CN103839261B - SAR image segmentation method based on decomposition evolution multi-objective optimization and FCM - Google Patents

Abstract

The invention discloses an SAR image segmentation method based on decomposition evolution multi-objective optimization and FCM. The method mainly solves the problem that in the prior art of image segmentation, image segmentation precision is not high, the evaluation index is single, and the segmentation effect is not ideal. The method comprises the steps that the Gabor feature and gray level symbiotic feature of each pixel of an image are extracted, and a superpixel is obtained through rough segmentation of a watershed, superpixel features are used as data to be clustered, a clustering center is used as individual species, the species are optimized through the decomposition evolution multi-objective method, the species obtained after evolution are used as the clustering center to initialize the FCM algorithm, a new clustering center is obtained and used as new species for participating in the next evolution of the decomposition evolution multi-objective algorithm. According to the SAR image segmentation method, the better clustering center is obtained through cross adoption of the decomposition evolution multi-objective algorithm and the FCM algorithm, the defect that the FCM initial value is sensitive and falls into a local optimal solution easily is overcome, and the better image segmentation result can be obtained.

Description

Based on the sar image partition method decomposing Evolutionary multiobjective optimization and fcm

Technical field

The invention belongs to intelligent image process field, it is related to Remote Sensing Image Segmentation technology, specifically a kind of being based on is decomposed The sar image partition method of Evolutionary multiobjective optimization and fcm, for remote sensing image and synthetic aperture radar (sar) figure The purpose to reach target recognition for the segmentation of picture, can be used for remote sensing mapping, Missile Terminal Guidance, marine resources monitoring, military surveillance, The multiple fields such as ground mineral resource exploration, urban planning, earthquake relief work.

Background technology

With the rise of theory on computer vision, the segmentation to image has become the heat that image understanding field is paid close attention to Point, image segmentation is filled with challenge as front subject, has attracted numerous scholars to be engaged in this area research.Image segmentation is just It is the feature according to image, segment the image into some specific, the region of peculiar property simultaneously extracts target interested Technology and process.Its application widely, occurs nearly in all spectra about image procossing.

Image partition method can be divided into the list using simple target function according to the number of the optimization object function adopting Objective optimization algorithm and the multi-objective optimization algorithm simultaneously being optimized using multiple target, in actual applications, if it is known that with regard to asking The clearly solution target of topic, can adopt single object optimization algorithm, but, the pixel distribution of real image is often relatively difficult to estimate Meter and modeling, ideal mode is exactly to simultaneously scan for from multiple directions, and this just inspires researchers using more wide in range Multi-objective optimization algorithm is improving the combination property of Solve problems.So, multi-objective optimization question application in practice is more next More it is subject to people's attention, multi-objective optimization algorithm is used for image segmentation field and is increasingly becoming the heat that scholars study Point.

Occurred in that the image Segmentation Technology that some application multi-target methods are realized in recent years, multiple mutual exclusions simultaneously complementation Target combines, and reaches more preferable segmentation result and segmentation precision using more image informations, such as " based on immune many mesh The image segmentation algorithm of mark cluster ", this algorithm is a kind of image segmentation algorithm based on immune multi-object clustering it is proposed that one kind Add the immunization method of Local Search extreme value, and clonal plant population scale carried out with self adaptationization and then uses it for image segmentation, Although the method has certain advantage in terms of region consistency and edge holding, the deficiency existing is, due to employing Excessive evolution technology, increased the computation complexity of whole cutting procedure so that splitting speed is slower, and meanwhile, the method is selected Two object functions are incorrect, and an object function comprises another object function, thus can not embody multiple target and calculate In place of the advantage of method, so leading to segmentation result unsatisfactory.

Content of the invention

The purpose of the present invention is: leads to image information using relatively for above-mentioned single-object problem evaluation index is single Few and some multi-objective optimization algorithms are high in computation complexity, and image detail keeps that performance is bad to wait deficiency it is proposed that a kind of base In the sar image partition method decomposing Evolutionary multiobjective optimization and fcm.Fusion feature is extracted as band cluster numbers in the present invention According to, the ability in feature extraction of preferable performance complement can be reached, preferably keep image detail；Choose two complementary target letters Number, just can simultaneously scan for optimizing so that algorithm can be in more broad range searching from multiple directions, it is to avoid algorithm is absorbed in office Portion's optimal solution, improves the single shortcoming of object function in existing method；And take full advantage of the spy of fcm algorithm Fast Convergent Property, decrease the time complexity of algorithm.

The technical scheme is that a kind of sar image partition method based on decomposition Evolutionary multiobjective optimization and fcm, It is characterized in that: comprise the following steps:

Step 1: input remote sensing images to be split；

Step 2: extract characteristics of image to be split: extract the gabor characteristic vector of image using gabor wave filter, utilize Algorithm of co-matrix extracts the gray scale symbiosis characteristic vector of image, and will be every as image to be split for fusion feature vector The characteristic vector of one pixel；

Step 3: produce data features to be clustered: treat segmentation figure picture with watershed algorithm and carry out watershed rough segmentation Cut, obtain the super-pixel of artwork；The all pixels point feature that each super-pixel is comprised is averaged, and to represent initial clustering The characteristic vector of each super-pixel of data, with the set of the characteristic vector of all super-pixel as data to be clustered The size of features, features is nf × fl, and wherein nf represents the number of the super-pixel after coarse segmentation, and fl represents each The dimension of the characteristic vector of individual super-pixel；

Step 4: using the initial population x={ x for n for the data initialization size to be clustered₁,x₂,…,x_n, each individual x_n All represent a cluster centre, also represent a segmentation result, n=1 simultaneously, 2 ..., n, n are initial population size；

Step 5: respectively each individual target function value f is calculated according to index xb and jm_n: drawn according to index xb Value is as target function value f_nFirst aim value, using the value being drawn according to index jm as target function value f_nSecond Desired value:

f_n=[f1, f2]=[xb, jm]

Step 6: initialization ideal point z^*；

Wherein It is the 1st minima that up to the present object function xb finds,It is the 2nd mesh The minima that up to the present scalar functions jm finds；

Step 7: multi-objective problem f (x)=min (f1 (x), f2 (x)) Chebyshev's decomposition method is resolved into n son Problem, specifically the object function of each subproblem is as follows:

$\min imize{g}_j^{te}\left(x\right|{\mathrm{\λ}}^j,z^{*})=\underset{1\≤i\≤m}{max}\left\{{\mathrm{\λ}}_i^j\right|f_{ji}\left(x\right)-z_i^{*}\left|\right\}$

Wherein,Current reference point, i.e. the vector of the current optimal value composition of each target, In the present invention, the value of m is 2；Represent the object function of j-th subproblem；It is j-th subproblem Weights；J=1,2 ..., n；X represents a population at individual, f_jiX () represents j-th subproblem Corresponding i-th object function of individuality value, in the present invention value of i be equal to m value, value be 2；

Step 8: according to each subproblemWeights λ^j, calculate the s_n neighbours of each subproblem Subproblem nbor (j)=(nbor_j1,nbor_j2,…,nbor_{js_n}), nbor_jiRepresent that i-th neighbours' of j-th subproblem is asked The index of topic, so nbor_jiValue be integer；Take s_n=10；I=1,2 ..., s_n；

Step 9: by each subproblemIndividual p_jT () is initialized as x_j, x_j∈ x, wherein t are iteration Number of times, t=0；And calculate individual p_j(t) corresponding target function value ft_j；

