Image segmentation method and system using validity index of fuzzy clustering of multiple interactions

Abstract

The application discloses an image segmentation method and system of a plurality of interaction fuzzy clustering validity index, comprising: 1, using the improved fuzzy C-means clustering algorithm based on kernel to classify the pixel points of the given image; 2, establishing a target function, checking whether the termination condition is met or the maximum iteration number is reached; 3, initializing and updating the membership matrix and the clustering center; 4, calculating the intra-class compactness value through the ratio of the fuzzy cardinality and the fuzzy weighted distance to the sample variance and the disturbance factor, and calculating the inter-class separation value from four aspects of separation relation, using the product of two factors and the iteration number to obtain the index value; 5, comparing the validity index of all classes, selecting the clustering number corresponding to the maximum validity index and the corresponding membership matrix to perform image segmentation. The application can effectively segment the image, cluster the pixel points and obtain effective image clustering results, and is suitable for unbalanced, complex, overlapped and noisy pixel sets.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of data mining, and particularly relates to an image segmentation method and system of validity index of multi-item interaction fuzzy clustering. BACKGROUND

[0002] The purpose of image segmentation is to extract a specific target from a complex image, and it is an important basis for image recognition, image understanding and image analysis. With the development of technology, image segmentation based on fuzzy clustering has been widely used in many fields, such as medical image processing, face recognition, traffic road analysis and the like. Therefore, more and more scholars study various indexes for evaluating the related image segmentation algorithm to determine the pros and cons of the algorithm. The index can objectively analyze the practicality of the clustering algorithm in some scenes. Of course, the result under the measurement of an index cannot explain everything, and the comprehensive investigation of various indexes is also needed. After numerous studies and discussions of scholars, many kinds of algorithm indexes based on fuzzy clustering improvement have been proposed.

[0003] The clustering validity index can be divided into three categories: internal validity index, external validity index and relative validity index. The clustering validity problem is to establish a clustering validity index function, run the function in different situations, and then take the optimal value of the function as the optimal partition. Specifically, under different clustering numbers, a clustering algorithm is run, and the optimal clustering number is obtained when the clustering validity index function is optimal.

[0004] The existing fuzzy clustering index has the following three problems when applied to the field of image segmentation:

[0005] 1) The basic criterion of clustering is to put data objects with the same feature into the same cluster, and data objects across different clusters are heterogeneous. For this purpose, the compactness and separation of data clusters are usually measured. The compactness measures the concentration of data objects within the cluster. The distance between objects with homogeneous features should be relatively small. However, when part of the cluster centers in the cluster are distributed close to each other, this processing strategy will fail.

[0006] 2) On the other hand, the separation is to measure the isolation degree between clusters. Objects with heterogeneous features should be separated as much as possible. This can be evaluated by the distance between each pair of centroids, or by the distance between two heterogeneous objects from two different clusters. The greater the distance, the better the separation effect of the cluster. Most of the existing indexes are too simple in expressing the separation degree, which will make the data set not well characterized when analyzing the data set, and a more comprehensive and stereoscopic expression form is needed.

[0007] 3) Poor performance on noisy datasets. In real-world datasets, most contain varying proportions of noise. Traditional metrics, which only consider the dataset's geometric structure (e.g., CH, DBI, and Dunn), can lead to errors in evaluating noisy datasets. NPC overcomes the tendency for metrics to change monotonically with the number of clusters, but it is less effective with dense data. Similarly, while WLI, VCVI, IMI, I, and SMI metrics can accurately determine the number of clusters on some datasets, their performance on noisy datasets is also unsatisfactory. Summary of the Invention

[0008] In order to overcome the shortcomings of the existing technology, this invention proposes an image segmentation method and system with a multi-interaction fuzzy clustering effectiveness index, which is intended to be applicable to the accurate segmentation of pixel sets with imbalance, high dimension, complexity, overlap and noise, thereby achieving good image segmentation results.

