CN106846326A - Image partition method based on multinuclear local message FCM algorithms - Google Patents

Abstract

The invention discloses a kind of image partition method based on multinuclear local message FCM algorithms, it is characterized in that carrying out as follows：1 pair of pixel set carries out optimal dividing so that target function value is minimum；2 obtain initial subordinated-degree matrix and initialization cluster centre；3 iteration are obtained and are subordinate to angle value and cluster centre；4 obtain the object function introduced after weighted index.The present invention can accurately evade that FCM is more sensitive to noise spot and common accounting method for Selection of kernel function uncertain problem, can find to be best suitable for weighted value and the current size for being subordinate to angle value simultaneously, and then improve the reliability and convergence of algorithm, and be applied in image segmentation, the image segmentation result that can be worked well.

Description

Image partition method based on multinuclear local message FCM algorithms

Technical field

The invention belongs to the algorithm that Data Mining carries out data classification, specifically a kind of multinuclear local message Fuzzy c-Means Clustering Algorithm, and it is applied to image segmentation.

Background technology

Cluster is a critically important branch of non-supervised recognition, and the final purpose of cluster is to make between similar pixel Distance it is small as far as possible, make the distance between different pixels big as far as possible, distinguish data in this way, number of classifying According to.Image procossing is the important component of computer vision, and two demands of aspect, first human eye are met using fuzzy clustering The subjectivity of vision makes image be well suited for being processed with fuzzy means, and secondly, the deficient of training pixel image needs to carry out Unsupervised analysis, it is image segmentation that fuzzy clustering is most commonly used in image processing field, that is, equivalent to image Pixel carries out unsupervised classification, and the image partition method based on fuzzy clustering has a lot, and in Study Of Segmentation Of Textured Images, it is colored Image segmentation aspect also makes great progress.Fuzzy C-Means Cluster Algorithm (FCM) is of people's research fuzzy clustering Basic skills, is a kind of fuzzy clustering algorithm grown up via Bezdek by Dunn propositions, and the algorithm is based primarily upon minimum The concept of square error, and specify all pixels degree of membership sum be 1.The FCM algorithms feelings uneven to number of pixels When being clustered under condition, often cannot get preferable result.

Face Krishnapuram and Keller relax the constraint bar of degree of membership on the basis of Fuzzy c-Means Clustering Algorithm Part, it is proposed that possibility clustering algorithm PCM.PCM algorithms are subordinate to angle value and can reflect data point to the actual distance of cluster centre, The reason for this is also PCM algorithms relatively good to noise robustness, this is also the improvements compared to FCM algorithms, but PCM algorithms Globally optimal solution could can only be really obtained when all of cluster centre overlaps.

A kind of improved possibility clustering algorithm cluster mode is proposed based on above reason Zhang in the literature, increases by one Plant new parameter η_iTo reduce the error of algorithm, although the clustering algorithm of possibility can overcome the problem that uniformity is clustered, so And for original m_pThe selection quite sensitive of parameter, different m_pEven if value difference very little, the cluster centre for finally obtaining also can It is two completely different numerical value.The c means clustering algorithms (PFCM) that a kind of improvement that Nikhil is proposed is improved, that is, obscure C means clustering algorithms.PFCM algorithms have good noise robustness, will not also produce the cluster of coincidence, but PFCM algorithms The selection of parameter is generally needed it is artificial specify and lack theoretic foundation, with stronger dependence.Krinidis is carried Go out a kind of c means clustering algorithms based on fuzzy local message, the algorithm is by introducing local parameter G_kiEffectively prevent original Selection of the beginning FCM algorithm to parameter, at the same by build fusion local spatial information fuzzy factor come suppress picture noise and Image detail is kept, the segmentation accuracy of image is effectively raised, achieved on containing noisy image segmentation good Effect.But the clustering algorithm has good Clustering Effect for linear data, but for the cluster of nonlinear data Often effect is less desirable, meanwhile, when image is by noise severe contamination, the neighborhood territory pixel of pixel is likely to dirty Dye.Now, the local spatial information of pixel cannot play effectively positive effect in the image segmentation of Noise.

