CN108389211A - Based on the image partition method for improving whale Optimization of Fuzzy cluster - Google Patents
Based on the image partition method for improving whale Optimization of Fuzzy cluster Download PDFInfo
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Abstract
The invention discloses a kind of based on the image partition method for improving whale Optimization of Fuzzy cluster, mainly solves the serious loss after the segmentation of prior art image information, the problem of sliced time length.Implementation step is：1. input picture and the gray level for obtaining all pixels point；2. choosing c cluster centre divides the image into c classes；3. generating n whale, each whale has c dimensional vectors, represents the possibility solution at a group cluster center；4. searching for Optimal cluster centers as adaptive value by the inverse of Fast Fuzzy C mean cluster object functions；5. realizing image segmentation according to the maximum adaptation angle value corresponding group cluster center searched, the pixel that gray level is same degree of membership section is classified as one kind, the image after output segmentation.The present invention improves the effect of image segmentation, can be used for target detection, video monitoring and medical imaging by being combined optimizing result with fuzzy clustering image segmentation.
Description
Technical field
The invention belongs to technical field of image processing, further relate to a kind of image of improvement whale Optimization of Fuzzy cluster
Dividing method can be used for target detection, video monitoring and medical imaging.
Background technology
Image segmentation is one of the important technology in image procossing and computer vision, according to gray level, shape and line
Piece image is divided into multiple nonoverlapping regions by the characteristics such as reason, and the same area has similar characteristic, and between different zones not
With similar characteristic.Image segmentation is important step of the image procossing to image analysis, and purpose is exactly to divide the image into
Subsequent processing procedure, such as feature extraction, target identification are convenient in several significant regions.The method of image segmentation has
Many kinds, the dividing method such as based on cluster centre, the dividing method based on region and the dividing method for merging specific theory.Base
In Fuzzy Set Theory fuzzy clustering algorithm for a kind of image segmentation constantly labeling process after non-supervisory fuzzy clustering,
Human intervention can be reduced in application process, meet in image and there are uncertain and ambiguity actual conditions, effectively improve
The precision of image segmentation.
Fuzzy C-means FCM clustering algorithms are simple and efficient, and are widely used in image segmentation at present, can be effectively prevented from poly-
There are problems that multiple-limb in class centralization segmentation.FCM algorithms are a kind of Local Optimization Algorithms, quicker to the selection of initial value
Sense, and is easily trapped into local optimum, so FCM is in place of when carrying out image segmentation, there are many deficiencies, wherein Major Difficulties
It is the selection of initial cluster center with key point and how algorithm is avoided to be absorbed in local optimum.
Whale algorithm is one kind in swarm intelligence algorithm, and swarm intelligence algorithm is mainly based upon to nature biotechnology life-form structure
Imitation optimization algorithm, group is made of numerous individuals, each individual one kind of problem as an optimization wherein in group
Potential solution, it is optimal when searching first by all individual selection initial solutions, then constantly being updated to current solution
It solves or terminates when reaching maximum search number.Blum is at article " Swarm intelligence in optimization. "
Group in swarm intelligence algorithm is mentioned in Swarm Intelligence.Springer Berlin Heidelberg, 2008.43-85.
Each individual function in body is simple, but by the information exchange between individual, entire group can solve the problems, such as complexity,
There is compared with traditional algorithm stronger high efficiency and robustness simultaneously.Yang is in article " Swarm intelligence
based algorithms:a critical analysis."Evolutionary Intelligence 7.1(2014):17-
It is mentioned in 28. since population size is larger in swarm intelligence algorithm, the possibility of initial value selection is more, degree of freedom bigger.
Each of group individual can regard a different set of possible solution as in swarm intelligence algorithm, and entire group is made to have very strong solution
Diversity, and swarm intelligence algorithm does not need excessive priori can optimize complicated problem.
