CN113674295B - Image segmentation method and system for validity index of three-degree separation-guided fuzzy clustering - Google Patents

Image segmentation method and system for validity index of three-degree separation-guided fuzzy clustering Download PDF

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CN113674295B
CN113674295B CN202110974971.6A CN202110974971A CN113674295B CN 113674295 B CN113674295 B CN 113674295B CN 202110974971 A CN202110974971 A CN 202110974971A CN 113674295 B CN113674295 B CN 113674295B
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唐益明
李冰
黄佳佳
孙晓
李书杰
吴文斌
陈锐
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Hefei University of Technology
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Abstract

The invention discloses an image segmentation method and an image segmentation system based on an effectiveness index of fuzzy clustering of three-degree separation guidance, wherein the method comprises the following steps: 1, dividing pixel points in an image by using a fuzzy C-means clustering algorithm; 2, establishing a target function, and setting a termination condition or achieving the maximum iteration times; initializing and updating an iteration membership matrix and a clustering center, and judging whether a termination condition is reached or the maximum iteration frequency is reached; 4, calculating the separability value among classes according to the separation relation of the three layers, obtaining the compactness value in the class through the fuzzy weighting distance and the base number of the fuzzy cluster, and obtaining the index value by using the ratio of the latter to the former; and 5, comparing the effectiveness indexes of all the classes, and selecting the clustering number corresponding to the maximum effectiveness index and the corresponding membership matrix for image segmentation. The method can effectively divide the image, cluster the pixel points to obtain an effective clustering result, and is suitable for a complex, overlapped and noisy pixel set.

Description

Image segmentation method and system for validity index of three-degree separation-guided fuzzy clustering
Technical Field
The invention belongs to the field of data mining, and particularly relates to an image segmentation method and an image segmentation system for validity indexes of fuzzy clustering guided by three-degree separation.
Background
The purpose of image segmentation is to extract a specific target from a complex image, and the image segmentation 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 related to evaluating the related image segmentation algorithm to judge the quality of the algorithm. The indexes can objectively analyze the practical degree of the clustering algorithm in certain scenes. Of course, the result of measurement of one index does not indicate all the problems, and comprehensive examination of various indexes is also required. Through research and discussion of countless scholars, a plurality of algorithm indexes improved based on fuzzy clustering have been proposed.
The clustering validity index can be divided into three categories: an internal validity indicator, an external validity indicator, and a relative validity indicator. The problem of the clustering effectiveness is that a clustering effectiveness index function is established, the function is operated under different conditions, and then the condition corresponding to the function optimum value is taken as the optimal division. Specifically, a clustering algorithm is operated under different clustering numbers, so that the optimal clustering number is obtained when the clustering effectiveness index function is optimal.
The problems existing when the existing fuzzy clustering index is applied to the field of image segmentation mainly include the following 3:
1) Some validity indexes only consider geometric structure information, for example, the CH indexes respectively describe the compactness and the separation degree by using an intra-class dispersion matrix and an inter-class dispersion matrix. The DB index describes intra-class compactness by the distance from an intra-class sample point to the clustering center thereof, and represents the separability between classes by the distance between the clustering centers.
2) Some clustering effectiveness indexes only analyze membership degrees, such as effectiveness index separation coefficient PC and separation entropy PE indexes for fuzzy clustering which are provided at the earliest, only take membership degree information into consideration, and do not take other sample information such as data structures and the like into consideration when designing indexes. The standard separation coefficient NPC index is only for overcoming the disadvantage of monotone change of the PC index, and does not really consider the information of the integrated sample set.
3) Also, structural information of the data set and indexes of membership, such as XBI indexes and FS indexes, are considered at the same time. The XBI index is a fuzzy clustering effectiveness index of a ratio value, compactness and separability are scaled to different degrees through the introduced scale factor, although the performance of the XBI index is improved to a certain degree, the performance of the XBI index is not very stable. Later WLI indexes are obtained by adding the median distance between the clustering centers on the basis of the XBI indexes, and better clustering results can be obtained. Although the VCVI index can achieve better clustering results in some cases, the VCVI index is not satisfactory when the data set contains more noise points.