[0009] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0010] The image segmentation method of the present invention, which uses a multi-interaction fuzzy clustering effectiveness index, is characterized by the following steps:

[0011] Step 1: Use the kernel-based improved fuzzy C-means clustering algorithm to cluster the set of pixels {x1, x2, ..., x3} in any image X. i ,…,x N} Divide into K pixel classes {C k |k=1,2,…,K}, and obtain K pixel point classes {C k The membership matrix U = {μ} corresponding to |k=1,2,…,K} ik |i=1,2,...,N;k=1,2,...,K} and cluster centers V={v1,v2,…,v k ,…,v K}; where x i μ represents the i-th pixel in image X. ik Represents the i-th pixel x i Belongs to the class C of the k-th pixel. k The membership value, and 0 ≤ μ ik ≤1, v k Represents the class C of the k-th pixel. k The cluster centers; i = 1, 2, ..., N; k = 1, 2, ..., K; N represents the number of pixels in image X;

[0012] Set the maximum number of iterations to iter_max, the termination condition error of the iteration to ε, and initialize K=2;

[0013] Step 2: Construct the iterth iteration objective function of image X in the KFCM blur algorithm using equation (1).

[0014]

[0015] In equation (1), C represents the class of the k-th pixel in the iter-th iteration. k Cluster centers Let x represent the i-th pixel in the iter-th iteration. i With the k-th pixel, class C k Cluster center The distance between them mapped to the higher-dimensional kernel space. Let x represent the i-th pixel in the iter-th iteration. i Belongs to the k-th pixel class C k The membership degree, where m is the weighted index, represents the degree of fuzziness in clustering;

[0016] Step 3: Set the initial iteration number iter = 0, and use the membership matrix U and cluster centers V as the membership matrix U for the iter-th iteration. iter and the cluster center V in the iterth iteration iter ;

[0017] Step 4: Update the membership matrix U of the iterth iteration using equation (2). iter The membership matrix of the (iter+1)th iteration is obtained.

[0018]

[0019] In equation (2), U represents the membership matrix of the (iter+1)th iteration. iter+1 The i-th pixel x i Belongs to the k-th pixel class C k Membership degree; v j Represents the class C of the j-th pixel. j The cluster centers are GK(·), where GK(·) is the Gaussian kernel function; j = 1, 2, ..., K, j ≠ k;

[0020] Step 5: Update the cluster center V of the iterth iteration using equation (3). iter The cluster centers of the (iter+1)th iteration are obtained.

[0021]

[0022] In equation (3), V represents the cluster center in the (iter+1)th iteration. iter+1 The k-th pixel is of class C k Cluster centers;

[0023] Step 6, if ||V iter+1 -V iter If ||<ε, then stop the iteration and set the cluster center V of the (iter+1)th iteration to ε. iter+1 The optimal cluster center V corresponding to the number of clusters K * Otherwise, increment iter by 1 and assign iter to iter, then check if iter > iter_max. If it is true, then set the cluster center V of the iter_max-th iteration to... iter_max The optimal cluster center V corresponding to the number of clusters K * Otherwise, return to step 4 and execute sequentially;

[0024] Step 7: Calculate the intra-class compactness com(K):

[0025] Step 7.1: Initialize k = 1, define the intra-cluster compactness corresponding to the number of clusters k as com(k), and initialize com(k) = 0;

[0026] Step 7.2: After assigning k+1 to k, check if k > K is true. If true, proceed to step 7.3; otherwise, calculate... After assigning the value to com(k), repeat step 7.2, where v0 represents the mean value of the pixel, α represents the perturbation factor, and d represents the Euclidean distance;

[0027] Step 7.3: Calculate the intra-cluster compactness com(K) corresponding to the number of clusters K using equation (4):

[0028]

[0029] Step 8: Use equation (5) to calculate the class {C} of K pixels. k The inter-class separability sep(K) for k = 1, 2, ..., K:

[0030]

[0031] In equation (5), Let represent the median of K cluster centers, min represents the function to find the minimum value, mean represents the function to find the mean value, and max represents the function to find the maximum value.

[0032] Step 9: Calculate the class {C} of K pixels using equation (6). k|k=1,2,…,K} corresponding to the validity index V MI (K):

[0033]

[0034] Step 10, K+1 is assigned to K, and it is judged If it is true, it indicates that the validity index of K pixel point classes {C k |k=1,2,…,K} is obtained, and step 11 is executed; otherwise, step 2 is returned to be sequentially executed.

[0035] Step 11, the validity indexes of K pixel point classes {C k |k=1,2,…,K} are compared, and the cluster number corresponding to the maximum validity index and the corresponding membership matrix are selected to segment the image X, so that the segmentation result of the image X is obtained.

[0036] The image segmentation system of the present application has the following characteristics:

[0037] An image acquisition module is used to acquire the pixel point set of the image X.

