CN110634141B - Image segmentation method based on improved intuitionistic fuzzy c-means clustering and storage medium - Google Patents

Image segmentation method based on improved intuitionistic fuzzy c-means clustering and storage medium Download PDF

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CN110634141B
CN110634141B CN201910887555.5A CN201910887555A CN110634141B CN 110634141 B CN110634141 B CN 110634141B CN 201910887555 A CN201910887555 A CN 201910887555A CN 110634141 B CN110634141 B CN 110634141B
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杨真真
许鹏飞
康彬
匡楠
乐俊
郑艺欣
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Nanjing University of Posts and Telecommunications
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Abstract

The invention discloses an image segmentation method and a storage medium based on improved intuitive fuzzy c-means clustering, wherein the method comprises the following steps: 1) calculating a maximum dominance inhibition similarity function according to local pixel gray information of the image; 2) calculating the membership degree of the fuzzy set of the pixels; 3) constructing a nonlinear fuzzy complementary function, and calculating the non-membership degree and the hesitation degree of a fuzzy set; 4) according to the membership degree, the non-membership degree and the hesitation degree, image data are intuitively blurred; 5) constructing an intuitive fuzzy factor according to the local spatial relationship of the image pixels; 6) according to the intuitive fuzzy factor, carrying out solution optimization in the intuitive fuzzy set; 7) and performing image segmentation by using a clustering algorithm according to the optimization solution. The invention solves the problems of noise sensitivity and data uncertainty of the existing method, effectively improves the quality of image segmentation, can well inhibit noise when applied to the MRI brain image, and can well express picture details.

Description

Image segmentation method based on improved intuitionistic fuzzy c-means clustering and storage medium
Technical Field
The present invention relates to an image segmentation method and a storage medium, and more particularly, to an image segmentation method and a storage medium based on improved intuitive fuzzy c-means clustering.
Background
Image segmentation is a classic problem in the field of image processing and is widely applied in various fields, among which human brain image segmentation. In human brain Magnetic Resonance Images (MRI), three different brain tissues can be seen: brainstem, gray matter and white matter. Due to the complex structure of the human brain, the boundaries of different tissues are difficult to distinguish. To solve this problem, researchers have proposed many segmentation algorithms, such as image segmentation algorithms based on thresholds, regions, neural networks, Markov random fields, and clustering.
Wherein the clustering algorithm is a classic human brain MR image segmentation algorithm. However, the classical clustering algorithm is limited, and each pixel in the clustering algorithm can only belong to one cluster center. In fact, there are some pixels that belong to the intersection of two clusters. This also leads to uncertainty in the data. Thereafter, based on the Fuzzy Set (FS) principle, Bezdek proposes a fuzzy c-means (FCM) clustering algorithm to deal with the uncertainty of the data. However, this algorithm has two drawbacks: (1) the algorithm is sensitive to noise; (2) this algorithm does not fully resolve the uncertainty of the data.
To this end, researchers have proposed many improvements over FCM. To eliminate the effects of noise, Chen et al propose FCM-S1, FCM-S2 algorithms. The FCM-S1 performs mean filtering on the image and the FCM-S2 performs median filtering on the image. But both images alter the original image, losing a lot of image detail information. By combining local spatial information, Krinnidis proposes a fuzzy local information c-means (FLICM) clustering algorithm. The algorithm adds a fuzzy local neighborhood factor to the objective function of the standard FCM algorithm. This factor combines the grey scale information and the spatial relationship of the pixels and does not require any parameter adjustment. However, the running time of the algorithm is too long, and the effect is not good. To further handle 1 data uncertainty, ataanassov proposes an Intuitive Fuzzy Set (IFS) based on the fuzzy set. The intuition fuzzy set is to add functions of non-membership degree and hesitation degree on the fuzzy set, namely, the functions of membership degree, non-membership degree and hesitation degree are used for describing the fuzziness of the set, which is more accurate than the fuzziness represented by a classical fuzzy set. Xu et al proposed an intuitive fuzzy c-means clustering (IFCM) algorithm based on this theory.
