CN105678798A - Multi-target fuzzy clustering image segmentation method combining local spatial information - Google Patents

Abstract

The invention discloses a multi-target fuzzy clustering image segmentation method combining local spatial information. The multi-target fuzzy clustering image segmentation method comprises the steps of: 1, inputting an image to be segmented; 2, calculating a nonlinear weighted sum image; 3, carrying out multi-target fuzzy clustering on the weighted image obtained in step 2; 4, acquiring a group of Pareto solution sets through the above development, and selecting an optimal individual from the Pareto solution sets by adopting a clustering index I; 5, and utilizing the optimal individual, namely, a group of optimal clustering centers for clustering pixels of the weighted sum image, and finally carrying out class marking on the pixels in the weighted sum image to obtain a final segmentation result of the image. The multi-target fuzzy clustering image segmentation method can effectively separate a target from a background, is accurate in segmentation results and is simple in algorithm implementation.

Description

A kind of multi objective fuzzy in conjunction with local spatial information clusters image partition method

Technical field

The invention belongs to image processing field, be specifically related to a kind of multi objective fuzzy in conjunction with local spatial information and cluster image partition method.

Background technology

Image segmentation is the committed step that image procossing arrives graphical analysis, its objective is to divide the image into several disjoint regions according to the gray scale of pixel, color and Texture eigenvalue in image, and make to be characterized by the same area similarity, and feature has obvious diversity between zones of different.

Being typically based on some clustering criteria based on the image partition method of fuzzy clustering and differentiate the ownership of pixel in image, the image segmentation result therefore obtained is optimum under this criterion or close to optimum. In actual applications, image segmentation is the different demands needed according to people or different applied environments, from the problem that multiple angles consider. It addition, the maximum shortcoming of fuzzy clustering is not account for spatial information any in image so that method is for the noise-sensitive in image, it is impossible to obtain satisfied segmentation result in Noise image is split.

Summary of the invention

It is an object of the invention to provide a kind of multi objective fuzzy in conjunction with local spatial information and cluster image partition method, with the defect overcoming above-mentioned prior art to exist, target and background can be separated by the present invention effectively, and segmentation result is accurate, and algorithm realizes simple.

For reaching above-mentioned purpose, the present invention adopts the following technical scheme that

A kind of multi objective fuzzy in conjunction with local spatial information clusters image partition method, comprises the following steps:

First step 1: input image to be split, if image to be split is RGB image, then transform the image into gray level image;

Step 2: calculate nonlinear weight and image ξ;

Step 3: the weighted sum image that step 2 is obtained carries out multi objective fuzzy cluster;

Step 4: obtain one group of Pareto disaggregation by step 3, adopts clustering target I therefrom to select an optimum individual;

Step 5: then utilize optimum individual that weighted sum image pixel is clustered, finally the pixel in weighted sum image is carried out category label, obtains the final segmentation result of image.

Further, step 2 calculates nonlinear weight and image ξ method particularly includes:

${\mathrm{\ξ}}_j=\frac{\underset{p\∈S_j}{\Σ}{E}_{jp}^{\′}{x}_p}{\underset{p\∈S_j}{\Σ}{E}_{jp}^{\′}}$

Wherein, ξ_jRepresent the jth pixel value of weighted sum image ξ, S_jRepresent the neighborhood window centered by pixel j, E'_jpRepresent the local similarity between pixel j and pixel p, E'_jpConcrete form as follows:

$E_{jp}^{\′}=\left\{\begin{array}{cc}\exp (-\frac{|a_j-a_p|+|b_j-b_p|}{{\mathrm{\λ}}_s}-\frac{\left|\right|x_j-x_p\left|\right|}{{\mathrm{\λ}}_g{\mathrm{\σ}}_j^2})& j\≠p\\ 0,& j=p\end{array}\right.$

Wherein, | a_j-a_p|+|b_j-b_p| represent the manhatton distance of pixel j and pixel p locus, x_j, x_pRepresent pixel j and pixel p gray value, λ_sAnd λ_gIt is two scale parameters, σ_jExpression formula beWherein, S_RIt is neighborhood window S_jThe number of interior pixel.