Disclosure of Invention
The invention provides an image segmentation method and an image segmentation system for an effectiveness index of fuzzy clustering guided by three-degree separation, aiming at overcoming the defects in the prior art, so that a pixel point set can be accurately divided, and the method and the system are suitable for the pixel set with high dimension, complexity, overlapping and noisy points, so that a good image segmentation effect can be achieved.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention relates to an image segmentation method of a three-degree separation-guided fuzzy clustering effectiveness index, which is characterized by comprising the following steps of:
step 1, a fuzzy C-means clustering algorithm is utilized to collect pixel points { X ] in any image X 1 ,x 2 ,…,x i ,…,x N Divide it into K classes and obtain membership matrix U = { mu = ik | i＝1,2,...,N；k＝1,2,...,K And cluster center V = { V = } 1 ,v 2 ,…,v k ,…,v K }; wherein x is i Representing the ith pixel point, μ, in image X ik Representing the ith pixel point x i Belonging to the kth class C k A membership value of 0 to mu ik ≤1，
Figure BDA0003227323690000021
v k A cluster center representing a kth class; i =1,2, \ 8230;, N; k =1,2, \ 8230;, K; n represents the number of pixel points in image X;
setting the maximum iteration number as M, the error of the termination condition of the iteration as epsilon, and initializing K =2;
step 2, constructing the iter-time iteration objective function of the FCM fuzzy algorithm by using the formula (1)
Figure BDA0003227323690000022
Figure BDA0003227323690000023
In the formula (1), the reaction mixture is,
Figure BDA0003227323690000024
the cluster center of the kth class representing the iter iteration,
Figure BDA0003227323690000025
the ith pixel point x representing the iter iteration i Clustering center with kth class
Figure BDA0003227323690000026
In between the distance between the first and second electrodes,
Figure BDA0003227323690000027
the ith pixel point x representing the iter iteration i The membership degree of the kth class, m is a weighting index and represents the clustering fuzzy degree;
step 3, enabling the initial iteration number iter =0, and taking the membership degree matrix U and the clustering center V as the initial membership degree matrix U 0 And an initial clustering center V 0 ；
Step 4, updating the membership degree matrix U of the iter order by using the formula (2) iter To obtain the ith +1 degree membership matrix
Figure BDA0003227323690000028
Figure BDA0003227323690000029
In the formula (2), the reaction mixture is,
Figure BDA0003227323690000031
represents the iter +1 degree membership matrix U iter+1 Middle ith pixel point x i Membership belonging to the kth class; v. of j Represents the cluster center of the jth class, j =1,2, \ 8230;, K; j is not equal to k;
step 5, updating the iter-th clustering center V by using the formula (3) iter To obtain the iter + 1-degree clustering center
Figure BDA0003227323690000032
Figure BDA0003227323690000033
In the formula (3), the reaction mixture is,
Figure BDA0003227323690000034
represents the iter +1 th cluster center V iter+1 Cluster center of the kth class;
step 6, if V | | iter+1 -V iter If | | < epsilon, stopping iteration, otherwise, assigning an value of iter +1 to iter, and returning to the step 4 until iter = M;
and 7, calculating the close relation fcp (K) in the class through the fuzzy weighted distance and the base number of the fuzzy cluster:
step 7.1, letting k =1, defining a close relationship corresponding to the cluster number k as fcp (k), and initializing fcp (k) =0;
step 7.2, after K +1 is assigned to K, judging whether K is more than K, if so, indicating that the close relationship fcp (K) in the class is obtained, otherwise, calculating
Figure BDA0003227323690000035
And assigns fcp (k), then returns to step 7.2:
and 8, calculating the separation relation fsp1 (K) of the first layer between the classes by using the formula (4):
Figure BDA0003227323690000036
in the formula (4), the reaction mixture is,
Figure BDA0003227323690000037
represents the median of the K cluster centers;
and 9, calculating the separation relation fsp2 (K) of the second layer between the classes by using the formula (5):
Figure BDA0003227323690000038
in the formula (5), mean represents a mean function;
and 10, calculating the separation relation fsp3 (K) of the third layer between the classes by using the formula (6):
Figure BDA0003227323690000039
in the formula (5), min represents a minimum function;
step 11, obtaining three-degree separation indexes V of K classes by using the formula (7) TDS (K)：
Figure BDA0003227323690000041
Step 10, assigning K +1 to K and judging
Figure BDA0003227323690000042
Whether the K classes are established or not is judged, if yes, the effectiveness indexes of all the K classes are obtained, and step 11 is executed; otherwise, returning to the step 2 for execution;
and 11, comparing the effectiveness indexes of all the K classes, and selecting the clustering number corresponding to the maximum effectiveness index and the corresponding membership degree matrix to segment the image X so as to obtain a segmentation result of the image X.
