CN110245666A - Multiple target Interval Valued Fuzzy based on dual membership driving clusters image partition method - Google Patents
Multiple target Interval Valued Fuzzy based on dual membership driving clusters image partition method Download PDFInfo
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Abstract
The invention discloses a kind of multiple target Interval Valued Fuzzies based on dual membership driving to cluster image partition method, it mainly solves the problems, such as in image segmentation to noise-sensitive, be easily trapped into local optimum, scheme is: inputting image to be split and initial parameter value is arranged；Construct interval value blurred picture；Construct the global Interval Valued Fuzzy compactness function J of dual membership drivingLNWith the Interval Valued Fuzzy separability function S of dual membership drivingLN, and multi-target evolution is carried out to the two objective functions, obtain non-dominant disaggregation P；The interval value choosing solution index W index for calculating dual membership driving, selects optimal chromosome from non-dominant disaggregation P with the index and is decoded to it, obtain Optimal cluster centers；Joint subordinated-degree matrix is updated with Optimal cluster centers, and the classification results of pixel are obtained according to maximum membership grade principle.The present invention can effectively inhibit noise, prevent from falling into local optimum, improve segmentation accuracy rate, can be used for the identification of natural image.
Description
Technical field
The invention belongs to field of image processings, and in particular to a kind of fuzzy clustering image partition method can be used for nature figure
The identification of picture.
Background technique
Image segmentation is as its name suggests that piece image is divided into each tool characteristic and several mutually disjoint parts, it
It is the committed step from image procossing to image analysis.In recent years, the research of image partition method is constantly subjected to researchers'
It pays high attention to, including the method based on cluster, the method based on threshold value, the method based on edge and based on the method in region,
In the method based on cluster be research emphasis.Cluster, as the term suggests it is exactly the process for the element in set being divided into multiple classes,
Wherein similar object is divided into one kind, and different objects is classified as different classes.Common clustering method includes that K- mean cluster is calculated
Method, fuzzy clustering algorithm, spectral clustering and hierarchical clustering algorithm etc., wherein fuzzy clustering algorithm causes numerous researchers'
Interest.
But traditional fuzzy clustering algorithm, such as the image mould based on two-dimensional histogram that Liu Jianzhuan was proposed in 1992
When paste cluster segmentation method is applied to image segmentation, there are problems that two: first problem is that algorithm is sensitive to initial value, is easy
Fall into local optimum.In order to solve this problem, evolution algorithm is introduced into fuzzy clustering algorithm by Majdi in 2019, is proposed
Fuzzy clustering image segmentation algorithm based on evolution algorithm.Second Problem is that traditional fuzzy clustering algorithm compares noise
Sensitivity, the image effect for handling Noise is bad, so spatial information was introduced into fuzzy clustering algorithm in 2018 by Zhang
In, the enhanced space constraint Remote Sensing Image Segmentation based on the double neighborhood information C- means clustering algorithms in fuzzy part is proposed, is reached
The effect of removal noise and full segmentation image is arrived.But these algorithms all only considered single when being applied to image segmentation
Objective function, since in the production and living of reality, single target function is unable to satisfy many-sided demand of user, 2011,
Mukhopadhyay proposes the segmentation that the fuzzy clustering algorithm based on multi-target evolution is applied to brain image, and the algorithm is simultaneously
Optimize two fitness functions of connectivity and population deviation, coordinates tradeoff between multiple objective functions, so that all target letters
Number is optimal as far as possible.But algorithm above all uses single-value data, cannot preferably mining data uncertainty.
For this purpose, De Carvalho proposes Interval Valued Fuzzy C- mean value IVFCM algorithm, which replaces monodrome using interval valued data
Data, can preferably mining data uncertainty, but still remain to noise-sensitive, be easily trapped into local optimum and
The problem of only considered single target function is not able to satisfy the various demands of user.
Summary of the invention
It is an object of the invention to for above there is deficiency existing for technology, provide a kind of more mesh based on dual membership driving
It marks Interval Valued Fuzzy and clusters image partition method, to reduce the sensibility to noise, avoid falling into local optimum, and from many aspects
Consider the segmentation problem of image, improves segmentation accuracy.