Step 10: to each subproblemCorresponding individuality p_j(t) carry out evolutional operation obtain temporarily individual Body p_j(t+1)”

10.1 randomly choose 3 neighbours subproblem s, k in s_n neighbour subproblem nbor (j) of j-th subproblem, L, to s, the individual p of k, l neighbours subproblem_s(t), p_k(t), p_lT () is simulated two and enters crossover operation, obtain one newly Interim offspring individual p_j(t+1)'；

10.2 couples of temporary individual p_j(t+1) ' carry out multinomial mutation operation, obtain individual p_j(t+1)”；

Step 11: to the individual p obtaining_j(t+1) " carry out an iteration operation with fcm algorithm and obtain new individual p_j(t+ 1)；

Step 12: calculate new temporary individual p_j(t+1) two target function value newf_j1And newf_j2, and according to newf_j1And newf_j2Update ideal point z^*；By new temporary individual p_jAnd its desired value newf (t+1)_j1And newf_j2To update All s_n neighbours subproblem nbor (j) of j-th subproblem corresponding individuality and each individual corresponding target letter respectively Numerical value；

Step 13: judge whether current iteration number of times t meets t ＜ t max, such as meet, then execution step 13；Otherwise, make Iterationses t adds a t=t+1, and return to step 11, wherein t max are maximum iteration time, take t max=20；

Step 14: select suitably individuality from population as cluster centre: by each subproblem's Parent individuality p_jT () takes out, using each individual cluster centre as the super-pixel that will cluster, these cluster centres are made For final output disaggregation；And a selection individual is concentrated as cluster from final output solution according to third party's index p bm The heart；

Step 15: obtain the classification number of each pixel: calculate the characteristic vector of each pixel and obtain from step 14 The Euclidean distance of cluster centre, is grouped into this pixel in the classification of the minimum cluster centre of its Euclidean distance, obtains every The classification of one pixel；

Step 16: output segmentation figure picture.

The process of the extraction characteristics of image to be split described in above-mentioned steps 2 includes the following:

2.1.1 the process being extracted the medium and low frequency texture feature vector of image using gabor wave filter is included: bidimensional Gabor kernel function can be defined as:

$g(x,y)=\frac{1}{2{\mathrm{\π\σ}}_x{\mathrm{\σ}}_y}\exp \[-\frac{1}{2}(\frac{x^2}{{\mathrm{\σ}}_x^2}+\frac{y^2}{{\mathrm{\σ}}_y^2})+j2\mathrm{\π}f(xcos\mathrm{\θ}+ysin\mathrm{\θ})\]$

Wherein, σ_xAnd σ_yRepresent oval Gaussian function respectively along the standard deviation on x and y direction, f is modulating frequency, and θ is The direction of gabor kernel function.

2.2.1 included using the process of algorithm of co-matrix texture feature extraction vector: first by pending image It is quantified as certain gray level, local window size can design according to object of experiment, the distance between pixel is d_n, then according to The secondary angular separation making two pixel lines and transverse axis is certain angle, calculates the direction number of requirement according to the following formula respectively Gray level co-occurrence matrixes:

P (i, j)=# { (x₁,y₁),(x₂,y₂)∈m×n|f(x₁,y₁)=r, f (x₂,y₂)=s }

Wherein, p (i, j) is element on coordinate (i, j) position for the gray level co-occurrence matrixes, and # is the element number of set { }, (x₁,y₁) and (x₂,y₂) be two pixel point coordinates that distance is equal to d_n, ∈ be set in belong to symbol, m × n be wait to locate The size of reason image, | for the conditional code in theory of probability, r is (x₁,y₁) gray value after place's pixel vector quantization, s is (x₂, y₂) gray value after place's pixel vector quantization.

The calculating process calculating each individual target function value described in above-mentioned steps 5 includes:

The formula of 5.1 target function value f1 and f2 being obtained according to xb index and jm index respectively is as follows:

$f1=xb=\frac{\underset{p=1}{\overset{k}{\mathrm{\σ}}}\underset{i,j=1}{\overset{nf}{\mathrm{\σ}}}{u}_{pj}^2\left|\right|{\mathrm{features}}_j-c_p|{|}^2}{{\mathrm{nfmin}}_{i,j}\left|\right|c_i-c_j\left|\right|}$

$f2=jm=\underset{j=1}{\overset{nf}{\σ}}\underset{p=1}{\overset{k}{\σ}}{u}_{pj}^2\left|\right|{\mathrm{features}}_j-c_p|{|}^2$

$u_{pj}=\frac{1}{\underset{j=1}{\overset{k}{\σ}}{\left(\frac{\left|\right|c_p-{\mathrm{features}}_j\left|\right|}{\left|\right|c_i-{\mathrm{features}}_j\left|\right|}\right)}^2}$

Wherein, features_jIt is the pixel characteristic matrix extracting, j=1,2 ..., nf is the feature extracted after feature The line number of matrix, i.e. the number of the image block after image coarse segmentation, c_p, p=1,2 ... k, be image pixel cluster in The heart, k is the number of the cluster centre specified, u_k×nfIt is fuzzy membership matrix；

5.2 each individual target function value f_n=[f_n1,f_n2], wherein, f_n1=f1=xb, f_n2=f2=jm.

To the individual p obtaining in above-mentioned steps 11_j(t+1) " carry out an iteration operation with fcm algorithm and obtain new individuality p_j(t+1) implication described in is as follows:

11.1 individual p_j(t+1) " as cluster centre c, according to this cluster centre c to data features to be clustered Euclidean distance obtain the fuzzy membership matrix u of this cluster centre_ij, u_ijBe calculated as follows:

$u_{ij}=\frac{1}{\underset{k=1}{\overset{c}{\σ}}{\left(\frac{d_{ij}}{d_{kj}}\right)}^{2/(m-1)}}$

u_ijIt is between 0, between 1, c_iIt is the cluster centre of ambiguity group i, d_ij=| | c_i-features_j| | represent i-th The Euclidean distance of j-th data point of cluster centre and features, and m ∈ [1, ∞), m=2 in the present invention；

11.2 according to the 11.1 fuzzy membership matrix u obtaining_ijCluster centre c' after being updated, c' is calculated as follows:

$c_i^{\′}=\frac{\underset{j=1}{\overset{nf}{\σ}}{u}_{ij}^m{\mathrm{features}}_j}{\underset{j=1}{\overset{nf}{\σ}}{u}_{ij}^m}$

features_jIt is j-th data point, nf is the number of the data point that features comprises；

11.3 c' obtaining are as new individual p_j(t+1)；

Above-mentioned steps 12 ideal point z^*Renewal process and the more parent individuality of new neighbor subproblem and its corresponding target The process of value includes the following:

12.1 ideal point z^*Renewal process include: ifOtherwise constant；IfOtherwise constant；

The process of all individual and its corresponding desired value of 12.2 more new neighbor subproblems includes: for new interim Individual p_j(t+1) each neighbours subproblem, nbor_ji∈ nbor (j), i=1,2 ..., s_n, wherein s_n are that neighbours' is asked The number of topic, if for all of nbor_jiHaveThen use New temporary individual p_j(t+1) substitute the corresponding individuality of i-th neighbours subproblem of j-th subproblemAnd use newf_j1 And newf_j2Substitute the corresponding target function value of i-th neighbours subproblem of j-th subproblemOtherwise, constant.