The intuitive fuzzy C mean clustering (IFCM) algorithm is an improved algorithm based on the classic Fuzzy C Mean (FCM) clustering algorithm. The algorithm adds a non-membership function and a hesitation function on the basis of the fuzzy set, namely, the membership function, the non-membership function and the hesitation function are used for describing the fuzziness of the set. Therefore, the algorithm can obtain more accurate segmentation effect. The intuitive fuzzy set adds a non-membership function and a hesitation function to the fuzzy set, but the algorithm has two defects: (1) the algorithm is sensitive to noise; (2) the resolution of the uncertainty problem remains incomplete.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide an image segmentation method and a storage medium based on improved intuitive fuzzy c-means clustering, solve the problems of sensitivity to noise and uncertainty of data in the existing method and effectively improve the quality of image segmentation.
The technical scheme is as follows: the invention discloses an image segmentation method based on improved intuitive fuzzy c-means clustering, which comprises the following steps of:
(1) calculating a maximum dominance inhibition similarity function according to local pixel gray information of the image;
(2) calculating the membership degree of the fuzzy set of the pixels;
(3) constructing a nonlinear fuzzy complementary function, and calculating the non-membership degree and the hesitation degree of a fuzzy set;
(4) according to the membership degree, the non-membership degree and the hesitation degree, image data are subjected to intuitive fuzzification to form an intuitive fuzzy set;
(5) constructing an intuitive fuzzy factor according to the local spatial relationship of the image pixels;
(6) according to the intuitive fuzzy factor, carrying out solution optimization in the intuitive fuzzy set in the step (4);
(7) and performing image segmentation by using a clustering algorithm according to the optimization solution.
Further, the step (1) is specifically as follows:
(1.1) with the jth pixel x in the imagejAs a center, take NRPutting pixels in a rectangular window of size into a set NjIn (A), itExpression is { xk|k∈Nj,k＝1,2,...,NR-1}，NRIs a set NjTotal number of middle pixels, xkIs an element xjN of the neighborhood windowjThe kth pixel in;
(1.2) adding NjThe inner pixels are sorted in ascending order according to the gray value, and N is divided into golden section pointsjDivided into reward sets
Figure BDA0002207777990000021
And penalty set
Figure BDA0002207777990000022
Mixing [0.618 × (N)R-1)]Put into one pixel
Figure BDA0002207777990000023
In, the rest of the pixels are put into
Figure BDA0002207777990000024
(1.3) punishing or rewarding the pixel according to the set to which the pixel belongs, wherein the maximum dominance inhibition similarity function is as follows:
Figure BDA0002207777990000025
wherein α is a suppression factor, SjkIs the jth pixel xjAnd set NjK-th pixel x in (b)kThe local similarity function between the two is expressed as follows:
Figure BDA0002207777990000026
wherein,
Figure BDA0002207777990000027
is a set NjDiffusion scale factor of medium gray scale similarity, xpIs a set NjThe p-th element in (b).
Further, the membership degree in the step (2) is as follows:
Figure BDA0002207777990000031
wherein, mu (x)j) The jth pixel xjThe fuzzy membership function of (a) is,
Figure BDA0002207777990000032
further, the fuzzy complement function in the step (3) is,
Figure BDA0002207777990000033
wherein gamma is a segmentation point of the fuzzy complementary function, and gamma is more than or equal to 0 and less than or equal to 0.5;
the hesitation function is:
π(xj)＝1-μ(xj)-v(xj)。
further, the intuitive fuzzy set in the step (4) is as follows:
A＝{(x,μ(x),v(x),π(x))|x∈X}，
where X is the set of image pixels.
Further, the intuitive fuzzy factor in the step (5) is:
Figure BDA0002207777990000034
wherein HijFor the intuitive blur factor, K is the number of cluster centers, N is the total number of pixels in the image, uilRepresents NjMembership function of the ith element and the ith clustering center, m is fuzzy coefficient, m is not less than 1, USilIs NjThe similarity function between the ith element and the ith cluster center is expressed as:
Figure BDA0002207777990000035
further, the solution optimization in the intuitive fuzzy set in the step (6) is specifically as follows:
Figure BDA0002207777990000041
Figure BDA0002207777990000042
wherein m is a blurring coefficient, m is not less than 1,
Figure BDA0002207777990000043
a set of noise robust intuitively blurred representations representing pixels of an image,
Figure BDA0002207777990000044
a set of noise robust intuitively-blurred representations representing the cluster centers,
Figure BDA0002207777990000045
and
Figure BDA0002207777990000046
respectively the ith cluster center and pixel xjIs a noise-robust, intuitive fuzzy representation ofijDenotes xjA membership value of 0 to u of the ith cluster centerij≤1，
Figure BDA0002207777990000047
Is that
Figure BDA0002207777990000048
And
Figure BDA0002207777990000049
the expression of (1) is as follows:
Figure BDA00022077779900000410
solving the optimization problem by using a Lagrange multiplier method to obtain the membership degree uijAnd a cluster center
Figure BDA00022077779900000411
The expression of (a) is:
Figure BDA00022077779900000412
Figure BDA00022077779900000413
the storage medium of the present invention has stored thereon a computer program which, when executed by a computer processor, implements the above-described image segmentation method based on improved intuitive fuzzy c-means clustering.