The invention relates to an image segmentation system of fuzzy clustering effectiveness indexes guided by three-degree separation, which is characterized by comprising the following steps:
an image acquisition module: the method comprises the steps of acquiring a pixel point set of an image X;
a cluster initialization module: the system comprises a parameter for initializing image segmentation and constructing an objective function; the parameters include: terminating conditions or reaching the maximum iteration times, an initial membership matrix and an initial clustering center;
a clustering calculation module: the membership matrix and the clustering center are updated and iterated, so that a final membership matrix and a final clustering center are obtained;
an index forming module: calculating an intra-class compact relationship and an inter-class separation relationship, wherein the inter-class separation relationship comprises: the first layer of inter-class separation relation, the second layer of separation relation and the third layer of separation relation, the intra-class compact relation is used as a numerator, and the product of the three inter-class separation relations is used as a denominator, so that an effectiveness index is obtained;
the index checking module: and the method is used for comparing the effectiveness indexes of all the classes, acquiring the clustering number corresponding to the maximum effectiveness index and the corresponding membership matrix, and clustering and segmenting the image X.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention adopts a separability and compactness scale factor method, integrates the advantages of a Fuzzy Clustering (FCM) index method, and simultaneously reduces the influence of more classification numbers on experimental results, so that the clustering results are more accurate.
2. The invention solves the problem that the classification result of the existing index on overlapped data, a high-dimensional data set, a data set containing more noise and a data set with closer mass center distribution is inaccurate by calculating the distance between the cluster center and the average cluster center of each class and the minimum cluster center distance between the two classes, can give consideration to the cluster and individual data in a complex and dispersed data set, also fully considers the position of each cluster center of the data set, prevents the condition that different cluster centers are distributed very closely to a certain extent, ensures that the TDS index expression mode is fuller and more stereoscopic, allows the mass centers to distribute similar clusters to a certain extent, and has better effect on the data sets with closer cluster center distribution.
3. According to the invention, the clustering number can be judged more accurately by the fuzzy clustering method, and the influence of the distance between different clustering centers on the classification accuracy is smaller and smaller, so that the method is more suitable for a multi-dimensional and complex-distribution data set than other methods.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2a is a diagram of two types of original images according to the present invention;
FIG. 2b is a class two noise image of the present invention;
FIG. 2c is a diagram of two types of segmented images according to the present invention;
FIG. 3a is a diagram of three types of original images according to the present invention;
FIG. 3b is a diagram of three types of noise images according to the present invention
FIG. 3c is a diagram of three types of segmented images according to the present invention;
FIG. 4a is a diagram of an original image of a natural image according to the present invention;
FIG. 4b is a natural image noise image of the present invention;
FIG. 4c is a segmented image of a natural image according to the present invention;
FIG. 5a is the original image of the natural images Coins according to the present invention;
FIG. 5b is a noise image of the natural images Coins according to the present invention;
FIG. 5c is a Coins segmented image of the natural image according to the present invention.