The process according to third party's index p bm selection generation optimum segmentation result described in above-mentioned steps 14 is as follows:

14.1 values being obtained according to third party's index p bm obtaining each cluster centre first:

$ic\left(index\right)=pbm\left(k\right)={(\frac{1}{k}\×\frac{ec}{e_k}\×d_k)}^2,$

$e_k=\underset{p=1}{\overset{k}{\σ}}\underset{j=1}{\overset{n}{\σ}}{u}_{pj}\left|\right|{\mathrm{features}}_j-c_p\left|\right|,d_k={\max }_{i,j=1}^k\left|\right|c_i-c_j\left|\right|$

Wherein, features_j,c_p,u_pjConsistent with the description in step 2, index=1 ... n, n are currently available gathering The number at class center, k is intended to the class number split, e_kIt is the corresponding cluster centre of super-pixel that a splitting scheme obtains Apart from sum d_kIt is the maximum separation between cluster centre, ec is each features_j, j=1 ... nf to features Geometric center apart from sum, it is equal that each cluster centre obtains ec.

By studying the document with regard to clustering target performance, referring to document maulik u., and bandyopadhyay s.performance evaluation of some clustering algorithms and validity indices, ieee transactions on pattern analysis and machine intelligence,vol.24,n0.12, Pp:1650-1654,2002, the document points out that pbm index is that current segmentation performance is best, and index passes through k, e_k, and d_kThree Between collective effect reach find a suitable splitting scheme purpose.

The thinking that the present invention realizes goal of the invention is: carries out feature extraction in the image to input and watershed segmentation obtains After cluster data, first randomly generate initial population, then choose two complementary indexs xb and jm to evaluate as object function poly- Class performance, by based on the multi-objective Algorithm moea decomposing d and two algorithms of common clustering algorithm fcm combine and plant to initial Individuality in group is iterated optimizing, and obtains final population after meeting stopping criterion for iteration, according to the from final population Tripartite's index p bm selects an individual as the cluster centre of cluster data, according to the cluster centre obtaining to cluster data Carry out clustering the classification number obtaining each cluster data, obtain the segmentation result of image.

The invention has the beneficial effects as follows:

First, the present invention is due to, in image segmentation with process, employing gabor filtering and gray level co-occurrence matrixes this two Complementary feature extracting method extracts medium and low frequency texture feature vector and the high frequency texture characteristic vector of image respectively, solves existing Technology is had to filter the disappearance extracting the image information that image feature vector leads to so that the present invention can be preferable merely with gabor Keep image detail；And, after having extracted gabor feature, using the big gaussian filtering of window gabor filtering more used The image information extracted is smoothed, preferably can keep image border, improve overall segmentation precision.

Second, the present invention employs two complementary object function evaluation cluster property in the cluster process of image segmentation Can, overcome the single shortcoming of prior art evaluation index so that evaluation index of the present invention is diversified, it is possible to obtain one group of segmentation Result.

3rd, the present invention employs based on decomposing Evolutionary multiobjective optimization and fcm in the cluster process of image segmentation Multi-target evolution problem is changed into single goal subproblem one by one by decomposition and is processed, each height is asked by clustering algorithm Topic is updated according to the neighbours around it, effectively can be searched in complicated solution space；And can be calculated using fcm The characteristic of method fast convergence rate, overcomes fcm initial value sensitive and defect that is being easily trapped into locally optimal solution, so that after combining Algorithm can have the quick ability finding optimal solution in global scope so that the present invention can obtain more accurate region one Cause property and more preferable edge retention energy.

Brief description

Fig. 1 is the flow chart of the present invention；

Fig. 2 is the present invention and segmentation result comparison diagram on two class texture images of a width synthetic for the prior art；

Fig. 3 is the present invention and segmentation result comparison diagram on three class texture images of a width synthetic for the prior art；

Fig. 4 is the present invention and segmentation result comparison diagram on four class texture images of a width synthetic for the prior art；

Fig. 5 is the present invention and segmentation result comparison diagram on five class texture images of a width synthetic for the prior art；

Fig. 6 is for the present invention and prior art on two class sar image sar_1 (size 256 × 256) of a width synthetic Segmentation result comparison diagram；

Fig. 7 is segmentation with prior art on the sar image sar_2 (size 256 × 256) of one four segmentation for the present invention Comparative result figure；

Fig. 8 is segmentation with prior art on the sar image sar_3 (size 512 × 512) of one three segmentation for the present invention Comparative result figure；

Fig. 9 is segmentation with prior art on the sar image sar_4 (size 440 × 440) of one four segmentation for the present invention Comparative result figure；

Specific embodiment

Below in conjunction with the accompanying drawings the present invention is described in further detail.

Embodiment 1

The present invention is to propose a kind of sar image partition method based on decomposition Evolutionary multiobjective optimization and fcm, belongs to figure As processing technology field, further relate to a kind of dividing method of Study Of Segmentation Of Textured Images technical field.The emulation of this example be The pentium dual_core cpu e5200 of dominant frequency 2.3ghz, the hardware environment of internal memory 4gb and matlab r2009a's is soft Carry out under part environment.

The present invention is a kind of sar image partition method based on decomposition Evolutionary multiobjective optimization and fcm, for prior art The evaluation index existing is single, computation complexity is high, details keeps the deficiencies such as performance is bad, the present invention propose a kind of based on point Solution Evolutionary multiobjective optimization and the sar image partition method of fcm.It is extracted fusion feature as data to be clustered, more in method Good holding image detail；Choose two complementary object functions, improve that object function in existing method is single, object function bag The shortcomings of containing image information less.Referring to Fig. 1, the present invention comprises the following steps to image segmentation:

Step 1: input texture image to be split；

Step 2: extract characteristics of image to be split；

2.1 utilize gabor wave filter to extract the gabor characteristic vector of image；

2.2 utilize algorithm of co-matrix to extract the gray scale symbiosis characteristic vector of image；

The gray scale symbiosis characteristic vector of 2.3 images being obtained with the gabor characteristic vector and 2.2 of 2.1 images obtaining Fusion feature vector is exactly the characteristic vector of each pixel of image to be split；

Step 3: produce data features to be clustered: treat segmentation figure picture with watershed algorithm and carry out watershed rough segmentation Cut, obtain the super-pixel of artwork；The all pixels point feature that each super-pixel is comprised is averaged, and to represent initial clustering The characteristic vector of each super-pixel of data, with the set of the characteristic vector of all super-pixel as data to be clustered The size of features, features is nf × fl, and wherein nf represents the number of the super-pixel after coarse segmentation, and fl represents each The dimension of the characteristic vector of individual super-pixel；

Step 4: using the initial population x={ x for n for the data initialization size to be clustered₁,x₂,…,x_n, each individual x_n All represent a cluster centre, also represent a segmentation result, n=1,2 ..., n, n are initial population size, take n=simultaneously 100；

Step 5: respectively each individual target function value f is calculated according to index xb and jm_n: drawn according to index xb Value is as target function value f_nFirst aim value, using the value being drawn according to index jm as target function value f_nSecond Desired value:

f_n=[f1, f2]=[xb, jm]

The formula of 5.1 target function value f1 and f2 being obtained according to xb index and jm index respectively is as follows:

$f1=xb=\frac{\underset{p=1}{\overset{k}{\σ}}\underset{i,j=1}{\overset{nf}{\σ}}{u}_{pj}^2\left|\right|{\mathrm{features}}_j-c_p|{|}^2}{{\mathrm{nfmin}}_{i,j}\left|\right|c_i-c_j\left|\right|}$

$f2=jm=\underset{j=1}{\overset{nf}{\σ}}\underset{p=1}{\overset{k}{\σ}}{u}_{pj}^2\left|\right|{\mathrm{features}}_j-c_p|{|}^2$

