CN110245666B - Multi-target interval value fuzzy clustering image segmentation method based on dual-membership-degree driving - Google Patents

Multi-target interval value fuzzy clustering image segmentation method based on dual-membership-degree driving Download PDF

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CN110245666B
CN110245666B CN201910495205.4A CN201910495205A CN110245666B CN 110245666 B CN110245666 B CN 110245666B CN 201910495205 A CN201910495205 A CN 201910495205A CN 110245666 B CN110245666 B CN 110245666B
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赵凤
李超琦
刘汉强
范九伦
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Xian University of Posts and Telecommunications
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Abstract

The invention disclosesA multi-target interval value fuzzy clustering image segmentation method based on dual membership degree driving is provided, which mainly solves the problems of sensitivity to noise and easy falling into local optimum in image segmentation, and has the scheme that: inputting an image to be segmented and setting an initial parameter value; constructing an interval value blurred image; constructing a double-membership-driven global interval value fuzzy compactness function JLNAnd dual membership driven interval value fuzzy separability function SLNPerforming multi-objective evolution on the two objective functions to obtain a non-dominated solution set P; calculating an interval value selection solution index W index driven by double membership degrees, and selecting an optimal chromosome from the non-dominated solution set P by using the index to decode the optimal chromosome to obtain an optimal clustering center; and updating the joint membership matrix by using the optimal clustering center, and obtaining a classification result of the pixel points according to the maximum membership principle. The invention can effectively inhibit noise, prevent local optimization, improve the segmentation accuracy and can be used for identifying natural images.

Description

Multi-target interval value fuzzy clustering image segmentation method based on dual-membership-degree driving
Technical Field
The invention belongs to the field of image processing, and particularly relates to a fuzzy clustering image segmentation method which can be used for identifying natural images.
Background
Image segmentation, as the name implies, is to segment an image into several portions that have characteristics and do not intersect each other, which is a key step from image processing to image analysis. In recent years, researches on image segmentation methods have been receiving high attention from researchers, including a clustering-based method, a threshold-based method, an edge-based method, and a region-based method, wherein the clustering-based method is the focus of the researches. Clustering, as the name implies, is the process of dividing elements in a collection into multiple classes, where similar objects are classified into one class and different objects are classified into different classes. Common clustering methods include a K-means clustering algorithm, a fuzzy clustering algorithm, a spectral clustering algorithm, a hierarchical clustering algorithm and the like, wherein the fuzzy clustering algorithm arouses the interest of researchers.
However, when the conventional fuzzy clustering algorithm, such as the image fuzzy clustering segmentation method based on the two-dimensional histogram proposed by liujianzhuang in 1992, is applied to image segmentation, there are two problems: the first problem is that the algorithm is sensitive to initial values and tends to fall into local optima. In order to solve the problem, in 2019, Majdi introduces an evolutionary algorithm into a fuzzy clustering algorithm, and provides a fuzzy clustering image segmentation algorithm based on the evolutionary algorithm. The second problem is that the traditional fuzzy clustering algorithm is sensitive to noise and has poor effect on processing images containing noise, so that Zhang introduces spatial information into the fuzzy clustering algorithm in 2018, and provides enhanced spatial constraint remote sensing image segmentation based on the fuzzy local double-neighborhood information C-mean clustering algorithm, so that the effects of removing noise and completely segmenting images are achieved. However, when the algorithms are applied to image segmentation, only a single objective function is considered, and in the real production life, the single objective function cannot meet the requirements of users in various aspects, and in 2011, Mukhopadhyay proposes a fuzzy clustering algorithm based on multi-objective evolution to be applied to segmentation of brain images, and the algorithm optimizes two fitness functions of connectivity and total deviation at the same time, and coordinates and balances among a plurality of objective functions, so that all objective functions are optimized as far as possible. However, the above algorithms all use single-valued data, and cannot better mine the uncertainty of the data. Therefore, De Carvalho provides an interval value fuzzy C-mean IVFCM algorithm, the algorithm replaces single-value data with interval value data, uncertainty of data can be better mined, but the algorithm still has the problems of sensitivity to noise, easiness in falling into local optimization and consideration of only a single objective function, and cannot meet various requirements of users.
Disclosure of Invention
The invention aims to provide a multi-target interval value fuzzy clustering image segmentation method based on dual-membership driving, aiming at overcoming the defects of the prior art, so as to reduce the sensitivity to noise, avoid falling into local optimization, consider the image segmentation problem from multiple aspects and improve the segmentation accuracy.
