Brain image segmentation method based on evolutionary multi-view transfer rough fuzzy clustering

Abstract

The present invention discloses a brain image segmentation method based on evolutionary multi-view migration rough fuzzy clustering, which mainly solves the problem that the existing brain magnetic resonance image segmentation uses a single view, resulting in insufficient brain tissue information representation capability and slow calculation speed. Its implementation scheme is: input the image to be segmented and set the initial parameter value; perform bilateral filtering on the image; introduce the multi-view migration mechanism and the image spatial information obtained after filtering into the rough fuzzy clustering objective function, and design a migration multi-view rough fuzzy clustering objective function; use an accelerated differential evolution method based on convergence point estimation to optimize the objective function to obtain the optimal solution; calculate the global membership of the view based on the optimal solution, and obtain the image segmentation result according to the maximum membership principle. The present invention improves the impact of insufficient brain tissue information representation capability caused by a single view, improves the efficiency of segmentation, can be used to process brain magnetic resonance images, and provide a reference for doctors to analyze lesions.

Description

Technical Field

[0001] The present invention belongs to the technical field of medical image processing, and in particular relates to a brain image segmentation method, which can be used for processing brain magnetic resonance imaging images. Background Art

[0002] Magnetic resonance imaging (MRI) is one of the most commonly used imaging techniques in medical imaging. It can noninvasively provide high-contrast, high-spatial-resolution images of different tissues, and has therefore been widely studied and applied in clinical practice. To study human brain diseases, precise segmentation of white matter, gray matter, and cerebrospinal fluid (CSF) in brain MRI images is often required. However, due to issues such as imaging equipment, brain images are often contaminated by noise, intensity inhomogeneities, and local volume effects. Furthermore, factors such as tissue imbalance and pixel overlap between different tissues make brain image segmentation a challenging task. Existing techniques primarily rely on manual brain segmentation by human experts. While reliable, this manual method is time-consuming and susceptible to subjectivity. To effectively segment brain MRI images, researchers have proposed a variety of methods, including threshold-based, region-based, edge-based, clustering-based, and neural network-based methods. Clustering is an effective technique for brain image segmentation, grouping pixels according to specific clustering criteria. Common clustering methods include fuzzy C-means clustering, rough C-means clustering, rough fuzzy C-means clustering and possibility C-means clustering. Rough fuzzy C-means clustering uses rough set and fuzzy set theory to simultaneously deal with uncertainty problems such as fuzziness and overlap in data.

[0003] In 2012, Ji et al. proposed a generalized rough fuzzy C-means clustering algorithm for brain MRI image segmentation. This algorithm utilizes rough fuzzy clustering and spatial information to achieve brain image segmentation. This method suffers from two issues when implementing image segmentation: First, it is a single-view clustering algorithm and can only be used to segment images of a single morphology. It cannot effectively segment the three sequence-weighted images of T1, T2, and proton density in brain MRI images, resulting in insufficient representation of brain tissue information. Second, the optimization solution based on the Lagrange multiplier method is sensitive to cluster center initialization, easily trapped in local optima, and unable to stably obtain a global optimal solution.

[0004] To address the first problem, Liu et al. proposed a multi-space weighted fuzzy clustering algorithm for image segmentation in 2020. It simultaneously segments the original image, mean filtered image and median filtered image through multi-view clustering. However, during the clustering process, since there is no interaction between the information of each view, it is unable to effectively utilize the complementary information between different views, resulting in poor segmentation effect.

[0005] To address the second problem, Alireza et al. proposed a differential evolution brain magnetic resonance image segmentation algorithm guided by RBF kernel FCM in 2017. The algorithm used a population-based differential evolution method to optimize the clustering algorithm to avoid the algorithm falling into local optimality and improve the robustness of the algorithm. However, since the algorithm uses traditional differential evolution methods for optimization, the convergence speed is slow. Summary of the Invention

[0006] The purpose of the present invention is to address the shortcomings of the existing technologies and provide a brain image segmentation method based on evolutionary multi-view migration rough fuzzy clustering, so as to fully utilize the complementary information under three weighted sequences of brain magnetic resonance images, accelerate the convergence speed of differential evolution, improve computational efficiency, and achieve accurate segmentation of brain magnetic resonance images.