$u_{pj}=\frac{1}{\underset{j=1}{\overset{k}{\σ}}{\left(\frac{\left|\right|c_p-{\mathrm{features}}_j\left|\right|}{\left|\right|c_i-{\mathrm{features}}_j\left|\right|}\right)}^2}$

Wherein, features_j, j=1,2 ..., nf is the line number extracting the eigenmatrix after feature, i.e. image rough segmentation The number of the image block after cutting, c_p, p=1,2 ... k, is the cluster centre of image pixel, and k is the cluster centre specified Number, u_k×nfIt is fuzzy membership matrix；

5.2 each individual target function value f_n=[f_n1,f_n2], wherein, f_n1=f1=xb, f_n2=f2=jm；

Step 6: initialization ideal point z^*；

Wherein It is the 1st minima that up to the present object function xb finds,It is the 2nd mesh The minima that up to the present scalar functions jm finds；

Step 7: multi-objective problem f (x)=min (f1 (x), f2 (x)) Chebyshev's decomposition method is resolved into n son Problem, specifically the object function of each subproblem is as follows:

$\min imize{g}_j^{te}\left(x\right|{\mathrm{\λ}}^j,z^{*})=\underset{1\≤i\≤m}{max}\left\{{\mathrm{\λ}}_i^j\right|f_{ji}\left(x\right)-z_i^{*}\left|\right\}$

Wherein,Current reference point, i.e. the vector of the current optimal value composition of each target, In the present invention, the value of m is 2；Represent the object function of j-th subproblem；It is j-th subproblem Weights；J=1,2 ..., n；X represents a population at individual, f_jiX () represents j-th subproblem Corresponding i-th object function of individuality value, in the present invention value of i be equal to m value, value be 2；

Step 8: according to each subproblemWeights λ^j, calculate the s_n neighbours of each subproblem Subproblem nbor (j)=(nbor_j1,nbor_j2,...,nbor_{js_n}), nbor_jiRepresent that i-th neighbours' of j-th subproblem is asked The index of topic, so nbor_jiValue be integer；Take s_n=10；I=1,2 ..., s_n；

Step 9: by each subproblemIndividual p_jT () is initialized as x_j, x_j∈ x, wherein t are iteration Number of times, t=0；And calculate individual p_j(t) corresponding target function value ft_j；

Step 10: to each subproblemIndividual p_jT () carries out evolutional operation and obtains temporary individual p_j(t +1)”

10.1 randomly choose 3 neighbours subproblem s, k in s_n neighbour subproblem nbor (j) of j-th subproblem, L, to s, the individual p of k, l neighbours subproblem_s(t), p_k(t), p_lT () carries out crossover operation, obtain a new interim son Generation individual p_j(t+1)'；

10.2 couples of temporary individual p_j(t+1) ' carry out multinomial mutation operation, obtain individual p_j(t+1)”；

Randomly choose and select 3 neighbours subproblems, the scope of search space can be expanded, enter in bigger search space Line search, it is possible to jump out local optimum, finds more preferable solution.

Step 11: to the individual p obtaining_j(t+1) " carry out an iteration operation with fcm algorithm and obtain new individual p_j(t+ 1)

11.1 individual p_j(t+1) " as cluster centre c, according to this cluster centre c to data features to be clustered Euclidean distance obtain the fuzzy membership matrix u of this cluster centre_ij, u_ijBe calculated as follows:

$u_{ij}=\frac{1}{\underset{k=1}{\overset{c}{\σ}}{\left(\frac{d_{ij}}{d_{kj}}\right)}^{2/(m-1)}}$

u_ijIt is between 0, between 1, c_iIt is the cluster centre of fuzzy i, d_ij=| | c_i-features_j| | represent i-th and gather The Euclidean distance of j-th data point of class center and features, and m ∈ [1, ∞), m=2 in the present invention；

11.2 according to the 11.1 fuzzy membership matrix u obtaining_ijCluster centre c' after being updated, c' is calculated as follows:

$c_i^{\′}=\frac{\underset{j=1}{\overset{nf}{\σ}}{u}_{ij}^m{\mathrm{features}}_j}{\underset{j=1}{\overset{nf}{\σ}}{u}_{ij}^m}$

features_jIt is j-th data point, nf is the number of the data point that features comprises；

11.3 c' obtaining are as new individual p_j(t+1)；

Step 12: calculate new temporary individual p_j(t+1) two target function value newf_j1And newf_j2, and according to newf_j1And newf_j2Update ideal point z^*；By new temporary individual p_jAnd its desired value newf (t+1)_j1And newf_j2To update All s_n neighbours subproblem nbor (j) of j-th subproblem corresponding individuality and each individual corresponding target letter respectively Numerical value；

Step 13: judge whether current iteration number of times t meets t ＜ tmax, such as meet, then execution step 13；Otherwise, order changes Generation number t adds a t=t+1, and return to step 11, wherein tmax are maximum iteration time, take tmax=20；

Step 14: select suitably individuality from population as cluster centre: by each subproblem's Parent individuality p_jT () takes out, using each individual cluster centre as the super-pixel that will cluster, these cluster centres are made For final output disaggregation；And a selection individual is concentrated as cluster from final output solution according to third party's index p bm The heart；

Step 15: obtain the classification number of each pixel: calculate the characteristic vector of each pixel and obtain from step 14 The Euclidean distance of cluster centre, is grouped into this pixel in the classification of the minimum cluster centre of its Euclidean distance, obtains every The classification of one pixel, and contrasted with segmentation Prototype drawing, obtain error parameter；

Step 16: output segmentation figure picture.

Embodiment 2

Based on decomposing the sar image partition method of Evolutionary multiobjective optimization and fcm with embodiment 1, can implement to possess Property, described in further detail to the present invention as follows:

Wherein in step 2, image characteristics extraction is described in further detail as follows:

2.1.1 the process being extracted the medium and low frequency texture feature vector of image using gabor wave filter is included: bidimensional Gabor kernel function can be defined as:

$g(x,y)=\frac{1}{2{\mathrm{\π\σ}}_x{\mathrm{\σ}}_y}\exp \[-\frac{1}{2}(\frac{x^2}{{\mathrm{\σ}}_x^2}+\frac{y^2}{{\mathrm{\σ}}_y^2})+j2\mathrm{\π}f(xcos\mathrm{\θ}+ysin\mathrm{\θ})\]$

Wherein, σ_xAnd σ_yRepresent oval Gaussian function respectively along the standard deviation on x and y direction, f is modulating frequency, and θ is The direction of gabor kernel function, because gabor wave filter is in the conjugate symmetry of frequency domain, therefore only need in 0-180 degree selecting party To parameter θ.We are according to document clausi d.a and deng h.design-based texture in the present invention feature fusion using gabor filters and co-occurrence probabilities,ieee Transaction on image processing, vol.14, no.7, pp:925-936,2005. choose six mid frequency f =6.1876,4.3878,3.9135,3.6751,3.3991,2.9551, and six kernel function directionsParameter as wave filter.Obtain the texture feature vector of 36 dimensions of each pixel.