By introducing kernel function, initial data is passed through into mercer cores condition by pixel data x={ x₁,x₂,···, x_nBe mapped in high-dimensional feature space F, mapping data are respectively { φ (x₁),φ(x₂),···,φ(x_n), and in space F In pixel is clustered, formed based on core fuzzy clustering algorithm, the difference between nuclear space can amplify pixel, increase The accuracy rate of cluster.The fuzzy clustering algorithm KFCM, Genton based on core that Yang is proposed in the literature are from statistical angle The machine learning mode of a seed nucleus is illustrated, Tzortzis and Likas proposes a kind of determination and the algorithm of increment is poly- to overcome Class initialization matter：Their Algorithm mapping to a data point for high-dimensional feature space, by using kernel function and optimization Cluster mistake.Make it that there is good robustness for noise and outlier, also overcome PFCM algorithms quick to parameter setting The problem of sense, but the fuzzy clustering algorithm based on core is relatively good for spherical effect data, but for non-spherical data, it is past It is past to cannot get preferable effect.

Zhao et al. previously in the literature propose multinuclear maximum kernel segmentation clustering algorithm more focus on supervision and Semi-supervised clustering learning, this be based on limit cluster to greatest extent, it is evident that a shortcoming be exactly their poly- Class algorithm is used for hard cluster.Selection and combination of the kernel method of the multinuclear that Mr. Hsin-Chien proposes to basic kernel are provided Very big flexibility, this also increased information source from different angles, in addition this also increases the code capacity of domain knowledge, It is evident that one of these many Clustering Algorithm of Kernel has the disadvantage, what the index of the weight of kernel was typically to be difficult to determine is difficult real Now good kernel weight distribution.

The content of the invention

The present invention is proposed a kind of based on multinuclear local message FCM for the weak point for overcoming above-mentioned prior art to exist The image partition method of algorithm, to evade, FCM is more sensitive to noise spot and FILCM algorithms are contaminated in neighborhood territory pixel Problem, while it can be found that be best suitable for weights and return currently is subordinate to the size of angle value, thus improve the reliability of algorithm with Convergence, and then improve the accuracy of image segmentation.

In order to realize foregoing invention purpose, the present invention is adopted the following technical scheme that：

A kind of the characteristics of image partition method based on multinuclear local message FCM algorithms of the present invention is to enter as follows OK：

Step 1, to the n image of pixel, making X={ x₁,x₂,…,x_j,…,x_nRepresent described image set of pixels Close, x_jRepresent j-th pixel；1≤j≤n；Optimal dividing is carried out to pixel set X so that the target function value J shown in formula (1) It is minimum：

In formula (1), i represents the i-th class, and c represents the classification number of division, and 1≤i≤c, u_ijRepresent j-th pixel x_jIt is subordinate to Belong to the angle value that is subordinate to of the i-th class, and U={ u_ij|_{I=1,2 ..., c；J=1,2 ..., n}Represent subordinated-degree matrix；0≤u_ij≤1；Represent the J pixel belongs to the m power of the degree of membership of the i-th class, and m is Weighted Index, represents clustering fuzzy degree；P_ijIt is balance factor, instead Reflect j-th pixel to the spatial information of the center pixel of the i-th class；D_ijRepresent multinuclear high-dimensional feature space j-th pixel and The pixel center v of i-th class in multinuclear high-dimensional feature space_iThe distance between, and have：

In formula (2), φ (x_j) represent j-th pixel-map to the mapping function in multinuclear high-dimensional feature space；φ(v_i) table Show that the pixel center of the i-th class is mapped to the mapping function in multinuclear high-dimensional feature space, φ represents data point in a high position in formula Expression way in special category space distinguishes general data point with this；

Step 2, using Fuzzy C-Means Cluster Algorithm to the pixel set X treatment, obtain subordinated-degree matrix U= {u_ij|_{I=1,2 ..., c；J=1,2 ..., n}And pixel center V={ v₁,v₂,···,v_i,···,v_c}；With the subordinated-degree matrix U With pixel center V as initial subordinated-degree matrix U⁰With initial cluster center V⁰；

The spatial information balance factor of step 3, j-th pixel of random initializtion to the pixel center of the i-th classDefinition Iterations is λ, and maximum iteration is λ_max；And initialize λ=1；Then the λ times subordinated-degree matrix of iteration is U^(λ)；The λ times The pixel center of iteration is V^(λ)；

Step 4, using formula (4) obtain the λ times j-th pixel x of iteration_jBe under the jurisdiction of the i-th class is subordinate to angle value