Therefore swarm intelligence algorithm and fuzzy clustering image segmentation are combined by more and more researchers, for example,
Yang is in paper " Fuzzy c-means image segmentation algorithm based on chaotic
simulated annealing[C]."International Conference on Mechatronics,Materials
and Manufacturing.Chengdu,2014:A kind of Fuzzy C-means based on simulated annealing are proposed in 536-539
Image partition method is clustered, solves the disadvantage that be easily trapped into local optimum to a certain extent, but simulated annealing pair
Initial temperature and cooling ratio are more sensitive, and algorithm is hard to reach balance in convergence rate and convergence precision.Ankita exists "
Fuzzy-based artificial bee colony optimization for gray image segmentation"
.Signal, proposed in Image and Video Processing.2016/02/02. by by the mould of artificial bee colony algorithm
Paste C- mean cluster image segmentations, selection of this method independent of initial cluster center, in convergence, time complexity, Shandong
Stick and segmentation precision etc. have preferable performance.The exploring ability of artificial bee colony algorithm is stronger, but development ability compared with
It is weak, therefore Searching efficiency is poor in an iterative process.According to Fuzzy Set Theory, cluster image segmentation is realized, with traditional figure
As dividing method compares, the fuzzy clustering image segmentation algorithm calculating process required time based on swarm intelligence algorithm is significantly
Shorten, but since the fuzzy clustering image segmentation itself based on swarm intelligence algorithm is difficult to balance the spy in searching process well
Suo Nengli and development ability cause that the problem of best Optimal cluster centers may solve can not be found, and lead to the cluster acquired point
Image information after cutting is lost seriously, and segmentation effect is not good enough, further influences the process of computer vision analysis.
Invention content
It is a kind of poly- based on whale Optimization of Fuzzy is improved it is an object of the invention in view of the above shortcomings of the prior art, propose
The image partition method of class shortens the time for finding Optimal cluster centers to reduce the loss situation of image information, improves image
Segmentation effect.
The technical scheme is that：First by each individual in gam respectively represent one group of difference cluster centre can
It can solve, corresponding fitness is calculated according to fitness function；Again by behavior pattern different in whale algorithm be iterated with
Update, the corresponding cluster centre combination solution of maximum adaptation degree that final output searches；Further according to cluster centre combination to figure
Pixel as in is classified, and implementation step includes as follows：
To achieve the above object, technical scheme is as follows：
(1) input picture, gray level image and the number M × N and dimension D for extracting pixel in gray level image, each picture
The gray level of vegetarian refreshments is k, and gray level value range is [0, L-1], and wherein M and N respectively represent the row and column of pixel in image,
If the number of pixels of gray level k is hk, L is expressed as the number of gray level；
(2) initialization gam scale n, fuzzy factor ω and clusters number c, if iterations t=0, greatest iteration time
Number is MaxT and terminal error σ；
(3) clusters number c is set, c different grey-scale is randomly choosed from all gray levels as a group cluster center
Possibility solution, selecting n groups altogether may solve, wherein being expressed as per the possibility solution at group cluster centera,
B ... p ∈ c and a ≠ b ≠ ... ≠ p, i ∈ [1, n]；
(4) take the n group clusters center selected in (3) that may solve, by the gray level in every group of possible solution according to from small to large
Sequence rearrange, the possibility solution after being sorted：And it willAs whale
The initial solution of i-th of whale in shoal of fish body, whereinIt indicatesM-th of cluster centre in the corresponding possible solution of the group, m ∈ [1,
c]；
(5) gray level k and initial solution are calculatedIn c cluster centre distance
(6) the grey level histogram h for obtaining image, if the number for the pixel that gray level is j is hj,j∈[0,L-1]；
(7) initialization subordinated-degree matrix U0, in conjunction in (5)With the h in (6)j, it is initial to calculate each whale
SolutionFitnessAnd preserving in n whale initial solution, there is a group cluster center of maximum adaptation degree may solve