In order to achieve the above object, the technique of the present invention comprises the steps of:
(1) inputting an image to be segmented, and converting the image to be segmented into a gray image if the image to be segmented is a color image;
(2) setting parameters: setting the population size as 100, the iteration times as 50, the maximum class number as 10 and the variation probability as 0.1, and for Gaussian noisy images, limiting the parameters of local spatial information
Figure BDA0002088346870000021
And the non-local spatial information restriction item parameter psi is 6 and 16 respectively, and for the salt-pepper noisy image, the two parameters are set to 16 and 1 respectively;
(3) method for constructing interval value membership of gray level image by using Gaussian fuzzy number
Figure BDA0002088346870000022
And constructing interval value non-membership degree of gray level image by using m-fuzzy compensation operator
Figure BDA0002088346870000023
According to the degree of membership u of the interval valueI(δi) Sum interval value non-membership vI(δi) Obtaining interval value fuzzy image
Figure BDA00020883468700000218
Wherein: deltaiAre the points of pixels that are to be imaged,u(δi) And
Figure BDA0002088346870000024
respectively a left end point and a right end point of the interval value membership degree,v(δi) And
Figure BDA0002088346870000025
the left end point and the right end point of the interval value non-membership degree are respectively;
(4) respectively constructing local membership function eta by using local spatial information and non-local spatial informationkiAnd a non-local membership function uki：
Figure BDA0002088346870000026
Figure BDA0002088346870000027
Wherein m-2 represents a fuzzy weighting index, Y represents the number of classes,
Figure BDA0002088346870000028
the pixel points of the interval value are represented,
Figure BDA0002088346870000029
represents the clustering center of the interval values, d (-) represents the Euclidean distance,
Figure BDA00020883468700000210
to represent
Figure BDA00020883468700000211
Local spatial information of, NiRepresents
Figure BDA00020883468700000212
M is the total number of pixels in the neighborhood, a probability function
Figure BDA00020883468700000213
NkiIs that
Figure BDA00020883468700000214
The number of pixels in the neighborhood that belong to the kth class,
Figure BDA00020883468700000215
obtained by iterative non-local mean algorithm
Figure BDA00020883468700000216
Psi is a non-local spatial information restriction item parameter;
(5) calculating a joint membership function Z according to the result of (4)kiAnd designing a double-membership-driven global interval value fuzzy compactness function JLNAnd dual membership driven interval value fuzzy separability function SLN：
Figure BDA00020883468700000217
Figure BDA0002088346870000031
Figure BDA0002088346870000032
Wherein n is the total number of pixel points, xi 1 and ζ 2 are respectively a local membership function limiting item parameter and a non-local membership function limiting item parameter,
Figure BDA0002088346870000033
and
Figure BDA0002088346870000034
are all interval value clustering centers, ηkiIs that
Figure BDA0002088346870000035
Is subject to
Figure BDA0002088346870000036
Of local membership function ukiIs that
Figure BDA0002088346870000037
Is subject to
Figure BDA0002088346870000038
Is determined by the non-local membership function of (a),
Figure BDA0002088346870000039
is a local spatial information restriction item parameter, # is a non-local spatial information restriction item parameter, ZpqIs that
Figure BDA00020883468700000310
Is subject to
Figure BDA00020883468700000311
A joint membership function of (a);
(6) performing multi-objective evolution on the two objective functions obtained in the step (5) to obtain a final group of interval value non-dominated solution sets P;
(7) combining the interval value blurred image obtained in the step (3)
Figure BDA00020883468700000312
Constructing a dual-membership-driven interval value selection solution index W by the pixel points, selecting an optimal chromosome from the interval value non-dominated solution set P obtained in the step (6) by using the index W, and taking an interval value clustering center coded on the chromosome as an optimal clustering center;
(8) updating the joint membership matrix by using the optimal clustering center obtained in the step (7)
Figure BDA00020883468700000313
And classifying the pixel points according to the maximum membership principle to obtain a segmentation result of the gray level image.
Compared with the prior art, the invention has the following beneficial technical effects:
first, the invention introduces multi-objective evolution into the interval value fuzzy clustering algorithm, solves the problem that the clustering algorithm of a single clustering criterion is easy to fall into local optimum, and the clustering result can meet various requirements of users.
Secondly, the local space information and the non-local space information of the image are respectively utilized to construct a local membership function and a non-local membership function, two interval value fuzzy fitness functions driven by double membership are designed by fusing the two membership functions, and the influence of noise on the image segmentation process is overcome.