In formula (4), D_sjIt is j-th pixel in multinuclear high-dimensional feature space and the s classes in multinuclear high-dimensional feature space Pixel center v_sThe distance between, 1≤s≤c,It is λ -1 balance factor of renewal；

Step 5, using formula (5) calculate the λ times pixel center of the i-th class of iteration

Step 6, using formula (6) obtain j-th pixel x_jTo the λ times pixel center of the i-th class of iterationSpace letter Breath balance factor

In formula (6),The pixel average of pixel set X is represented,Represent j-th pixel x_jAnd pixel averageBetween Euclidean distance, d_ijRepresent j-th pixel x_jWith the i-th class pixel center v_iLocus distance,Table Show j-th pixel x_jWith λ -1 the i-th class pixel center v of iteration_iBetween Euclidean distance；

Step 7, using formula (7) obtain introduce weighted index after object function J (β)：

In formula (7), β_kThe weighted value in k heavy nucleus space is represented, and is had：α_ijkCombination multinomial is represented, and is had：

In formula (8), k represents the check figure of nuclear space, k (x_j,x_j) represent gaussian kernel function, and k (x_j,x_j)=1；

Step 8, judgementOr λ ＞ λ_maxWhether set up, if so, then representIt is optimal degree of membership Value,Be optimal pixel center,It is optimal balance factor value；And makeAfter substitute into In formula (1)；So as to realize the optimal dividing to pixel set X, ε is threshold value set in advance；If not, then by the assignment of λ+1 To λ, the order of repeat step 4 is performed, until meeting condition untill, finally give the image after segmentation.

Compared with the prior art, beneficial effects of the present invention are embodied in：

1st, the present invention has concentrated the advantage of fuzzy clustering (FCM) method and the mould of local message using the method for multinuclear The advantage of paste clustering algorithm (FILCM), while reducing the influence of the selection for experimental result of core, the clustering algorithm pair of multinuclear More sensitive in the selection of kernel function, the concept that local message is added under the basis of multinuclear is balance factor, makes cluster result It is more accurate；So that image segmentation is more accurate.

2nd, the present invention use the algorithm of local core can be while carry out nonlinear data operation, can be by common Data linear operation in data increased the antitypy and robustness of algorithm, in this hair by being mapped to high-dimensional data space The concept of weight is it is also proposed in bright, the weight that data point is under the jurisdiction of each kernel clustering center in nuclear space is different, examination Test middle different image and data set pair weight (β_k) requirement be different, if corresponding to unified weight does not meet reality Rule is tested, therefore is tested by iterating to calculate out the weighted value of best match.

3rd, the segmentation clustering algorithm of multinuclear is extended to fuzzy clustering aspect by the present invention, and the ownership of pixel is obscured Change, accuracy, while in view of the local spatial information of pixel, pixel pair is judged by calculating the distance between pixel The influence power of cluster centre, it is smaller apart from the more remote influence power of cluster centre, therefore, this method is than other method more suitable for relation Data.

Brief description of the drawings

Fig. 1 is the original image of bianry image in the prior art；

Fig. 2 is the bianry image of the salt-pepper noise of addition 10% in the prior art；

Fig. 3 is the binary segmentation image that FCM algorithms are obtained in the prior art；

Fig. 4 is the binary segmentation image that FILCM algorithms are obtained in the prior art；

Fig. 5 is the binary segmentation image that MKFILCM algorithms proposed by the present invention are obtained.

Specific embodiment

In the present embodiment, a kind of image partition method based on multinuclear local message FCM algorithms is to enter in accordance with the following steps OK：

Step 1, to the n image of pixel, making X={ x₁,x₂,…,x_j,…,x_nRepresent image pixel set, x_j Represent j-th pixel；1≤j≤n, n are the numbers of pixel；Optimal dividing is carried out to pixel set X so that the mesh shown in formula (1) Offer of tender numerical value J is minimum：