Further, described multi objective fuzzy cluster includes chromosome and generates and initialization of population, selects, intersects and mutation operation.

Further, the weighted sum image in step 3, step 2 obtained carries out multi objective fuzzy cluster method particularly includes:

3a) initiation parameter: clusters number c, population scale is 100, and maximum algebraically is 200, and crossover probability is 0.9 mutation probability is 0.1, gene code scope 0～255, λ_sIt is 3, λ_gIt is 8, S_RIt is 8;

3b) initialization of population, randomly generates 100 individualities, it is assumed that being divided into K class then each chromosome to have K gene position, each gene position value is 0～255, G=1;

3c) calculate 2 target function values of each individuality in population, two target function values are respectively added to chromosomal K+1, K+2 gene position;

3d) utilize step 3c) in the target function value that calculates population is carried out non-dominated ranking, and individual non-of inferior quality level and crowding distance are respectively added to chromosomal K+3, K+4 gene position;

3e) start to evolve, with tournament method, from population, select the individuality of half quantity as parent according to sequence value and crowding distance;

3f) parent individuality is intersected and mutation operation, produce filial generation;

3g) current population is merged with progeny population, then sort and delete, it is thus achieved that the of new generation population consistent with initial population number of individuals;

If 3h) G > 200, then perform step 4; Otherwise, G=G+1, jump to step 3c).

Further, in step 4, clustering target I is:

$I={(\frac{1}{c}\×\frac{E_1}{E_c}\×D_{max})}^2$

Wherein E_c, D_maxDefinition as follows:

$E_c=\underset{i=1}{\overset{c}{\Σ}}\underset{k=1}{\overset{n}{\Σ}}{u}_{ik}D(v_i,x_k)$

$D_{max}={\max }_{i,j=1}^{c}D(v_i,v_j)$

In formula, c is cluster centre number, and n is the number of sample data to be clustered, E_cIt is weigh the function of compactness, E in class₁It is E_cMiddle i takes value when 1, is a constant, D_maxBe measure all clusters to the function of maximum separability, D (v_i,x_k) it is ith cluster center and the distance of kth sample, D (v_i,v_j) it is ith cluster center and the distance of jth cluster centre, u_ikIndicate that the kth sample degree of membership to ith cluster center.

Further, described step 3c) in two object functions: one is the function CJ of class compactness in embodying, and another is to embody the function CS of separating degree between class, it is assumed that one group of cluster centre is V={v₁,v₂,...,v_c, then degree of membership u_ik(i=1,2 ..., c, k=1,2 ..., calculation expression n) is:

$u_{ik}=\frac{1}{\underset{j=1}{\overset{c}{\Σ}}{\left(D\right(v_i,x_k)/D(v_j,x_k\left)\right)}^{2/(m-1)}},1\≤i\≤c;1\≤k\≤n$

Wherein, c is cluster centre number, and n is sample data number to be clustered, D (v_i,x_k) it is ith cluster center and the distance of kth sample, D (v_j,x_k) it is jth cluster centre and the distance of kth sample, m takes 2, the definition according to cluster centre and degree of membership, two kinds of clustering target of separating degree CS between compactness CJ and class in class, namely

$CJ=\underset{i=1}{\overset{c}{\Σ}}\frac{\underset{k=1}{\overset{n}{\Σ}}{u}_{ik}^{m}D(v_i,x_k)}{\underset{k=1}{\overset{n}{\Σ}}{u}_{ik}}$

$CS=\underset{i=1}{\overset{c}{\Σ}}\underset{j=1,j\≠i}{\overset{c}{\Σ}}{\mathrm{\δ}}_{ij}^{m}D(v_i,v_j)$

Wherein, D (v_i,v_j) it is ith cluster center and the distance of jth cluster centre, δ_ijIt is defined as:

${\mathrm{\δ}}_{ij}=\frac{1}{\underset{l=1,l\≠j}{\overset{c}{\mathrm{\Σ}}}{\left(D\left(v_i,v_j\right)/D\left(v_l,v_j\right)\right)}^{2/\left(m-1\right)}},i\≠j.$

In order to obtain Optimal cluster centers, while minimizing CJ, maximize CS, adopt CJ and 1/CS two object functions clustered as multi objective fuzzy.