2.2.1 included using the process of algorithm of co-matrix texture feature extraction vector: first by pending image It is quantified as 32 gray levels, local window size is 9 × 9, and the distance between pixel is 1, then make two pixel lines successively It is 0 °, 45 °, 90 ° and 135 ° with the angular separation of transverse axis, calculate the gray level co-occurrence matrixes of four direction according to the following formula respectively:

P (i, j)=# { (x₁,y₁),(x₂,y₂)∈m×n|f(x₁,y₁)=r, f (x₂,y₂)=s }

Wherein, p (i, j) is element on coordinate (i, j) position for the gray level co-occurrence matrixes, and # is the element number of set { }, (x₁,y₁) and (x₂,y₂) be two pixel point coordinates that distance is equal to 1, ∈ be set in belong to symbol, m × n be pending The size of image, | for the conditional code in theory of probability, r is (x₁,y₁) gray value after place's pixel vector quantization, s is (x₂,y₂) Gray value after place's pixel vector quantization.

Choose contrast on this matrix four direction, homogeneity and energy value according to gray level co-occurrence matrixes respectively, finally Obtain 12 dimension texture feature vectors of pixel.

Treat segmentation figure picture using dividing ridge method in step 3 and carry out coarse segmentation, the concrete watershed that the present invention uses is divided Segmentation method is the watershed segmentation methods based on gradient.

The method can be found in k.haris, s.n.efstratiadis, n.maglaveras, and a.k.katsaggelos,“hybrid image segmentation using watersheds and fast region merging,”ieee transactions on image processing,vol.7,no.12,pp.1684-1699,1998.

In step 5, the present invention adopts xb index and jm index as two complementary mesh in the cluster process of image segmentation Scalar functions evaluate clustering performance, overcome the single shortcoming of prior art evaluation index.Referring to document bandyopadhyay s., maulik u.,and mukhopadhyay a.multi-objective genetic clustering for pixel classification in remote sensing imagery,ieee transaction on geoscience and remote sensing,vol.45,no.5,pp:1506-1511,2007.The combination of this two complementary target makes the present invention comment The variation of valency index, is more suitable for the complex information that remote sensing images are comprised, can obtain more preferable effect.Single goal method is run The result repeatedly obtaining, multi-target method only needs to run and is once obtained with one group of segmentation result.

In step 7, the present invention employs based on decomposition Evolutionary multiobjective optimization in the cluster process of image segmentation Moea d algorithm, by moea d algorithm multi-target evolution problem changed into single goal subproblem one by one processed, often One subproblem is updated according to the neighbours around it, can effectively be searched for, overcome in complicated solution space Prior art is easily trapped into local optimum affects the shortcoming of segmentation result, and it is complicated to reduce the calculating of the every generation of holistic approach Degree.

Being implemented as follows of step 10.1 in the individual evolution operation of each of step 10 subproblem:

10.1.1 simulation two is entered to intersect and is produced new temporary individual p_j(t+1) ' process as follows:

3 neighbours subproblem s, k, l are randomly choosed in s_n neighbour subproblem nbor (j) of j-th subproblem, right The individual p of s, k, l neighbours subproblem_s(t), p_k(t), p_lT () is simulated two and enters crossover operation, each individuality is The vector of one fl dimension, for example, individual p_sT () is represented byThe formula producing is as follows:

${p_j}^i{(t+1)}^{\&prime;}=\left\{\begin{array}{cc}{p}_s^i\left(t\right)+f\left(p_k^i\right(t)-p_l^i\left(t\right)),if& {\mathrm{rand}}_n(0,1)<cr\\ p_j^i\left(t\right),& otherwise\end{array}\right.$

Wherein cr ∈ [0,1] is crossover probability, and f is an invariant, is set to 0.5,Represent individual the I position.

10.2.1 the method adopting multinomial variation is to individual p_j(t+1) ' enter the new new individual p of row variation generation_j(t+ 1) ", to make a variation it isI.e. individual p_j(t+1) ' kth (1≤k≤fl) position, its its span is [l_k, u_k] then formula as follows:

${p_j}^i{(t+1)}^{\&prime;\&prime;}=\left\{\begin{array}{cc}{p_j}^i{(t+1)}^{\&prime;},& i\&notequal;k\\ c_k,& i=k\end{array}\right.$

Whereinδ is referred to as the step-length that makes a variation, and its computing formula is: δ=δ × (u_k-l_k), its Middle δ is expressed as follows:

$\mathrm{\&delta;}=\left\{\begin{array}{cc}{\&lsqb;2u+(1-2u){(1-{\mathrm{\&delta;}}_1)}^{{\mathrm{\&eta;}}_m+1}\&rsqb;}^{\frac{1}{{\mathrm{\&eta;}}_m\mathrm{+1}}-1}if& u\&le;0.5\\ 1-{\&lsqb;2(1-u)+2(u-0.5){(1-{\mathrm{\&delta;}}_2)}^{{\mathrm{\&eta;}}_m+1}\&rsqb;}^{\frac{1}{{\mathrm{\&eta;}}_m\mathrm{+1}}-1}if& u>0.5\end{array}\right.$

δ in formula₁=(ν_k-l_k)/(u_k-l_k), δ₂=(u_k-ν_k)/(u_k-l_k), u is the random number in [0,1] interval, η_mIt is Profile exponent.

Produce optimum segmentation result detailed process in step 14 to include:

14.1 values being obtained according to third party's index p bm obtaining each cluster centre first:

$ic\left(index\right)=pbm\left(k\right)={(\frac{1}{k}\&times;\frac{ec}{e_k}\&times;d_k)}^2,$

$e_k=\underset{p=1}{\overset{k}{\&sigma;}}\underset{j=1}{\overset{n}{\&sigma;}}{u}_{pj}\left|\right|{\mathrm{features}}_j-c_p\left|\right|,d_k={\max }_{i,j=1}^k\left|\right|c_i-c_j\left|\right|$

Wherein, features_j,c_p,u_pjDescription in claim 2 is consistent, index=1 ... n, n are current obtaining The number of the cluster centre arriving, k is intended to the class number split, e_kIt is that the super-pixel that a splitting scheme obtains is corresponding poly- Class center apart from sum d_kIt is the maximum separation between cluster centre, ec is each features_j, j=1 ... nf arrives The geometric center of features apart from sum, it is equal that each cluster centre obtains ec；

14.2 find, from the ic vector that 14.1 steps obtain, subscript en that the value of maximum is located, then from final output disaggregation In select the en cluster centre, here it is the cluster centre out according to pbm index.

Embodiment 3

Based on the multiple-target remote sensing image dividing method decomposing with embodiment 1-2, the segmentation effect of the present invention can pass through Hereinafter experiment further illustrates:

Experiment simulation environment is: the pentium dual_core cpu e5200 of dominant frequency 2.3ghz, the hardware of internal memory 2gb Environment and the software environment of matlab r2009a.

Also by Fuzzy c-Means Clustering Algorithm of the prior art (fcm) in experiment, imis (merges gabor filtering and gray scale The immune multi-object image segmentation algorithm of symbiosis complementary characteristic), nsga-ii (a fast and elitist multi- Objective genetic algorithm) algorithm is also separately in the segmentation of artwork, with the present invention with above-mentioned three kinds points Segmentation method is compared.