Has the advantages that: the invention provides an improved intuitionistic fuzzy c-means clustering algorithm, applies the algorithm to image segmentation, applies an intuitionistic fuzzy set with noise robustness to human brain MRI image segmentation, and can obtain better anti-noise performance. In addition, in order to process the uncertainty of the data, the invention also provides a new efficient intuitive fuzzy factor. The fuzzy factor combines the local gray information and the spatial information of the image and can be used for adjusting the membership degree in the algorithm objective function. Therefore, the invention can simultaneously solve the problems of noise and data uncertainty of the human brain MRI image and effectively improve the quality of image segmentation. The algorithm is applied to a simulated MRI human brain image, and experiments show that the algorithm has good performance of inhibiting noise and can well express details of pictures.
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FIG. 1 is an overall flowchart of the method of the present embodiment;
fig. 2 is a comparison graph of the segmentation effect of different algorithms on a simulated brain image.
Detailed Description
The image segmentation method (NR-IFCM for short) based on the improved intuitive fuzzy c-means clustering is based on a clustering algorithm, each image block segmented in the clustering algorithm is a cluster, pixels in the same cluster have the largest membership degree and the shortest distance in relative clustering, and therefore the original image segmentation problem is converted into an optimization problem. Firstly, the algorithm applies the noise robust intuitionistic fuzzy set to the human brain MRI image segmentation, and obtains better anti-noise performance. Then, in order to process the uncertainty of the data, the method also provides a new efficient intuitive fuzzy factor. The blurring factor is combined with local gray information and spatial information of the image, and can be used for adjusting the magnitude of membership in the NR-IFCM objective function. The flow of the method is shown in fig. 1, and the specific implementation mode is as follows:
step 1, in order to determine membership function of fuzzy set, the algorithm calculates jth element x in image according to local pixel gray information of imagejAnd its neighborhood window NjInner kth pixel xkMaximum dominant inhibitory similarity function SSjk. This function classifies pixels within the neighborhood using competitive learning and the concept of golden section points. The details of the calculation of this function are as follows:
1. with the jth pixel x in the imagejAs a center, take NRPutting pixels in a rectangular window of size into a set NjIn (1), its expression is { xk|k∈Nj,k＝1,2,...,NR-1}；
2. Will NjThe pixels in the set are sorted in ascending order of gray value, and the set is divided into two sets with the golden section point as the boundary, and the two sets are divided into [0.618 × (N)R-1)]Putting individual pixels into a reward set
Figure BDA0002207777990000051
In, remaining put penalty set
Figure BDA0002207777990000052
3. And punishing or rewarding the pixel according to the reward or punishment set to which the pixel belongs, wherein the function expression of the maximum dominance inhibition similarity function is as follows:
Figure BDA0002207777990000053
wherein α is a suppression factor, SjkIs the jth pixel xjAnd set NjK-th pixel x in (b)kThe local similarity function between the two is expressed as follows:
Figure BDA0002207777990000054
wherein,
Figure BDA0002207777990000061
is a set NjDiffusion scale factor of medium gray scale similarity, xpIs a set NjThe p-th element in (b).
