CN108288267B - Dark channel-based non-reference evaluation method for image definition of scanning electron microscope - Google Patents

Abstract

The invention provides a dark channel-based non-reference evaluation method for image definition of a scanning electron microscope, which comprises the following steps of: carrying out dark channel preprocessing on the original scanning electron microscope blurred image, calculating the edge of the preprocessed image again, carrying out enhanced denoising on the edge by using an edge-preserving filter based on weighted multiplication, and finally, taking the weighting of the maximum gradient and the average gradient as the quality fraction of the image according to the visual characteristics of human beings. The invention applies the dark channel to the quality evaluation of the scanning electron microscope image for the first time, and the performance of the proposed method is superior to that of the current typical fuzzy image quality evaluation method.

Description

Dark channel-based non-reference evaluation method for image definition of scanning electron microscope

Technical Field

The invention relates to the field of image quality evaluation, in particular to a non-reference evaluation method for the image definition of a scanning electron microscope based on a dark channel.

Background

The scanning electron microscope images broaden human vision and provide a way for acquiring fine structure information. Various types of distortions can be caused in the process of acquiring the scanning electron microscope image, and the distortions directly influence the judgment of human beings on the researched object, so that the quality evaluation of the scanning electron microscope image has very important significance, but the quality evaluation of the scanning electron microscope image is not concerned at present. The definition of the scanning electron microscope image is the most important technical index in the imaging process, and generally, a clear image needs to be obtained by repeatedly adjusting imaging parameters and setting, which is time-consuming and labor-consuming, so that a method specially for evaluating the definition of the scanning electron microscope is urgently needed.

There are many methods for evaluating image sharpness, and these methods are described below.

Definition no-reference quality evaluation: some image blur evaluation algorithms have been proposed in recent years. The document Marziliano [1] et al first proposed to detect image edges with the Sobel operator and then calculate the edge width. Ferzli [2] et al propose Just Noticeable Blur (JNB) methods that can predict the relative blur amount of images of different contents by combining the concept of JNB with a probability sum model. Niranjan [3] et al, based on human fuzzy perception studies of different contrast values, calculate the fuzzy probability of each edge and propose a method for detecting fuzzy Cumulative Probability (CPBD), which improves the JNB method. Bahrami [4] et al in the literature define the maximum local difference (MLV) of each pixel as the maximum intensity difference of this pixel from its 8-neighborhood, and the standard deviation of the MLV distribution of each pixel is a representation of sharpness.

The methods are not designed aiming at the scanning electron microscope image, and the performance of the methods in the aspect of evaluating the quality of the scanning electron microscope image is not ideal through experiments, so that a method for specially evaluating the definition of the scanning electron microscope image is urgently needed.

[1]Marziliano P,Dufaux F,Winkler S,et al.Perceptual blur and ringing metrics:application to JPEG2000[J].Signal processing:Image communication,2004,19(2):163-172.

[2]Ferzli R,Karam L J.A no-reference objective image sharpness metric based on the notion of just noticeable blur(JNB)[J].IEEE Transactions on Image Processing,2009,18(4):717-728.

[3]Narvekar N D,Karam L J.A no-reference image blur metric based on the cumulative probability of blur detection(CPBD)[J].IEEE Transactions on Image Processing,2011,20(9):2678-2683.

[4]Bahrami K,Kot A C.A fast approach for no-reference image sharpness assessment based on maximum local variation[J].IEEE Signal Processing Letters,2014,21(6):751-755.

Disclosure of Invention

The purpose of the invention is as follows: the invention provides a method specially for evaluating the definition of a scanning electron microscope image, which aims at the problem that the existing definition evaluation method is not suitable for the scanning electron microscope image, and discloses a non-reference evaluation method for the definition of the scanning electron microscope image based on a dark channel.

The technical scheme is as follows: the technical scheme provided by the invention is as follows:

a non-reference evaluation method for the definition of a scanning electron microscope image based on a dark channel comprises the following steps:

(1) acquiring a scanning electron microscope blurred image I, and performing dark channel pretreatment on the I;

(2) extracting an edge image of the image subjected to dark channel preprocessing by using a Sobel edge operator;

(3) filtering the edge image by using an edge-preserving smoothing filter based on a weighted least square method;

(4) and weighting the maximum gradient and the average gradient of the filtered image to be used as an objective quality score for evaluating the scanning electron microscope blurred image I.