The setting of the setting of inventive algorithm and contrast algorithm is as follows, and the maximum iteration time of fcm is 120 times, obscures and refers to Number is 2, independent operating 30 times, therefrom chooses best result.The algorithm of nsga-ii, imis and this paper is all that multiple-objection optimization is entered Change algorithm, the setting such as table 1 below of parameter:

Table 1

Algorithm	Population Size	Iterationses	Crossover probability	Mutation probability	Clustering target	Clone pool
							nsga-ii	100	30	0.8	1/n	xb jm	50
imis	100	20	0.8	0.1	xb jm	20
							Inventive algorithm	100	20	0.8	0.1	xb jm	---

Fig. 2 (a), 3 (a), 4 (a), synthetic texture maps two Texture Segmentation used in 5 (a), respectively emulation experiment Artwork, three Texture Segmentation artwork, four Texture Segmentation artwork and five Texture Segmentation artwork, image size is 256 × 256；2 (b), 3 (b), 4 (b), the segmentation template of the synthetic texture maps two Texture Segmentation figure used in 5 (b), respectively emulation experiment, three The segmentation template of Texture Segmentation figure, the segmentation template of the segmentation template of four Texture Segmentation figures and five Texture Segmentation figures；2 (c), 3 (c), 4 (c), use fcm algorithm that the segmentation of synthetic texture maps two Texture Segmentation figure is tied in 5 (c), respectively emulation experiment Really, the segmentation result of three texture segmentation figures, the segmentation result of the segmentation template of four Texture Segmentation figures and five Texture Segmentation figures；2 (d), 3 (d), 4 (d), with imis algorithm, synthetic texture maps two Texture Segmentation figure is divided in 5 (d), respectively emulation experiment Cut result, the segmentation result of three texture segmentation figures, the segmentation result of the segmentation template of four Texture Segmentation figures and five Texture Segmentation figures； 2 (e), 3 (e), 4 (e), use nsga-ii algorithm in 5 (e), respectively emulation experiment to synthetic texture maps two Texture Segmentation figure Segmentation result, the segmentation result of three texture segmentation figures, the segmentation of the segmentation template of four Texture Segmentation figures and five Texture Segmentation figures Result；2 (f), 3 (f), 4 (f), use the algorithm of the present invention in 5 (f), respectively emulation experiment to synthetic texture maps two texture The segmentation result of segmentation figure, the segmentation result of three texture segmentation figures, the segmentation template of four Texture Segmentation figures and five Texture Segmentation figures Segmentation result be shown in Table 2；

Table 2

Table 2 gives the xb value of four kinds of methods, jm value, pbm value, clusters accuracy ar (accuracy rate) value, and The comparison of ari (adjusted rand index) desired value, the wherein result of fcm are that isolated operation takes best result 30 times.

Best value, the analysis of experimental result in four algorithms of expression of overstriking mark, Fig. 2,3,4 and 5 respectively describe Algorithm fcm, nsga-ii algorithm, imis algorithm, and inventive algorithm is respectively used to split two classes synthesis texture maps, three classes synthesis Texture maps, four class synthesis texture maps, and five classes synthesize the result of texture maps, and table 2 gives this four algorithms to different stricture of vaginas The xb of reason figure segmentation result, the result of jm, pbm, ari evaluation index, the value of xb is the smaller the better, the index of jm be also more little more Good, and two indices cannot concurrently reach minimum, and the value of pbm is to be the bigger the better, and the value of ari is also to be the bigger the better.

Can draw from Fig. 2, four algorithms all have reasonable segmentation result to two class Texture Segmentation figures it is possible to After drawing the Feature Fusion that use gabor of this paper and gray level co-occurrence matrixes extract respectively, can preferably catch the information of image, greatly Decrease greatly data volume, simplify the cutting procedure of image, Fig. 2,3 and 4 can be seen that algorithm fcm, imis, the calculation of the present invention Method all achieves preferable segmentation result, but combine table 2 find the present invention algorithm segmentation result accuracy except two Texture Segmentation by fcm leading outside, in three texture maps, four texture maps, the cluster of five texture maps strives for that rate will be calculated higher than other Method, segmentation result also will be better than other algorithms, although the fcm algorithm of single goal can obtain once preferably segmentation knot Really, but find during experiment, its segmentation result is unstable, isolated operation 30 times, and its average statistical is unstable, Other algorithms to be inferior in this respect,

It should be noted that as seen from Table 2, in three segmentation figures, fcm achieves the jm value of minimum, but pbm, ar, It is not but best that ari refers to target value, although and the algorithm of the present invention cannot obtain the minima of xb and jm, segmentation simultaneously The index of result is but optimum, illustrates that optimal solution is not present in the extreme value place of this two targets, but is present in them Compromise position, therefore, the model of multi-objective Algorithm can preferably mate this demand, find single object optimization algorithm and be not easy The compromise position finding, is conducive to the solution of problem, obtains the target solution more suitable for this problem.

Embodiment 4

Based on the multiple-target remote sensing image dividing method decomposing with embodiment 1-2, the segmentation effect of the present invention can pass through Hereinafter experiment further illustrates:

Experiment simulation environment is: the pentium dual_core cpu e5200 of dominant frequency 2.3ghz, the hardware of internal memory 2gb Environment and the software environment of matlab r2009a.

Also by Fuzzy c-Means Clustering Algorithm of the prior art (fcm) in experiment, imis (merges gabor filtering and gray scale The immune multi-object image segmentation algorithm of symbiosis complementary characteristic), nsga_ii (a fast and elitist multi- Objective genetic algorithm) algorithm is also separately in the segmentation to sar image, with the present invention with above-mentioned Three kinds of dividing methods are compared.

The setting of the setting of inventive algorithm and contrast algorithm is as follows, and the maximum iteration time of fcm is 120 times, obscures and refers to Number is 2, independent operating 30 times, therefrom chooses best result.The algorithm of nsga-ii, imis and this paper is all that multiple-objection optimization is entered Change algorithm, the setting of parameter is as follows:

Table 3

Algorithm	Population Size	Iterationses	Crossover probability	Mutation probability	Clustering target	Clone pool
							nsga-ii	100	30	0.8	1/n	xb jm	50
imis	100	20	0.8	0.1	xb jm	20
							Inventive algorithm	100	20	0.8	0.1	xb jm	---

Fig. 6 (a), the artwork of the two class sar image sar_1 of synthetic using in 7 (a) respectively emulation experiment, four The artwork of the sar image sar_2 of segmentation, image size is 256 × 256, and 8 (a) is the other width used in emulation experiment The sar image sar_3 artwork of three segmentations, size is 512 × 512, and 9 (a) is other four segmentations used in emulation experiment Sar image sar_4 artwork, size is 440 × 440；6 (b), is two classes sar of the synthetic figure used in emulation experiment The segmentation template of image sar_1；6 (c), 7 (b), 8 (b), 9 (b) are respectively algorithm fcm to sar_1, sar_2, sar_3 and sar_ 4 segmentation result；6 (d), 7 (c), 8 (c), 9 (c) are respectively the segmentation to sar_1, sar_2, sar_3 and sar_4 for the imis algorithm Result；6 (e), 7 (d), 8 (d), 9 (d) are respectively nsag-ii algorithm and the segmentation of sar_1, sar_2, sar_3 and sar_4 are tied Really；The segmentation result to sar_1, sar_2, sar_3 and sar_4 for the algorithm of 6 (f), 7 (e), 8 (e), 9 (e) the respectively present invention；

Table 4 gives the xb value of four kinds of methods, jm value, pbm value, clusters accuracy ar (accuracy rate) value, and The comparison of ari (adjusted rand index) desired value, the wherein result of fcm are that isolated operation takes best result 30 times.

