value, then calculate the error mean and variance. The error mean and variance include the one-way errors δ _U and δ _V in the horizontal and vertical directions, and the comprehensive error δ _UV in the two directions. The calculation steps are as follows:

First, find the mean and variance of the errors Δδ _U , Δδ _V , Δδ _UV for each pixel, denoted as E(Δδ _U ), D(Δδ _U ), E(Δδ _V ), D(Δδ _V ), E( Δδ _UV ), D(Δδ _UV ), the calculation method is as follows:

Then, the influence of the sub-region size on the error is introduced, and the overall error of the sub-region is calculated. The mean values are respectively recorded as: E(δ _U ), E(δ _V ), E(δ _UV ), and the variances are respectively recorded as D(δ _U ) , D(δ _V ), D(δ _UV ), the results are:

Step 7: Re-select the target sub-area, repeat steps 4, 5, and 6 until the target sub-area is selected, and record the error mean and variance of each sub-area. The _total error _mean and _variance are obtained by using _the error _mean and variance _of each sub-area _. δ _U ), D _total (δ _V ), D _total (δ _UV ) are calculated as follows:

The final error mean is used as the main factor to consider the speckle quality.

Using the above measurement methods, the actual speckle quality analysis is performed for several speckles. A series of speckles with a radius of 2 and different duty ratios were obtained by numerical simulation software. The quality of the speckle is analyzed by the above calculation method, and the analysis result is shown in Figure 3. It can be seen from the implementation result that the experimental result and the theoretical analysis fit well.

Claims (4)

1. A method for evaluating the quality of binarized speckle based on power spectrum analysis, characterized in that the experimental device of the method comprises a camera, a speckle pattern fixing plate, a binarized speckle to be measured, a white light source, an optical table, Electronic computer, the method includes the following steps: Step 1. The camera collects the binarized speckle pattern; Step 2, extracting the gray value of the collected binarized speckle pattern, and saving it in the form of a matrix, extracting and removing noise components from the matrix, and obtaining the expression of the speckle duty ratio and the camera noise; Step 3. Set the size of the sub-area, and frame several target sub-areas; Step 4, select the target sub-region, obtain the power spectrum of the corresponding sub-region of the picture: utilize the autocorrelation Fourier transform of the image sub-region to obtain the power spectrum of the picture sub-region, and store the result in the matrix S _xx ; Step 5. Set the size of the sub-region, subtract the product of the fixed value component determined by the size of the sub-region and the square of the speckle duty cycle from the power spectrum, and then solve the probability density function that two adjacent points of the speckle are the same speckle primitive ; The constant value component is expressed as

The result is as follows:

Among them, u and v are power spectrum variables, and L is the sub-region size parameter; The probability density function is solved as follows: Multiply the speckle duty cycle by the fixed value component determined by the size of the sub-area, and calculate the difference between the speckle power spectrum and it and store it in the form of a matrix. The obtained difference is expressed as

The result is:

solve

Inverse Fourier transform F _same (x,y) of the quotient with (δ-δ ² ), the result is stored in matrix form:

Solve the probability density function f _same (x, y) that two adjacent points of the speckle are the same speckle primitive:

Step 6. Set the error solving accuracy, the unit of error solving accuracy is pixel, solve the speckle error value and the probability corresponding to each value, and obtain the error mean and variance; The steps for solving the speckle error value and the probability corresponding to each value are as follows: Delineate the 3σ area as the possible error range, and use the set two-direction error solution accuracy ε _i , ε _j to divide the area, and obtain the coordinates of each sampling point:

i=-N _i , -N _i +1...0...N _i -1,N _i , _j =-Nj, _-Nj +1...0... _Nj -1, _Nj in,

Confirm the coherence value Ri _,j between the two-point grayscales:

Among them, I～N(1, 2σ ² ); Find the probability of obtaining the maximum value for each sampling point

Among them, erf(x) is the error function, f(R _{i, j} ) is the probability density distribution function satisfied by R _{i, j} , and its expression is:

in,

The above maximum value is obtained by numerical solution method; The error mean and variance include the one-way errors δ _U , δ _V in the horizontal and vertical directions, and the comprehensive error δ _UV in the two directions. The calculation method is as follows: Find the error Δδ _U , Δδ _V , Δδ _UV mean and variance of each pixel, denoted as E(Δδ _U ), D(Δδ _U ), E(Δδ _V ), D(Δδ _V ), E(Δδ _UV ) ), D(Δδ _UV ), the calculation method is as follows:

The influence of the size of the sub-region on the error is introduced, and the overall error of the sub-region is calculated. The mean values are respectively recorded as: E(δ _U ), E(δ _V ), E(δ _UV ), and the variances are respectively recorded as D(δ _U ), D( δ _V ), D(δ _UV ), the result is: E(δ _U )=E(Δδ _U ),

E(δ _V )=E(Δδ _V ),

E(δ _UV )=E(Δδ _UV ),

Step 7, re-select the target sub-area, repeat steps 4 to 6, until the target sub-area is selected, use the error mean and variance of each sub-area to obtain the total error mean and variance; The mean and variance of the total error are recorded as: E _total (δ _U ), E _total (δ _V ), E _total (δ _UV ), and the variance is recorded as: D _total (δ _U ), D _total (δ _V ) , D _total (δ _UV ), calculated as follows:

2. The method for evaluating the quality of binarized speckle based on power spectrum analysis according to claim 1, wherein the specific methods for removing noise components and extracting noise forms in step 2 are as follows: Step 2-1, divide the grayscale matrix into two sub-matrices, calculate the average value of the two sub-matrices respectively, and record the difference between the actual value of each pixel and the average, and record the difference as each pixel. noise value; Step 2-2, the noise is regarded as a Gaussian probability distribution with a mean value of zero, and the variance of the pixel noise value is the expression variance, then the noise probability density distribution expression f(I) is:

Among them, I is the noise gray value, and σ is the noise variance. 3. The binarized speckle quality evaluation method based on power spectrum analysis according to claim 2, wherein the speckle duty ratio in step 2 is the number of elements of the sub-matrix with a larger value and the entire grayscale. The ratio of the number of elements in the degree matrix, denoted as δ. 4 . The binarized speckle quality evaluation method based on power spectrum analysis according to claim 1 , wherein the sub-region in step 3 is a L*L rectangular region, and the number of target sub-regions is N. 5 .

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