Thirdly, the invention automatically adjusts the cross probability according to the fitness function value, improves the searching performance and the searching goodness and leads the segmentation effect to be more ideal.
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FIG. 1 is a flow chart of an implementation of the method of the present invention;
FIG. 2 is a comparison of results of a simulation segmentation of an image numbered 238011 in a Berkeley image database using the present invention and a prior art method;
fig. 3 is a comparison graph of the results of simulation segmentation of the image with number 3096 in the Berkeley image database using the present invention and the existing method.
Detailed Description
The following further describes the practice and effects of the invention in detail:
referring to fig. 1, the implementation steps of the present invention are as follows:
step 1: inputting an image to be segmented and setting initial parameter values.
Inputting all images to be segmented, and converting the images to be segmented into gray images if the images to be segmented are color images;
setting the population size as 100, the iteration times as 50, the maximum class number as 10 and the variation probability as 0.1, and for Gaussian noisy images, limiting the parameters of local spatial information
Figure BDA0002088346870000041
And the non-local spatial information restriction parameter psi is 6 and 16, respectively, which are set to 16 and 1, respectively, for noisy salt-and-pepper images.
Step 2: constructing interval value blurred images
Figure BDA0002088346870000042
2.1) construction of the Pixel Point δ by means of Gauss fuzzy numberiDegree of membership u (delta)i,ε,σ)：
Figure BDA0002088346870000043
Wherein epsilon is 150, sigma is 120;
2.2) calculating the Pixel Point deltaiDegree of membership of interval value of (a):
Figure BDA0002088346870000044
wherein:
u(δi) Is the left end point of the interval value membership degree,
Figure BDA0002088346870000045
the right end points of the interval value membership degrees are respectively expressed as follows:
Figure BDA0002088346870000046
Figure BDA0002088346870000047
wherein e is 2;
2.3) constructing the pixel point delta by using the m-fuzzy compensation operatoriIs not degree of membership v (delta)i) The formula is as follows:
Figure BDA0002088346870000048
wherein w is 0.2;
2.4) calculating the Pixel Point deltaiInterval value of (2) non-membership degree
Figure BDA0002088346870000049
Wherein:
v(δi) The left end point of interval value non-membership degree,
Figure BDA00020883468700000410
the right end points of the interval value non-membership degree are respectively expressed as follows:
v(δi)＝v(δi)+απ(δi)，
Figure BDA00020883468700000411
wherein, alpha is 0.1,
Figure BDA00020883468700000412
π(δi)＝1-u(δi,ε,σ)-v(δi)。
and step 3: and performing multi-objective evolution on the two objective functions to obtain a non-dominated solution set P.
3.1) population initialization: coding each chromosome into 2-10 clustering centers by using a variable length coding method, randomly generating 100 parent chromosomes to form a population, and setting the current iteration number to be 1;
3.2) calculating two objective function values of each chromosome in the population;
3.2.1) calculating the clustering center of interval values
Figure BDA0002088346870000051
And interval value pixel point
Figure BDA0002088346870000052
Euclidean distance of
Figure BDA0002088346870000053
Figure BDA0002088346870000054
3.2.2) calculating interval value pixel points
Figure BDA0002088346870000055
Local spatial information of
Figure BDA0002088346870000056
Figure BDA0002088346870000057
Wherein N isiRepresents
Figure BDA0002088346870000058
The 3 x 3 neighborhood window of (a),
Figure BDA0002088346870000059
is that
Figure BDA00020883468700000510
Neighborhood window NiPixel points with interval values in the neighborhood window, wherein M is the number of the total pixel points in the neighborhood window;
3.2.3) calculating the clustering center of interval values
Figure BDA00020883468700000511
And local spatial information
Figure BDA00020883468700000512
European distance of
Figure BDA00020883468700000513
Figure BDA00020883468700000514
3.2.4) calculating interval value pixel points
Figure BDA00020883468700000515
Is a probability function fki：
Figure BDA00020883468700000516
Wherein N iskiIs that
Figure BDA00020883468700000517
Neighborhood window NiThe number of pixels belonging to the kth class;
3.2.5) calculating a local membership function eta based on the results of 3.2.3) and 3.2.4)ki：
Figure BDA00020883468700000518
Wherein d (-) is Euclidean distance, fkiIs a likelihood function, m-2 represents a fuzzy weighting index, and Y represents the number of categories;
3.2.6) calculating interval value pixel points by using iterative non-local mean algorithm
Figure BDA00020883468700000519
Non-local spatial information of
Figure BDA00020883468700000520
Figure BDA00020883468700000521
Wherein t is the iteration number of the iterative non-local mean algorithm, Wi rRepresenting pixel points by interval values
Figure BDA00020883468700000522
A search window of size 21 x 21 centered,