[0007] To achieve the above objectives, the technology of the present invention includes the following:

[0008] (1) Input three different sequence weighted images to be segmented X = {X1, X2, X3} and set the initial parameter values: number of views L, number of clusters C, lower approximation weight w, spatial coefficient α, coefficient of variation F, crossover coefficient CR, maximum evolutionary generations T, population size I, elite rate r, and fuzzy factor m;

[0009] (2) Perform bilateral filtering on the three images to be segmented to obtain the filtered images

[0010]

[0011] (3) Introducing the multi-view migration mechanism and image spatial information into the rough fuzzy clustering objective function, the migration multi-view rough fuzzy clustering objective function J is designed:

[0012]

[0013] Where L represents the number of views, ω l represents the view weight, λ l represents the migration coefficient, γ l represents the regularization parameter, J1 represents the rough fuzzy clustering objective function, and J2 represents the multi-view information migration objective function;

[0014] (4) Set the initial evolutionary generation t = 1, use the uniform sampling method to randomly generate the initial population, and calculate the fitness value of each individual in the initial population according to the migration multi-view rough fuzzy clustering objective function J;

[0015] (5) Design an accelerated evolution strategy based on convergence point estimation to update the initial population;

[0016] (5a) For the initial population, the mutation and crossover operators in the differential evolution method are used to obtain a new population, and the fitness value of each individual in the new population is calculated according to the migration multi-view rough fuzzy clustering objective function J;

[0017] (5b) Select the best k individuals from the new population to form an elite subpopulation, and use the mean of the elite subpopulation as the estimated approximate convergence point;

[0018] (5c) Perform Gaussian sampling around the estimated approximate convergence point and use the sampled k individuals to replace the worst k individuals in the new population to form the offspring population;

[0019] (5d) According to the size of the fitness value, individuals with small fitness values ​​are selected one-to-one from the initial population and the offspring population to form the final population;

[0020] (5e) Compare the initial evolutionary number t with the maximum evolutionary number T:

[0021] If t>T, stop updating and output the final population, execute (6),

[0022] Otherwise, let t = t + 1, and use the final population to replace the initial population, and return to (5a);

[0023] (6) Decode the individual with the smallest fitness value in the output final population to obtain the cluster center v of each view lc ;

[0024] (7) According to the decoded cluster center v lc Calculate the weight ω of each view l and membership μ lic , get the global membership u ic ;

[0025] (8) Using the obtained global membership u ic , classify each pixel according to the maximum membership principle, obtain the cluster label of the image pixel, and output the segmentation result of image X.

[0026] Compared with the prior art, the present invention has the following beneficial technical effects:

[0027] First, since the present invention introduces the multi-view migration mechanism into the rough fuzzy clustering algorithm, it can effectively utilize the complementary information between the three sequences of brain magnetic resonance images, T1, T2 and proton density weighted views, and reduce the impact of insufficient brain tissue information representation ability caused by a single view.

[0028] Secondly, the present invention designs a migration multi-view rough fuzzy clustering objective function and simultaneously utilizes the membership information and spatial information of three sequences T1, T2 and proton density weighted views of brain magnetic resonance images, thereby improving the resistance of the rough fuzzy clustering algorithm to factors such as noise in brain magnetic resonance images.

[0029] Third, the present invention designs an accelerated evolution strategy based on convergence point estimation, uses the elite subpopulation in each generation of the population to approximately estimate the convergence point, and samples around it to improve the accuracy of the convergence point estimation, thereby solving the problem of slow convergence speed of traditional differential evolution methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 Flowchart for the implementation of the present invention;

[0031] Figure 2 A comparison chart of simulation results of segmenting the 80th slice image containing 9% noise and 20% intensity non-uniformity in the BrainWeb dataset using the present invention and the existing method;

[0032] Figure 3 This is a comparison chart of the results of simulating segmentation of the 123rd slice image containing 9% noise and 20% intensity non-uniformity in the BrainWeb dataset using the present invention and the existing method; DETAILED DESCRIPTION

[0033] The following is a further detailed description of the implementation and effects of the invention with reference to the accompanying drawings:

[0034] See also Figure 1 The implementation steps of this example include the following:

[0035] Step 1: Input the image to be segmented X and set the initial parameter values.