Table 4

Fig. 6 (a) is the sar figure of two segmentations to synthetic it can be seen that four algorithms all achieve preferable segmentation As a result, this illustrates that our feature extracting method is applied to sar figure is also feasible, and the texture that can preferably catch sar figure is special Reference ceases, and can be further used for splitting.Fig. 7 is the segmentation result contrast of the true sar figure of four classes secondary to, and 7 (a) comprises machine Field runway, residential quarter, four, the lawn region of top-right lawn and lower left, dividing property of frontier district is required very high, especially Around residential quarter, existing runway has lawn region again.From the point of view of segmentation result, runway is demarcated by imis algorithm well Come, but two pieces of lawns region does not make a distinction, and also has much mixed and disorderly region around residential quarter, leads to segmentation result unclear Clear, four regions are not had separated by fcm algorithm and nsga-ii algorithm, and block region is preferably made a distinction by the present invention, And it is better than imis algorithm that image detail is processed.Fig. 8 is also the sar figure of real three segmentations of a width, comprises farmland, shrub And river, the atural object such as bridge it can be seen that the algorithm of fcm, imis and the present invention will be substantially separated for all river and shrubs, Nsga-ii but divide into a class farmland and river, middle part and one of the upper upper left corner on the right of the segmentation result image of fcm algorithm Point farmland has been divided into river, in the segmentation result of imis algorithm, some quilt of the farmland of mid portion on the right of image It is divided into river one class, and the algorithm of the present invention compares other three algorithms, wrong point of image area is minimum, table in 4 originally simultaneously The pbm value that the algorithm of invention obtains with regard to Fig. 8 (a) is also maximum.Fig. 9 (a) is also the sar figure of real four segmentations of a width, by occupying People area and different farmlands composition, segmentation difficult point is the differentiation between the division of residential block and different croplands, comes from segmentation result See, four algorithms are more or less the same to the local division result of residential block and farmland handing-over, but farmland in the middle part of image in Fig. 9 (b) Segmentation result has mixed and disorderly point, and Fig. 9 (c) is also that the farmland division in the middle part of image is unintelligible, and a part of farmland of top right-hand side is drawn Result is divided to obscure, in Fig. 9 (d), farmland divides unclassified really, and the farmland of image top has been also divided into residential block, figure 9 (e) divides clear for farmland out, and the interface portion in residential block and farmland is also clearer, in conjunction with table 4, the present invention The pbm of algorithm is also maximum.

In sum it was demonstrated that the algorithm of the present invention achieves more satisfied result in sar image segmentation.The present invention proposes Based on the sar image partition method decomposing Evolutionary multiobjective optimization and fcm, extract fusion feature as data to be clustered, more Good holding image detail；Choose two complementary object functions, improve that object function in existing method is single, a target letter The shortcomings of number comprises another object function.Multi-objective problem is resolved into a series of bands in based on the method decomposed by the present invention The subproblem of weights, to solve, reduces computation complexity, improves the precision of general image segmentation.And take full advantage of fcm The characteristic of Fast Convergent, simultaneously with overcoming fcm initial value sensitivity based on decomposition Evolutionary Multiobjective Optimization and being easily trapped into The defect of locally optimal solution, so that the algorithm after combining can have the quick ability finding optimal solution in global scope, obtains To more satisfied image segmentation result.

Claims (6)

1. based on the sar image partition method decomposing Evolutionary multiobjective optimization and fcm it is characterised in that: comprise the following steps:

Step 1: input remote sensing images to be split；

Step 2: extract characteristics of image to be split: extract the gabor characteristic vector of image using gabor wave filter, using gray scale Co-occurrence matrix method extract image gray scale symbiosis characteristic vector, and using fusion feature vector as image to be split each The characteristic vector of pixel；

Step 3: produce data features to be clustered: treat segmentation figure picture with watershed algorithm and carry out watershed coarse segmentation, obtain The super-pixel of artwork；The all pixels point feature that each super-pixel is comprised is averaged, and to represent initial clustering data Each super-pixel characteristic vector, with the set of the characteristic vector of all super-pixel as data features to be clustered, The size of features is nf × fl, and wherein nf represents the number of the super-pixel after coarse segmentation, and fl represents each super-pixel Characteristic vector dimension；

Step 4: using the initial population x={ x for n for the data initialization size to be clustered₁,x₂,...,x_n, each individual x_nAll generations One cluster centre of table, also represent a segmentation result, n=1 simultaneously, and 2 ..., n, n are initial population size；

Step 5: respectively each individual target function value f is calculated according to index xb and jm_n: the value being drawn according to index xb is made For target function value f_nFirst aim value, using the value being drawn according to index jm as target function value f_nSecond target Value:

f_n=[f1, f2]=[xb, jm]

Step 6: initialization ideal point z^*；

Wherein It is the 1st minima that up to the present object function xb finds,It is the 2nd target letter The minima that up to the present number jm finds；

Step 7: multi-objective problem f (x)=min (f1 (x), f2 (x)) is resolved into n son with Chebyshev's decomposition method and asks Topic, specifically the object function of each subproblem is as follows:

$\begin{array}{cc}\min imize& g_j^{te}\left(x\right|{\mathrm{\&lambda;}}^j,z^{*})=\underset{1\&le;i\&le;m}{max}\left\{{\mathrm{\&lambda;}}_i^j\right|f_{ji}\left(x\right)-z_i^{*}\left|\right\}\end{array}$

Wherein,Current reference point, i.e. the vector of the current optimal value composition of each target, the present invention The value of middle m is 2；Represent the object function of j-th subproblem；It is the power of j-th subproblem Value； J=1,2 ..., n；X represents a population at individual, f_jiX () represents the individual of j-th subproblem The value of corresponding i-th object function of body, in the present invention, the value of i is equal to the value of m, and value is 2；

Step 8: according to each subproblemWeights λ^j, calculate the s_n neighbours subproblem of each subproblem Nbor (j)=(nbor_j1,nbor_j2,...,nbor_{js_n}), nbor_jiRepresent the rope of i-th neighbours subproblem of j-th subproblem Draw, so nbor_jiValue be integer；Take s_n=10；I=1,2 ..., s_n；

Step 9: by each subproblemIndividual p_jT () is initialized as x_j, x_j∈ x, wherein t are iterationses, T=0；And calculate individual p_j(t) corresponding target function value ft_j；

Step 10: to each subproblemCorresponding individuality p_jT () carries out evolutional operation and obtains temporary individual p_j(t +1)”

10.1 randomly choose 3 neighbours subproblem s, k, l in s_n neighbour subproblem nbor (j) of j-th subproblem, right The individual p of s, k, l neighbours subproblem_s(t), p_k(t), p_lT () is simulated two and enters crossover operation, obtain new facing When offspring individual p_j(t+1)'；

10.2 couples of temporary individual p_j(t+1) ' carry out multinomial mutation operation, obtain individual p_j(t+1)”；

Step 11: to the individual p obtaining_j(t+1) " carry out an iteration operation with fcm algorithm and obtain new individual p_j(t+1)；

Step 12: calculate new temporary individual p_j(t+1) two target function value newf_j1And newf_j2, and according to newf_j1With newf_j2Update ideal point z^*；By new temporary individual p_jAnd its desired value newf (t+1)_j1And newf_j2To update j-th son All s_n neighbours subproblem nbor (j) of problem corresponding individuality and each individual corresponding target function value respectively；

Step 13: judge whether current iteration number of times t meets t ＜ tmax, such as meet, then execution step 13；Otherwise, make iteration time Number t adds a t=t+1, and return to step 11, wherein tmax are maximum iteration time, take tmax=20；

Step 14: select suitably individuality from population as cluster centre: by each subproblemParent Individual p_jT () takes out, using each individual cluster centre as the super-pixel that will cluster, using these cluster centres as Whole output disaggregation；And a selection individual is concentrated as cluster centre from final output solution according to third party's index p bm；

Step 15: obtain the classification number of each pixel: the characteristic vector calculating each pixel and the cluster obtaining from step 14 The Euclidean distance at center, is grouped into this pixel in the classification of the minimum cluster centre of its Euclidean distance, obtains each The classification of pixel；

Step 16: output segmentation figure picture.

