CN104657949A - Method for optimizing structural elements during denoising of coal slime flotation froth image - Google Patents

Abstract

The invention relates to processing of a coal slime flotation froth image, particularly to a method for optimizing structural elements during denoising of the coal slime flotation froth image. The method for optimizing the structural elements during denoising of the coal slime flotation froth image comprises steps as follows: the coal slime flotation froth image acquired from a flotation site of a coal preparation plant is denoised by a morphological opening and closing filter, the structural elements used during denoising of the coal slime flotation froth image are optimized, and the optimized structural elements are used for image reconstruction morphological opening and closing filtering denoising processing. With the adoption of the method, selection processes are simple, convenient and time-saving, selection results are more scientific, reasonable and accurate, the blindness of selection of the structural elements is overcome, and the reconstruction morphological opening and closing filtering denoising effect is improved.

Description

A Method for Structural Element Optimization in Slime Flotation Foam Image Denoising

technical field

The invention relates to coal slime flotation foam image processing, in particular to a method for optimizing structural elements in coal slime flotation foam image denoising.

Background technique

The coal slime flotation foam image is an image actually acquired during the flotation production process of the coal preparation plant. Because the bubbles in the coal slime flotation are water bubbles carrying fine coal particles, and the boundaries are not clear and the size is inconsistent, and the image acquisition It was performed in an unenclosed natural light and lighting environment, and the air bubbles in the image contain many small reflective bright spots. In addition, there are still noises such as CCD sensors in the process of image acquisition, which bring great difficulties to the subsequent image segmentation. Therefore, in order to remove the noise existing in the slime flotation froth image, it is very necessary to use the morphological open-close filter to denoise the froth image.

In the image denoising process of reconstructed morphological open-close filter, the role of structural elements is very important, and its selection determines the final filter performance. However, there are often no fixed methods and rules to follow for the selection of structural elements, and how to determine the shape and size of structural elements has become a problem that plagues people. Choosing structural elements of different shapes in image filtering will produce different filtering effects; similarly, its size is also very critical in filtering. If you choose too large structural elements, the details of the filtered image will be lost at this time; otherwise , it will make denoising incomplete. Due to the importance mentioned above, the rational selection of structural elements has become the subject of many researchers. When performing morphological filtering, in order to obtain a good filtering effect, the structural elements should be screened and optimized, not only considering its geometric shape but also optimizing its size. Choosing a reasonable structural element can not only remove noise but also better protect The details of the image ensure the accuracy of segmentation based on watershed.

Contents of the invention

The technical problem to be solved by the present invention is: how to better remove the noise existing in the coal slime flotation foam image when using the morphological open-close filter to denoise the foam image.

The technical solution adopted in the present invention is: a method for optimizing structural elements in the denoising of coal slime flotation foam images, using a morphological open-close filter for the coal slime flotation foam images obtained from the flotation site of the coal preparation plant Denoise the coal slime flotation foam image, optimize the structural elements used in the denoising of the coal slime flotation foam image, and optimize the structural elements for image reconstruction morphological opening and closing filter denoising processing. Structural elements used in mud flotation froth image denoising are optimized according to the following steps

Step 1. Select the coal slime flotation foam images captured in production, with a pixel size of 256×256, and use circular structural elements with radii r of 2, 3, 4, and 5 to test their information capacity one by one. Find the structural element corresponding to the largest information capacity and the second largest information capacity, and then select a d×d full "1" matrix as a new structural element between the two, d is between the largest information capacity and the second largest information capacity Between the dimensions of the corresponding circular structural elements, the d×d matrix is expanded into 1 row during the optimization iteration, thereby forming the initial antibody group, and the chromosome of the initial antibody group is coded by d×d bit 0/1, That is, the number of coding fields is L=d×d, and d is a natural number;

Step 2. For each antibody in the initial antibody population, calculate its fitness value, namely

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; info</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; log</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; Norm</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, f _i represents the fitness value of the i-th antibody in the antibody group, i is a natural number, C _info represents the improved information capacity, Norm(G ₁ ,G ₂ ) represents a two-dimensional histogram based on peak normalization, G ₁ Indicates the gray level of a certain pixel in the image after filtering by the i-th antibody, _G2 indicates the gray level of its right neighbor pixel, ω is the cumulative constraint area of information capacity, which can be expressed as:

$\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ <span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

T ₁ and T ₂ are called non-negative constraint thresholds, G _max and G _min respectively represent the maximum and minimum values of the gray level in the two-dimensional histogram used for logarithmic normalization, in the optimization of structural elements Take G _min =0, G _max =255, T ₁ =128, T ₂ =2;

Step 3: Adopt the elite retention strategy, select the m antibodies with the largest fitness value as memory antibodies, put them into the elite library and retain them as an elite group, do not participate in the selection, crossover and mutation operations, and are directly added to the generated new ones as excellent individuals In the first generation population, wherein m=(15%～20%)N, m is an integer, and N is the population size;