[0038] A cluster initialization module is used to initialize the parameters of image segmentation and construct a target function; the parameters include: a termination condition or a maximum iteration number, a radial basis function parameter sigma, an initial membership matrix and an initial cluster center.

[0039] A cluster calculation module is used to update and iterate the membership matrix and the cluster center, so as to obtain the final membership matrix and the cluster center.

[0040] An index forming module is used to calculate the intra-class compactness and the inter-class separation relationship based on the image segmentation method of claim 1, so as to obtain the validity index.

[0041] An index verification module is used to compare the validity indexes of all classes, and obtain the cluster number corresponding to the maximum validity index and the corresponding membership matrix, which is used for clustering and segmenting the image X.

[0042] Compared with the prior art, the present application has the following advantages:

[0043] 1. The present application adopts the product method of the cluster number and the separation y and the reciprocal of compactness, which concentrates the advantages of the fuzzy clustering (KFCM) index method, reduces the influence of the large number of classifications on the experimental results, makes the image clustering result more accurate, and greatly improves the robustness of the image segmentation method due to the mutual competition and balance among the three factors.

[0044] 2. In terms of compactness processing, this invention adds an α perturbation factor, which greatly improves the noise resistance of the index. Secondly, in terms of separation processing, it utilizes the product of the sample variance of the pixel set cluster center and the sum of its maximum value, minimum value, and twice the mean, comprehensively considering the separation characteristics between clusters. This not only effectively handles pixel sets with very close cluster centers but also avoids over-division of normal clusters, and greatly improves the robustness of the image segmentation method.

[0045] 3. This invention uses fuzzy clustering to more accurately determine the number of clusters in a pixel set. The distance between the cluster centers of different pixel sets also has less and less influence on the classification accuracy. Therefore, this method is more suitable for multidimensional and complex pixel sets than other methods. Attached Figure Description

[0046] Figure 1 This is a flowchart of the method of the present invention;

[0047] Figure 2a The original image of the house in this invention is a natural image.

[0048] Figure 2b This invention relates to a natural image of a house with noise.

[0049] Figure 2c This is a natural image of a house segmentation image according to the present invention;

[0050] Figure 3a These are the four types of original images used in this invention;

[0051] Figure 3b These are the four types of noise images of this invention;

[0052] Figure 3c These are the four types of segmented images of this invention. Detailed Implementation

[0053] In this embodiment, as Figure 1 As shown, an image segmentation method based on the effectiveness index of multi-interaction fuzzy clustering is performed according to the following steps:

[0054] Step 1: Use the kernel-based improved fuzzy C-means clustering algorithm to cluster the set of pixels {x1, x2, ..., x3} in any image X. i ,…,x N} Divide into K pixel classes {C k |k=1,2,…,K}, and obtain K pixel point classes {C k The membership matrix U = {μ} corresponding to |k=1,2,…,K} ik |i=1,2,...,N;k=1,2,...,K} and cluster centers V={v1,v2,…,vk ,…,v K}; where x i μ represents the i-th pixel in image X. ik Represents the i-th pixel x i Belongs to the class C of the k-th pixel. k The membership value, and 0 ≤ μ ik ≤1, v k Represents the class C of the k-th pixel. k The cluster centers; i = 1, 2, ..., N; k = 1, 2, ..., K; N represents the number of pixels in image X;

[0055] Set the maximum number of iterations to iter_max, the iteration termination condition error to ε, and initialize K=2;

[0056] Step 2: Construct the iterth iteration objective function of image X in the KFCM blur algorithm using equation (1).

[0057]

[0058] In equation (1), C represents the class of the k-th pixel in the iter-th iteration. k Cluster centers Let x represent the i-th pixel in the iter-th iteration. i With the k-th pixel, class C k Cluster center The distance between them mapped to the higher-dimensional kernel space. Let x represent the i-th pixel in the iter-th iteration. i Belongs to the k-th pixel class C k The membership degree, where m is the weighted index, represents the degree of fuzziness in clustering;

[0059] In the specific experiment, the parameter setting is as follows: m is set to a range between 1.5 and 2.5, and in this invention, it is set to 2.