In formula (1), i represents the i-th class, and c represents the classification number of division, and 1≤i≤c, u_ijRepresent j-th pixel x_jIt is subordinate to Belong to the angle value that is subordinate to of the i-th class, and U={ u_ij|_{I=1,2 ..., c；J=1,2 ..., n}Represent subordinated-degree matrix；0≤u_ij≤1；Represent the J pixel belongs to the m power of the degree of membership of the i-th class, and m is Weighted Index, represents clustering fuzzy degree；P_ijIt is balance factor, instead Reflect j-th pixel to the spatial information of the center pixel of the i-th class；D_ijRepresent multinuclear high-dimensional feature space j-th pixel and The pixel center v of i-th class in multinuclear high-dimensional feature space_iThe distance between, and have：

In formula (2), φ (x_j) represent j-th pixel-map to the mapping function in multinuclear high-dimensional feature space；φ(v_i) table Show that the pixel center of the i-th class is mapped to the mapping function in multinuclear high-dimensional feature space, φ represents data point high-order extraordinary empty Between in expression way general data point is distinguished with this；

The cluster centre that J values minimum is obtained is optimal, and the effect of image segmentation is also best, segmentation effect such as table 1, Shown in figure Fig. 3, Fig. 4, Fig. 5, Fig. 1 is the original image of bianry image, and Fig. 2 is the image after the salt-pepper noise of addition 10%, examination Test the setting of middle parameter, m sets in test scope and floated between 1.5 to 2.5 setting, is traditionally arranged to be 2, ε and is set to 0.001, iterations 100 times, window size is set to 3 × 3, from Fig. 3, as can be seen that because MKFILCM algorithms fill in 4,5 Divide the influence that take into account neighbors around pixel, and using many accounting methods of self adaptation, by Experimental comparison's MKFILCM algorithms Noise spot after segmentation is substantially zeroed, and its segmentation effect is substantially better than FCM algorithms and FILCM algorithms.

Split accuracy rate contrast (%) under the different noise conditions of table 1

The present invention verifies application effect of the FCM algorithms based on multinuclear local message in image segmentation by many experiments Really, FCM Algorithms (FCM) are compared, Fcm_S1 algorithms, Fcm_s2 algorithms, En_FCM algorithms, GFCM algorithms, MSOFCM is calculated The different grass of method, FILCM algorithms and the FCM algorithms (MKFILCM) based on multinuclear local message in two-value gray level image Segmentation accuracy rate under part, it can be found that the segmentation accuracy rate of MKFILCM algorithms is universal more than 99%, calculates compared to other classics Method is greatly improved.By running of the invention can obtain image segmentation to be substantially better than FCM algorithms with And FILCM algorithms.

Step 2, using Fuzzy C-Means Cluster Algorithm to pixel set X treatment, obtain subordinated-degree matrix U={ u_ij |_{I=1,2 ..., c；J=1,2 ..., n}And cluster centre V={ v₁,v₂,···,v_i,···,v_c}；With subordinated-degree matrix U and cluster Center V is used as initial subordinated-degree matrix U⁰With initial cluster center V⁰；

The spatial information balance factor of step 3, j-th pixel of random initializtion to the cluster centre of the i-th classDefinition Iterations is λ, and maximum iteration is λ_max；And initialize λ=1；Then the λ times subordinated-degree matrix of iteration is U^(λ)；The λ times The cluster centre of iteration is V^(λ)；

Step 4, using formula (4) obtain the λ times j-th pixel x of iteration_jBe under the jurisdiction of the i-th class is subordinate to angle value

In formula (4), D_sjIt is j-th pixel in multinuclear high-dimensional feature space and the s classes in multinuclear high-dimensional feature space Cluster centre v_sThe distance between, 1≤s≤c,It is the balance factor of λ -1 renewals；

Step 5, using formula (5) calculate the λ times cluster centre of iteration

Step 6, the spatial information for obtaining the λ time j-th pixel of iteration to the cluster centre of the i-th class using formula (6) are flat Weighing apparatus factor

In formula (6),Represent the average value of pixel, x_jIt is j-th pixel value, c represents classification number,Represent jth Individual pixel x_jAnd pixel averageBetween Euclidean distance, d_ijRepresent the locus of j-th pixel and ith pixel away from From, | | x_j-v_i| | represent j-th pixel x_jWith the i-th class cluster centre v_iBetween Euclidean distance；

Step 7, using formula (7) obtain introduce weighted index after object function J (β)：

In formula (7), β_kThe weighted value in k heavy nucleus space is represented, and is had：α_ijkIt is in order that function expression is simple The clean and combination multinomial that sets, and has：