Xbest, obtain fitness maximum value f (Xbest)；
(8) n whale solution is iterated to calculate：
(8a) sets t as current iteration number, and t ∈ [0, MaxT], wherein t=0 represent the original state before starting iteration, if
The fitness of i-th of whale, the t times iteration isI ∈ [1, n], enable t=1；
(8b) selects the t-1 times higher n of iteration fitness1A whale solutionWith the lower n of fitness3A whale solutionAnd by remaining n2A whale solutionIt is updated toI ∈ [1, n], and n1+n2+n3=n；
(8c) is by the n in (8b)1A whale solutionIt is updated to intersection behavior
(8d) randomly generates number r, r a ∈ [0,1], if r>0.5, by n3A whale solutionCountermeasures are tieed up using Lay
It is updated toIt otherwise, will using local variations behaviorIt is updated to
(8e) is according to all updated whale solutionsIn c cluster centre, it is a to calculate the t time iteration gray level k and c
The Euclidean distance of cluster centreAnd subordinated-degree matrix
It is obtained in (8f) basis (8e)WithCalculate each whale solution of the t times iterationFitnessi∈[1,n]；
(8g) is by all fitness in (8f)With the fitness maximum value f (X in (7)b) be compared：
IfThen fitness maximum value is updated toBy optimal cluster
The possible solution in center is updated toOtherwise, it does not update；
(8h) judges end condition, if t>MaxT, iteration ends, output f (Xbest) and Xbest, execute step (9) otherwise
T=t+1 is enabled, is returned (8b)；
(9) update calculates subordinated-degree matrix UtAnd cluster centre；
(10) if | | Ut-Ut-1||<σ, algorithm terminate, and execute step (11)；Otherwise jump procedure (9)；
(11) cluster segmentation of image, C are completed according to maximum membership grade principlek=arg { max (uik), wherein CkIt represents
K-th of gray level belongs to the degree of the i-th class.
Compared with the prior art, the present invention has the following advantages：
First, invention introduces crossover operations, for the highest preceding n of fitness in group1Individual is intersected, and is led to
The information exchange between outstanding small population size is crossed, more excellent possibility solution is remained, improves in group's searching process
Exploring ability.
Second, the present invention ties up the search strategy of flight characteristic due to introducing Lay, balances local search and global search
Ratio accelerates search speed, so as to shorten the time of determining Optimal cluster center, accelerates image segmentation rate.
Third, the present invention are combined by that will improve whale algorithm with Segmentation by Fuzzy Clustering thought, are had using the algorithm
There is the advantage that can further balance exploring ability and development ability in searching process to be split image, it then follows improved
Fuzzy C-means criterion solves the maximum value that suitable cluster centre meets fitness function, improves image segmentation precision.
Simulation result shows that the present invention can improve the exploring ability of group, enhances the diversity of entire group, avoids simultaneously
It is absorbed in local extremum, development ability and exploring ability in searching process are preferably balanced, so as to select best cluster
Center so that the image after segmentation avoids losing multi information, makes image segmentation better performances.
Description of the drawings
Fig. 1 is the implementation flow chart of the present invention.
Fig. 2 is the input original image in the present invention.
It is the segmentation result figure with of the invention and existing method to Fig. 2 in Fig. 3.
Fig. 4 is the fitness maximum value curve in the present invention and existing method iterative process.
Specific implementation mode
Below in conjunction with the accompanying drawings, the present invention is described in further detail.
The present invention is improved the optimizing ability of original gam algorithm, introduces intersection behavior and variation behavior, leads to
It crosses and chooses suitable gray level as segmentation cluster centre, every whale individual in group is enabled to represent one group of segmentation cluster centre
It may solve, by the iterations of setting, all possibility solutions are updated based on cross and variation gam algorithm.Each
In iterative process, every whale is defeated when reaching maximum iteration by selecting different behavior patterns to update self information
Go out the corresponding Optimal cluster centers solution of the fitness function maximum value searched, finally according to Optimal cluster centers solution segmentation figure
Picture.