Compared with prior art, the present invention has following useful technique effect:

The present invention defines a new nonlinear weight and image first with the gray value in original image and neighborhood of pixels window and locus, thus overcomes the noise impact on segmentation effect in image segmentation process. Then multi-target evolution clustering clustering is utilized. Compared with the clustering algorithm based on single clustering criteria, multi-target evolution clustering is almost no longer to initializing cluster centre sensitivity and being not easily absorbed in local optimum, and cluster result more meets the diverse requirements of people. Owing to invention make use of multi objective fuzzy clustering method so that target can than more completely be separated from background, it is thus achieved that ideal segmentation effect.

Accompanying drawing explanation

Fig. 1 is the overall flow figure of the inventive method;

Fig. 2 is Berkeley image data base the first image segmentation result comparison diagram used in emulation experiment of the present invention;

Fig. 3 is Berkeley image data base the second image segmentation result comparison diagram used in emulation experiment of the present invention:

Wherein, (a) artwork; (b) Standard Segmentation result; (c) salt-pepper noise figure; (d) FGFCM (salt-pepper noise) method segmentation result; (e) the inventive method (locus adopts Chebyshev's distance, salt-pepper noise); (f) the inventive method (salt-pepper noise). (g) Gaussian noise figure; (h) FGFCM (Gaussian noise) method segmentation result; (i) the inventive method (locus adopts Chebyshev's distance, Gaussian noise) (j) the inventive method (Gaussian noise). (k) mixed noise figure; (l) FGFCM (mixed noise) method segmentation result; (m) the inventive method (locus adopts Chebyshev's distance, mixed noise) (n) the inventive method (mixed noise).

Detailed description of the invention

Below the implementation process of the present invention is further described:

Referring to Fig. 1, the present invention comprises the following steps in conjunction with the multi objective fuzzy cluster image partition method of local spatial information:

1. first the image that input is to be split, if image to be split is RGB image, then transform the image into gray level image;

2. calculate nonlinear weight and image ξ. It is specially;

Utilizing the original image in step 1 and the gray scale in neighborhood of pixels window and locus to define a nonlinear weight and image, it is defined as follows:

${\mathrm{\ξ}}_j=\frac{\underset{p\∈S_j}{\Σ}{E}_{jp}^{\′}{x}_p}{\underset{p\∈S_j}{\Σ}{E}_{jp}^{\′}}$

Wherein, ξ_jRepresenting the jth pixel value of weighted sum image ξ, view picture nonlinear weight and image ξ are through pixel one by one and calculate, S_jRepresent the neighborhood window centered by pixel j, E'_jpRepresent the local similarity between pixel j and pixel p, E'_jpConcrete form as follows:

$E_{jp}^{\′}=\left\{\begin{array}{cc}\exp (-\frac{|a_j-a_p|+|b_j-b_p|}{{\mathrm{\λ}}_s}-\frac{\left|\right|x_j-x_p\left|\right|}{{\mathrm{\λ}}_g{\mathrm{\σ}}_j^2})& j\≠p\\ 0,& j=p\end{array}\right.$

Wherein, | a_j-a_p|+|b_j-b_p| represent the manhatton distance of pixel j and pixel p locus, x_j, x_pRepresent pixel j and pixel p gray value, λ_sAnd λ_gIt is two scale parameters, σ_jExpression formula beWherein, S_RIt is neighborhood window S_jThe number of interior pixel.

3. the weighted image that pair step 2 obtains carries out multi objective fuzzy cluster, and multi objective fuzzy cluster is a kind of evolutionary optimization algorithm, and multi objective fuzzy cluster mainly includes chromosome and generates and initialization of population, selects, intersects and mutation operation, specific as follows:

3a) initiation parameter: clusters number c, population scale is 100, and maximum algebraically is 200, and crossover probability is 0.9 mutation probability is 0.1, gene code scope 0～255. λ_sIt is 3, λ_gIt is 8, S_RIt is 8.