In formula (8), k represents the check figure of nuclear space, k (x_j,x_j) represent kernel function；And：k(x_j,x_j)=1；

Bianry image to Fig. 1 adds 10% Gaussian noise of same level, obtains contrast table as shown in Table 2.From table two In, it can be seen that when windows radius are 1, no matter in the case where noise variance is how many, the segmentation precision under level of the same race Highest.With being continuously increased for segmentation radius, segmentation precision is gradually reduced.Because segmentation radius is bigger, the texture information of image Obscure, meanwhile, under same segmentation radius, noise addition is more, and segmentation precision can also be reduced.When noise variance reaches When 50, no matter split radius reaches how many, segmentation precision can all be remarkably decreased.After the complexity of other algorithm increases, Segmentation effect will decline naturally, therefore picture noise is when be not very big, and segmentation radius is typically chosen 1, and noise is very big When selection it is 3 proper.

Segmentation precision (%) of the present invention of table 2 under different radii, different noise conditions

Step 8, judgementOr λ ＞ λ_maxWhether set up, if so, then representIt is optimal degree of membership Value,Be optimal pixel center,It is optimal balance factor value；And makeAfter substitute into In formula (1)；So as to realize the optimal dividing to pixel set X, ε is threshold value set in advance；If not, then by the assignment of λ+1 To λ, the order of repeat step 4 is performed, until meeting condition untill, finally give the image after segmentation.

In sum, the present invention is extended on the basis of FCM algorithms and then proposes MKFLICM algorithms, this calculation The result of method be it is incoherent, it is immune.It has evaded that FCM is more sensitive to noise spot and FILCM algorithms are in neighborhood territory pixel Be contaminated this how the problem of segmentation figure picture, while reduce the influence of the selection for experimental result of core, the cluster of multinuclear is calculated Method is more sensitive for the selection of kernel function, set forth herein algorithm can simultaneously find to be best suitable for weights and return is currently subordinate to The size of angle value.Kinds of experiments result shows that algorithm of the invention can produce more preferable overall performance, the segmentation figure picture for obtaining Obtained by better than other algorithms, with practicality very high.

Claims (1)

1. a kind of image partition method based on multinuclear local message FCM algorithms, it is characterized in that carrying out as follows：

Step 1, to the n image of pixel, making X={ x₁,x₂,…,x_j,…,x_nRepresent described image pixel set, x_j Represent j-th pixel；1≤j≤n；Optimal dividing is carried out to pixel set X so that the target function value J shown in formula (1) is minimum：

$J=\underset{i=1}{\overset{c}{\Σ}}\underset{j=1}{\overset{n}{\Σ}}{u}_{ij}^m{D}_{ij}^2+P_{ij}---\left(1\right)$

In formula (1), i represents the i-th class, and c represents the classification number of division, and 1≤i≤c, u_ijRepresent j-th pixel x_jIt is under the jurisdiction of I-th class is subordinate to angle value, andRepresent subordinated-degree matrix；0≤u_ij≤1；Represent j-th pixel category In the m power of the degree of membership of the i-th class, m is Weighted Index, represents clustering fuzzy degree；P_ijIt is balance factor, reflects j-th picture Spatial information of the element to the center pixel of the i-th class；D_ijRepresent that j-th pixel and multinuclear in multinuclear high-dimensional feature space are high-dimensional The pixel center v of the i-th class of feature space_iThe distance between, and have：

$D_{ij}^2=\mathrm{\φ}\left(x_j\right)\mathrm{\φ}\left(x_j\right)-2\mathrm{\φ}\left(x_j\right)\mathrm{\φ}\left(v_i\right)+\mathrm{\φ}\left(v_i\right)\mathrm{\φ}\left(v_i\right)---\left(2\right)$

In formula (2), φ (x_j) represent j-th pixel-map to the mapping function in multinuclear high-dimensional feature space；φ(v_i) represent the The pixel center of i classes is mapped to the mapping function in multinuclear high-dimensional feature space, and φ represents data point high-order extraordinary in formula Expression way in space distinguishes general data point with this；

Step 2, using Fuzzy C-Means Cluster Algorithm to the pixel set X treatment, obtain subordinated-degree matrixWith pixel center V={ v₁,v₂,…,v_i,…,v_c}；With the subordinated-degree matrix U and pixel center V is used as initial subordinated-degree matrix U⁰With initial cluster center V⁰；