Further, the expression of performing dark channel preprocessing on the image I in the step (1) is as follows:

wherein, s (I) represents the image after the image I is subjected to dark channel preprocessing, and s (I), (t) represents the pixel value at the pixel point t in s (I); Ω (t) represents a window of m × m with the pixel point t as the center, and m is the width of the window; i (z) represents the pixel value at pixel point z in image I.

Further, the expression of the edge image extracted in step (2) is as follows:

g(x,y)＝|Δ_xh(x,y)|+|Δ_yv(x,y)| (2)

Δ_xh(x,y)＝s(x+1,y-1)+2s(x+1,y)+s(x+1,y+1)-s(x-1,y-1)-2s(x-1,y)-s(x-1,y+1)

Δ_yv(x,y)＝s(x-1,y+1)+2s(x,y+1)+s(x+1,y+1)-s(x-1,y-1)-2s(x,y-1)-s(x+1,y-1)

wherein g represents an edge image, g (x, y) represents a pixel value at a pixel point (x, y) in the edge image g, and Δ_xh (x, y) and Δ_yv (x, y) represents the first derivative of the image s (i) in the horizontal direction and the first derivative in the vertical direction, respectively.

Further, the step (3) of filtering the edge image with an edge-preserving smoothing filter based on a weighted least square method specifically includes:

(4-1) constructing an objective function:

wherein,

wherein u represents the target image, u_pRepresents the pixel value at a point p on the image u; λ is a regularization term parameter, a_xP (g) and a_y,p(g) Respectively representing a smoothing weight in the horizontal direction and a smoothing weight in the vertical direction; l represents the logarithmic luminance channel of the edge image g; alpha is an exponent, and epsilon is a very small constant;

(4-2) converting the objective function into a matrix form:

in the formula, A_xFor diagonal matrices containing smooth weights in the horizontal direction, A_yIs a diagonal matrix containing smooth weights in the vertical direction; d_xAnd D_yRespectively a horizontal direction discrete difference operator and a vertical direction discrete difference operator;

(4-3) solving u which minimizes the objective function.

Further, the step of solving u that minimizes the objective function is:

let the objective function equal to 0, convert the objective function to:

(Q+λL_g)u＝g (5)

wherein L is_gIs a five-point space anisotropic Laplacian matrix which is used for deriving a piecewise smooth adjustment graph from a sparse constraint set,

is a reaction of with D_xThe backward difference operator in the opposite direction is,

is a reaction of with D_yBackward difference operators in opposite directions; q is an identity matrix;

u can be calculated according to the formula (5).

Further, the maximum gradient and the average gradient of the image filtered in the step (4) are respectively as follows:

MG＝max(u(x,y))

AG＝(∑_x,yu(x,y)/(w×h))

in the formula, MG and AG are the maximum gradient and average gradient of the filtered image respectively, and w and h are the length and width of the filtered image respectively;

the objective quality fraction of the scanning electron microscope blurred image I is as follows: iQA ═ MG × AG^-α。

Has the advantages that: compared with the existing definition non-reference image quality evaluation method, the method provided by the invention has the advantages that the dark channel is used for the quality evaluation of the scanning electron microscope image for the first time, and the performance is obviously improved.

Drawings

FIG. 1 is a flow chart of the present invention.

Detailed Description

The technical scheme of the invention is further explained by combining the drawings and the embodiment.

The invention relates to a dark channel-based non-reference evaluation method for image definition of a scanning electron microscope. Because there is no scanning electron microscope image database, this embodiment first constructs a database with 650 scanning electron microscope images, obtains the subjective quality score of the image through subjective experiments, extracts 150 blurred images and their corresponding subjective quality scores from 650 scanning electron microscope images, then performs dark channel preprocessing on the original scanning electron microscope blurred image, calculates its edge on the preprocessed image again, uses an edge preserving filter based on weighted multiplication to perform enhanced denoising after obtaining the edge, and finally takes the weighting of the maximum gradient and the average gradient as the objective quality score of the image according to the human visual characteristics. The invention applies the dark channel to the image quality evaluation for the first time, and the performance of the proposed method is superior to that of the current typical fuzzy image quality evaluation method.

The invention will be further described with reference to fig. 1.