To achieve the above object, technology of the invention includes the following steps:
(1) image to be split is inputted, if image to be split is color image, is first converted into gray level image；
(2) parameter is arranged: setting population scale is 100, the number of iterations 50, and maximum classification number is 10, and mutation probability is
0.1, for Gauss noisy image, local spatial information limit entry parameterDistinguish with non local spatial information limit entry parameter ψ
For 6 and 16, for spiced salt noisy image, the two parameters are respectively set to 16 and 1；
(3) the interval value degree of membership of Gaussian Blur number construction gray level image is utilizedAnd utilize m-
The interval value non-affiliated degree of fuzzy complementary operator construction gray level imageAccording to interval value degree of membership uI(δi)
With interval value non-affiliated degree vI(δi) obtain Interval Valued Fuzzy imageWherein: δiIt is pixel,u(δi) andIt is respectively
The left end point and right endpoint of interval value degree of membership,v(δi) andIt is the left end point and right endpoint of interval value non-affiliated degree respectively；
(4) local subordinating degree function η is constructed respectively using local spatial information and non local spatial informationkiWith non local person in servitude
Category degree function uki:
Wherein, m=2 represents FUZZY WEIGHTED index, and Y represents classification number,Indicate interval value pixel,Indicate interval value
Cluster centre, d () represent Euclidean distance,It indicatesLocal spatial information, NiIt represents3 × 3 neighborhoods
Window, M are total pixel number in neighborhood, plausibility functionNkiIt isBelong to the pixel of kth class in neighborhood
Number,It is to be acquired using iteration non-local mean algorithmNon local spatial information, ψ is the limitation of non-local spatial information
Item parameter；
(5) joint subordinating degree function Z is calculated according to the result of (4)ki, and design the global interval value mould of dual membership driving
Paste compactness function JLNWith the Interval Valued Fuzzy separability function S of dual membership drivingLN:
Wherein, n is pixel total number, and ξ=1 and ζ=2 are local subordinating degree function limit entry parameter respectively and non local
Subordinating degree function limit entry parameter,WithIt is interval value cluster centre, ηkiIt isIt is under the jurisdiction ofLocal subordinating degree function,
ukiIt isIt is under the jurisdiction ofNon local subordinating degree function,It is local spatial information limit entry parameter, ψ is non-local spatial information
Limit entry parameter, ZpqIt isIt is under the jurisdiction ofJoint subordinating degree function；
(6) multi-target evolution is carried out to two objective functions that (5) obtain, obtains a final class interval value non-domination solution
Collect P；
(7) the Interval Valued Fuzzy image obtained in conjunction with (3)Pixel construct dual membership driving interval value choosing
Index W is solved, selects an optimal chromosome from the non-dominant disaggregation P of interval value that (6) obtain using index W, and by the dye
The interval value cluster centre encoded on colour solid is as Optimal cluster centers；
(8) Optimal cluster centers for utilizing (7) to obtain update joint subordinated-degree matrixAnd it is subordinate to according to maximum
Category degree principle classifies pixel, obtains the segmentation result of gray level image.
Compared with prior art, the invention has the following beneficial technical effects:
First, multi-target evolution is introduced into Interval Valued Fuzzy clustering algorithm by the present invention, solves single clustering criteria
Clustering algorithm the problem of easily falling into local optimum, and cluster result can satisfy many-sided demand of user.
Second, the present invention is utilized respectively the local spatial information of image and non local spatial information constructs local degree of membership
Function and non local subordinating degree function, and the interval value that two dual memberships drive is devised by merging two subordinating degree functions
Fuzzy fitness function, overcomes the influence of noise on image cutting procedure.
Third, the present invention automatically adjust crossover probability according to fitness function value, improve search property and optimizing, so that
Segmentation effect is even more ideal.