[0060] The cluster centers corresponding to the minimum J value are optimal, and the image segmentation effect is also the best. Figure 2a It is the original image of the natural house. Figure 2b This is the image after adding 8.5% Gaussian noise. Figure 2c This is the segmentation effect of the KFCM algorithm on natural house images; Figure 3a The original images are divided into four categories. Figure 3b For the image after adding 10% salt and pepper noise, Figure 3cThe image segmentation effect of the FCM algorithm on four types of images is shown. Through the operation process of this invention, it can be seen that the image segmentation method with multiple interactive fuzzy clustering effectiveness indicators is significantly better than the traditional fuzzy C-means clustering algorithm.

[0061] Step 3: Set the initial iteration number iter = 0, and use the membership matrix U and cluster centers V as the initial membership matrix U. iter and the initial cluster center V iter ;

[0062] Step 4: Update the membership matrix U of the iterth iteration using equation (2). iter The membership matrix of the (iter+1)th iteration is obtained.

[0063]

[0064] In equation (2), U represents the membership matrix of the (iter+1)th iteration. iter+1 The i-th pixel x i Belongs to the k-th pixel class C k Membership degree; v j Represents the class C of the j-th pixel. j The cluster centers are defined by the following formulas: j = 1, 2, ..., K; j ≠ k. GK(x, v) is a Gaussian kernel function. In this embodiment, GK(x, v) = exp{-||xv|| 2 / σ 2},σ 2 >0, where σ is the parameter of the radial basis function;

[0065] Step 5: Update the cluster center V of the iterth iteration using equation (3). iter The cluster centers of the (iter+1)th iteration are obtained.

[0066]

[0067] In equation (3), V represents the cluster center in the (iter+1)th iteration. iter+1 The k-th pixel is of class C k Cluster centers;

[0068] Step 6, if ||V iter+1 -V iter If ||<ε, then stop the iteration and set the cluster center V of the (iter+1)th iteration to ε. iter+1 The optimal cluster center V corresponding to the number of clusters K *Otherwise, increment iter by 1 and assign iter to iter, then check if iter > iter_max. If it is true, then set the cluster center V of the iter_max-th iteration to iter_max. iter_max The optimal cluster center V corresponding to the number of clusters K * Otherwise, return to step 4 and execute sequentially;

[0069] Step 7: Calculate the compactness com(K) within the class:

[0070] Step 7.1: Initialize k = 1, define the compactness corresponding to the number of clusters k as com(k), and initialize com(k) = 0;

[0071] Step 7.2: After assigning k+1 to k, check if k > K is true. If true, proceed to step 7.3; otherwise, calculate... After assigning the value to com(k), repeat step 7.2; where v0 represents the mean value of the pixel, α represents the perturbation factor, and d represents the Euclidean distance;

[0072] Step 7.3: Calculate the intra-cluster compactness com(K) corresponding to the number of clusters K using equation (4).

[0073]

[0074] Step 8: Use equation (5) to calculate the class {C} of K pixels. k The inter-class separability sep(K) of |k=1,2,…,K}:

[0075]

[0076] In equation (5), Let represent the median of K cluster centers, min represents the function to find the minimum value, mean represents the function to find the mean value, and max represents the function to find the maximum value.

[0077] Step 9: Calculate the class {C} of K pixels using equation (6). k The effectiveness index V corresponding to |k=1,2,…,K} MI (K):

[0078]

[0079] Step 10: Assign K+1 to K and then determine... Does it hold true? If it does, then it means that K pixels of type {C} have been obtained. k If the validity index of |k=1,2,…,K} is not found, proceed to step 11; otherwise, return to step 2 and execute sequentially.

[0080] In order to verify the segmentation effect of the method in natural images, a house, four types of images are used for experiment. Figure 2a The natural image house original image, Figure 2b is a natural image house added 8.5% Gaussian noise image, Figure 2c is a segmentation image of the natural image house; the parameter setting k=3, m=2, the size of a is set to 1.0, L is set to 5.0, epsilon is set to 0.001, the iteration number is 100 times, the window size is set to 3*3, and the following Figure 3a- Figure 3c It can be seen that the method of the application better maintains the detail features of the image and can also segment the arc partition, showing good segmentation effect.

[0081] Step 11, compare the effectiveness indexes of K pixel point classes {C k |k=1, 2, …, K}, and select the cluster number and the corresponding membership matrix corresponding to the maximum effectiveness index to segment the image X, thereby obtaining the segmentation result of the image X.