Detailed Description
In this embodiment, as shown in fig. 1, an image segmentation method for validity index of three-degree separation-guided fuzzy clustering is performed according to the following steps:
step 1, a fuzzy C-means clustering algorithm is utilized to collect pixel points { X ] in any image X 1 ,x 2 ,…,x i ,…,x N Divide it into K classes and obtain membership matrix U = { mu = ik | i＝1,2,...,N；k＝1,2,...,K And cluster center V = { V = } 1 ,v 2 ,…,v k ,…,v K }; wherein x is i Representing the ith pixel point, μ, in image X ik Representing the ith pixel point x i Belonging to the kth class C k A membership value of 0 to mu ik ≤1，
Figure BDA0003227323690000051
v k A cluster center representing a kth class; i =1,2, \ 8230;, N; k =1,2, \ 8230;, K; n represents the number of pixel points in image X;
setting the maximum iteration number as M, the error of the termination condition of the iteration as epsilon, and initializing K =2;
step 2, constructing the iter-time iteration objective function of the FCM fuzzy algorithm by using the formula (1)
Figure BDA0003227323690000052
Figure BDA0003227323690000053
In the formula (1), the acid-base catalyst,
Figure BDA0003227323690000054
the cluster center of the kth class representing the iter iteration,
Figure BDA0003227323690000055
the ith pixel point x representing the iter iteration i Clustering center with kth class
Figure BDA0003227323690000056
The distance between the two or more of the two or more,
Figure BDA0003227323690000057
the ith pixel point x representing the iter iteration i Membership degree belonging to the kth class, wherein m is a weighting index and represents clustering fuzzy degree;
the parameters in the specific test are set, m is set to be in a floating setting range between 1.5 and 2.5 in the test, and the parameter setting range is set to be 2;
the corresponding cluster center is optimal when the J value is minimum, and the image segmentation effect is also the best. Fig. 2a is an original image of a class two image, fig. 2b is an image after 10% salt and pepper noise is added, and fig. 2c is a segmentation effect of the FCM algorithm on the class two image; fig. 3a is an original image divided into three types, fig. 3b is an image after 10% gaussian noise is added, and fig. 3c is a segmentation effect of the FCM algorithm on the three types of images; the image segmentation method capable of obtaining the effectiveness index of the three-degree separation-guided fuzzy clustering in the operation process is obviously superior to the fuzzy C-means clustering algorithm in the traditional technology.
Step 3, enabling the initial iteration number iter =0, and taking the membership degree matrix U and the clustering center V as the initial membership degree matrix U 0 And an initial clustering center V 0 ；
Step 4, updating the membership degree matrix U of the iter order by using the formula (2) iter To obtain the ith +1 degree membership matrix
Figure BDA0003227323690000061
Figure BDA0003227323690000062
In the formula (2), the reaction mixture is,
Figure BDA0003227323690000063
represents the iter +1 degree membership matrix U iter+1 Middle ith pixel point x i Membership belonging to the kth class; v. of j Represents the cluster center of the jth class, j =1,2, \ 8230;, K; j is not equal to k;
step 5, updating the iter-th clustering center V by using the formula (3) iter To obtain the iter +1 th clustering center
Figure BDA0003227323690000064
Figure BDA0003227323690000065
In the formula (3), the reaction mixture is,
Figure BDA0003227323690000066
represents the iter +1 th cluster center V iter+1 The cluster center of the kth class;
step 6, if V | | | iter+1 -V iter If | | < epsilon, stopping iteration, otherwise, assigning an value of iter +1 to iter, and returning to the step 4 until iter = M;
and 7, calculating the close relation fcp (K) in the class:
step 7.1, letting k =1, defining a close relationship corresponding to the cluster number k as fcp (k), and initializing fcp (k) =0;
step 7.2, after K +1 is assigned to K, judging whether K is more than K, if so, indicating that the close relationship fcp (K) in the class is obtained, otherwise, calculating
Figure BDA0003227323690000067
And assigning to fcp (k), returning to step 7.2:
and 8, calculating the separation relation fsp1 (K) of the first layer among the classes by using the formula (4):
Figure BDA0003227323690000071
in the formula (4), the reaction mixture is,
Figure BDA0003227323690000072
represents the median of the K cluster centers;
