CN104794483A - Image division method based on inter-class maximized PCM (Pulse Code Modulation) clustering technology - Google Patents

Abstract

The invention discloses an image division method based on an inter-class maximized PCM (Pulse Code Modulation) clustering algorithm. The method comprises the following steps: carrying out classified labeling on pixel points of an input image according to a gray value; obtaining a clustering label when a clustering analysis method is used for dividing a target image; and carrying out performance evaluation on a label obtained by image division and an original label according to an evaluation index by a clustering method. The novel inter-class maximized PCM clustering algorithm considers the inter-class penalty, and parameters are adjusted and adjusted to enlarge the distance between class centers, so that the optimal classification of the pixel points in the image is realized.

Description

Based on the image partition method of the PCM clustering technique maximized between class

[technical field]

The present invention relates to data mining and mode identification technology, particularly based on the image partition method of cluster analysis.

[background technology]

Iamge Segmentation be image is divided into each tool characteristic region and extract technology and the process of effective target, it is the important step that image procossing arrives graphical analysis, and the target of segmentation refers to the information based on imaging data collection, object in image is divided into different regions or classification, in essence, Iamge Segmentation is exactly the process of pixel being carried out to cluster.Image segmentation algorithm all plays vital effect in the application of a lot of fields, and such as medical treatment is biological, military, remote sensing, meteorological etc.Existing partitioning algorithm roughly can be divided into following a few class ^[2]: based on threshold value partitioning algorithm, based on detect, based on region, based on cluster and based on the method etc. of some Specific Theory Tools.Initial Iamge Segmentation takes manual segmentation, and these class methods are very complicated and very consuming time, occurred auto Segmentation thereupon, and it is a very important field in image analysis process, and the Iamge Segmentation afterwards based on artificial intelligence is proposed in succession.In recent years, the Unsupervised clustering technology of FCM is widely used in the auto Segmentation process of graphical analysis.

Cluster analysis refer to when without when priori by Data Placement to different classifications, and ensure that the object in same class keeps maximum similarity, and the object between class has larger otherness.Cluster analysis has been widely used in a lot of field, comprises the segmentation of medical image, market survey, pattern-recognition, data analysis and image procossing etc.The type of clustering algorithm has a lot, but is mainly divided into two large classes: hard cluster and soft cluster.Hard clustering algorithm typically has the k-means algorithm based on hard plot, and soft cluster is for representative with the FCM algorithm based on fuzzy partitioning, namely soft or hard herein represents the fog-level difference of degree of membership, the degree of degree of membership fuzzyyer then " soft " is larger, the more accurate degree of being then more partial to " firmly " of degree of membership.

FCM algorithm is the representational algorithm of most in fuzzy theory, is proposed at first and promoted by Bezdek by Dunn.Although FCM has very large advantage in image segmentation process, in FCM algorithm sample degree of membership and be 1 constraint condition make its to noise spot and outlier very sensitive.In order to overcome this shortcoming of FCM, some algorithms based on FCM propose in succession, and relatively more outstanding has, and PFCM, CFCM and algorithm that some combine with kernel function are as KFCM.Wherein, the most outstanding is the possibility C-mean algorithm (PCM) that Krishnapuram and Keller proposes.Due to relax degree of membership and be 1 constraint condition, PCM than FCM process noise and outlier in have more robustness.Although in process noise, PCM has more superiority than FCM, but when processing the data that between class, plyability is higher, PCM does not take into full account the distance between class center, this makes PCM clustering algorithm when processing cluster centre coincidence phenomenon, does not still reach gratifying effect.Someone proposes the possibility C-mean algorithm (KPCM) based on core, the thought based on accounting method, by kernel function, the point in luv space is mapped in feature space, directly or indirectly in feature space carry out algorithm design, analyze and calculate, thus obtain the clustering of luv space, this type of algorithm has the ability finding non-convex cluster structures, be mapped to higher-dimension from low-dimensional and carry out cluster, reduce time complexity, but show from a large amount of interpretations, still some problems existed in primal algorithm have been left over, comparatively responsive to the initialization of parameter, and easily form coincidence cluster.In addition, also someone proposes the algorithm strengthening subspace clustering, compared to other algorithm, this algorithm take into account the problem of class centre distance, but weak point is, it considers the maximization of the spacing of the central point at each class center and these class centers, does not consider the maximization of class center distance each other.