Figure BDA00020883468700000523
is shown in
Figure BDA00020883468700000524
Interval-value pixel point in centered neighborhood window
Figure BDA00020883468700000525
The formula is as follows:
Figure BDA00020883468700000526
wherein h is a control weight function
Figure BDA0002088346870000061
The parameters of the attenuation are such that,
Figure BDA0002088346870000062
is of GaussWeighted Euclidean distance, χ is the standard deviation of the Gaussian kernel, N (-) is the similarity window, ZiTo normalize the constants, the formula is as follows:
Figure BDA0002088346870000063
3.2.7) calculating the clustering center of the interval value according to the result of 3.2.6)
Figure BDA0002088346870000064
And non-local spatial information
Figure BDA0002088346870000065
European distance of
Figure BDA0002088346870000066
Figure BDA0002088346870000067
3.2.8) calculating a non-local membership function u) based on the results of 3.2.3) and 3.2.7)ki：
Figure BDA0002088346870000068
Wherein n is the total number of pixel points, and psi is a non-local spatial information restriction item parameter;
3.2.9) calculating a double-membership-driven global interval value fuzzy compactness function J) according to the results of 3.2.4), 3.2.5) and 3.2.8)LNThe value of (c):
Figure BDA0002088346870000069
wherein,
Figure BDA00020883468700000610
is a local spatial information constraint term parameter;
3.2.10) calculating a joint membership function Z based on the results of 3.2.5) and 3.2.8)ki：
Figure BDA00020883468700000611
Where ξ ═ 1 and ζ ═ 2 are the local membership function constraint term parameter and the non-local membership function constraint term parameter, respectively;
3.2.11) calculating an interval value clustering center
Figure BDA00020883468700000612
And
Figure BDA00020883468700000613
european distance of
Figure BDA00020883468700000614
Figure BDA00020883468700000615
3.2.12) according to the results of 3.2.10) and 3.2.11), calculating a dual-membership-driven interval value fuzzy separability function SLNThe value of (c):
Figure BDA00020883468700000616
wherein,
Figure BDA00020883468700000617
and
Figure BDA00020883468700000618
are all interval value clustering centers, ZpqIs that
Figure BDA00020883468700000619
Is subject to
Figure BDA00020883468700000620
A joint membership function of (a);
3.2.13) encoding the two objective function values sequentially onto the chromosome;
3.3) carrying out non-dominated sorting on the parent chromosomes by using the target numerical value, and sequentially coding the obtained sequence value and the obtained crowding distance on the chromosomes;
3.4) selecting 50 chromosomes from the population as parents by using a binary tournament method;
3.5) pairing of parent chromosomes
Figure BDA0002088346870000071
And
Figure BDA0002088346870000072
performing a Laplace crossover to generate offspring chromosomes, wherein,
Figure BDA0002088346870000073
representing a code on the parent chromosome P1The upper tau interval values cluster the center,
Figure BDA0002088346870000074
representing a code on the parent chromosome P2The upper gamma interval value clustering centers;
3.5.1) calculating the crossover probability pc：
Figure BDA0002088346870000075
Wherein p iscmax0.9 is the maximum crossover probability, pcmin0.5 is the minimum cross probability, two indices σ1And σ2The calculation formula of (a) is as follows:
Figure BDA0002088346870000076
Figure BDA0002088346870000077
wherein,
Figure BDA0002088346870000078
and
Figure BDA0002088346870000079
respectively representing two objective function values of the first parent chromosome,
Figure BDA00020883468700000710
and
Figure BDA00020883468700000711
respectively representing two objective function values of the second parent chromosome,
Figure BDA00020883468700000712
and
Figure BDA00020883468700000713
respectively, the average values of the two objective function values of all chromosomes in the population;
3.5.2) calculating offspring chromosome C(1)Upper interval value clustering center
Figure BDA00020883468700000714
And progeny chromosome C(2)Upper interval value clustering center
Figure BDA00020883468700000715
The formula is as follows:
Figure BDA00020883468700000716
Figure BDA00020883468700000717
wherein, | - | represents an absolute value,
Figure BDA00020883468700000718
and
Figure BDA00020883468700000719
are all the interval value cluster centers on the first parent chromosome,
Figure BDA00020883468700000720
and
Figure BDA00020883468700000721
is the clustering center of the interval value on the second parent chromosome, and is a random number obeying Laplace distribution, and the calculation formula is as follows:
Figure BDA00020883468700000722
wherein rand is a random number between 0 and 1 which accords with normal distribution, and the values of the positioning parameter a and the scale parameter b are both 0.5;
3.5.3) obtaining the offspring chromosome C according to the result of 3.5.2)(1)And progeny chromosome C(2)The formula is as follows:
Figure BDA0002088346870000081
Figure BDA0002088346870000082
wherein,
Figure BDA0002088346870000083
is encoded in offspring chromosome C(1)The upper theta interval values cluster the center,