Detailed description of the invention
Fig. 1 is the implementation flow chart of the method for the present invention；
Fig. 2 is that the image for being 238011 to the number in Berkeley image data base with the present invention and existing method carries out
Emulate the comparative result figure of segmentation；
Fig. 3 is that the image for being 3096 to the number in Berkeley image data base with the present invention and existing method is imitated
The comparative result figure really divided.
Specific embodiment
The implementation of invention and effect are described in further detail below:
Referring to Fig. 1, steps are as follows for realization of the invention:
Step 1: inputting image to be split and initial parameter value is set.
Input it is all want image to be split, if image to be split be color image, be first converted into gray level image；
If population scale is 100, the number of iterations 50, maximum classification number is 10, and mutation probability 0.1 contains Gauss
It makes an uproar image, local spatial information limit entry parameterIt is respectively 6 and 16 with non local spatial information limit entry parameter ψ, for green pepper
Salt noisy image, the two parameters are respectively set to 16 and 1.
Step 2: building Interval Valued Fuzzy image
2.1) pixel δ is constructed using Gaussian Blur numberiDegree of membership u (δi, ε, σ):
Wherein, ε=150, σ=120；
2.2) pixel δ is calculatediInterval value degree of membership:Wherein:
u(δi) be interval value degree of membership left end point,For the right endpoint of interval value degree of membership, respectively indicate as follows:
Wherein, e=2；
2.3) complementary operator is obscured using m- construct pixel δiNon-affiliated degree v (δi), formula is as follows:
Wherein, w=0.2；
2.4) pixel δ is calculatediInterval value non-affiliated degreeWherein:
v(δi) be interval value non-affiliated degree left end point,For the right endpoint of interval value non-affiliated degree, respectively indicate as
Under:
v(δi)=v (δi)+απ(δi),
Wherein, α=0.1,π(δi)=1-u (δi,ε,σ)-v(δi)。
Step 3: multi-target evolution being carried out to two objective functions, obtains non-dominant disaggregation P.
3.1) initialization of population: using variable-length coding method by each chromosome coding be 2 to 10 cluster centres, with
Machine generates 100 parent chromosomes and constitutes a population, and sets current iteration number as 1；
3.2) two target function values of each chromosome in population are calculated；
3.2.1) computation interval value cluster centreWith interval value pixelEuclidean distance
3.2.2) computation interval value pixelLocal spatial information
Wherein, NiIt represents3 × 3 neighborhood windows,It isNeighborhood window NiInterior interval value pixel, M are in neighborhood window
The number of total pixel；
3.2.3) computation interval value cluster centreWith local spatial informationEuclidean distance
3.2.4) computation interval value pixelA possibility that function fki:
Wherein, NkiIt isNeighborhood window NiInside belong to the number of the pixel of kth class；
3.2.5) according to 3.2.3) and 3.2.4) as a result, calculating local subordinating degree function ηki:
Wherein, d () is Euclidean distance, fkiIt is plausibility function, m=2 represents FUZZY WEIGHTED index, and Y represents classification number；
3.2.6 iteration non-local mean algorithm computation interval value pixel) is usedNon local spatial information
Wherein, t is the number of iterations of iteration non-local mean algorithm, Wi rIt indicates with interval value pixelCentered on it is big
Small is 21 × 21 search window,Indicate withCentered on neighborhood window in interval value pixelWeight, formula is such as
Under:
Wherein, h is weight functionThe parameter of decaying,It is Gauss weighted euclidean distance, χ is Gaussian kernel mark
Quasi- deviation, N () are similar window, ZiTo normalize constant, formula is as follows:
3.2.7) according to 3.2.6) as a result, computation interval value cluster centreWith non local spatial informationIt is European away from
From
3.2.8) according to 3.2.3) and 3.2.7) as a result, calculating non local subordinating degree function uki:
Wherein, n is the total number of pixel, and ψ is non-local spatial information limit entry parameter；
3.2.9) according to 3.2.4), 3.2.5) and 3.2.8) as a result, calculate dual membership driving global interval value mould