Referring to Fig.1, the present invention is implemented as follows.
Step 1, input gray level image.
A width gray level image is obtained in picture library and is inputted, and extracts M × N number of pixel and dimension D in gray level image, each
The gray level of pixel is k, and gray level k value ranges are [0, L-1], wherein M and N respectively represent in image the row of pixel and
Row, if the number of pixels of gray level k is hk, L is expressed as the series of gray level.
Step 2：Initialize gam scale n, fuzzy factor ω, if iterations t=0, maximum iteration MaxT
With
Terminal error σ；
Step 3：The cluster centre number c of setting segmentation image.
Since the number of targets of image segmentation depends on cluster centre number c, can be divided the image by c cluster centre
C target, therefore the cluster centre number c of setting segmentation image is needed before dividing, implementation step is as follows：
2.1) c gray level is randomly selected out of grey level range as c cluster centre, then by this c cluster centre
It may be solved as a group cluster center；
2.2) choosing n group clusters center may solve, and possible solution will be expressed as per group cluster center
Wherein ka,kb,...,kpIndicate a, b in image ... gray level a, the b of p pixel ... p ∈ [1, M × N], and a ≠ b
≠ ... ≠ p, i ∈ [1, n], M × N indicate pixel sum in image.
Step 4：Initialize whale algorithm.
Whale algorithm is a kind of optimization algorithm based on group, and each individual in group can be used as and solve the problems, such as
A kind of solution may be solved if there is n whale in group wherein each whale represents a group cluster center, whale initialization then table
Show and obtain n whale initial solution, process is as follows：
Take the n group clusters center chosen in step 2 that may solve, by every group cluster center may be in solution gray level according to from
Small to be rearranged to big sequence, the possible solution of cluster centre after sequence is expressed as：
Whereini∈[1,n]；
It willAs the initial solution of i-th of whale in whale group, whereinIt indicatesThe corresponding group may be the in solution
M cluster centre, m ∈ [1, c].
Step 5：Calculate gray level k and initial solutionIn c cluster centre distance
Wherein, viIndicate that ith cluster center, k indicate gray level, | | | | expression, which is adjusted the distance, seeks two norms.
Step 6：Obtain the grey level histogram h of image.
According to the gray level d of all pixels point and each pixel that are obtained in step 1k, gray level j is obtained from 0 to L-1
All hj, wherein hjIndicate that gray level is the pixel number of j, j ∈ [0, L-1]；Use hjAs the longitudinal axis, made using gray level j
For horizontal axis, obtained schematic diagram is grey level histogram h.
Step 7：Initialize subordinated-degree matrix U0, calculate whale initial solution fitness value, preserve fitness maximum value and
Cluster centre may solve.
7.1) it takes in step 5Subordinated-degree matrix U is obtained according to following calculation formula0In each degree of membership
Element uik：
Wherein uikIndicate that gray level k is under the jurisdiction of the degree of the i-th class, djk(k,vj) indicate gray level k to cluster centre vj's
Euclidean distance；
7.2) combine above-mentioned uik,With the h in step 6j, the fitness of n whale initial solution of calculating, i-th
Whale initial solutionFitness be expressed asSteps are as follows for its calculating：
First, it calculates about subordinated-degree matrix U0With cluster centre matrix V0Object function JFFCM(U0,V0), value is smaller
It is better to represent Clustering Effect, calculation formula is as follows：
Wherein, c indicates that clusters number, L-1 indicate number of grayscale levels, hkFor the number for the pixel that gray level is k, ω tables
Show fuzzy factor；
Then, the fitness of n whale initial solution, i-th of whale initial solution are calculatedFitness be expressed as
Its calculation formula is as follows：
7.3) fitness maximum value f (X are calculatedbest)：
Wherein XbestIndicate that fitness maximum group cluster center may solve in n whale solution, also referred to as optimum cluster
Center may solve.Fitness can weigh the ability of segmentation image, and fitness value is bigger, illustrates that image segmentation is better.