Figure BDA0002088346870000084
is encoded in offspring chromosome C(2)P interval value cluster centers;
3.6) selecting the k-th interval value clustering center
Figure BDA0002088346870000085
D-th dimension value c ofkdCarrying out interval value fuzzy Poisson variation, and obtaining the gene locus value after variation
Figure BDA0002088346870000086
The following were used:
Figure BDA0002088346870000087
wherein u (c)kd) Is ckdDegree of membership of, pi (c)kd) Is ckdHesitation degree of;
3.7) circulating from 3.2) to 3.6), and stopping iteration when the maximum iteration times is reached to obtain a filial generation population;
3.8) selecting 100 chromosomes from the parent population and the child population obtained in the step 3.4) and the step 3.7) by using an elite strategy, decoding the 100 chromosomes to obtain an interval value clustering center, wherein the interval value clustering center is the final non-dominated solution set P.
And 4, step 4: the optimal chromosome is selected.
4.1) calculating a double-membership-driven interval value solution index W:
Figure BDA0002088346870000088
wherein,
Figure BDA0002088346870000089
is the center of the interval value cluster and,
Figure BDA00020883468700000810
is an interval value pixel point, d (-) represents the Euclidean distance, m 2 represents the fuzzy weighting index,
Figure BDA00020883468700000811
is a regionMean value clustering center
Figure BDA00020883468700000812
Average value of (2), ZkiIs a joint membership function, nkRepresenting the total number of pixel points belonging to the kth class;
4.2) selecting a solution index W by using an interval value driven by double membership degrees, selecting an optimal chromosome from the interval value non-dominated solution set P obtained in the step 3, and taking an interval value clustering center coded on the chromosome as an optimal clustering center.
And 5: and outputting the result of the image segmentation.
Updating the joint membership matrix by using the optimal clustering center obtained in the step 4
Figure BDA0002088346870000091
And classifying the pixel points according to the maximum membership principle to obtain a segmentation result of the gray level image.
The technical effects of the invention are further explained by combining simulation experiments as follows:
1. simulation conditions are as follows:
the simulation experiment was performed in the software environment of computer Inter (R) core (TM) i5-3230M 2.60GHZ CPU, 4G memory, MATLAB R2014 a.
2. Simulation content:
simulation 1, selecting an image with the number of 238011 in a Berkeley image database, and segmenting the image by using the method of the invention and the existing FCM method, FCM _ S1 method, IFCM method, IT2FCM method, IVFCM method, MOVGA method and MSFCA method respectively, wherein the result is shown in FIG. 2, wherein:
2(a) is an original image of the 238011 image;
2(b) is a standard segmentation map of the 238011 image;
2(c) is a salt-and-pepper noisy image of 238011 images, with a noise intensity of 0.05;
2(d) is the segmentation result of the salt-pepper noisy image of 238011 image by the existing FCM method;
2(e) is the segmentation result of the salt-pepper noisy image of 238011 image by the existing FCM _ S1 method;
2(f) is the segmentation result of the salt-pepper noisy image of the 238011 image by the existing IFCM method;
2(g) is the segmentation result of the salt-pepper noisy image of 238011 image by the existing IT2FCM method;
2(h) is the segmentation result of the salt-pepper noisy image of 238011 image by the existing IVFCM method;
2(i) is the segmentation result of the noisy pepper salt image of 238011 image by the existing MOVGA method;
2(j) is the segmentation result of the salt-pepper noisy image of 238011 image by the existing MSFCA method;
2(k) is the segmentation result of the salt-pepper noisy image of 238011 image by the present invention;
2(l) is a gaussian noise-containing image of 238011 images, with a noise intensity of 0.005;
2(m) is the result of segmentation of the gaussian noisy image of 238011 images using the existing FCM method;
2(n) is the result of segmentation of a gaussian noisy image of 238011 images using the existing FCM _ S1 method;
2(o) is a result of segmenting a gaussian noisy image of the 238011 image by the existing IFCM method;
2(p) is the result of segmentation of the gaussian noisy image of the 238011 image using the existing IT2FCM method;
2(q) is a result of segmenting a gaussian noisy image of the 238011 image by the existing IVFCM method;
2(r) is the result of segmentation of the gaussian noisy image of the 238011 image using the existing MOVGA method;
2(s) is a result of segmenting a gaussian noisy image of the 238011 image by using the existing MSFCA method;
2(t) is the result of the segmentation of the gaussian noisy image of 238011 images using the present invention;
as can be seen from FIG. 2, the background and the target can be separated on the basis of noise suppression, so the segmentation effect of the method on the noisy image is better than that of the existing FCM method, FCM _ S1 method, IFCM method, IT2FCM method, IVFCM method, MOVGA method and MSFCA method.