Paste compactness function JLNValue:
Wherein,It is local spatial information limit entry parameter；
3.2.10) according to 3.2.5) and 3.2.8) as a result, calculate joint subordinating degree function Zki:
Wherein, ξ=1 and ζ=2 are local subordinating degree function limit entry parameter and non local subordinating degree function limit entry respectively
Parameter；
3.2.11) computation interval value cluster centreWithEuclidean distance
3.2.12) according to 3.2.10) and 3.2.11) as a result, calculate dual membership driving Interval Valued Fuzzy separability
Function SLNValue:
Wherein,WithIt is interval value cluster centre, ZpqIt isIt is under the jurisdiction ofJoint subordinating degree function；
3.2.13) two target function values are successively encoded on chromosome；
3.3) non-dominated ranking carried out to parent chromosome using target value, and by obtained sequence value and crowding distance according to
It is secondary to be encoded on chromosome；
3.4) 50 chromosomes are selected from population as parent using binary system tournament method；
3.5) to parent chromosomeWithLaplace intersection is carried out, is generated
Child chromosome, whereinCoding is represented in parent chromosome P1On τ interval value cluster centre,Coding is represented in parent chromosome P2On γ interval value cluster centre；
3.5.1 crossover probability p) is calculatedc:
Wherein, pcmax=0.9 is maximum crossover probability, pcmin=0.5 is minimum crossover probability, two index σ1And σ2's
Calculation formula is as follows:
Wherein,WithTwo target function values of first parent chromosome are respectively indicated,WithRespectively
Indicate two target function values of second parent chromosome,WithIt is two mesh of all chromosomes in population respectively
The average value of offer of tender numerical value；
3.5.2 child chromosome C) is calculated(1)On interval value cluster centreWith child chromosome C(2)On interval value
Cluster centreFormula is as follows:
Wherein, | | absolute value is represented,WithIt is all the interval value cluster centre on first parent chromosome,WithIt is all the interval value cluster centre on second parent chromosome, δ is the random number for obeying Laplace distribution, is calculated
Formula is as follows:
Wherein, rand is the random number met between 0 to the 1 of normal distribution, and positional parameter a and scale parameter b are
Value is 0.5；
3.5.3) according to 3.5.2) as a result, obtaining child chromosome C(1)With child chromosome C(2), formula is as follows:
Wherein,It is coding in child chromosome C(1)On θ interval value cluster centre,It is coding in child chromosome C(2)On ρ interval value cluster centre；
3.6) k-th of interval value cluster centre is chosenD dimension value ckdInterval Valued Fuzzy Poisson variation is carried out, is become
Gene place value after differentIt is as follows:
Wherein, u (ckd) it is ckdDegree of membership, π (ckd) it is ckdHesitation degree；
3.7) circulation when the maximum number of iterations is reached, then stops iteration, obtains a progeny population 3.2) to 3.6)；
3.4) and 3.7) 3.8) 100 chromosomes are selected from the parent and progeny population obtained using elitism strategy,
This 100 chromosomes are decoded, interval value cluster centre is obtained, which is final non-domination solution
Collect P.
Step 4: selecting optimal chromosome.
4.1) the interval value choosing solution index W of dual membership driving is calculated:
Wherein,It is interval value cluster centre,It is interval value pixel, d () represents Euclidean distance, and m=2 represents mould
Weighted Index is pasted,It is interval value cluster centreAverage value, ZkiIt is joint subordinating degree function, nkRepresentative belongs to
The pixel total number of kth class；
4.2) the interval value choosing solution index W driven with dual membership, from the non-dominant disaggregation P of interval value that step 3 obtains,
An optimal chromosome is selected, and using the interval value cluster centre encoded on the chromosome as Optimal cluster centers.
Step 5: the result after output image segmentation.
Joint subordinated-degree matrix is updated using the Optimal cluster centers that step 4 obtainsAnd it is subordinate to according to maximum
Degree principle classifies pixel, obtains the segmentation result of gray level image.