And 2, according to the maximum dominance inhibition similarity function obtained in the step 1. The function is normalized first, and the function value of the function is used as the weighting factor of the image pixel. Then, N is addedjThe fuzzy membership degree of the jth pixel can be obtained by weighted average of the pixels in (1), and the expression is as follows:
Figure BDA0002207777990000062
wherein,
Figure BDA0002207777990000063
and 3, calculating a non-membership function according to a novel nonlinear fuzzy complementary function, wherein compared with a classical fuzzy complementary function, the fuzzy complementary function is nonlinear, and the parameter gamma is well determined. The expression is as follows:
Figure BDA0002207777990000064
wherein gamma (gamma is more than or equal to 0 and less than or equal to 0.5) is a segmentation point of the fuzzy complementary function. The expression of the hesitation degree then available is as follows:
π(xj)＝1-μ(xj)-v(xj)
and 4, intuitively blurring the image data according to the membership degree, the non-membership degree and the hesitation degree. The set of intuitive blur for this image is represented as follows:
A＝{(x,μ(x),v(x),π(x))|x∈X}
where X is the set of image pixels.
Step 5, the invention fully utilizes the local spatial relationship of image pixels and provides a novel intuitionistic fuzzy factor HijThe expression is as follows:
Figure BDA0002207777990000065
where K represents the number of cluster centers, N represents the total number of pixels in the image, uilRepresents NjMembership function of the ith element and the ith clustering center, m (m is more than or equal to 1) is a fuzzy coefficient, USilIs NjThe similarity function between the ith element and the ith cluster center, wherein the expression of the similarity function is as follows:
Figure BDA0002207777990000071
step 6, the NR-IFCM algorithm transforms the original image segmentation problem into an optimization problem, which is nonlinear as follows:
Figure BDA0002207777990000072
wherein m (m is more than or equal to 1) is a blurring coefficient,
Figure BDA0002207777990000073
a set of noise robust intuitively blurred representations representing pixels of an image,
Figure BDA0002207777990000074
is a collection of noise robust intuitively fuzzy representations of cluster centers,
Figure BDA0002207777990000075
and
Figure BDA0002207777990000076
is the ith cluster center and pixel x, respectivelyjIs robust and intuitive to blur. u. ofij(0≤uij1) represents xjA membership value to the ith cluster center,
Figure BDA0002207777990000077
is that
Figure BDA0002207777990000078
And
Figure BDA0002207777990000079
the expression of (1) is as follows:
Figure BDA00022077779900000710
in the following, we solve the optimization problem of equation (1) by using the lagrangian multiplier method, the lagrangian function is as follows:
Figure BDA00022077779900000711
wherein λ isjRepresenting the lagrange multiplier. Are respectively paired
Figure BDA00022077779900000712
Find uijAnd λjAnd make it equal to0, the following equation is obtained:
Figure BDA00022077779900000713
Figure BDA00022077779900000714
the method is simplified and can be obtained:
Figure BDA0002207777990000081
also, for
Figure BDA0002207777990000082
Calculating mu (c)i)、υ(ci) And pi (c)i) And let it equal 0, we get:
Figure BDA0002207777990000083
Figure BDA0002207777990000084
Figure BDA0002207777990000085
the method is simplified and can be obtained:
Figure BDA0002207777990000086
each image block divided from the image is called a cluster.
Figure BDA0002207777990000087
The position of the cluster center of each image after segmentation is determined. u. ofijIs an Icircuitj, each pixel having i membership values, wherein the i value corresponding to the item with the largest membership value represents the jth element xjThe cluster belongs to the second cluster. And when each pixel finds the cluster to which each pixel belongs, each cluster has the element to which each pixel belongs, and the image segmentation process is completed. The algorithm is realized through Python software, and the task of image segmentation is completed.
To verify the effect of NR-IFCM, a simulation experiment was performed using a simulated brain image and the segmentation effect was compared to 5 image segmentation algorithms FCM _ S1, FCM _ S2, FLICM, IFCM, IIFCM. All algorithms were implemented by Python and tested on a computer equipped with an Intel Core i7-7700HQ CPU, 8G memory and Win 10 system. All the parameters required for the algorithm are shown in table 1.
TABLE 1 corresponding parameter settings
Figure BDA0002207777990000088
Figure BDA0002207777990000091
Simulated Brain images, which are slices of the 3D human Brain, 217 x 181 in size, are available on the published Brain Web site. A 2D axial view of T1 weight and slice thickness 1 mm was chosen and simulation experiments were performed at different intensity non-uniformities (INU 0, INU 20) and different noise intensities (0%, 1%, 3%). In the experiment, the brain image was divided into 4 parts, brainstem, white matter, gray matter and background, respectively. The background did not participate in this experiment. Fig. 2 is a graph showing the segmentation effect of the above algorithms, and fig. 2(a) to 2(f) are graphs showing the segmentation effect of FCM _ S1, FCM _ S2, FLICM, IFCM, IIFCM, and NR-IFCM, respectively. It is clear that the FLICM is least effective and that the NR-IFCM retains more detail than the remaining four methods, and therefore the NR-IFCM segmentation is best.