The method comprises the following steps: 150 scanning electron microscope blurred images I_iI1, 2, … … 150, pair I_iDark channel pre-processing is performed. For image I_iThe dark channel is defined as:

s(I_i) (x) is the image after dark channel preprocessing; omega (t) represents a window of m multiplied by m with the pixel point t as the center, and m is most suitable for taking a value of 15 through experiments; min in the formula represents the minimum value operation;

representing an image I_iThe pixel value at pixel point z on the chrominance component c. Because the scanning electron microscopic images are all gray level images and only have one channel, the invention

I.e. the formula for the dark channel is:

step two: extracting an edge image of the image after dark channel preprocessing by using a Sobel edge operator:

g_i(x,y)＝|Δ_xh_i(x,y)|+|Δ_yv_i(x,y)|

Δ_xh_i(x,y)＝s_i(x+1,y-1)+2s_i(x+1,y)+s_i(x+1,y+1)-s_i(x-1,y-1)-2s_i(x-1,y)-s_i(x-1,y+1)

Δ_yv_i(x,y)＝s_i(x-1,y+1)+2s_i(x,y+1)+s_i(x+1,y+1)-s_i(x-1,y-1)-2s_i(x,y-1)-s_i(x+1,y-1)

in the formula, g_i(x, y) denotes an edge image g_iPixel value, Δ, at the middle pixel point (x, y)_xh_i(x, y) and Δ_yv_i(x, y) respectively denote the dark channel preprocessed image s_i(I) The first derivative in the horizontal direction and the first derivative in the vertical direction.

Step three: edge image g using edge-preserving smoothing filter based on weighted least square method_i(x, y) is enhanced while removing noise. For the input image g_iWe set the target image to u_i. On the one hand, we want it to be as close as possible to g_iAt the same time, u_iExcept that in g_iSome regions where the edge gradient changes more greatly should be as smooth as possible in their entirety. Therefore, the specific step of filtering the edge image by the edge-preserving smoothing filter based on the weighted least square method includes:

a solution is solved that minimizes the following objective function.

Wherein,

in the formula, the first term (u) of the objective function_ip-g_ip)²For making the input image and the output image more similar, the better, the second term is a regular term, by minimizing u_iSuch that the smoother the output image, the better. λ is a regularization term parameter, which balances the specific gravity of the two, and the larger λ is, the smoother the image is. The smoothed weights are each a_x,p(g_i) And a_y,p(g_i). Wherein l_iIs to be transportedInput image g_iThe logarithmic luminance channel of (a) is exponential and epsilon is a very small constant (typically 0.0001).

Writing the above equation in matrix form:

here, A_ixAnd A_iyIs a diagonal matrix containing smoothing weights, D_ixAnd D_iyIs a discrete difference operator.

Let the objective function equal to 0, convert the objective function to:

(Q+λL_ig)u_i＝g_i

wherein L is_igIs a five-point spatial anisotropic laplacian matrix,

the method is mainly used for deriving a piecewise smoothing adjustment graph from a sparse constraint set;

and

is a backward difference operator.

Step four: and finally, weighting the maximum gradient and the average gradient of the filtered image to serve as the quality score of the evaluated image. The maximum and average gradients of the image are defined as:

MG_i＝max(u_i(x,y))

AG_i＝(∑_x,yu_i(x,y)/(w_i×h_i))

wherein, MG_iAnd AG_iThe maximum and average gradients of the image after filtering, w and h are the length and width of the filtered image, respectively.

Scanning electron microscope blurred image I_iThe objective mass fraction of (a) is:

IQA_i＝MG_i×AG_i ^-α

experimental tests have shown that the results are optimal when alpha is 0.4366.

Experimental results and performance:

in order to verify the performance of the method provided by the invention, the objective quality score obtained by prediction in the embodiment is compared with the subjective quality score, namely whether the result obtained by the technical scheme is consistent with the human visual sense is judged. Since the objective quality score and the subjective quality score obtained by the implementation are nonlinear, the objective quality score is subjected to appropriate nonlinear transformation, namely, the image objective quality score is mapped to the same scale as the subjective quality score through a nonlinear fitting function. Usually, a five-parameter fitting function is selected, v is set to represent the objective quality score, and f (v) is expressed as follows:

wherein, tau_iAnd i is 1,2,3,4 and 5 as fitting parameters.

After nonlinear fitting, three common indexes can be selected to judge the performance of the invention. Defining the subjective quality fraction and the objective quality fraction after nonlinear conversion of the ith scanning electron microscope image as k_iAnd q is_iThe calculation processes of the three indexes are described below.

(1) Pearson Linear Correlation Coefficient (PLCC):

wherein N represents the number of scanning electron microscope images,

and

respectively representing N scanning electron microscope imagesThe subjective mass fraction mean and the objective mass fraction mean.

(2) Root Mean Square Error (RMSE):

(3) spearman correlation coefficient (SRCC):

wherein d is_iShowing scanning Electron microscope image I_iThe subjective quality score and the objective quality score of (1).