Step 4, adopting the rapid calculation method of Hamming distance based on XOR operation to calculate the antibody concentration of the antibody group, and calculate the replication rate e _k on the basis of the antibody concentration;

Replication rate: $e_k=\frac{f_k}{{\left(C_k\right)}^{\mathrm{\&beta;}}}---\left(3\right)$

f _k is the fitness of antibody k, C _k is the concentration of antibody k, and β is an important parameter reflecting the proportion of antibody concentration and fitness in the expected reproduction rate. Here, β=2, and the concentration of antibody k C _k The fast algorithm of Hamming distance based on XOR operation is used for calculation, that is

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; kw</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; kw</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; t</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; t</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

C _k is the concentration of antibody k, N is the population size, a _kw is the affinity between two antibodies k and w, D is the Hamming distance of two antibodies, t is the threshold of Hamming distance, t=0.3*L, L The length of the string is the number of encoded fields, and k and w are natural numbers;

Step 5. Calculate the selection probability p _sk . According to step 4, the selection probability p _sk can be obtained, and the antibody population is selected based on the value of p _sk , and the crossover operation is performed.

${\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; sk</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Among them, e _k is the replication rate of antibody k, N is the population size, i is a natural number less than or equal to N, e _i is the replication rate of any antibody i;

Step 6, adopt to add adjustable factor θ, obtain new antibody group; Add the calculating formula of the adaptive variation probability of adjustable factor as:

${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\frac{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; avg</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ></span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; avg</span>}}\\ {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; avg</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; k</span>}}{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

In the formula, f _max represents the maximum value of fitness; f _avg represents the arithmetic average fitness value; f is the individual fitness value; k ₃ and k ₄ refer to the adjustment coefficients between 0 and 1, taking k ₃ =k ₄ =0.1, θ is the adjustable factor, G is the evolutionary algebra; G _max is the maximum evolutionary algebra; k is the value of the adjustable factor θ in the first generation, where k=0.005;

Step 7. Update the antibody group, and call the individuals with high fitness value in the elite group to replace the individuals with low fitness value in the antibody group to generate the next generation antibody group;

Step 8, judge according to the termination condition, if it is satisfied, end the optimization, output the optimized structural element, if not, jump to step 2 and repeat the execution, the termination condition is one of the following: a, define the threshold ε=0.0001, For each antibody group, calculate the average fitness of the antibody group, the difference between the arithmetic mean fitness value of this antibody group and the arithmetic mean fitness value of the previous generation antibody group is less than ε, b, the highest fitness of 15 consecutive generation antibody groups The degree value remains unchanged, c, reaches the maximum evolution algebra. The present invention has the following advantages:

The beneficial effects of the present invention are:

1. On the basis of the selection mechanism, the concentration adjustment selection mechanism is adopted, and the Hamming distance similarity criterion based on XOR operation is introduced, and the traditional information entropy method is abandoned, which can avoid cumbersome logarithmic calculations and improve efficiency .

2. The improved self-adaptive variation method is adopted, and the variation adjustment factor is added, so as to increase the diversity of initial individuals and avoid premature convergence.

3. The excellent gene individuals can be retained, further speeding up the algorithm search process.

4. In the process of optimizing the structural elements of the slime flotation image denoising, for the particularity of the no-reference evaluation of the slime flotation foam image, the improved information capacity based on the gray level co-occurrence matrix is used as the slime flotation Fitness functions in structural element optimization algorithms for foam image denoising.

5. Use an improved generation method of the initial antibody population to generate the initial antibody population, take the circular structural element as the object, gradually expand its size, test the improved information capacity based on the gray level co-occurrence matrix as the standard, and finally lock The range of structural elements that may obtain the best filtering effect is used as the length of the chromosome code.

The present invention finds an effective method for selecting structural elements of a coal slime flotation foam image, which makes the selection process simple and time-saving, makes the selected results more scientific, reasonable and accurate, overcomes the blindness in the selection of structural elements, and improves Reconstructing the denoising effect of morphological opening and closing filtering.

Description of drawings

Fig. 1 is a flow chart of structural element optimization in morphological opening and closing denoising of coal slime flotation foam image reconstruction;

Fig. 2 is the domain of definition and the constraint area of two-dimensional histogram;

Figure 3 is the adjustable factor change curve θ.