Step 8：Iterate to calculate n whale solution.
T is taken to indicate that current iteration number, MaxT indicate that iteration total degree, t ∈ [0, MaxT], wherein t=0 representative start to change
For preceding original state, if the fitness of i-th of whale, the t times iteration isI ∈ [1, n], iterative step is as follows:
8.1) t=1 is enabled；
8.2) the t-1 times higher n of iteration fitness is selected1A whale solutionWith the lower n of fitness3A whale solutionAnd by remaining n2A whale solutionIt is updated toI ∈ [1, n], and n1+n2+n3=n；
8.3) n in update 8.2)1A whale solution
Use the n intersected in behavior update 8.2)1A whale solutionRenewal process is calculated as follows：
Wherein, intersection behavior is a kind of mode of more new explanation, pcIndicate crossover probability, value pc=0.5,Represent n1
I-th of whale be in the position of the t times iteration in a whale,WithFor the n selected1One of a whale solution, i, j ∈
[1,n1], i ≠ j；
8.4) n in update 8.2)3A whale solutionIts detailed process is as follows：
8.4.1 number r, r a ∈ [0,1]) is randomly generated；
8.4.2 location Update Strategy) is selected according to the value of r：
If r>0.5, then by n3A whale solutionIt is updated to using Lay dimension countermeasuresIt is public that Lay ties up countermeasures update
Formula is as follows：
Wherein,Represent n3I-th of whale be in the position of the t times iteration in a whale,Indicate point-to-point multiplication, α tables
Show step size controlling amount, its value Normal Distribution；L (λ) be Levy random searches path, arbitrary width meet L (s, λ)~
s-λLevy distributions, s is the arbitrary width that Levy flies, and λ is power number, 0<λ<3.
If r≤0.5, use local variations behavior willIt is updated toMore new formula is as follows for it：
Wherein, rand (0,1) indicates the random number between 0 to 1,Represent n3The t times iteration, i-th of whale in a whale
Fish solution XiM-th of cluster centre, Xbest,mRepresent XbestIn m-th of cluster centre；
8.5) according to all updated whale solutionsIn c cluster centre, it is a to calculate the t time iteration gray level k and c
The Euclidean distance of cluster centreWith subordinated-degree matrix Ut, calculating process is as follows：
8.5.1) according to formulaI ∈ [1, c] calculate gray level k to ith cluster center
Euclidean distance
8.5.2) according to 8.5.1) inCalculate subordinated-degree matrixIn each degree of membership uik, calculation formula is such as
Under：
Wherein, uikIndicate that gray level k is under the jurisdiction of the degree of the i-th class；
8.6) it is obtained in basis (8.5)And Ut, calculate each whale solution of the t times iterationFitnessI ∈ [1, n], calculating process is as follows：
First, it calculates about subordinated-degree matrix UtWith cluster centre matrix VtObject function JFFCM(Ut,Vt), value is smaller
It is better to represent Clustering Effect, calculation formula is as follows：
Wherein, c indicates that clusters number, L-1 indicate number of grayscale levels, hkFor the number for the pixel that gray level is k, ω tables
Show fuzzy factor.
Then, each whale solution of the t times iteration is calculatedFitnessIts calculation formula is as follows：
8.7) judge whether to update fitness maximum value and Optimal cluster centers solution：
Take n fitness f (X in step 8.6)t), wherein i-th of fitness is expressed asCompareWith step
7) f of fitness maximum value described in (Xbest) size：
IfThen by fitness maximum value f (Xbest) be updated toAnd it will step
It is rapid 7) described in Optimal cluster centers may solve XbIt is updated toOtherwise, without update.