TABLE 1 Experimental data Table on SPECTF heart of the present invention
Index (es) Class 2 Class 3 Class 4 Class 5 Class 6 Class 7 Class 8 Class 9 Class 10
CH + 0.5428 0.5543 0.2706 0.2549 0.1243 0.1155 0.1213 0.1067 0.0928
DB - 109.2186 292.9729 207.8232 266.7252 557.1038 101.6500 105.7082 104.1051 119.9793
PC + 0.5000 0.3334 0.2501 0.2001 0.1668 0.1429 0.1250 0.1112 0.1001
PE - 0.9999 0.5727 1.9998 2.3216 0.8087 2.8069 2.9995 3.1697 1.0354
FS - 7690.6 5087.8 3817.7 3056.3 2521.5 2180.4 1905.7 1681.9 1515.1
XB - 36.2452 51.2162 30.8201 64.3935 48.9373 79.4901 101.7217 81.0978 90.7100
NPC + -0.6968 -1.1059 -1.3974 -1.6241 -1.8100 -1.9682 -2.1056 -2.2274 -2.3366
WLI - 24.6578 21.1556 26.9917 34.6935 25.1479 37.6424 23.1215 34.5336 29.7515
VCVI - 56.8260 56.2808 55.9367 56.6848 54.9396 52.2441 51.5878 54.5937 53.2441
TCR - 31.6301 33.7628 87.7579 71.4417 39.6394 33.0926 50.1074 87.0055 45.7900
Table 1 gives the clustering results for some of the indices used for comparison herein in 6 data sets. The dimension of the data set is many, and the division result judged by most indexes is wrong; the invention adopts a method that the average clustering center and the minimum value of the clustering centers between any two classes are all involved in separability measurement, thereby solving the problems and obtaining a good segmentation result.
And 9, calculating the separation relation fsp2 (K) of the second layer among the classes by using the formula (5):
Figure BDA0003227323690000073
in the formula (5), mean represents a mean function;
and step 10, calculating a separation relation fsp3 (K) of a third layer among the classes by using the formula (6):
Figure BDA0003227323690000074
in the formula (5), min represents a minimum function;
in order to verify the segmentation effect of the proposed algorithm under natural images, the most commonly used images of Camerman and Coins were used for experiments. FIG. 4a is a natural image Camerman original image, FIG. 4b is a natural image Camerman added with salt and pepper noise image of 10%, and FIG. 4c is a segmentation image of the natural image Camerman; the size of the parameter setting k =3,m =2,a is set to 1.0, l is set to 5.0, epsilon is set to 0.001, the number of iterations is 100, and the window size is set to 3 × 3, as can be seen from fig. 3 a-3 c below, the method of the invention better preserves the detail features of the image and also allows segmentation of sky and grassy areas.
Fig. 5a is an original image of the natural images conis, fig. 5b is an image of the natural images conis with 10% salt-pepper noise added thereto, and fig. 5c is a divided image of the natural images conis. The method also achieves good segmentation effect.
And 11, comparing the effectiveness indexes of all the K classes, and selecting the clustering number corresponding to the maximum effectiveness index and the corresponding membership degree matrix to segment the image X so as to obtain a segmentation result of the image X.
In this embodiment, an image segmentation system based on a three-degree separation-guided fuzzy clustering validity index includes:
an image acquisition module: the method comprises the steps of acquiring a pixel point set of an image X;
a cluster initialization module: the system comprises a parameter for initializing image segmentation and constructing an objective function; the parameters include: terminating conditions or reaching the maximum iteration times, an initial membership matrix and an initial clustering center;
a clustering calculation module: the method comprises the steps of updating and iterating a membership matrix and a clustering center to obtain a final membership matrix and a final clustering center;
an index formation module: calculating an intra-class compact relationship and an inter-class separation relationship, wherein the inter-class separation relationship comprises: a first layer of inter-class separation relation, a second layer of separation relation and a third layer of separation relation, wherein the intra-class compact relation is used as a numerator, and the product of the three inter-class separation relations is used as a denominator, so that an effectiveness index is obtained;
the index checking module: and the method is used for comparing the effectiveness indexes of all the classes, acquiring the clustering number corresponding to the maximum effectiveness index and the corresponding membership matrix, and clustering and segmenting the image X.