The spatial information balance factor of step 3, j-th pixel of random initializtion to the pixel center of the i-th classDefine iteration Number of times is λ, and maximum iteration is λ_max；And initialize λ=1；Then the λ times subordinated-degree matrix of iteration is U^(λ)；The λ times iteration Pixel center be V^(λ)；

Step 4, using formula (4) obtain the λ times j-th pixel x of iteration_jBe under the jurisdiction of the i-th class is subordinate to angle value

$u_{ij}^{\left(\mathrm{\λ}\right)}=\frac{1}{\underset{s=1}{\overset{c}{\Σ}}{\left(\frac{D_{ij}^2+P_{ij}^{(\mathrm{\λ}-1)}}{D_{sj}^2+P_{ij}^{(\mathrm{\λ}-1)}}\right)}^{\frac{1}{m-1}}}---\left(4\right)$

In formula (4), D_sjIt is the picture of the s classes of j-th pixel and multinuclear high-dimensional feature space in multinuclear high-dimensional feature space Plain center v_sThe distance between, 1≤s≤c,It is λ -1 balance factor of renewal；

Step 5, using formula (5) calculate the λ times pixel center of the i-th class of iteration

$v_i^{\left(\mathrm{\λ}\right)}=\frac{\underset{j=1}{\overset{n}{\Σ}}\left({\left(u_{ij}^{(\mathrm{\λ}-1)}\right)}^m{x}_j\right)}{\underset{j=1}{\overset{n}{\Σ}}{\left(u_{ij}^{(\mathrm{\λ}-1)}\right)}^m}---\left(5\right)$

Step 6, using formula (6) obtain j-th pixel x_jTo the λ times pixel center of the i-th class of iterationSpatial information put down Weighing apparatus factor

$p_{ij}^{\left(\mathrm{\λ}\right)}=\underset{i=1}{\overset{c}{\Σ}}\underset{j=1}{\overset{n}{\Σ}}\frac{\left|\right|x_j-\stackrel{\‾}{x}|{|}^2}{d_{ij}+1}{(1-u_{ij}^{(\mathrm{\λ}-1)})}^m\left|\right|x_j-v_i^{(\mathrm{\λ}-1)}|{|}^2---\left(6\right)$

In formula (6),The pixel average of pixel set X is represented,Represent j-th pixel x_jAnd pixel averageIt Between Euclidean distance, d_ijRepresent j-th pixel x_jWith the i-th class pixel center v_iLocus distance,Represent jth Individual pixel x_jWith λ -1 the i-th class pixel center v of iteration_iBetween Euclidean distance；

Step 7, using formula (7) obtain introduce weighted index after object function J (β)：

$J\left(\mathrm{\β}\right)=\underset{i=1}{\overset{c}{\Σ}}\underset{j=1}{\overset{n}{\Σ}}\underset{k=1}{\overset{L}{\Σ}}{\mathrm{\β}}_k^2{\mathrm{\α}}_{ijk}\[u_{ij}^m+\frac{\left|\right|x_j-\stackrel{\‾}{x}|{|}^2}{d_{ij}+1}{(1-u_{ij})}^m\]---\left(7\right)$

In formula (7), β_kThe weighted value in k heavy nucleus space is represented, and is had：α_ijkCombination multinomial is represented, and is had：

${\mathrm{\α}}_{ijk}=\underset{k=1}{\overset{L}{\Σ}}k(x_j,x_j)\[1-2\underset{j=1}{\overset{n}{\Σ}}{u}_{ij}^m+\underset{j=1}{\overset{n}{\Σ}}\underset{j=1}{\overset{n}{\Σ}}{u}_{ij}^m{u}_{ij}^m\]---\left(8\right)$

In formula (8), k represents the check figure of nuclear space, k (x_j,x_j) represent gaussian kernel function, and k (x_j,x_j)=1；

Step 8, judgementOr λ ＞ λ_maxWhether set up, if so, then representFor it is optimal be subordinate to angle value, Be optimal pixel center,It is optimal balance factor value；And makeFormula (1) is substituted into afterwards In；So as to realize the optimal dividing to pixel set X, ε is threshold value set in advance；If not, λ+1 is then assigned to λ, weight Multiple step 4 order is performed, until meeting condition untill, finally give the image after segmentation.