8.8) judge whether to terminate iterative process:
Compare the size of t and MaxT, if t<MaxT then enables t=t+1, return to step 8.2), otherwise, export step 7)
In f (Xbest) and Xbest, terminate iterative process, execute step (9), wherein t indicates that current iteration number, MaxT indicate iteration
Sum.
Step 9：According to 7) output as a result, calculating subordinated-degree matrix UtWith cluster centre matrix Vt。
9.1) gray level k to X is calculatedbThe Euclidean distance at ith cluster centerIt is updated and is subordinate to according to following formula
Category degree uik：
Then subordinated-degree matrix Ut={ uik, i=1,2 ..., c, k=0,1 ..., L-1, L-1 is number of grayscale levels, and c is
Cluster centre number；
9.2) according to 9.1) updated subordinated-degree matrix U={ uik, i=1,2 ..., c, k=0,1 ..., L-1 } it calculates
Cluster centre matrix V, calculation formula are as follows：
Wherein, viIndicate ith cluster center, hkIt is the number for the pixel that gray level is k, ω indicates fuzzy factor, xk
Indicate gray value, then cluster centre matrix Vt={ vi, i=1,2 ..., c }.
Step 10：Judge end condition, if | | Ut-Ut-1||<σ, algorithm terminate, and execute step (11)；Otherwise step is redirected
Rapid 9.
Step 11：The cluster segmentation of image, C are completed according to maximum membership grade principlek=arg { max (uik), wherein CkGeneration
K-th of gray level of table belongs to the degree of the i-th class.
The result of the present invention can be further illustrated by following simulation result：
1. simulated environment and condition：
Using software Matlab 2013b, it is 512x512x3 to input a width size from picture library, as shown in Figure 2；Setting
Iteration sum M axT=150, population scale n=20, fuzzy factor ω=2, error σ=10-3, artificial bee colony Fuzzy C-means are poly-
The parameter of class algorithm and simulated annealing Fuzzy C-Means Clustering Algorithm in corresponding bibliography in background technology according to being arranged.
2. emulation content：
Emulation one：
If cluster centre number c=5, moved back respectively using the present invention, artificial bee colony Fuzzy C-Means Clustering Algorithm and simulation
Fiery Fuzzy C-Means Clustering Algorithm carries out 1 segmentation emulation to Fig. 2, and image after segmentation is as shown in figure 3, wherein Fig. 3 (a) charts
Show that the image after being divided to Fig. 2 using the present invention, Fig. 3 (b) figures are indicated using simulated annealing Fuzzy C-Means Clustering Algorithm to Fig. 2
Image after segmentation, Fig. 3 (c) are the images after artificial bee colony Fuzzy C-Means Clustering Algorithm divides Fig. 2.Iteration of simulations process
The simulation curve of middle fitness maximum value is as a result, as shown in Figure 4.
Emulation two：
If cluster centre number c is respectively 2,3,4,5, the present invention, artificial bee colony Fuzzy C-Means Clustering Algorithm are used
AFCM and simulated annealing Fuzzy C-Means Clustering Algorithm SFCM are split emulation to Fig. 2, each cluster centre number is taken
Value all carries out 30 segmentation emulation, and segmentation emulation every time has corresponding data result, including fitness maximum value and most
Excellent cluster centre may solve.Show the primary corresponding data results in 30 segmentation emulation with best segmentation effect and 30 times
The mean value of fitness maximum value in data resultWith standard deviation std, as a result as shown in table 1.
Table 1
3. analysis of simulation result：
The evaluation criterion of fuzzy clustering image segmentation algorithm is：Image after segmentation and artwork are closer to illustrating segmentation effect
Better.To find out from Fig. 3 (b), the missing image information after the Fuzzy C-Means Clustering Algorithm segmentation of simulated annealing is most, from
It can be seen that the missing image information after the Fuzzy C-Means Clustering segmentation of artificial bee colony algorithm is also more in Fig. 3 (c), cannot
Content in comprehensive display diagram 2, it is closer from (a) in Fig. 3 as can be seen that the image information loss after present invention segmentation is less
Artwork illustrates that segmentation effect of the present invention is more preferable, this is because the present invention improves the precision that group searches optimal result, enhancing
The diversity of entire group and the ability for jumping out Local Extremum, it is thus possible to select more suitable cluster centre, make
Image after must dividing can overcome the shortcomings that losing multi information.