Detailed ways:

Below in conjunction with accompanying drawing 1,2,3 concrete implementation of the present invention is described:

1. The individual chromosomes of the initial antibody group are determined using the principle of one-by-one determination of typical structural elements. When reconstructing the open-close filter of the flotation foam image, the circular structural elements with radii of 2, 3, 4, and 5 were selected to determine the dimension of the initial antibody population. Select the slime flotation foam image captured in production, with a pixel size of 256×256, and use circular structural elements with radii r of 2, 3, 4, and 5 to reconstruct the morphological open-close filter to remove Then the information capacity of the denoised image is tested one by one. The information capacity of the filtered image obtained by the circular structural elements with a radius of 2, 3, and 4 increases sequentially with the increase of the radius, especially when the radius is 4 Structural element, the information capacity of the filtered image is the largest; but when the radius of the structural element is 5, the information capacity of the filtered flotation image decreases instead. For further testing, between the structural elements with a radius of 3 (5 dimensions) and a radius of 4 (7 dimensions), a d×d full “1” matrix is selected as a new structural element, and d is between the maximum information Between the capacity and the dimension of the circular structural element corresponding to the next largest information capacity, a 6×6 full “1” matrix is selected as the structural element for fitness testing, and the measured 6×6 full “1” matrix The fitness of the flotation foam image reconstructed after morphological opening and closing filtering is greater than the information capacity of the image filtered by the structure element with a radius of 4. Therefore, in various optimizations, the structural elements are determined to be a 6×6 matrix, and the matrix is expanded into 1 row in the optimization iteration, that is, the chromosomes of the initial antibody population are coded with 36 bits 0, 1, that is, the number of coded fields: L= 36. To generate a sequence group with an initial population of 30 and a chromosome number of 36, a 30×36 matrix can be used, each row of the matrix is used as an antibody, and the maximum evolutionary generation is set to 50.

2. Select a foam image obtained by an industrial CCD camera at the coal slime flotation production site, and its pixel size is 256×256. For each antibody, it is arranged into a 6×6 matrix in order, which is its corresponding structural element, which is used as the structural element in the reconstruction morphology filter to denoise the foam image, and the processed image The fitness value is calculated using the improved information capacity based on the gray level co-occurrence matrix, namely

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; info</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; log</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; Norm</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, f _i represents the fitness value of the i-th antibody in the antibody group, i is a natural number, C _info represents the improved information capacity, Norm(G ₁ ,G ₂ ) represents a two-dimensional histogram based on peak normalization, G ₁ Indicates the gray level of a certain pixel in the image after filtering by the i-th antibody, _G2 indicates the gray level of its right neighbor pixel, ω is the cumulative constraint area of information capacity, which can be expressed as:

$\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ <span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Calculate the fitness value of each antibody.

3. Sort the fitness, and select the largest m=5 as elite antibodies for retention.

4. Apply the expected replication rate formula:

${\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Calculate the expected replication rate of the antibody, take β=2 in the formula; at the same time, according to the formula

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; kw</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; kw</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; t</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; t</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Calculate the concentration of antibody k; D is the Hamming distance between the two antibodies, t=10, and an improved XOR algorithm is used, that is, a bit-by-bit XOR operation is performed on the binary coded sequences of the two antibodies, and the XOR result is "1 "The number of digits is accumulated, and the final accumulated sum is the Hamming distance;

5. Based on step 4, the formula is:

${\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; sk</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Calculate the selection probability of the antibody; select the antibody population based on the value of p _sk , and perform a crossover operation.

6. Based on the improved adaptive mutation method, the antibody is mutated, and the mutation rate of the antibody is determined by the formula $P_m=\left\{\begin{array}{c}\frac{k_3\left[(f_{\max }-f)\right]}{f_{\max }-f_{\mathrm{avg}}}+\mathrm{\&theta;},f>f_{\mathrm{avg}}\\ k_4,f\&le;f_{\mathrm{avg}}\end{array}\right.---\left(6\right)$

$\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; k</span>}}{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

Calculation is performed, where k ₃ =k ₄ =0.1, k=0.005, and a new antibody group is generated after mutation.

7. Call individuals with high fitness value in the elite group to replace individuals with low fitness value in the antibody group, update the antibody group, and generate the next generation of antibody group.

8. For each generation of antibody groups, if one of the following conditions is met, the optimization ends and the optimized structural elements are output; if not, jump to 2 and repeat. 1) Calculate the average fitness of the antibody population; if the difference ε between the average fitness of this antibody population and the average fitness of the previous generation antibody population is less than or equal to 0.0001, that is, ε≤0.0001; 2) The highest fitness of 15 consecutive generations of antibody populations 3) Reach the maximum evolution algebra.

9. After the iteration is over, select the individual with the greatest fitness in the population, and arrange it into a 6×6 matrix according to the order, which is the structural element obtained from the final optimization.