[summary of the invention]

The object of the invention is to make PCM algorithm can process the data set that between class, plyability is higher, the present invention is on the basis of PCM algorithm, introduce very big penalty term and regulatory factor λ between class, construct brand-new objective function, control the distance between class by adjustment regulatory factor, thus avoid the generation of the comparatively near even coincidence phenomenon of cluster centre position.

In order to reach object of the present invention, clustering method according to the present invention is in the application of Iamge Segmentation, and the center that can effectively solve is near the problem even overlapped, and the present invention has taken into full account the information between class and class.Product between distance between cluster centre point and subordinated-degree matrix is sued for peace, and introduce regulatory factor, to the Section 3 of the similarity between class and class as objective function, and realize controlling the distance adjustment between class by regulatory factor, the distance realized between cluster centre maximizes.And the concrete method in Iamge Segmentation comprises the pixel to input picture, carry out tag along sort according to gray-scale value; Cluster labels is obtained when clustering method being used for the segmentation to target image; Clustering method carries out label that Iamge Segmentation obtains and original tag carries out performance evaluation according to evaluation index.

Given sample space X={x ₁, x ₂..., x _n, then the objective function of FCM algorithm can be expressed as:

$J_{\mathrm{FCM}}(U,V)=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{i=1}{\overset{c}{\mathrm{\Σ}}}{\left(u_{\mathrm{ij}}\right)}^m{\left|\right|x_j-v_i\left|\right|}^2$

In formula, c represents the cluster numbers of given sample set X, and n represents total sample number, and m is then weighted index, and m > 1; v _irepresent the cluster centre of the i-th class; u _ijwhat represent that a jth sample belongs to the i-th class is subordinate to angle value; || x _j-v _i|| represent the Euclidean distance between a jth sample and i-th cluster centre.Above formula meets following constraint condition:

$\underset{i=1}{\overset{c}{\mathrm{\Σ}}}{u}_{\mathrm{ij}}=\mathrm{1,0}\≤u_{\mathrm{ij}}\≤\mathrm{1,1}\≤i\≤c,1\≤j\≤n$

In FCM algorithm, the cluster numbers of sample X is c, and the degree of membership sum that same sample belongs to all classes is 1, this make it to noise and outlier comparatively responsive.

Further, in order to overcome this problem, the people such as Keller relax degree of membership and be 1 constraint condition, propose possibility C mean cluster (PCM), its objective function is as follows:

$J_{\mathrm{PCM}}(U,V)=\underset{i=1}{\overset{c}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{u_{\mathrm{ij}}}^m{d}_{\mathrm{ij}}^2+\underset{i=1}{\overset{c}{\mathrm{\Σ}}}{\mathrm{\η}}_i\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{(1-u_{\mathrm{ij}})}^m$

Constraint condition is:

$0\&le;u_{\mathrm{ij}}\&le;\mathrm{1,0}<\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}<N,$ And $d_{\mathrm{ij}}^2={\left|\right|x_j-v_i\left|\right|}^2={(x_j-v_i)}^T(x_j-v_i)$

Wherein, η _i> 0 is penalty factor, and

${\mathrm{\&eta;}}_i=K\frac{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u_{\mathrm{ij}}}^m{d}_{\mathrm{ij}}^2}{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u_{\mathrm{ij}}}^m}$ (K > 0, usual K=1)

P is sample dimension, and m is weighted index, and m formula is:

Further, according to clustering criteria, try to achieve J _pCMthe degree of membership of (U, V) and the iterative formula of cluster centre as follows:

$u_{\mathrm{ij}}=\frac{1}{1+{\left(\frac{d_{\mathrm{ij}}^2}{{\mathrm{\&eta;}}_j}\right)}^{\frac{1}{m-1}}},v_i=\frac{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u_{\mathrm{ij}}}^m{x}_j}{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u_{\mathrm{ij}}}^m}$

The Section 1 of the objective function of PCM is identical with the objective function of FCM, embodies the Weighted distance of different pieces of information point to all kinds of central point; Section 2 is penalty term, be used for avoiding Likelihood matrix be 0 situation.Although PCM relaxes degree of membership relative to FCM and be 1 constraint, less to the degree of membership of noise and outlier, reduce the impact of noise, have good robustness, PCM still comes with some shortcomings.Because PCM only considers the similarity of class interior element, and have ignored the distance between class and class, so when the data set that processing overlapping degree is higher, cluster centre position can be produced near the phenomenon very overlapped.In order to effectively solve center near the problem even overlapped, take into full account the information between class and class herein.Product between distance between cluster centre point and subordinated-degree matrix is sued for peace, and introduce λ as regulatory factor, to the Section 3 of the similarity between class and class as objective function, and realize controlling the distance adjustment between class by regulatory factor λ, the distance realized between cluster centre maximizes.Between class, the expression formula of very big penalty term is: $P=\mathrm{\&lambda;}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{k=1,k\&NotEqual;i}{\overset{c}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m{(v_i-v_k)}^2,$

In formula, v _krefer to the central point except i-th central point; λ is regulatory factor, λ > 0.