Figure 4, it is seen that in an iterative process, the fitness of the Fuzzy C-Means Clustering Algorithm of simulated annealing
Although curve constantly rises, the fitness maximum value searched is too poor, illustrates that the Fuzzy C-means of simulated annealing are poly-
The exploring ability of class algorithm is stronger, but development ability is weak；The fitness curve of artificial bee colony Fuzzy C-Means Clustering Algorithm is
It is always maintained at faster growth trend before 10 iterations, but is tended to be steady quickly, illustrates that artificial bee colony Fuzzy C-is equal
The development ability for being worth clustering algorithm is stronger, but exploring ability is weaker, is absorbed in local optimum；The present invention is in longer iterative process
In the fitness maximum value that searches keep larger slope to increase, illustrate that the development ability of the present invention is stronger, while can be with
Find out that the present invention can search the maximum value of fitness in short-term iterative process, illustrates the whole search capability of the present invention more
By force, the development ability and exploring ability in searching process can be preferably balanced, therefore segmentation effect is more preferable.
From the mean value of fitness maximum value, fitness maximum value in table 1It can be seen that with standard deviation std
Under cluster centre number same case, fitness maximum value bigger of the invention, mean value is maximum, and standard deviation is minimum, explanation
The segmentation effect of the present invention is more preferably and the effect in repeated segmentation emulation is more stablized.
Claims (8)
1. based on the image partition method for improving whale Optimization of Fuzzy cluster, including：
(1) input picture, gray level image and the number M × N and dimension D for extracting pixel in gray level image, each pixel
Gray level be k, gray level value range is [0, L-1], and wherein M and N respectively represent the row and column of pixel in image, if grey
The number of pixels for spending grade k is hk, L is expressed as the number of gray level；
(2) initialization gam scale n, fuzzy factor ω, if iterations t=0, maximum iteration is MaxT and terminates mistake
Poor σ；
(3) set clusters number c, from all gray levels randomly choose c different grey-scale as a group cluster center can
It can solve, selecting n groups altogether may solve, wherein the possibility solution per group cluster center is expressed asa,b,...p
∈ c and a ≠ b ≠ ... ≠ p, i ∈ [1, n]；
(4) take the n group clusters center selected in (3) that may solve, every group of gray level that may be in solution is suitable according to from small to large
Sequence rearranges, the possibility solution after being sorted：And it willAs gam
The initial solution of i-th of whale in body, whereinIt indicatesM-th of cluster centre in the corresponding possible solution of the group, m ∈ [1, c]；
(5) gray level k and initial solution are calculatedIn c cluster centre distance
(6) the grey level histogram h for obtaining image, if the number for the pixel that gray level is j is hj,j∈[0,L-1]；
(7) initialization subordinated-degree matrix U0, in conjunction in (5)With the h in (6)j, calculate each whale initial solution
FitnessAnd preserving in n whale initial solution, there is a group cluster center of maximum adaptation degree may solve Xbest, obtain
To fitness maximum value f (Xbest)；
(8) n whale solution is iterated to calculate：If t is current iteration number, before t ∈ [0, MaxT], wherein t=0 represent beginning iteration
Original state, if the fitness of i-th of whale, the t times iteration isi∈[1,n]；
(8a) enables t=1；
(8b) selects the t-1 times higher n of iteration fitness1A whale solutionWith the lower n of fitness3A whale solution
And by remaining n2A whale solutionIt is updated toI ∈ [1, n], and n1+n2+n3=n；
(8c) is by the n in (8b)1A whale solutionIt is updated to intersection behavior