Simulation 2, selecting an image with the number of 3096 in a Berkeley image database, and segmenting the image by using the method of the present invention and the existing FCM method, FCM _ S1 method, IFCM method, IT2FCM method, IVFCM method, MOVGA method and MSFCA method, respectively, wherein the result is shown in FIG. 3, wherein:
3(a) is an original image of 3096 image;
3(b) is a standard segmentation map of the 3096 image;
3(c) is a noisy pepper salt image of 3096 image with a noise intensity of 0.05;
3(d) is the segmentation result of the salt-pepper noisy image of 3096 image by the existing FCM method;
3(e) is the segmentation result of the salt-pepper noisy image of 3096 image by the existing FCM _ S1 method;
3(f) is the segmentation result of the salt-pepper noisy image of 3096 image by the existing IFCM method;
3(g) is the segmentation result of the salt-pepper noisy image of 3096 image by the existing IT2FCM method;
3(h) is the segmentation result of the salt-pepper noisy image of 3096 image by the existing IVFCM method;
3(i) is the segmentation result of the pepper salt noisy image of 3096 image by the existing MOVGA method;
3(j) is the segmentation result of the salt-pepper noisy image of 3096 image by the existing MSFCA method;
3(k) is the segmentation result of the salt-pepper noisy image of 3096 image by the invention;
3(l) is a Gaussian noisy image of image 3096, with a noise intensity of 0.005;
3(m) is the result of segmentation of the gaussian noisy image of 3096 images using the existing FCM method;
3(n) is the result of segmentation of the gaussian noisy image of 3096 image using the existing FCM _ S1 method;
3(o) is a result of segmenting the gaussian noisy image of 3096 image by the existing IFCM method;
3(p) is the result of segmentation of the gaussian noisy image of 3096 images using the existing IT2FCM method;
3(q) is a result of segmenting the gaussian noisy image of 3096 image by the existing IVFCM method;
3(r) is the result of segmentation of the gaussian noisy image of 3096 image by the existing MOVGA method;
3(s) is the result of segmentation of the gaussian noisy image of 3096 images using the existing MSFCA method;
3(t) is the result of the segmentation of the Gaussian noisy image of 3096 image by the present invention;
as can be seen from fig. 3, the present invention can separate the background and the object based on the noise suppression, and the segmentation effect on the noisy image is better than that of the existing FCM method, FCM _ S1 method, IFCM method, IT2FCM method, IVFCM method, MOVGA method and MSFCA method.