Further, the objective function of the PCM algorithm (being called for short MPCM) maximized between class is:

$J_{\mathrm{MPCM}}(U,V)=\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u_{\mathrm{ij}}}^m{\left|\right|x_j-v_i\left|\right|}^2+\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}{\mathrm{\&eta;}}_i\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{(1-u_{\mathrm{ij}})}^m-\mathrm{\&lambda;}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{k=1,k\&NotEqual;i}{\overset{c}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m{(v_i-v_k)}^2$

In formula, c is the cluster numbers of given sample set X, and n represents total sample number, and m is weighted index, and m > 1; v _irepresent the cluster centre of the i-th class; u _ijwhat represent that a jth sample belongs to the i-th class is subordinate to angle value, wherein

$0\&le;u_{\mathrm{ij}}\&le;\mathrm{1,0}<\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}<N,m=\frac{\min (n,p)}{\min (n,p-1)-2}\mathrm{orm}=2.$

Can find out, new target function type adds very big penalty term between a class on the basis of PCM objective function, constructs brand-new objective function, in objective function, can find out, work as v _i≠ v _kand during λ > 0, the phenomenon overlapped can not appear in the central point between class with class, thus efficiently avoid the drawback of cluster centre coincidence.

MPCM can regard the extensive version of one of PCM as, if λ gets 0, then obtains classical PCM algorithm.Equally, objective function can the solving of PCM solution strategies equally, namely carries out differentiate to U, V, obtain:

$\frac{\&PartialD;J}{\&PartialD;u_{\mathrm{ij}}}=m{u}_{\mathrm{ij}}^{m-1}{d}_{\mathrm{ij}}^2-m{\mathrm{\&eta;}}_i{(1-u_{\mathrm{ij}})}^{m-1}-\mathrm{m\&lambda;}\underset{k=1,k\&NotEqual;i}{\overset{c}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^{m-1}{(v_i-v_k)}^2$

$\frac{\&PartialD;J}{\&PartialD;v_i}=-2\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m(x_j-v_i)-2\mathrm{\&lambda;}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1,k\&NotEqual;i}{\overset{c}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m(v_i-v_k)$

Further order the iterative formula that can obtain its degree of membership and cluster centre is as follows:

$u_{\mathrm{ij}}=\frac{1}{1+{\left(\frac{{\left|\right|x_j-v_k\left|\right|}^2-\mathrm{\&lambda;}\underset{k=1,k\&NotEqual;i}{\overset{c}{\mathrm{\&Sigma;}}}{(v_i-v_k)}^2}{{\mathrm{\&eta;}}_i}\right)}^{\frac{1}{m-1}}}$

$v_i=\frac{\mathrm{\&lambda;}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1,k\&NotEqual;i}{\overset{c}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m{v}_k-\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m{x}_j}{\mathrm{\&lambda;c}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m-\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m}$

The optimizing process of subordinated-degree matrix U and cluster centre V is consistent with PCM, and undertaken by the mode of iteration optimizing, the span of regulatory factor lambda parameter provides at experimental section, in the process upgraded by the mutual iteration of U, V, until find U, till the optimal value of V.

The present invention effectively to image and with salt-pepper noise image pixel carry out cluster, realize the best cluster of pixel, have good segmentation effect.

[accompanying drawing explanation]

In conjunction with reference accompanying drawing and ensuing detailed description, the present invention will be easier to understand, and Fig. 1 is the process flow diagram of the image partition method based on the PCM clustering technique maximized between class in the present invention.

[embodiment]

For enabling above-mentioned purpose of the present invention, feature and advantage become apparent more, and below in conjunction with the drawings and specific embodiments, the present invention is further detailed explanation.

Embodiments provide a kind of image partition method of the PCM clustering technique based on maximizing between class, the present invention is on the basis of PCM algorithm, introduce very big penalty term and regulatory factor λ between class, construct brand-new objective function, control the distance between class by adjustment regulatory factor, avoid the generation of the comparatively near even coincidence phenomenon of cluster centre position.In the process of Iamge Segmentation process, according to the gray-scale value of pixel, based on the method for cluster analysis, by good segmentation effect in the image that process gray-scale value is nearer.