Below in conjunction with emulation experiment, technical effect of the invention is described further:
1. simulated conditions:
Emulation experiment is in computer Inter (R) Core (TM) i5-3230M 2.60GHZ CPU, 4G memory, MATLAB
It is carried out under R2014a software environment.
2. emulation content:
The image that the number in Berkeley image data base is 238011 is chosen in emulation 1, with the present invention and existing FCM
Method, FCM_S1 method, IFCM method, IT2FCM method, IVFCM method, MOVGA method and MSFCA method respectively to its into
Row segmentation, as a result as shown in Figure 2, in which:
2 (a) be the original image of 238011 images；
2 (b) be the Standard Segmentation figure of 238011 images；
2 (c) be the spiced salt noisy image of 238011 images, noise intensity 0.05；
2 (d) be the segmentation result with existing FCM method to the spiced salt noisy image of 238011 images；
2 (e) be the segmentation result with existing FCM_S1 method to the spiced salt noisy image of 238011 images；
2 (f) be the segmentation result with existing IFCM method to the spiced salt noisy image of 238011 images；
2 (g) be the segmentation result with existing IT2FCM method to the spiced salt noisy image of 238011 images；
2 (h) be the segmentation result with existing IVFCM method to the spiced salt noisy image of 238011 images；
2 (i) be the segmentation result with existing MOVGA method to the spiced salt noisy image of 238011 images；
2 (j) be the segmentation result with existing MSFCA method to the spiced salt noisy image of 238011 images；
2 (k) be the segmentation result with the present invention to the spiced salt noisy image of 238011 images；
2 (l) be the Gauss noisy image of 238011 images, noise intensity 0.005；
2 (m) be the segmentation result with existing FCM method to the Gauss noisy image of 238011 images；
2 (n) be the segmentation result with existing FCM_S1 method to the Gauss noisy image of 238011 images；
2 (o) be the segmentation result with existing IFCM method to the Gauss noisy image of 238011 images；
2 (p) be the segmentation result with existing IT2FCM method to the Gauss noisy image of 238011 images；
2 (q) be the segmentation result with existing IVFCM method to the Gauss noisy image of 238011 images；
2 (r) be the segmentation result with existing MOVGA method to the Gauss noisy image of 238011 images；
2 (s) be the segmentation result with existing MSFCA method to the Gauss noisy image of 238011 images；
2 (t) be the segmentation result with the present invention to the Gauss noisy image of 238011 images；
Figure it is seen that the present invention can separate background and target on the basis of inhibiting noise, so this
Invention is better than existing FCM method, FCM_S1 method, IFCM method, IT2FCM method, IVFCM to the segmentation effect of noisy image
Method, MOVGA method and MSFCA method.
The image that the number in Berkeley image data base is 3096 is chosen in emulation 2, with the present invention and the existing side FCM
Method, FCM_S1 method, IFCM method, IT2FCM method, IVFCM method, MOVGA method and MSFCA method respectively carry out it
Segmentation, as a result as shown in Figure 3, in which:
3 (a) be the original image of 3096 images；
3 (b) be the Standard Segmentation figure of 3096 images；
3 (c) be the spiced salt noisy image of 3096 images, noise intensity 0.05；
3 (d) be the segmentation result with existing FCM method to the spiced salt noisy image of 3096 images；
3 (e) be the segmentation result with existing FCM_S1 method to the spiced salt noisy image of 3096 images；
3 (f) be the segmentation result with existing IFCM method to the spiced salt noisy image of 3096 images；
3 (g) be the segmentation result with existing IT2FCM method to the spiced salt noisy image of 3096 images；
3 (h) be the segmentation result with existing IVFCM method to the spiced salt noisy image of 3096 images；
3 (i) be the segmentation result with existing MOVGA method to the spiced salt noisy image of 3096 images；
3 (j) be the segmentation result with existing MSFCA method to the spiced salt noisy image of 3096 images；
3 (k) be the segmentation result with the present invention to the spiced salt noisy image of 3096 images；
3 (l) be the Gauss noisy image of image 3096, noise intensity 0.005；
3 (m) be the segmentation result with existing FCM method to the Gauss noisy image of 3096 images；
3 (n) be the segmentation result with existing FCM_S1 method to the Gauss noisy image of 3096 images；
3 (o) be the segmentation result with existing IFCM method to the Gauss noisy image of 3096 images；
3 (p) be the segmentation result with existing IT2FCM method to the Gauss noisy image of 3096 images；
3 (q) be the segmentation result with existing IVFCM method to the Gauss noisy image of 3096 images；
3 (r) be the segmentation result with existing MOVGA method to the Gauss noisy image of 3096 images；
3 (s) be the segmentation result with existing MSFCA method to the Gauss noisy image of 3096 images；
3 (t) be the segmentation result with the present invention to the Gauss noisy image of 3096 images；
From figure 3, it can be seen that the present invention can separate background and target on the basis of inhibiting noise, to containing
Make an uproar image segmentation effect better than existing FCM method, FCM_S1 method, IFCM method, IT2FCM method, IVFCM method,
MOVGA method and MSFCA method.