In order to verify the validity of the fuzzy clustering validity index of the three-degree separation guidance, some experiments are carried out. The experimental platform is a Window10 system, the compiling environment is Intel (R) Core (TM) 5-7400 CPU @300GHz 3.00GHz, RAM8.00GB and Windows 10OS, and the programming language is Matlab2018b. During the course of the experiment, a lateral comparison was required with some of the previously presented relatively well-performing indices, which were referred to as CHI (+), DBI (-), PC (+), PE (-), FSI (-), XBI (-), NPC (+), WLI (-), VCVI (-), TDS (-). Six data sets are used for verification, and the related data sets comprise a Pima data set, a WDBC data set, a Hayes-Roth data set, an Austra data set, a Monk data set and a SPECTF heart data set. As shown in table 1, the performance of the fuzzy clustering validity index of the three-degree separation guide obtained finally in the experiment is the most excellent, and then the clustering number corresponding to the validity index and the corresponding membership matrix are selected to segment the image, so as to obtain the image segmentation result.
Table 2 experimental results of the invention in multiple data sets
Figure BDA0003227323690000091
As shown in table 2, the results of the experiment were analyzed to find that: under the condition of a complex distributed data set, no index can have a good effect on the data sets with different characteristics, the CH, PE and DB indexes obtain wrong results on a Hayes-Roth data set and a SPECTF heart data set, and the overlapping degree of different data clusters of the two data sets is high; the PC and NPC indexes have clustering result deviation on the Hayes-Roth data set; FS only obtains correct classification results on the Pima and WDBC data sets; the XB index obtains wrong clustering results on Austra and SPECTF heart data sets, and the overlapping degree of different data clusters of the two data sets is high; VCVI obtains wrong clustering results on the Pima and SPECTF heart data sets, the clustering centers of the two data sets are very close to each other, the different class overlapping degrees are also high, and some noise points are provided; under the condition that other indexes do not obtain good effects, the validity indexes of the fuzzy clustering guided by the three-degree separation of the new indexes all obtain correct results, and the new indexes are proved to have good characteristics. The effectiveness index of the fuzzy clustering guided by three-degree separation divides the data sets of Austra, hayes-Roth and Monk into 2 types, which shows that the index realizes the correct clustering of overlapped data; the fact that three data sets, namely the Pima data set, the WDBC data set and the SPECTF data set, have different characteristics respectively, the SPECTF data set is a data set with relatively small number of samples and more dimensions, the WDBC data set has a plurality of sample attributes although the number of the samples is not large, the number of the Monk data set attributes is relatively balanced with the number of the samples, and the validity indexes of fuzzy clustering guided by three-degree separation all obtain correct results. Therefore, the validity index of the fuzzy clustering guided by three-degree separation has strong adaptability. Therefore, the invention can obtain better effect on image segmentation.

Claims (2)

1. An image segmentation method of fuzzy clustering validity indexes guided by three-degree separation is characterized by comprising the following steps of:
step 1, utilizing a fuzzy C-means clustering algorithm to collect pixel points { X ] in any one image X 1 ,x 2 ,…,x i ,…,x N Divide it into K classes and obtain a membership matrix U = { mu = ik | i＝1,2,...,N；k＝1,2,...,K And cluster center V = { V = } 1 ,v 2 ,…,v k ,…,v K }; wherein x is i Representing the ith pixel point, μ, in image X ik Representing the ith pixel point x i Belonging to the kth class C k A membership value of 0 to mu ik ≤1，
Figure FDA0003889529960000011
v k A cluster center representing a kth class; i =1,2, \ 8230;, N; k =1,2, \8230;, K; n represents the number of pixel points in image X;
setting the maximum iteration number as M, setting the error of the termination condition of the iteration as epsilon, and initializing K =2;
step 2, constructing the iter-time iteration objective function of the FCM fuzzy algorithm by using the formula (1)
Figure FDA0003889529960000012
Figure FDA0003889529960000013
In the formula (1), the acid-base catalyst,
Figure FDA0003889529960000014
the cluster center of the kth class representing the iter iteration,
Figure FDA0003889529960000015
the ith pixel point x representing the iter iteration i Clustering center with kth class
Figure FDA0003889529960000016
The distance between the two or more of the two or more,