3b) initialization of population, randomly generates 100 individualities. Assuming to be divided into K class then each chromosome to have K gene position, each gene position value is 0～255, G=1.

3c) calculate 2 target function values of each individuality in population, two target function values are respectively added to chromosomal K+1, K+2 gene position.

Described step 3c) in two object functions: one is the function CJ of class compactness in embodying, and another is to embody the function CS of separating degree between class, it is assumed that one group of cluster centre is V={v₁,v₂,...,v_c, then degree of membership u_ik(i=1,2 ..., c, k=1,2 ..., calculation expression n) is:

$u_{ik}=\frac{1}{\underset{j=1}{\overset{c}{\Σ}}{\left(D\right(v_i,x_k)/D(v_j,x_k\left)\right)}^{2/(m-1)}},1\≤i\≤c;1\≤k\≤n$

Wherein, c is cluster centre number, and n is sample data number to be clustered, D (v_i,x_k) it is ith cluster center and the distance of kth sample, D (v_j,x_k) it is jth cluster centre and the distance of kth sample, m takes 2, the definition according to cluster centre and degree of membership, two kinds of clustering target of separating degree CS between compactness CJ and class in class, namely

$CJ=\underset{i=1}{\overset{c}{\Σ}}\frac{\underset{k=1}{\overset{n}{\Σ}}{u}_{ik}^{m}D(v_i,x_k)}{\underset{k=1}{\overset{n}{\Σ}}{u}_{ik}}$

$CS=\underset{i=1}{\overset{c}{\Σ}}\underset{j=1,j\≠i}{\overset{c}{\Σ}}{\mathrm{\δ}}_{ij}^{m}D(v_i,v_j)$

Wherein, D (v_i,v_j) it is ith cluster center and the distance of jth cluster centre, δ_ijIt is defined as:

${\mathrm{\δ}}_{ij}=\frac{1}{\underset{l=1,l\≠j}{\overset{c}{\mathrm{\Σ}}}{\left(D\left(v_i,v_j\right)/D\left(v_l,v_j\right)\right)}^{2/\left(m-1\right)}},i\≠j.$

In order to obtain Optimal cluster centers, it is necessary to minimize CJ, maximize CS simultaneously.This method adopts CJ and 1/CS two object functions clustered as multi objective fuzzy.

3d) utilize step 3c) in the target function value that calculates population is carried out non-dominated ranking, and individual non-of inferior quality level and crowding distance are respectively added to chromosomal K+3, K+4 gene position.

3e) start to evolve, with tournament method, from population, select the individuality of half quantity as parent according to sequence value and crowding distance.

3f) parent individuality is intersected and mutation operation, produce filial generation.

3g) current population is merged with progeny population, then sort and delete, it is thus achieved that the of new generation population consistent with initial population number of individuals.

If 3h) G > 200, then perform step 4. Otherwise, G=G+1, jump to step 3c).

Step 4: by evolution above, obtains one group of Pareto disaggregation, adopts clustering target I therefrom to select an optimum individual. C is clusters number, particularly as follows:

$I={(\frac{1}{c}\×\frac{E_1}{E_c}\×D_{max})}^2$

Wherein E_c, D_maxDefinition as follows:

$E_c=\underset{i=1}{\overset{c}{\Σ}}\underset{k=1}{\overset{n}{\Σ}}{u}_{ik}D(v_i,x_k)$

$D_{max}={\max }_{i,j=1}^{c}D(v_i,v_j)$

In formula, c is cluster centre number, and n is the number of sample data to be clustered, E_cIt is weigh the function of compactness, E in class₁It is E_cMiddle i takes value when 1, is a constant, D_maxBe measure all clusters to the function of maximum separability, D (v_i,x_k) it is ith cluster center and the distance of kth sample, D (v_i,v_j) it is ith cluster center and the distance of jth cluster centre, u_ikIndicate that the kth sample degree of membership to ith cluster center.

Step 5: then utilize optimum individual that is one group Optimal cluster centers that weighted sum image pixel is clustered, finally the pixel in weighted sum image is carried out category label, obtain the final segmentation result of image.