[0036] 1.1) Input three different sequence weighted images to be segmented: X = {X1, X2, X3}, where X1 represents the T1-weighted image, X2 represents the T2-weighted image, and X3 represents the proton density-weighted image;

[0037] 1.2) Set the number of views L, the number of clusters C, the lower approximation weight w, the spatial coefficient α, the coefficient of variation F, the crossover coefficient CR, the maximum evolutionary generations T, the population size I, the elitist rate r, and the fuzzy factor m.

[0038] In this example, the settings are, but not limited to, w=0.8, α=0.6, F=0.5, CR=0.3, T=100, I=50, r=0.05, and m=2.

[0039] Step 2: Perform bilateral filtering on the three images to be segmented to obtain the filtered images

[0040]

[0041] For the i-th pixel x in the l-th image li , 1≤l≤L, assuming that its coordinate value in the two-dimensional plane coordinate system is (c x ,c y ), the pixel coordinate values ​​in its neighborhood are (s x ,s y ), calculate the filtered pixels

[0042]

[0043] Among them, f(c x ,c y ) represents the coordinate value (c x ,c y )’s pixel grayscale value;

[0044] is the kernel function,

[0045] σ d represents geometric diffusion, σ r Represents luminosity spread.

[0046] Step 3: Design the objective function J for migrating multi-view rough fuzzy clustering.

[0047] 3.1) Classify the image pixels and calculate the rough fuzzy clustering objective function J1 to measure the intra-class compactness of the pixels:

[0048]

[0049] in, R (v lc ) and B(v lc ) represent the lower approximation and boundary area in the rough fuzzy C-means clustering, w represents the lower approximation weight, represents the boundary weight, represents the empty set, and the specific representations of A1 and B1 are as follows:

[0050]

[0051]

[0052] Among them, x li represents the i-th pixel in the l-th view, Represents pixel x li The corresponding pixel after filtering, v lc represents the cth cluster center in the lth view, μ licrepresents the membership of the i-th pixel in the l-th view to the c-th class, C represents the number of clusters, α represents the spatial coefficient, m represents the fuzzy factor, 1≤l≤L;

[0053] 3.2) Migrate the membership information between different views and calculate the multi-view information migration objective function J2 to ensure the consistency of information between views:

[0054]

[0055] The specific calculation formulas for A2 and B2 are as follows:

[0056]

[0057]

[0058] Among them, x li represents the i-th pixel in the l-th view, Represents pixel x li The corresponding pixel after filtering, v lc represents the cth cluster center in the lth view, μ lic represents the membership of the i-th pixel in the l-th view to the c-th class, μ l′ic represents the membership of the i-th pixel in the l′-th view to the c-th class, C represents the number of clusters, α represents the spatial coefficient, m represents the fuzzy factor, 1≤l≤L, 1≤l′≤L, l′≠l;

[0059] 3.3) The rough fuzzy clustering objective function J1 and the multi-view information migration objective function J2 are integrated to obtain the migration multi-view rough fuzzy clustering objective function J:

[0060]

[0061] Where L represents the number of views, ω l represents the view weight, λ l represents the migration coefficient, γ l Represents the regularization parameter.

[0062] Step 4: Use the uniform sampling method to randomly generate the initial population, and calculate the fitness value of each individual in the initial population according to the migration multi-view rough fuzzy clustering objective function J.

[0063] 4.1) Set the initial evolutionary generation t = 1 and decode each individual in the initial population:

[0064] Suppose the i-th individual p in the initial population i for:

[0065] p i =[v11 v 12 … v 21 … v lc …],

[0066] will p i Transformed into a center matrix V of size L×C:

[0067]

[0068] Among them, v lc The element in row l and column c represents the cluster center of the cth class in the lth view;

[0069] 4.2) Decode the cluster center v obtained in 4.1) lc Substitute it into the migration multi-view rough fuzzy clustering objective function J and calculate p i The fitness value J(p i ).

[0070] Step 5: Design an accelerated evolution strategy based on convergence point estimation to update the initial population.