The performance of the technical scheme is judged from the two aspects of prediction accuracy and monotonicity by the three performance indexes, wherein PLCC and RMSE are indexes of the algorithm prediction accuracy, and the higher the PLCC and SRCC are, the higher the algorithm prediction accuracy is. The prediction monotonicity index of the checking algorithm is RMSE, the lower the RMSE is, the more consistent the algorithm can be kept with subjective evaluation, and the better the performance of the algorithm is on the whole.

Table 1 compares the performance of the present invention and 11 exemplary sharpness non-reference evaluation methods, the best performance being shown in bold for ease of viewing.

TABLE 1 Performance comparison of the method of the present invention and existing sharpness non-reference image quality evaluation algorithms

From the above table, we can obtain the obvious advantage of the proposed method compared with the existing typical sharpness non-reference image quality evaluation method, i.e. the PLCC/SRCC value is obviously higher than all methods, and the RMSE is the lowest.

The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (3)

1. A non-reference evaluation method for the definition of a scanning electron microscope image based on a dark channel is characterized by comprising the following steps:

(1) acquiring a scanning electron microscope blurred image I, and performing dark channel pretreatment on the I;

wherein, s (I) represents the image after the image I is subjected to dark channel preprocessing, and s (I), (t) represents the pixel value at the pixel point t in s (I); Ω (t) represents a window of m × m with the pixel point t as the center, and m is the width of the window; i (z) represents the pixel value at pixel point z in image I;

(2) extracting an edge image of the image subjected to dark channel preprocessing by using a Sobel edge operator;

(3) filtering the edge image by using an edge-preserving smoothing filter based on a weighted least square method; the method comprises the following specific steps:

31) constructing an objective function:

wherein,

wherein u represents the target image, u_pRepresents the pixel value at a point p on the image u; λ is a regularization term parameter, a_x,p(g) And a_y,p(g) Respectively representing the smoothing weight in the horizontal direction and the smoothing weight in the vertical directionWeighing; l represents the logarithmic luminance channel of the edge image g; alpha is an exponent, and epsilon is a very small constant;

32) converting the objective function to a matrix form:

in the formula, A_xFor diagonal matrices containing smooth weights in the horizontal direction, A_yIs a diagonal matrix containing smooth weights in the vertical direction; d_xAnd D_yRespectively a horizontal direction discrete difference operator and a vertical direction discrete difference operator;

is a reaction of with D_xThe backward difference operator in the opposite direction is,

is a reaction of with D_yBackward difference operators in opposite directions;

33) solving for u that minimizes the objective function;

(4) weighting the maximum gradient and the average gradient of the filtered image to be used as objective quality scores for evaluating the scanning electron microscope fuzzy image I; the maximum gradient and the average gradient of the filtered image are respectively:

MG＝max(u(x,y))

AG＝(∑_x,yu(x,y)/(w×h))

in the formula, MG and AG are the maximum gradient and average gradient of the filtered image respectively, and w and h are the length and width of the filtered image respectively;

the objective quality fraction of the scanning electron microscope blurred image I is as follows: iQA ═ MG × AG^-α。

2. The method for non-reference evaluation of the definition of a scanning electron microscope image based on a dark channel according to claim 1, wherein the edge image extracted in the step (2) has an expression as follows:

g(x,y)＝|Δ_xh(x,y)+|Δ_yv(x,y)| (2)

Δ_xh(x,y)＝s(x+1,y-1)+2s(x+1,y)+s(x+1,y+1)-s(x-1,y-1)-2s(x-1,y)-s(x-1,y+1)

Δ_yv(x,y)＝s(x-1,y+1)+2s(x,y+1)+s(x+1,y+1)-s(x-1,y-1)-2s(x,y-1)-s(x+1,y-1)

wherein g represents an edge image, g (x, y) represents a pixel value at a pixel point (x, y) in the edge image g, and Δ_xh (x, y) and Δ_yv (x, y) represents the first derivative of the image s (i) in the horizontal direction and the first derivative in the vertical direction, respectively.

3. The method for non-reference evaluation of the definition of a scanning electron microscope image based on a dark channel according to claim 2, wherein the step of solving u that minimizes the objective function is:

let the objective function equal to 0, convert the objective function to:

(Q+λL_g)u＝g (5)

wherein L is_gIs a five-point space anisotropic Laplacian matrix which is used for deriving a piecewise smooth adjustment graph from a sparse constraint set,

is a reaction of with D_xThe backward difference operator in the opposite direction is,

is a reaction of with D_yBackward difference operators in opposite directions; q is an identity matrix;

u is calculated according to equation (5).

Images