Referring to Fig. 2, Fig. 3, below in conjunction with concrete emulation experiment figure, the effect of the present invention is described in further detail. Simulated conditions is: computer IntelCorei3M3802.53GHZCPU, 4G internal memory, carries out under MATLAB2010b software environment.

In order to verify effectiveness of the invention, experiment is chosen the 2 width images (as shown in (a) of Fig. 2-3) in Berkeley image data base, three types noise respectively salt-pepper noise (0,0.03), Gaussian noise (0,0.02), the mixed noise (spiced salt (0,0.01) and Gauss (0,0.01)), invention and FGFCM method and weighted sum image are adopted the present invention (present invention-Chybechev) contrast of Chebyshev's distance. Experimental image comparison diagram under salt-pepper noise is illustrated in (c)-(f) of Fig. 2-3 respectively, comparison diagram under Gaussian noise is illustrated in (g)-(j) of Fig. 2-3 respectively, comparison diagram under mixed noise is illustrated in (k)-(n) of Fig. 2-3 respectively, and (b) of Fig. 2-3 is Standard Segmentation result.

Simulated effect is analyzed: the present invention is more accurate to the segmentation result of the ration of division FGFCM (fast generalized FuzzycMeans Clustering) of target and background. Under additionally on #135069 image, Gaussian noise and mixed noise affect, context of methods adopts the context of methods of Chebyshev's distance to achieve more preferably segmentation result than weighted sum image.

Claims (6)

1. the multi objective fuzzy in conjunction with local spatial information clusters image partition method, it is characterised in that comprise the following steps:

First step 1: input image to be split, if image to be split is RGB image, then transform the image into gray level image;

Step 2: calculate nonlinear weight and image ξ;

Step 3: the weighted sum image that step 2 is obtained carries out multi objective fuzzy cluster;

Step 4: obtain one group of Pareto disaggregation by step 3, adopts clustering target I therefrom to select an optimum individual;

Step 5: then utilize optimum individual that weighted sum image pixel is clustered, finally the pixel in weighted sum image is carried out category label, obtains the final segmentation result of image.

2. a kind of multi objective fuzzy in conjunction with local spatial information according to claim 1 clusters image partition method, it is characterised in that calculate nonlinear weight and image ξ in step 2 method particularly includes:

${\mathrm{\ξ}}_j=\frac{\underset{p\∈S_j}{\Σ}{E}_{jp}^{\′}{x}_p}{\underset{p\∈S_j}{\Σ}{E}_{jp}^{\′}}$

Wherein, ξ_jRepresent the jth pixel value of weighted sum image ξ, S_jRepresent the neighborhood window centered by pixel j, E'_jpRepresent the local similarity between pixel j and pixel p, E'_jpConcrete form as follows:

$E_{jp}^{\′}=\left\{\begin{array}{cc}\exp (-\frac{|a_j-a_p|+|b_j-b_p|}{{\mathrm{\λ}}_s}-\frac{\left|\right|x_j-x_p\left|\right|}{{\mathrm{\λ}}_g{\mathrm{\σ}}_j^2})& j\≠p\\ 0,& j=p\end{array}\right.$

Wherein, | a_j-a_p|+|b_j-b_p| represent the manhatton distance of pixel j and pixel p locus, x_j, x_pRepresent pixel j and pixel p gray value, λ_sAnd λ_gIt is two scale parameters, σ_jExpression formula beWherein, S_RIt is neighborhood window S_jThe number of interior pixel.

3. a kind of multi objective fuzzy in conjunction with local spatial information according to claim 2 clusters image partition method, it is characterised in that described multi objective fuzzy cluster includes chromosome and generates and initialization of population, selects, intersects and mutation operation.