Claims (6)
1. a kind of multiple target Interval Valued Fuzzy based on dual membership driving clusters image partition method, it is characterised in that: including
It is as follows
(1) image to be split is inputted, if image to be split is color image, is first converted into gray level image；
(2) be arranged parameter: set population scale be 100, the number of iterations 50, maximum classification number be 10, mutation probability 0.1 is right
In Gauss noisy image, local spatial information limit entry parameterIt is respectively 6 Hes with non local spatial information limit entry parameter ψ
16, for spiced salt noisy image, the two parameters are respectively set to 16 and 1；
(3) the interval value degree of membership of Gaussian Blur number construction gray level image is utilizedAnd it is fuzzy using m-
The interval value non-affiliated degree of complementary operator construction gray level imageAccording to interval value degree of membership uI(δi) and area
Between be worth non-affiliated degree vI(δi) obtain Interval Valued Fuzzy imageWherein: δiIt is pixel,u(δi) andIt is section respectively
It is worth the left end point and right endpoint of degree of membership,v(δi) andIt is the left end point and right endpoint of interval value non-affiliated degree respectively；
(4) local subordinating degree function η is constructed respectively using local spatial information and non local spatial informationkiWith non local degree of membership
Function uki:
Wherein, m=2 represents FUZZY WEIGHTED index, and Y represents classification number,Indicate interval value pixel,Indicate interval value cluster
Center, d () represent Euclidean distance,It indicatesLocal spatial information, NiIt represents3 × 3 neighborhood windows,
M is total pixel number in neighborhood, plausibility functionNkiIt isBelong to of the pixel of kth class in neighborhood
Number,It is to be acquired using iteration non-local mean algorithmNon local spatial information, ψ is the limitation of non-local spatial information
Item parameter；
(5) joint subordinating degree function Z is calculated according to the result of (4)ki, and the global Interval Valued Fuzzy for designing dual membership driving is tight
Cause property function JLNWith the Interval Valued Fuzzy separability function S of dual membership drivingLN:
Wherein, n is pixel total number, and ξ=1 and ζ=2 are local subordinating degree function limit entry parameter respectively and non local are subordinate to
Function limit entry parameter is spent,WithIt is interval value cluster centre, ηkiIt isIt is under the jurisdiction ofLocal subordinating degree function, uki
It isIt is under the jurisdiction ofNon local subordinating degree function,It is local spatial information limit entry parameter, ψ is non-local spatial information limit
Item parameter processed, ZpqIt isIt is under the jurisdiction ofJoint subordinating degree function；
(6) multi-target evolution is carried out to two objective functions that (5) obtain, obtains the final non-dominant disaggregation P of a class interval value；
(7) the Interval Valued Fuzzy image obtained in conjunction with (3)Pixel construct dual membership driving interval value select solution to refer to
W is marked, selects an optimal chromosome from the non-dominant disaggregation P of interval value that (6) obtain using index W, and by the chromosome
The interval value cluster centre of upper coding is as Optimal cluster centers；
(8) Optimal cluster centers for utilizing (7) to obtain update joint subordinated-degree matrixAnd according to maximum membership degree
Principle classifies pixel, obtains the segmentation result of gray level image.