Figure FDA0003889529960000017
the ith pixel point x representing the iter iteration i Membership degree belonging to the kth class, wherein m is a weighting index and represents clustering fuzzy degree;
step 3, enabling the initial iteration number iter =0, and taking a membership matrix U and a clustering center V as an initial membership matrix U 0 And an initial clustering center V 0 ；
Step 4, updating the membership degree matrix U of the iter order by using the formula (2) iter To obtain the ith +1 degree membership matrix
Figure FDA0003889529960000018
Figure FDA0003889529960000019
In the formula (2), the reaction mixture is,
Figure FDA00038895299600000110
represents the iter +1 degree membership matrix U iter+1 Middle ith pixel point x i Membership belonging to the kth class; v. of j Cluster centers representing the jth class, j =1,2, \8230; j is not equal to k;
step 5, updating the iter-th clustering center V by using the formula (3) iter To obtain the iter +1 th clustering center
Figure FDA00038895299600000111
Figure FDA0003889529960000021
In the formula (3), the reaction mixture is,
Figure FDA0003889529960000022
represents the iter +1 th cluster center V iter+1 The cluster center of the kth class;
step 6, if V | | iter+1 -V iter If | | < epsilon, stopping iteration, otherwise, assigning an value of iter +1 to iter, and returning to the step 4 until iter = M;
and 7, calculating the close relation fcp (K) in the class through fuzzy weighted distance and the base number of the fuzzy clusters:
step 7.1, let k =1, define the close relationship corresponding to the kth class as fcp (k), and initialize fcp (k) =0;
step 7.2, after K +1 is assigned to K, judging whether K is more than K, if so, indicating that the close relationship fcp (K) in the class is obtained, otherwise, calculating
Figure FDA0003889529960000023
And assigning to fcp (k), returning to step 7.2:
and 8, calculating the separation relation fsp1 (K) of the first layer between the classes by using the formula (4):
Figure FDA0003889529960000024
in the formula (4), the reaction mixture is,
Figure FDA0003889529960000025
represents the median of the K cluster centers;
and 9, calculating the separation relation fsp2 (K) of the second layer among the classes by using the formula (5):
Figure FDA0003889529960000026
in the formula (5), mean represents a mean function;
and 10, calculating the separation relation fsp3 (K) of the third layer between the classes by using the formula (6):
Figure FDA0003889529960000027
in the formula (5), min represents a minimum function;
step 11, obtaining three-degree separation indexes V of K classes by using the formula (7) TDS (K)：
Figure FDA0003889529960000028
Step 12, assigning K +1 to K and judging
Figure FDA0003889529960000029
If yes, the validity indexes of all K classes are obtained, and step 13 is executed; otherwise, returning to the step 2 for execution;
and step 13, comparing the validity indexes of all K classes, and selecting the clustering number corresponding to the maximum validity index and the corresponding membership matrix to segment the image X so as to obtain a segmentation result of the image X.
2. An image segmentation system of three-degree separation guided fuzzy clustering effectiveness index, which is used for realizing the image segmentation method of the three-degree separation guided fuzzy clustering effectiveness index according to claim 1, and comprises:
an image acquisition module: the method comprises the steps of acquiring a pixel point set of an image X;
a cluster initialization module: the system comprises a parameter for initializing image segmentation and constructing an objective function; the parameters include: terminating conditions or reaching the maximum iteration times, and obtaining an initial membership matrix and an initial clustering center;
a clustering calculation module: the method comprises the steps of updating and iterating a membership matrix and a clustering center to obtain a final membership matrix and a final clustering center;
an index forming module: calculating an intra-class compact relationship and an inter-class separation relationship, wherein the inter-class separation relationship comprises: a first layer of inter-class separation relation, a second layer of separation relation and a third layer of separation relation, wherein the intra-class compact relation is used as a numerator, and the product of the three inter-class separation relations is used as a denominator, so that an effectiveness index is obtained;
an index checking module: and the method is used for comparing the effectiveness indexes of all the classes, acquiring the clustering number corresponding to the maximum effectiveness index and the corresponding membership matrix, and clustering and segmenting the image X.
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