4. a kind of multi objective fuzzy in conjunction with local spatial information according to claim 3 clusters image partition method, it is characterised in that the weighted sum image in step 3, step 2 obtained carries out multi objective fuzzy cluster method particularly includes:

3a) initiation parameter: clusters number c, population scale is 100, and maximum algebraically is 200, and crossover probability is 0.9 mutation probability is 0.1, gene code scope 0～255, λ_sIt is 3, λ_gIt is 8, S_RIt is 8;

3b) initialization of population, randomly generates 100 individualities, it is assumed that being divided into K class then each chromosome to have K gene position, each gene position value is 0～255, G=1;

3c) calculate 2 target function values of each individuality in population, two target function values are respectively added to chromosomal K+1, K+2 gene position;

3d) utilize step 3c) in the target function value that calculates population is carried out non-dominated ranking, and individual non-of inferior quality level and crowding distance are respectively added to chromosomal K+3, K+4 gene position;

3e) start to evolve, with tournament method, from population, select the individuality of half quantity as parent according to sequence value and crowding distance;

3f) parent individuality is intersected and mutation operation, produce filial generation;

3g) current population is merged with progeny population, then sort and delete, it is thus achieved that the of new generation population consistent with initial population number of individuals;

If 3h) G > 200, then perform step 4; Otherwise, G=G+1, jump to step 3c).

5. a kind of multi objective fuzzy in conjunction with local spatial information according to claim 4 clusters image partition method, it is characterised in that in step 4, clustering target I is:

$I={(\frac{1}{c}\×\frac{E_1}{E_c}\×D_{max})}^2$

Wherein E_c, D_maxDefinition as follows:

$E_c=\underset{i=1}{\overset{c}{\Σ}}\underset{k=1}{\overset{n}{\Σ}}{u}_{ik}D(v_i,x_k)$

$D_{max}={\max }_{i,j=1}^{c}D(v_i,v_j)$

In formula, c is cluster centre number, and n is the number of sample data to be clustered, E_cIt is weigh the function of compactness, E in class₁It is E_cMiddle i takes value when 1, is a constant, D_maxBe measure all clusters to the function of maximum separability, D (v_i,x_k) it is ith cluster center and the distance of kth sample, D (v_i,v_j) it is ith cluster center and the distance of jth cluster centre, u_ikIndicate that the kth sample degree of membership to ith cluster center.

6. a kind of multi objective fuzzy in conjunction with local spatial information according to claim 4 clusters image partition method, it is characterized in that, described step 3c) in two object functions: one is the function CJ of class compactness in embodying, another is to embody the function CS of separating degree between class, it is assumed that one group of cluster centre is V={v₁,v₂,…,v_c, then degree of membership u_ik(i=1,2 ..c, k ,=1,2, n, calculation expression be:

$u_{ik}=\frac{1}{\underset{j=1}{\overset{c}{\Σ}}{\left(D\right(v_i,x_k)/D(v_j,x_k\left)\right)}^{2/(m-1)}},1\≤i\≤c;1\≤k\≤n$

Wherein, c is cluster centre number, and n is sample data number to be clustered, D (v_i,x_k) it is ith cluster center and the distance of kth sample, D (v_j,x_k) it is jth cluster centre and the distance of kth sample, m takes 2, the definition according to cluster centre and degree of membership, two kinds of clustering target of separating degree CS between compactness CJ and class in class, namely

$CJ=\underset{i=1}{\overset{c}{\Σ}}\frac{\underset{k=1}{\overset{n}{\Σ}}{u}_{ik}^{m}D(v_i,x_k)}{\underset{k=1}{\overset{n}{\Σ}}{u}_{ik}}$

$CS=\underset{i=1}{\overset{c}{\Σ}}\underset{j=1,j\≠i}{\overset{c}{\Σ}}{\mathrm{\δ}}_{ij}^{m}D(v_i,v_j)$

Wherein, D (v_i,v_j) it is ith cluster center and the distance of jth cluster centre, δ_ijIt is defined as:

${\mathrm{\δ}}_{ij}=\frac{1}{\underset{l=1,l\≠j}{\overset{c}{\Σ}}{\left(D\right(v_i,v_j)/D(v_l,v_j\left)\right)}^{2/(m-1)}},i\≠j.$

In order to obtain Optimal cluster centers, while minimizing CJ, maximize CS, adopt CJ and 1/CS two object functions clustered as multi objective fuzzy.