[0082] In this embodiment, a multi-item interactive fuzzy clustering effectiveness index image segmentation system comprises:

[0083] An image acquisition module is used to acquire the pixel point set of the image X;

[0084] A cluster initialization module is used to initialize the parameters of image segmentation and construct a target function; the parameters include: a termination condition or a maximum iteration number, a radial basis function parameter sigma, an initial membership matrix and an initial cluster center;

[0085] A cluster calculation module is used to update and iterate the membership matrix and the cluster center, thereby obtaining the final membership matrix and the cluster center;

[0086] An index formation module is used to calculate the intra-class compactness and the inter-class separability based on the above image segmentation method, thereby obtaining the effectiveness index;

[0087] An index verification module is used to compare the effectiveness indexes of all classes, and obtain the cluster number and the corresponding membership matrix corresponding to the maximum effectiveness index, which is used for clustering and segmenting the image X.

[0088] In order to verify the image segmentation effect of the validity index of multi-interaction fuzzy clustering, some experiments are carried out. The experimental platform is Window 10 system, the compiling environment is Intel(R)Core(TM)5-10400CPU@2.90GHz 2.90GHz and RAM 16.00GB and Windows 10 OS, and the programming language is Matlab2018b. In the process of the experiment, some relatively good indicators appeared before are needed to be compared horizontally, which involve CH(+), PC(+), Dunn(+), NPC(+), FS(-), XBI(-), DB(-), WLI(-), VCVI(-), IMI(-), I(+), SMI(-), and MI(-). Nine data sets are used for verification, which involve SPECTF-heart data set, Monk data set, Hayes-Roth data set, Seeds data set, Soybean-small data set, Glass data set, Zoo data set, Letter data set, and Libras data set. The performance of the validity index of multi-interaction fuzzy clustering is the best as shown in the following table, then the clustering number and the corresponding membership matrix corresponding to the validity index are selected to segment the image, so as to obtain the image segmentation result.

[0089] Table 2 Experimental results of the present application in multiple data sets

[0090] data sets #C CH (+) ]]> PC (+) ]]> Dunn (+) ]]> NPC (+) ]]> FS (-) ]]> XBI (-) ]]> DB (-) ]]> WLI (-) ]]> VCVI (-) ]]> IMI (-) ]]> I (+) ]] SMI (-) ]]> MI (-) ]]> SPECTF-heart 2 2 2 2 2 10 2 2 2 2 2 2 2 2 Monk 2 2 2 2 2 10 2 2 2 2 2 2 2 2 Hayes-Roth 3 2 2 2 2 9 3 2 3 3 3 3 3 3 Seeds 3 2 2 2 2 3 3 2 3 3 3 3 3 3 Soybean-small 4 2 2 2 2 2 2 2 2 2 2 2 2 2 Glass 6 2 2 2 2 5 6 2 6 6 2 6 2 6 Zoo 7 2 2 2 2 10 7 3 7 2 2 7 7 7 Letter 26 30 2 2 2 30 26 2 26 26 26 30 2 26 Libras 15 2 2 2 2 29 15 3 15 15 3 15 2 15

[0091] As shown in Table 2, analysis of the experimental results can know that: in the case of complex unbalanced distribution data set, no index can have good effect on these data sets with different characteristics, the MI index obtains the correct classification number on SPECTFheart, Monk, Hayes-Roth, Seeds, Glass, Zoo, Letter, Libras data sets. The I index obtains the correct classification number in 6 UCI low-dimensional data sets, but fails to obtain the correct data set result in high-dimensional data sets Letter and Libras data sets, and it is found through the experimental result that in the data set in which the I index obtains the correct classification, the MI index shows stronger stability and accuracy than the I index. For other data sets with better performance, the SMI index and the IMI index fail to obtain the correct classification number on Soybean-small, Glass, Letter, Libras data sets, the VCVI index fails to obtain the correct classification number on Soybean-small, Zoo data sets, the WLI index and the XBI index fail to obtain the correct classification number on Soybean-small data set. It is found that the MI index proposed in the application obtains the correct result in the case that other indexes do not have good effect, the MI index can obtain good result in different types of data sets, and can maintain stable evaluation ability in low-dimensional and high-dimensional data sets, which is not possessed by other indexes with slightly better performance, even in the case of other error results, it also approaches the correct result. Therefore, it can be concluded that the effectiveness index of multi-item interaction fuzzy clustering has strong adaptability. Therefore, the application can obtain better effect on image segmentation.