Please refer to Fig. 1, it illustrates the method flow diagram of specific embodiment of the image partition method 100 of the PCM clustering technique maximized between the class in the present invention.Described image partition method 100 comprises:

Step 102, according to gray-scale value, tag along sort is carried out to the pixel of input picture:

Experiment picture comes from the USI-SIPI image data base of American South University of California, and picture size is a point n × n, first coloured image etc. is converted to gray-scale map, then gray-scale value matrix permutation is become n ²the one dimension matrix of × 1, cluster number c=4, class label divides according to the gray-scale value of pixel: the pixel label between gray-scale value 0 to 63 is the 1st class; Pixel label between gray-scale value 64 to 127 is the 2nd class; Pixel label between gray-scale value 128 to 191 is the 3rd class; Pixel label between gray-scale value 192 to 255 is the 4th class.

Step 104, obtains cluster labels when clustering method being used for the segmentation to target image; First determine cluster classification number c, maximum iteration time Max_t and maximum error threshold epsilon are set, initialization regulatory factor λ=1/n; Set the subordinated-degree matrix U that returned by FCM, and cluster centre V, as MPCM initial degree of membership and cluster centre, now establish primary iteration number of times t=1;

Further, by U, V

$u_{\mathrm{ij}}=\frac{1}{1+{\left(\frac{{\left|\right|x_j-v_k\left|\right|}^2-\mathrm{\&lambda;}\underset{k=1,k\&NotEqual;i}{\overset{c}{\mathrm{\&Sigma;}}}{(v_i-v_k)}^2}{{\mathrm{\&eta;}}_i}\right)}^{\frac{1}{m-1}}}$

$v_i=\frac{\mathrm{\&lambda;}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1,k\&NotEqual;i}{\overset{c}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m{v}_k-\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m{x}_j}{\mathrm{\&lambda;c}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m-\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m}$

Upgrade subordinated-degree matrix and cluster centre matrix, until reach maximum iteration time Max_t as t or work as || U (t+1)-U (t) || _frobeniusduring < ε, algorithm stops, and U now, V are the optimum solution of algorithm.

Further according to subordinated-degree matrix, the label classification that each pixel in image obtains according to cluster analysis can be drawn.

Step 106, clustering method carries out label that Iamge Segmentation obtains and original tag carries out performance evaluation according to evaluation index;

According to original tag with carry out the label that Iamge Segmentation obtains according to clustering method and carry out performance evaluation according to two class indexs.The present invention selects following two large indexs, evaluates, can be evaluated the performance of this algorithm by two standards intuitively to the result of cluster, and two classes refer to target value, and larger to represent performance better.RandIndex evaluation index

$\mathrm{RI}=\frac{f_{00}+f_{11}}{N(N-1)/2}$

Wherein: f ₀₀represent that data point has different class labels, and belong to inhomogeneous data point number; f ₁₁represent that there is identical class label, and belong to other data point number of same class; N represents the amount of capacity of sample; NMI evaluation index:

$\mathrm{NMI}=\frac{\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{c}{\mathrm{\&Sigma;}}}{N}_{i,j}\log \frac{N\&times;N_{i,j}}{N_i\&times;N_j}}{\sqrt{(\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}{N}_i\log N_i/N)\&times;(\underset{j=1}{\overset{c}{\mathrm{\&Sigma;}}}{N}_j\log N_j/N)}}$

Wherein: N _{i, j}represent i-th compatible degree between cluster and class j; N represents the size of sample capacity; N _irepresent the number of samples of i-th cluster; N _jrepresent the number of samples of a jth cluster.

By the validity of the image partition method based on the PCM clustering technique maximized between class proposed by the invention, experiment will be divided into 3 parts, use muting Prof. Du Yucang texture image respectively, muting true picture and the true picture collection with salt-pepper noise.By algorithm of the present invention: the PCM algorithm (MPCM) maximized between class and possibility c average (PCM) clustering algorithm, fuzzy c-means (FCM) clustering algorithm, Comparison of experiment results analysis based on possibility C mean cluster (KPCM) algorithm of core, illustrate that segmentation effect of the present invention and the robustness to image salt-pepper noise promote to some extent than other clustering algorithm.