[0071] 5.1) For the initial population, use the mutation and crossover operators in the differential evolution method to obtain a new population:

[0072]

[0073] q j =p j +F×(p m -p n ),

[0074] Among them, j represents the jth individual in the new population, p j represents the jth individual in the initial population, p m and p n represent any two individuals in the initial population except the j-th individual, q j represents the individual after mutation, F represents the coefficient of variation, CR represents the crossover coefficient, and rand(0,1) represents a random number generated between 0 and 1;

[0075] 5.2) Calculate the fitness value of each individual in the new population:

[0076] Use the same method as 4.1) to decode each individual in the new population and calculate the fitness value of each individual in the new population;

[0077] 5.3) Select the k individuals with the smallest fitness in the new population to form an elite sub-population, and use the mean of the elite sub-population as the estimated approximate convergence point. The formula for calculating the k value is as follows:

[0078]

[0079] Among them, I represents the population size, r represents the elite rate, Indicates rounding down.

[0080] 5.4) Perform Gaussian sampling around the estimated approximate convergence point and use the k sampled individuals to replace the worst k individuals in the new population to form the offspring population;

[0081] 5.5) Based on the size of the fitness value, individuals with small fitness values ​​are selected one-to-one from the initial population and the offspring population to form the final population:

[0082]

[0083] Among them, J(p j ) and J(o j ) represent the jth individual p in the initial population j and the jth individual o in the new population j The fitness value, z j represents the jth individual in the final population;

[0084] 5.6) Compare the current evolutionary generation t with the maximum evolutionary generation T:

[0085] If t>T, stop updating and output the final population, and execute step 6.

[0086] Otherwise, set t = t + 1, and use the final population to replace the initial population, and return to step 5.1).

[0087] Step 6: Decode the final population and output the segmentation result of image X.

[0088] 6.1) Sort the final population output in order of fitness value from small to large, decode the individual with the smallest fitness value, and obtain the cluster center v of each view lc ;

[0089] 6.2) According to the decoded cluster center v lc Calculate the weight ω of each view l and membership μ lic :

[0090]

[0091]

[0092] in, is the distance metric, x li represents the i-th pixel in the l-th view, Represents pixel x li The corresponding pixel after filtering, v lc represents the cth cluster center in the lth view, α represents the spatial coefficient, λ l represents the migration coefficient, γ l represents the regularization parameter, 1≤l≤L;

[0093] is the distance metric, x l′i represents the i-th pixel in the l′-th view, Represents pixel x l′i The corresponding pixel after filtering, v l′c represents the cth cluster center in the l′th view, ω l′ represents the weight of the l′th view, 1≤l′≤L,l′≠l;

[0094] 6.3) According to the weight of the view ω l and membership μ lic , calculate the global membership u ic :

[0095]

[0096] 6.4) Using the global membership u ic , classify each pixel according to the maximum membership principle, obtain the cluster label of the image pixel, and output the segmentation result of X:

[0097]

[0098] Among them, C represents the number of clusters, h i represents the label of the i-th pixel.

[0099] The following is a further explanation of the technical effects of the present invention in conjunction with simulation experiments:

[0100] 1. Simulation conditions:

[0101] The simulation experiments were carried out on a computer with Intel(R)Core(TM)i5-10400F CPU@2.90GHz 2.90GHz, 16G memory, and MATLAB R2020a software environment.

[0102] 2. Simulation content:

[0103] Simulation 1: The 80th slice image with 9% noise level and 20% intensity non-uniformity in the BrainWeb dataset is segmented using the present invention, the existing FCM method, the RFCM method, the sRFCM method, the WFCM_MS method, and the T-MFC method. The results are shown in the figure. Figure 2 As shown, where:

[0104] 2(a) is the T1-weighted image of the 80th slice image;

[0105] 2(b) is the T2-weighted image of the 80th slice image;

[0106] 2(c) is the proton density weighted image of the 80th slice image;

[0107] 2(d) is the standard segmentation map of the 80th slice image;

[0108] 2(e) is the segmentation result of the 80th slice image using the method of the present invention;

[0109] 2(f) is the segmentation result of the 80th slice image using the existing FCM method;

[0110] 2(g) is the segmentation result of the 80th slice image using the existing RFCM method;

[0111] 2(h) is the segmentation result of the 80th slice image using the existing sRFCM method;

[0112] 2(i) is the segmentation result of the 80th slice image using the existing WFCM_MS method;

[0113] 2(j) is the segmentation result of the 80th slice image using the existing T-MFC method.

[0114] from Figure 2 It can be seen that the present invention can effectively remove noise interference from noisy brain MRI images and can more clearly display white matter, gray matter and cerebrospinal fluid tissue. Its segmentation effect is significantly better than the existing FCM method, RFCM method, sRFCM method, WFCM_MS method and T-MFC method.