2. the sar image partition method based on decomposition Evolutionary multiobjective optimization and fcm according to claim 1, its feature It is:

The process of the extraction characteristics of image to be split described in step 2 includes the following:

2.1.1 the process being extracted the medium and low frequency texture feature vector of image using gabor wave filter is included: the gabor of bidimensional Kernel function can be defined as:

$g(x,y)=\frac{1}{2{\mathrm{\&pi;\&sigma;}}_x{\mathrm{\&sigma;}}_y}\exp \&lsqb;-\frac{1}{2}(\frac{x^2}{{\mathrm{\&sigma;}}_x^2}+\frac{y^2}{{\mathrm{\&sigma;}}_y^2})+j2\mathrm{\&pi;}f(x\cos \mathrm{\&theta;}+y\sin \mathrm{\&theta;})\&rsqb;$

Wherein, σ_xAnd σ_yRepresent oval Gaussian function respectively along the standard deviation on x and y direction, f is modulating frequency, and θ is gabor The direction of kernel function；

2.2.1 included using the process of algorithm of co-matrix texture feature extraction vector: first by pending image quantization For certain gray level, local window size can design according to object of experiment, and the distance between pixel is d_n, then makes successively The angular separation of two pixel lines and transverse axis is certain angle, calculates the ash of the direction number of requirement according to the following formula respectively Degree co-occurrence matrix:

P (i, j)=# { (x₁,y₁),(x₂,y₂)∈m×nf(x₁,y₁)=r, f (x₂,y₂)=s }

Wherein, p (i, j) is element on coordinate (i, j) position for the gray level co-occurrence matrixes, and # is the element number of set { }, (x₁, y₁) and (x₂,y₂) be two pixel point coordinates that distance is equal to d_n, ∈ be set in belong to symbol, m × n be pending figure The size of picture, is the conditional code in theory of probability, and r is (x₁,y₁) gray value after place's pixel vector quantization, s is (x₂,y₂) place Gray value after pixel vector quantization.

3. the sar image partition method based on decomposition Evolutionary multiobjective optimization and fcm according to claim 1, its feature It is:

The calculating process calculating each individual target function value described in step 5 includes:

The formula of 5.1 target function value f1 and f2 being obtained according to xb index and jm index respectively is as follows:

$f1=xb=\frac{\underset{p=1}{\overset{k}{\&sigma;}}\underset{i,j=1}{\overset{nf}{\&sigma;}}{u}_{pj}^2\left|\right|{\mathrm{features}}_j-c_p|{|}^2}{{\mathrm{nfmin}}_{i,j}\left|\right|c_i-c_j\left|\right|}$

$f2=jm=\underset{j=1}{\overset{nf}{\&sigma;}}\underset{p=1}{\overset{k}{\&sigma;}}{u}_{pj}^2\left|\right|{\mathrm{features}}_j-c_p|{|}^2$

$u_{pj}=\frac{1}{\underset{j=1}{\overset{k}{\&sigma;}}{\left(\frac{\left|\right|c_p-{\mathrm{features}}_j\left|\right|}{\left|\right|c_i-{\mathrm{features}}_j\left|\right|}\right)}^2}$

Wherein, features_jIt is the pixel characteristic matrix extracting, j=1,2 ..., nf is the eigenmatrix extracting after feature Line number, i.e. the number of the image block after image coarse segmentation, c_p, p=1,2 ... k, is the cluster centre of image pixel, and k refers to The number of fixed cluster centre, u_k×nfIt is fuzzy membership matrix；

5.2 each individual target function value f_n=[f_n1,f_n2], wherein, f_n1=f1=xb, f_n2=f2=jm.

4. the sar image partition method based on decomposition Evolutionary multiobjective optimization and fcm according to claim 1, its feature It is:

To the individual p obtaining in step 11_j(t+1) " carry out an iteration operation with fcm algorithm and obtain new individual p_j(t+1) Implication is as follows:

11.1 individual p_j(t+1) " as cluster centre c, according to the Europe of this cluster centre c to data features to be clustered Family name's distance obtains the fuzzy membership matrix u of this cluster centreⁱ _j, uⁱ _jBe calculated as follows:

$u_{ij}=\frac{1}{\underset{k=1}{\overset{c}{\&sigma;}}{\left(\frac{d_{ij}}{d_{kj}}\right)}^{2/(m-1)}}$

u_ijIt is between 0, between 1, c_iIt is the cluster centre of ambiguity group i, d_ij=| | c_i-features_j| | represent ith cluster The Euclidean distance of j-th data point of center and features, and m ∈ [1, ∞), m=2 in the present invention；

11.2 according to the 11.1 fuzzy membership matrix u obtainingⁱ _jCluster centre c' after being updated, c' is calculated as follows:

$c_i^{\&prime;}=\frac{\underset{j=1}{\overset{nf}{\&sigma;}}{u}_{ij}^m{\mathrm{features}}_j}{\underset{j=1}{\overset{nf}{\&sigma;}}{u}_{ij}^m}$

features_jIt is j-th data point, nf is the number of the data point that features comprises；

11.3 c' obtaining are as new individual p_j(t+1).

5. the sar image partition method based on decomposition Evolutionary multiobjective optimization and fcm according to claim 1, its feature It is: step 12 ideal point z^*Renewal process and the more parent individuality of new neighbor subproblem and its corresponding desired value process Include the following:

12.1 ideal point z^*Renewal process include: ifOtherwise constant；If Otherwise constant；

The process of all individual and its corresponding desired value of 12.2 more new neighbor subproblems includes: for new temporary individual p_j(t+1) each neighbours subproblem, nbor_ji∈ nbor (j), i=1,2 ..., s_n, wherein s_n are neighbours subproblems Number, if for all of nbor_jiHaveThen with new Temporary individual p_j(t+1) substitute the corresponding individuality of i-th neighbours subproblem of j-th subproblemAnd use newf_j1With newf_j2Substitute the corresponding target function value of i-th neighbours subproblem of j-th subproblemOtherwise, constant.

6. the sar image partition method based on decomposition Evolutionary multiobjective optimization and fcm according to claim 1, its feature It is:

The process according to third party's index p bm selection generation optimum segmentation result described in step 14 is as follows:

14.1 values being obtained according to third party's index p bm obtaining each cluster centre first:

$ic\left(index\right)=pbm\left(k\right)={(\frac{1}{k}\&times;\frac{ec}{e_k}\&times;d_k)}^2,$

$e_k=\underset{p=1}{\overset{k}{\&sigma;}}\underset{j=1}{\overset{n}{\&sigma;}}{u}_{pj}\left|\right|{\mathrm{features}}_j-c_p\left|\right|,d_k={\max }_{i,j=1}^k\left|\right|c_i-c_j\left|\right|$

Wherein, features_j,c_p,u_pjConsistent with the description in step 2, index=1 ... n, n are in currently available cluster The number of the heart, k is intended to the class number split, e_kBe the corresponding cluster centre of super-pixel that a splitting scheme obtains away from From sum d_kIt is the maximum separation between cluster centre, ec is each features_j, j=1 ... nf to features's is several What center apart from sum, it is equal that each cluster centre obtains ec.