2. the method according to claim 1, wherein in (3) interval value degree of membership left end pointu(δi) and right end
PointIt respectively indicates as follows:
Wherein, e=2,ε=150, σ=120.
3. the method according to claim 1, wherein in (3) interval value non-affiliated degree left end pointv(δi) and it is right
EndpointIt respectively indicates as follows:
Wherein, α=0.1,π(δi)=1-u (δi,ε,σ)-v(δi)
ε=150, σ=120.
4. the method according to claim 1, wherein according to interval value degree of membership u in (3)I(δi) and interval value it is non-
Degree of membership vI(δi) obtain Interval Valued Fuzzy imageIt is expressed as follows:
5. the method according to claim 1, wherein carrying out multi-target evolution to two objective functions in (6), in fact
It is now as follows:
(6a) initialization of population: by each chromosome coding being 2 to 10 cluster centres using variable-length coding method, random to produce
Raw 100 parent chromosomes constitute a population, if current iteration number is 1；
(6b) calculates two target function values of each chromosome in population:
(6b1) computation interval value cluster centreWith interval value pixelEuclidean distance
(6b2) computation interval value pixelLocal spatial informationWherein NiIt represents3 × 3 neighborhoods
Window,It isNeighborhood window NiInterior interval value pixel, M are the numbers of total pixel in neighborhood window；
(6b3) computation interval value cluster centreWith local spatial informationEuclidean distance
(6b4) calculability functionWherein NkiIt isNeighborhood window NiInside belong to the number of the pixel of kth class,
M is the number of total pixel in neighborhood window；
(6b5) is by Euclidean distanceLocal spatial informationWith plausibility function fkiSubstitution formula<1>calculates part and is subordinate to
Category degree function ηki；
(6b6) uses iteration non-local mean algorithm computation interval value pixelNon local spatial information
(6b7) computation interval value cluster centreWith non local spatial informationEuclidean distance
(6b8) is by Euclidean distanceAnd Euclidean distanceSubstitution formula<2>, calculates non local subordinating degree function
uki；
(6b9) is by local subordinating degree function ηki, non local subordinating degree function ukiWith plausibility function fkiSubstitution formula<4>calculates double
The global Interval Valued Fuzzy compactness function J of degree of membership drivingLNValue；
(6b10) is by local subordinating degree function ηkiWith non local subordinating degree function ukiSubstitution formula<3>calculates joint subordinating degree function
Zki；
(6b11) computation interval value cluster centreWithEuclidean distance
(6b12) is by Euclidean distanceWith joint subordinating degree function ZkiSubstitution formula<5>calculates the area of dual membership driving
Between be worth fuzzy separability function SLNValue；
Two target function values are successively encoded on chromosome by (6b13)；
(6c) carries out non-dominated ranking to parent chromosome using target value, and obtained sequence value and crowding distance are successively compiled
On code to chromosome；
(6d) selects 50 chromosomes as parent using binary system tournament method from population；
(6e) carries out Laplace intersection to parent chromosome and Interval Valued Fuzzy Poisson variation generates filial generation；
(6f) recycles (6b) to (6e) and then stops iteration when reaching maximum number of iterations；
(6g) from the parent and progeny population that (6d) and (6e) is obtained, selects 100 chromosomes, to this using elitism strategy
100 chromosomes are decoded, and obtain interval value cluster centre, which is final non-dominant disaggregation P.
6. the method according to claim 1, wherein the interval value of the dual membership driving constructed in (7) selects solution
Index W, is expressed as follows:
Wherein,It is interval value cluster centre,It is interval value pixel, d () represents Euclidean distance, and m=2 represents fuzzy add
Index is weighed, Y is maximum classification number, and n is pixel total number,It is interval value cluster centreAverage value, Zki
It is joint subordinating degree function, nkRepresent the pixel total number for belonging to kth class.
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