[0115] Simulation 2: The 123rd slice image containing 9% noise and 20% intensity inhomogeneity in the BrainWeb dataset is segmented using the present invention, the existing FCM method, the RFCM method, the sRFCM method, the WFCM_MS method, and the T-MFC method. The results are shown in the figure. Figure 3 As shown, where:

[0116] 3(a) is the T1-weighted image of the 123rd slice image;

[0117] 3(b) is the T2-weighted image of the 123rd slice image;

[0118] 3(c) is the proton density weighted image of the 123rd slice image;

[0119] 3(d) is the standard segmentation map of the 123rd slice image;

[0120] 3(e) is the segmentation result of the 123rd slice image using the method of the present invention;

[0121] 3(f) is the segmentation result of the 123rd slice image using the existing FCM method;

[0122] 3(g) is the segmentation result of the 123rd slice image using the existing RFCM method;

[0123] 3(h) is the segmentation result of the 123rd slice image using the existing sRFCM method;

[0124] 3(i) is the segmentation result of the 123rd slice image using the existing WFCM_MS method;

[0125] 3(j) is the segmentation result of the 123rd slice image using the existing T-MFC method.

[0126] from Figure 3 It can be seen that the present invention can effectively remove noise interference from noisy brain MRI images, and the detailed information between brain tissues is more complete. Its segmentation effect is significantly better than the existing FCM method, RFCM method, sRFCM method, WFCM_MS method and T-MFC method.

Claims

1. A brain image segmentation method based on evolutionary multi-view migration rough fuzzy clustering, characterized by: These include: (1) Input three different sequence weighted images to be segmented X = {X1, X2, X3} and set the initial parameter values: number of views L, number of clusters C, lower approximation weight w, spatial coefficient α, coefficient of variation F, crossover coefficient CR, maximum evolutionary generations T, population size I, elite rate r, and fuzzy factor m; (2) Perform bilateral filtering on the three images to be segmented to obtain the filtered images (3) Introducing the multi-view migration mechanism and image spatial information into the rough fuzzy clustering objective function, the migration multi-view rough fuzzy clustering objective function J is designed: Where L represents the number of views, ω l represents the view weight, λ l represents the migration coefficient, γ l represents the regularization parameter, J1 represents the rough fuzzy clustering objective function, and J2 represents the multi-view information migration objective function; (4) Set the initial evolutionary generation t = 1, use the uniform sampling method to randomly generate the initial population, and calculate the fitness value of each individual in the initial population according to the migration multi-view rough fuzzy clustering objective function J; (5) Design an accelerated evolution strategy based on convergence point estimation to update the initial population; (5a) For the initial population, the mutation and crossover operators in the differential evolution method are used to obtain a new population, and the fitness value of each individual in the new population is calculated according to the migration multi-view rough fuzzy clustering objective function J; (5b) Select the best k individuals from the new population to form an elite subpopulation, and use the mean of the elite subpopulation as the estimated approximate convergence point; (5c) Perform Gaussian sampling around the estimated approximate convergence point and use the sampled k individuals to replace the worst k individuals in the new population to form the offspring population; (5d) According to the size of the fitness value, individuals with small fitness values ​​are selected one-to-one from the initial population and the offspring population to form the final population; (5e) Compare the initial evolutionary number t with the maximum evolutionary number T: If t>T, stop updating and output the final population, execute (6), Otherwise, let t = t + 1, and use the final population to replace the initial population, and return to (5a); (6) Decode the individual with the smallest fitness value in the output final population to obtain the cluster center v of each view lc ; (7) According to the decoded cluster center v lc Calculate the weight ω of each view l and membership μ lic , get the global membership u ic ; (8) Using the obtained global membership u ic , classify each pixel according to the maximum membership principle, obtain the cluster label of the image pixel, and output the segmentation result of image X.

2. The method according to claim 1, characterized in that In (2), the bilateral filtering operation is performed on the three images to be segmented respectively, and the pixel x in the ith image is li , 1≤l≤L, assuming that its coordinate value in the two-dimensional plane coordinate system is (c x ,c y ), the pixel coordinate values ​​in its neighborhood are (s x ,s y ), calculate the filtered pixels Among them, f(c x ,c y ) represents the coordinate value (c x ,c y )’s pixel grayscale value; is the kernel function, σ d represents geometric diffusion, σ r Represents luminosity spread.