Claims (1)

1. A method for optimization of structural elements in the denoising of coal slime flotation foam images. For the coal slime flotation foam images obtained from the flotation site of the coal preparation plant, the morphological open-close filter is used to analyze the coal slime flotation foam images. Carrying out denoising processing, which is characterized in that: the structural elements used in the denoising of the slime flotation foam image are optimized, and the optimized structural elements are used for image reconstruction morphological opening and closing filtering denoising processing, and the denoising of the coal slime flotation The optimization of structural elements used in foam image denoising is carried out according to the following steps Step 1. Select the coal slime flotation foam images captured in production, with a pixel size of 256×256, and use circular structural elements with radii r of 2, 3, 4, and 5 to test their information capacity one by one. Find the structural element corresponding to the largest information capacity and the second largest information capacity, and then select a d×d full "1" matrix as a new structural element between the two, d is between the largest information capacity and the second largest information capacity Between the dimensions of the corresponding circular structural elements, the d×d matrix is expanded into 1 row during the optimization iteration, thereby forming the initial antibody group, and the chromosome of the initial antibody group is coded by d×d bit 0/1, That is, the number of coding fields is L=d×d, and d is a natural number; Step 2. For each antibody in the initial antibody population, calculate its fitness value, namely ${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; info\; o</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; log</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; Norm</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ Among them, f _i represents the fitness value of the i-th antibody in the antibody group, i is a natural number, C _info represents the improved information capacity, Norm(G ₁ ,G ₂ ) represents a two-dimensional histogram based on peak normalization, G ₁ Indicates the gray level of a certain pixel in the image after filtering by the i-th antibody, _G2 indicates the gray level of its right neighbor pixel, ω is the cumulative constraint area of information capacity, which can be expressed as: $\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ <span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ T ₁ and T ₂ are called non-negative constraint thresholds, G _max and G _min respectively represent the maximum and minimum values of the gray level in the two-dimensional histogram used for logarithmic normalization, in the optimization of structural elements Take G _min =0, G _max =255, T ₁ =128, T ₂ =2; Step 3: Adopt the elite retention strategy, select m antibodies with the largest fitness value as memory antibodies, and put them into the elite pool as an elite group for retention, without participating in selection, crossover, and mutation operations, they are directly added as excellent individuals to the generated new In one generation group, wherein m=(15%～20%)N, m is an integer, and N is the population size; Step 4, adopting the rapid calculation method of Hamming distance based on XOR operation to calculate the antibody concentration of the antibody group, and calculate the replication rate e _k on the basis of the antibody concentration; Replication rate: $e_k=\frac{f_k}{{\left(C_k\right)}^{\mathrm{\&beta;}}}---\left(3\right)$ f _k is the fitness of antibody k, C _k is the concentration of antibody k, and β is an important parameter reflecting the proportion of antibody concentration and fitness in the expected reproduction rate. Here, β=2, and the concentration of antibody k C _k The fast algorithm of Hamming distance based on XOR operation is used for calculation, that is ${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; N</span>}}\underset{\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; kw</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; kw</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; t</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; t</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$ C _k is the concentration of antibody k, N is the population size, a _kw is the affinity between two antibodies k and w, D is the Hamming distance of two antibodies, t is the threshold of Hamming distance, t=0.3*L, L The length of the string is the number of encoded fields, and k and w are natural numbers; Step 5. Calculate the selection probability p _sk . According to step 4, the selection probability p _sk can be obtained, and the antibody population is selected based on the value of p _sk , and the crossover operation is performed. ${\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; sk</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$ Among them, e _k is the replication rate of antibody k, N is the population size, i is a natural number less than or equal to N, e _i is the replication rate of any antibody i; Step 6, adopt to add adjustable factor θ, obtain new antibody group; Add the calculating formula of the adaptive variation probability of adjustable factor as: ${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{c}\frac{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; avg</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; ></span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; avg</span>}}\\ {\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; \&le;</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; favg</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$ $\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; k</span>}}{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; k</span>}}{{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$ In the formula, f _max represents the maximum value of fitness; f _avg represents the arithmetic average fitness value; f is the individual fitness value; k ₃ and k ₄ refer to the adjustment coefficients between 0 and 1, taking k ₃ =k ₄ =0.1, θ is the adjustable factor, G is the evolutionary algebra; G _max is the maximum evolutionary algebra; k is the value of the adjustable factor θ in the first generation, where k=0.005; Step 7. Update the antibody group, and call the individuals with high fitness value in the elite group to replace the individuals with low fitness value in the antibody group to generate the next generation antibody group; Step 8, judge according to the termination condition, if it is satisfied, end the optimization, output the optimized structural element, if not, jump to step 2 and repeat the execution, the termination condition is one of the following: a, define the threshold ε=0.0001, For each antibody group, calculate the average fitness of the antibody group, the difference between the arithmetic mean fitness value of this antibody group and the arithmetic mean fitness value of the previous generation antibody group is less than ε, b, the highest fitness of 15 consecutive generation antibody groups The degree value remains unchanged, c, reaches the maximum evolution algebra.