Claims (6)

1. A multi-target interval value fuzzy clustering image segmentation method based on dual membership degree driving is characterized by comprising the following steps:
(1) inputting an image to be segmented, and converting the image to be segmented into a gray image if the image to be segmented is a color image;
(2) setting parameters: setting the population size as 100, the iteration times as 50, the maximum class number as 10 and the variation probability as 0.1, and for Gaussian noisy images, limiting the parameters of local spatial information
Figure FDA0002920359300000011
And the non-local spatial information restriction item parameter psi is 6 and 16 respectively, and for the salt-pepper noisy image, the two parameters are set to 16 and 1 respectively;
(3) method for constructing interval value membership of gray level image by using Gaussian fuzzy number
Figure FDA0002920359300000012
And constructing interval value non-membership degree of gray level image by using m-fuzzy compensation operator
Figure FDA0002920359300000013
According to the degree of membership u of the interval valueI(δi) Sum interval value non-membership vI(δi) Obtaining interval value fuzzy image
Figure FDA0002920359300000014
Wherein: deltaiAre the points of pixels that are to be imaged,u(δi) And
Figure FDA0002920359300000015
respectively a left end point and a right end point of the interval value membership degree,v(δi) And
Figure FDA0002920359300000016
the left end point and the right end point of the interval value non-membership degree are respectively;
(4) respectively constructing local membership function eta by using local spatial information and non-local spatial informationkiAnd a non-local membership function uki：
Figure FDA0002920359300000017
Figure FDA0002920359300000018
Wherein m-2 represents a fuzzy weighting index, Y represents the number of classes,
Figure FDA0002920359300000019
the pixel points of the interval value are represented,
Figure FDA00029203593000000110
an interval value cluster center representing the kth class,
Figure FDA00029203593000000111
an interval value cluster center representing the l-th class; d (-) represents the Euclidean distance,
Figure FDA00029203593000000112
to represent
Figure FDA00029203593000000113
The local spatial information of (a) the local spatial information,
Figure FDA00029203593000000114
is that
Figure FDA00029203593000000115
Neighborhood window NiPixel points with inner interval values; n is a radical ofiRepresents
Figure FDA00029203593000000116
3 x 3 neighborhood window of (a), M is the total number of pixels in the neighborhood, the probability function of pixel i to class k
Figure FDA00029203593000000117
NkiIs that
Figure FDA00029203593000000118
Number of pixels in the neighborhood that belong to the kth class, fliA likelihood function representing pixel i for class i;
Figure FDA00029203593000000119
obtained by iterative non-local mean algorithm
Figure FDA0002920359300000021
Psi is a non-local spatial information restriction item parameter;
(5) calculating a joint membership function Z according to the result of (4)kiAnd designing a double-membership-driven global interval value fuzzy compactness function JLNAnd dual membership driven interval value fuzzy separability function SLN：
Figure FDA0002920359300000022
Figure FDA0002920359300000023
Figure FDA0002920359300000024
Wherein n is the total number of pixel points, xi 1 and ζ 2 are respectively a local membership function limiting item parameter and a non-local membership function limiting item parameter,
Figure FDA0002920359300000025
and
Figure FDA0002920359300000026
are all interval value clustering centers, ηkiIs that
Figure FDA0002920359300000027
Is subject to
Figure FDA0002920359300000028
Of local membership function ukiIs that
Figure FDA0002920359300000029
Is subject to
Figure FDA00029203593000000210
Is determined by the non-local membership function of (a),
Figure FDA00029203593000000211
is a local spatial information restriction item parameter, # is a non-local spatial information restriction item parameter, ZpqIs that
Figure FDA00029203593000000212
Is subject to
Figure FDA00029203593000000213
A joint membership function of (a);
(6) for two objective functions J obtained in (5)LNAnd SLNPerforming multi-objective evolution to obtain a final group of interval value non-dominated solution sets P;
(7) combining the interval value blurred image obtained in the step (3)
Figure FDA00029203593000000219
Constructing a dual-membership-driven interval value selection solution index W by the pixel points, selecting an optimal chromosome from the interval value non-dominated solution set P obtained in the step (6) by using the index W, and taking an interval value clustering center coded on the chromosome as an optimal clustering center;
(8) updating the joint membership matrix by using the optimal clustering center obtained in the step (7)
Figure FDA00029203593000000214
And classifying the pixel points according to the maximum membership principle to obtain a segmentation result of the gray level image.