In order to quantify the effectiveness of the NR-IFCM algorithm, the image segmentation effect is to adopt a segmentation coefficient VpcSplit entropy VpeDavis-Boolten index DB, similarity rho, false negative rfnFalse positive rfp.6 indices were compared.
Division coefficient VpcSplit entropy VpeAre respectively:
Figure BDA0002207777990000092
Figure BDA0002207777990000093
Vpcand VpeIs a very representative index of fuzzy segmentation, VpcThe larger the image segmentation effect is better, VpeThe smaller the image segmentation, the better the image segmentation effect.
The definition of the davis-boolean index DB is:
Figure BDA0002207777990000094
wherein sigmaxIs the center of the cluster ciAverage distance to all elements in the cluster, d (c)i,cj) Representing a cluster ciAnd clustering cjThe distance of (c). The lower the DB value, the better the segmentation effect.
Similarity rho, false negative rfnFalse positive rfpAre respectively:
Figure BDA0002207777990000101
Figure BDA0002207777990000102
Figure BDA0002207777990000103
wherein, XiRepresenting an original image, YiRepresenting a segmented image, | XiI represents XiNumber of elements in (1). The higher the rho value, the better the segmentation effect, rfnAnd rfpThe lower the segmentation effect the better.
The results of the experiments are shown in tables 2-5. From Table 2, V of NR-IFCMpcMaximum, VpeAnd DB is the smallest, so the splitting effect of NR-IFCM is the best. From tables 3 to 5, it can be seen that the value of ρ, r, of NR-IFCM is the largestfnAnd rfpThe value NR-IFCM is larger than most algorithms. Therefore, the NR-IFCM splitting effect is the best. In summary, compared with other 5 image segmentation methods, the performance of the NR-IFCM algorithm proposed by the present invention is the best in terms of these 6 indicators.
TABLE 2V of the 6-segmentation algorithm at different intensity non-uniformities INU and different noise intensitiespc、VpeDB value comparison
Figure BDA0002207777990000104
Figure BDA0002207777990000111
TABLE 3 ρ, r of gray matter GM segmented by 6 segmentation algorithm under different intensity non-uniformity INU and different noise intensityfn、rfpValue comparison
Figure BDA0002207777990000112
Figure BDA0002207777990000121
TABLE 4. rho, r of white matter WM segmented by 6 segmentation algorithms under different intensity non-uniformity INU and different noise intensityfn、rfpValue comparison
Figure BDA0002207777990000122
TABLE 5 ρ, r of cerebrospinal fluid GSF segmented by 6 segmentation algorithms under different intensity non-uniformity INU and different noise intensityfn、rfpValue comparison
Figure BDA0002207777990000131
The experimental results show that the invention can simultaneously solve the problems of human brain MRI image noise and data uncertainty, and effectively improve the quality of image segmentation
The embodiments of the present invention, if implemented in the form of software functional modules and sold or used as independent products, may also be stored in a computer-readable storage medium. Based on such understanding, the technical solutions of the embodiments of the present invention may be essentially implemented or a part contributing to the prior art may be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the methods described in the embodiments of the present invention. The storage medium includes various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read Only Memory (ROM), a magnetic disk, or an optical disk. Thus, embodiments of the invention are not limited to any specific combination of hardware and software.