Claims

1. An image segmentation method of a fuzzy clustering validity index of multiple interaction, characterized by, is performed as follows: Step 1: Use the kernel-based improved fuzzy C-means clustering algorithm to cluster the set of pixels {x1, x2, ..., x3} in any image X. i ,…,x N } Divide into K pixel classes {C k |k=1,2,…,K}, and obtain K pixel point classes {C k The membership matrix U = {μ} corresponding to |k=1,2,…,K} ik |i=1,2,...,N;k=1,2,...,K} and cluster centers V={v1,v2,…,v k ,…,v K }; where x i μ represents the i-th pixel in image X. ik Represents the i-th pixel x i Belongs to the class C of the k-th pixel. k The membership value, and 0 ≤ μ ik ≤1, v k Represents the class C of the k-th pixel. k The cluster centers; i = 1, 2, ..., N; k = 1, 2, ..., K; N represents the number of pixels in image X; Set the maximum iteration number as iter_max, the termination condition error of iteration as ε, and initialize K=2; Step 2, constructing the image X using formula (1) in the KFCM fuzzy algorithm for the target function of the iter iteration In formula (1), represents the kth pixel point class C of the iterth iteration k the cluster center of the kth pixel point class C represents the distance between the ith pixel point x i and the cluster center of the kth pixel point class C k mapped to the high-dimensional kernel space, represents the membership degree of the ith pixel point x i to the kth pixel point class C k , and m is a weighted index, which represents the clustering fuzziness degree.​ Step 3, let initial iteration number iter = 0, and take membership matrix U and clustering center V as the membership matrix U of the iter iteration iter and the clustering center V of the iter iteration iter ; Step 4, update the membership matrix U of the iter iteration with formula (2) iter , to obtain the membership matrix U of the iter+1 iteration In formula (2), denotes the membership matrix U of the (iter+1)th iteration iter+1 the i-th pixel point x i in the k-th pixel point class C k ; v j denotes the cluster center of the j-th pixel point class C j ; GK(·) is a Gaussian kernel function; j=1,2,…,K,j≠k; Step 5, update the cluster center V of the iter iteration with formula (3) iter , to obtain the cluster center of the iter+1 iteration In formula (3), represents the clustering center V of the iter+1th iteration iter+1 the clustering center of the kth pixel point class C in the middle k the clustering center of the kth pixel point class C in the middle Step 6, if ||V iter+1 -V iter || < ε, stop iteration, and take the clustering center V iter+1 as the optimal clustering center V * corresponding to the clustering number K, and end the iteration; otherwise, let iter+1 assign iter, and judge whether iter > iter_max is true or not, if true, take the clustering center V iter_max as the optimal clustering center V * corresponding to the clustering number K, and end the iteration; otherwise, return to step 4 for sequential execution. Step 7, calculate the intra-class compactness com(K): Step 7.1, initialize k=1, define the intra-class compactness corresponding to the cluster number k as com(k), and initialize com(k)=0; Step 7.2, after assigning k+1 to k, judging whether k>K is true, if true, executing step 7.3, otherwise, calculating and assigning to com(k), repeating step 7.2, wherein v0 represents the mean value of the pixel points, a represents the perturbation factor, and d represents the Euclidean distance. Step 7.3, calculate the intra-class compactness com(K) corresponding to the cluster number K by using formula (4): Step 8, calculate the inter-class separability sep(K) of K pixel point classes {C k |k = 1, 2,..., K} using formula (5): In formula (5), denotes the median of the K cluster centers, min denotes the minimum function, mean denotes the mean function, and max denotes the maximum function. Step 9, calculate the validity index V k |k = 1, 2, …, K} corresponding to the K pixel points class {C MI (K): Step 10, assign K+1 to K, and judge whether it is true, if true, it indicates that the effectiveness index of K pixel point class {C k |k=1,2,…,K} is obtained, and step 11 is executed; otherwise, return to step 2 for sequential execution; Step 11, compare the validity indexes of K pixel point clusters {C k |k = 1, 2, …, K}, and select the cluster number corresponding to the maximum validity index and the corresponding membership matrix to segment the image X, thereby obtaining the segmentation result of the image X.

2. An image segmentation system of fuzzy clustering validity indices of multiple interations, characterized in that, com(K) = 1 / K * sum(com(k)) (4) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ^2)) (3) com(k) = 1 / n * sum(exp(-||x_i - c_k||^2 / σ

Images