3. The method according to claim 1, characterized in that The rough fuzzy clustering objective function J1 in the migration multi-view rough fuzzy clustering objective function J designed in step (3) is calculated by treating the brain magnetic resonance images weighted by the three sequences T1, T2 and proton density as three views and calculating it by the following formula: in, R (v lc ) and B(v lc ) represent the lower approximation and boundary area in the rough fuzzy C-means clustering, w represents the lower approximation weight, represents the boundary weight, represents the empty set, and the specific representations of A1 and B1 are as follows: Among them, x li represents the i-th pixel in the l-th view, Represents pixel x li The corresponding pixel after filtering, v lc represents the cth cluster center in the lth view, μ lic represents the membership of the i-th pixel in the l-th view to the c-th class, C represents the number of clusters, α represents the spatial coefficient, m represents the fuzzy factor, and 1≤l≤L.

4. The method according to claim 1, wherein The multi-view information transfer objective function J2 in the multi-view rough fuzzy clustering objective function J designed in step (3) is calculated by treating the brain magnetic resonance images weighted by the three sequences T1, T2 and proton density as three views and calculating them by the following formula: The specific calculation formulas for A2 and B2 are as follows: Among them, x li represents the i-th pixel in the l-th view, Represents pixel x li The corresponding pixel after filtering, v lc represents the cth cluster center in the lth view, μ lic represents the membership of the i-th pixel in the l-th view to the c-th class, μ l′ic represents the membership of the i-th pixel in the l′-th view to the c-th class, C represents the number of clusters, α represents the spatial coefficient, m represents the fuzzy factor, 1≤l≤L, 1≤l′≤L, l′≠l.

5. The method according to claim 1, wherein In (4), the fitness value of each individual in the initial population is calculated according to the migration multi-view rough fuzzy clustering objective function J, which is implemented as follows: 4a) Decode each individual in the initial population: Suppose the i-th individual p in the initial population i for: p i =[v 11 v 12 … v 21 … v lc …], will p i Transformed into a center matrix V of size L×C: Among them, v lc The element in row l and column c represents the cluster center of the cth class in the lth view; 4b) Calculate the fitness value: The decoded cluster center v lc Substitute it into the migration multi-view rough fuzzy clustering objective function J to get p i The fitness value J(p i ).

6. The method according to claim 1, characterized in that In (5a), the mutation and crossover operators in the differential evolution method are used to obtain a new population. The formula is as follows: q j =p j +F×(p m -p n ), Among them, j represents the jth individual in the new population, p j represents the jth individual in the initial population, p m and p n represent any two individuals in the initial population except the j-th individual, q j represents the individual after mutation, F represents the coefficient of variation, CR represents the crossover coefficient, and rand(0,1) represents a random number generated between 0 and 1.

7. The method according to claim 1, characterized in that In (5b), the best k individuals are selected from the new population to form an elite subpopulation. The calculation formula of k value is as follows: Among them, I represents the population size, r represents the elite rate, Indicates rounding down.

8. The method according to claim 1, characterized in that In (5d), individuals with smaller fitness values ​​are selected one-to-one from the initial population and the offspring population according to the fitness values. The formula is as follows: Among them, J(p j ) and J(o j ) represent the jth individual p in the original population j and the jth individual o in the new population j The fitness value, z j represents the jth individual in the final population.

9. The method according to claim 1, characterized in that The weight ω of each view is calculated in (7) l and membership μ lic , get the global membership u ic , the formula is as follows: in, is the distance metric, x li represents the i-th pixel in the l-th view, Represents pixel x li The corresponding pixel after filtering, v lc represents the cth cluster center in the lth view, α represents the spatial coefficient, λ l represents the migration coefficient, γ l represents the regularization parameter, 1≤l≤L; in, is the distance metric, x l′i represents the i-th pixel in the l′-th view, Represents pixel x l′i The corresponding pixel after filtering, v l′c represents the cth cluster center in the l′th view, ω l′ represents the weight of the l′th view, 1≤l′≤L,l′≠l; 10. The method according to claim 1, characterized in that The global membership u obtained in (8) is used ic , classify each pixel according to the maximum membership principle, the formula is as follows: Among them, C represents the number of clusters, h i Represents the label of the i-th pixel.

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