Accordingly, embodiments of the present invention also provide a computer storage medium having a computer program stored thereon. The computer program, when executed by a processor, may implement the aforementioned image segmentation method based on improved intuitive fuzzy c-means clustering. For example, the computer storage medium is a computer-readable storage medium.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

Claims (7)

1. An image segmentation method based on improved intuitive fuzzy c-means clustering is characterized by comprising the following steps:
(1) calculating a maximum dominance inhibition similarity function according to local pixel gray scale information of the image, which specifically comprises the following steps:
(1.1) with the jth pixel x in the imagejAs a center, take NRPutting pixels in a rectangular window of size into a set NjIn (1), its expression is { xk|k∈Nj,k＝1,2,...,NR-1}，NRIs a set NjTotal number of middle pixels, xkIs an element xjN of the neighborhood windowjThe kth pixel in;
(1.2) adding NjThe inner pixels are sorted in ascending order according to the gray value, and N is divided into golden section pointsjDivided into reward sets
Figure FDA0003346959180000011
And penalty set
Figure FDA0003346959180000012
Mixing [0.618 × (N)R-1)]Put into one pixel
Figure FDA0003346959180000013
In, the rest of the pixels are put into
Figure FDA0003346959180000014
(1.3) punishing or rewarding the pixel according to the set to which the pixel belongs, wherein the maximum dominance inhibition similarity function is as follows:
Figure FDA0003346959180000015
wherein α is a suppression factor, SjkIs the jth pixel xjAnd set NjK-th pixel x in (b)kThe local similarity function between the two is expressed as follows:
Figure FDA0003346959180000016
wherein,
Figure FDA0003346959180000017
is a set NjDiffusion scale factor of medium gray scale similarity, xpIs a set NjThe p-th element in (a);
(2) calculating the membership degree of the fuzzy set of the pixels;
(3) constructing a nonlinear fuzzy complementary function, and calculating the non-membership degree and the hesitation degree of a fuzzy set;
(4) according to the membership degree, the non-membership degree and the hesitation degree, image data are subjected to intuitive fuzzification to form an intuitive fuzzy set;
(5) constructing an intuitive fuzzy factor according to the local spatial relationship of the image pixels;
(6) according to the intuitive fuzzy factor, carrying out solution optimization in the intuitive fuzzy set in the step (4);
(7) and performing image segmentation by using a clustering algorithm according to the optimization solution.
2. The image segmentation method based on improved intuitive fuzzy c-means clustering according to claim 1, wherein the membership in step (2) is:
Figure FDA0003346959180000018
wherein, mu (x)j) The jth pixel xjThe fuzzy membership function of (a) is,
Figure FDA0003346959180000021
3. the image segmentation method based on the improved intuitive fuzzy c-means clustering of claim 2, characterized in that: the fuzzy complement function in step (3) is,
Figure FDA0003346959180000022
wherein gamma is a segmentation point of the fuzzy complementary function, and gamma is more than or equal to 0 and less than or equal to 0.5;
the hesitation function is:
π(xj)＝1-μ(xj)-v(xj)。
4. the image segmentation method based on improved intuitive fuzzy c-means clustering according to claim 3, characterized in that the set of intuitive fuzzy in step (4) is:
A＝{(x,μ(x),v(x),π(x))|x∈X}，
where X is the set of image pixels.
5. The image segmentation method based on improved intuitive fuzzy c-means clustering according to claim 4, characterized in that the intuitive fuzzy factor in step (5) is:
Figure FDA0003346959180000023
wherein HijFor the intuitive blur factor, K is the number of cluster centers, N is the total number of pixels in the image, uilRepresents NjMembership function of the ith element and the ith clustering center, m is fuzzy coefficient, m is not less than 1, USilIs NjThe similarity function between the ith element and the ith cluster center is expressed as:
Figure FDA0003346959180000024
6. the image segmentation method based on improved intuitive fuzzy c-means clustering according to claim 5, wherein the solution optimization in the intuitive fuzzy set in the step (6) is specifically:
Figure FDA0003346959180000031
Figure FDA0003346959180000032
wherein m is a blurring coefficient, m is not less than 1,
Figure FDA0003346959180000033
a set of noise robust intuitively blurred representations representing pixels of an image,
Figure FDA0003346959180000034
a set of noise robust intuitively-blurred representations representing the cluster centers,
Figure FDA0003346959180000035
and
Figure FDA0003346959180000036
respectively the ith cluster center and pixel xjIs a noise-robust, intuitive fuzzy representation ofijDenotes xjA membership value of 0 to u of the ith cluster centerij≤1，
Figure FDA0003346959180000037
Is that
Figure FDA0003346959180000038
And
Figure FDA0003346959180000039
the expression of (1) is as follows:
Figure FDA00033469591800000310
solving the optimization problem by using a Lagrange multiplier method to obtain the membership degree uijAnd a cluster center
Figure FDA00033469591800000311
The expression of (a) is:
Figure FDA00033469591800000312
Figure FDA00033469591800000313
7. a storage medium having a computer program stored thereon, characterized in that: the computer program, when executed by a computer processor, implements the method of any of claims 1 to 6.
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