(8d) randomly generates number r, r a ∈ [0,1], if r>0.5, by n3A whale solutionIt is updated using Lay dimension countermeasures
ForIt otherwise, will using local variations behaviorIt is updated to
(8e) is according to all updated whale solutionsIn c cluster centre, calculate the t time iteration gray level k and clustered with c
The Euclidean distance at centerWith subordinated-degree matrix Ut；
It is obtained in (8f) basis (8e)WithCalculate each whale solution of the t times iterationFitnessi∈[1,n]；
(8g) is by all fitness in (8f)With the fitness maximum value f (X in (7)best) be compared：
IfThen fitness maximum value is updated toIt can by optimal cluster centre
Energy solution is updated toOtherwise, it does not update；
(8h) judges end condition, if t>MaxT, iteration ends, output f (Xbest) and Xbest, execute step (9)；Otherwise t is enabled
=t+1 is returned (8b)；
(9) update calculates subordinated-degree matrix UtAnd cluster centre；
(10) if | | Ut-Ut-1||<σ, algorithm terminate, and execute step (11)；Otherwise jump procedure (9)；
(11) cluster segmentation of image, C are completed according to maximum membership grade principlek=arg { max (uik), wherein CkIt represents k-th
Gray level belongs to the degree of the i-th class.
2. according to the method described in claim 1, wherein calculating gray level k and initial solution in step (5)In c cluster in
The distance of the heartIt is calculated as follows：
Wherein, viIndicate that ith cluster center, k indicate gray level, | | | | expression, which is adjusted the distance, seeks two norms.
3. calculating the t times iteration, i-th of whale solution in method according to claim 1, wherein step (8)FitnessIt is calculated as follows：
Wherein, JFFCM(Ut,Vt) it is to be defined as follows about the function of subordinated-degree matrix U and cluster centre matrix V：
Wherein, c indicates that clusters number, L-1 indicate number of grayscale levels, hkFor the number for the pixel that gray level is k, ω indicates mould
Paste the factor, uikIndicate that gray level k is under the jurisdiction of the degree of the i-th class, subordinated-degree matrix function is as follows：
Wherein, djk(k,vj) indicate gray level k to cluster centre vjEuclidean distance.
4. calculating fitness maximum value f (X in method according to claim 1, wherein step (7)best), it counts as follows
It calculates：
Wherein, XbestIndicate Optimal cluster center,Indicate i-th of whale solution of the t times iteration.
5. by n in method according to claim 1, wherein step (8c)1A whale solutionIt is updated to intersection behavior
It is carried out by following formula：
Wherein, pcIndicate crossover probability, value pc=0.5,Represent n1I-th of whale is in the position of the t times iteration in a whale
It sets,WithFor the n selected1One of a whale solution, i, j ∈ [1, n1], i ≠ j.
6. will using the flight behavior of Lay dimension in method according to claim 1, wherein step (8d)It is updated toIt is more
New formula is as follows：
Wherein,Represent n3For i-th of whale in the position of the t times iteration, ⊕ indicates that point-to-point multiplication, α indicate step in a whale
Long controlled quentity controlled variable, its value Normal Distribution；L (λ) is Levy random searches path, and arbitrary width meets L (s, λ)~s-λ's
Levy is distributed, and s is the arbitrary width that Levy flies, and λ is power number, and 0<λ<3.
7. will using local variations behavior in method according to claim 1, wherein step (8d)It is updated to
More new formula is as follows for it：
Wherein rand (0,1) indicates the random number between 0 to 1,Represent n3The t times iteration, i-th of whale solution X in a whalei
M-th of cluster centre, Xb,mRepresent XbIn m-th of cluster centre.
8. method according to claim 1, wherein step (9) update cluster centre are calculated as follows：
Wherein viIndicate ith cluster center, xkRepresent pixel.
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