2. The method of claim 1, wherein (3) the left endpoint of the membership degree of the interval valueu(δi) And a right endpoint
Figure FDA00029203593000000215
Respectively, as follows:
Figure FDA00029203593000000216
Figure FDA00029203593000000217
wherein, e is 2,
Figure FDA00029203593000000218
ε＝150，σ＝120。
3. the method of claim 1, wherein (3) the left endpoint of interval value non-membershipv(δi) And a right endpoint
Figure FDA0002920359300000031
Respectively, as follows:
v(δi)＝v(δi)+απ(δi)，
Figure FDA0002920359300000032
wherein, alpha is 0.1,
Figure FDA0002920359300000033
π(δi)＝1-u(δi,ε,σ)-v(δi)
Figure FDA0002920359300000034
Figure FDA0002920359300000035
4. the method according to claim 1, wherein in (3), the degree of membership u is determined according to the interval valueI(δi) Sum interval value non-membership vI(δi) Obtaining interval value fuzzy image
Figure FDA0002920359300000036
It is represented as follows:
Figure FDA0002920359300000037
5. the method of claim 1, wherein the multi-objective evolution of the two objective functions in (6) is implemented as follows:
(6a) population initialization: encoding each chromosome into 2-10 clustering centers by using a variable length encoding method, randomly generating 100 parent chromosomes to form a population, and setting the current iteration number to be 1;
(6b) two objective function values for each chromosome in the population are calculated:
(6b1) calculating interval value clustering centers
Figure FDA0002920359300000038
And interval value pixel point
Figure FDA0002920359300000039
Euclidean distance of
Figure FDA00029203593000000310
(6b2) Calculating interval value pixel points
Figure FDA00029203593000000311
Local spatial information of
Figure FDA00029203593000000312
Wherein N isiRepresents
Figure FDA00029203593000000313
The 3 x 3 neighborhood window of (a),
Figure FDA00029203593000000314
is that
Figure FDA00029203593000000315
Neighborhood window NiPixel points with interval values in the neighborhood window, wherein M is the number of the total pixel points in the neighborhood window;
(6b3) calculating interval value clustering centers
Figure FDA00029203593000000316
And local spatial information
Figure FDA00029203593000000317
European distance of
Figure FDA00029203593000000318
(6b4) Computing a likelihood function
Figure FDA00029203593000000319
Wherein N iskiIs that
Figure FDA00029203593000000320
Neighborhood window NiThe number of pixels belonging to the kth class in the neighborhood window, and M is the number of total pixels in the neighborhood window;
(6b5) will Euclidean distance
Figure FDA00029203593000000321
Local spatial information
Figure FDA00029203593000000322
And a probability function fkiSubstituted type<1>Calculating a local membership function etaki；
(6b6) Calculating interval value pixel points by using iterative non-local mean algorithm
Figure FDA00029203593000000323
Non-local spatial information of
Figure FDA00029203593000000324
(6b7) Calculating interval value clustering centers
Figure FDA0002920359300000041
And non-local spatial information
Figure FDA0002920359300000042
European distance of
Figure FDA0002920359300000043
(6b8) Will Euclidean distance
Figure FDA0002920359300000044
And Euclidean distance
Figure FDA0002920359300000045
Substituted type<2>Calculating a non-local membership function uki；
(6b9) A function η of local membershipkiNon-local membership function ukiAnd a probability function fkiSubstituted type<4>Calculating a fuzzy compactness function J of the global interval value driven by the double membership degreesLNA value of (d);
(6b10) a function η of local membershipkiAnd a non-local membership function ukiSubstituted type<3>Calculating a joint membership function Zki；
(6b11) Calculating interval value clustering centers
Figure FDA0002920359300000046
And
Figure FDA0002920359300000047
european distance of
Figure FDA0002920359300000048
(6b12) Will Euclidean distance
Figure FDA0002920359300000049
And joint membership function ZkiSubstituted type<5>Calculating interval value of dual membership degree driveFuzzy separability function SLNA value of (d);
(6b13) encoding the two objective function values onto a chromosome in sequence;
(6c) carrying out non-dominated sorting on the parent chromosomes by using the target numerical values, and sequentially encoding the obtained sequence values and the crowding distances to the chromosomes;
(6d) selecting 50 chromosomes from the population as parents by using a binary tournament method;
(6e) carrying out Laplace crossing and interval value fuzzy Poisson variation on the parent chromosome to generate offspring;
(6f) looping (6b) through (6e), and stopping iteration when the maximum iteration number is reached;
(6g) and (3) selecting 100 chromosomes from the parent population and the child population obtained in the step (6d) and the step (6e) by using an elite strategy, and decoding the 100 chromosomes to obtain an interval value clustering center, wherein the interval value clustering center is the final non-dominated solution set P.
6. The method according to claim 1, wherein the interval value solution index W of the dual membership degree driving constructed in (7) is expressed as follows:
Figure FDA00029203593000000410
wherein,
Figure FDA00029203593000000411
is the center of the interval value cluster and,
Figure FDA00029203593000000412
is an interval value pixel point, d (-) represents an Euclidean distance, m 2 represents a fuzzy weighting index, Y is the maximum category number, n is the total number of the pixel points,
Figure FDA00029203593000000413
is interval value clustering center
Figure FDA00029203593000000414
Average value of (2), ZkiIs a joint membership function, nkRepresenting the total number of pixels belonging to the kth class.
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