MPCM is the extensive version of PCM, solves center superposition problem between class, thus in image segmentation, have larger lifting while the advantage keeping PCM algorithm.By muting Prof. Du Yucang texture image, muting true picture, and test with the true picture of salt-pepper noise, demonstrate segmentation effect of the present invention preferably, and applicability can be had more in actual applications.

It should be noted that: the method for above-mentioned cluster analysis, be only illustrated with above-mentioned a few class Iamge Segmentation, in practical application, can apply to as required and by said method split in different images.

Above-mentioned explanation fully discloses the specific embodiment of the present invention.It is pointed out that the scope be familiar with person skilled in art and any change that the specific embodiment of the present invention is done all do not departed to claims of the present invention.Correspondingly, the scope of claim of the present invention is also not limited only to described embodiment.

Claims (6)

1. based on an image partition method for the PCM clustering algorithm maximized between class, it is characterized in that, described method comprises:

According to gray-scale value, tag along sort is carried out to the pixel of input picture;

Cluster labels is obtained when clustering method being used for the segmentation to target image;

Clustering method carries out label that Iamge Segmentation obtains and original tag carries out performance evaluation according to evaluation index.

2. the PCM clustering algorithm maximized between class according to claim 1, the described pixel to input picture carries out tag along sort according to gray-scale value:

Cluster number c=4, class label divides according to the gray-scale value of pixel: the pixel label between gray-scale value 0 to 63 is the 1st class; Pixel label between gray-scale value 64 to 127 is the 2nd class; Pixel label between gray-scale value 128 to 191 is the 3rd class; Pixel label between gray-scale value 192 to 255 is the 4th class.

3. the PCM clustering algorithm maximized between class according to claim 2, is characterized in that, the objective function adding the PCM algorithm (being called for short MPCM) maximized between the class of maximum term between class is:

$J_{\mathrm{MPCM}}(U,V)=\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u_{\mathrm{ij}}}^m{\left|\right|x_j-v_i\left|\right|}^2+\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}{\mathrm{\&eta;}}_i\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{(1-u_{\mathrm{ij}})}^m-\mathrm{\&lambda;}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{k=1,k\&NotEqual;i}{\overset{c}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m{(v_i-v_k)}^2$

4. the PCM clustering algorithm maximized between class according to claim 2, the algorithm mechanism according to cluster principle obtains:

$\frac{\&PartialD;J}{\&PartialD;u_{\mathrm{ij}}}={\mathrm{mu}}_{\mathrm{ij}}^{m-1}{d}_{\mathrm{ij}}^2-{\mathrm{m\&eta;}}_i{(1-u_{\mathrm{ij}})}^{m-1}-\mathrm{m\&lambda;}\underset{k=1,k\&NotEqual;i}{\overset{c}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^{m-1}{(v_i-v_k)}^2$

$\frac{\&PartialD;J}{\&PartialD;v_i}=-2\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m(x_j-v_i)-2\mathrm{\&lambda;}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1,k\&NotEqual;i}{\overset{c}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m(v_i-v_k)$

Further order: $\frac{\&PartialD;J}{\&PartialD;u_{\mathrm{ij}}}=\frac{\&PartialD;J}{\&PartialD;v_i}=0$

And then the iterative formula obtaining its degree of membership and cluster centre is as follows:

$u_{\mathrm{ij}}=\frac{1}{1+{\left(\frac{{\left|\right|x_j-v_k\left|\right|}^2-\mathrm{\&lambda;}\underset{k=1,k\&NotEqual;i}{\overset{c}{\mathrm{\&Sigma;}}}{(v_i-v_k)}^2}{{\mathrm{\&eta;}}_i}\right)}^{\frac{1}{m-1}}}$

$v_i=\frac{\mathrm{\&lambda;}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1,k\&NotEqual;i}{\overset{c}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m{v}_k-\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m{x}_j}{\mathrm{\&lambda;c}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m-\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{u}_{\mathrm{ij}}^m}$

5. the PCM clustering algorithm maximized between class according to claim 1, obtains cluster labels when clustering method being used for the segmentation to target image:

The optimizing process of subordinated-degree matrix U and cluster centre V is consistent with PCM, and undertaken by the mode of iteration optimizing, the span of regulatory factor lambda parameter provides at experimental section, in the process upgraded by the mutual iteration of U, V, until find U, till the optimal value of V.Further according to subordinated-degree matrix, the label classification that each pixel in image obtains according to cluster analysis can be drawn.

6. the PCM clustering algorithm maximized between class according to claim 1, clustering method carries out label that Iamge Segmentation obtains and original tag and carries out performance evaluation according to evaluation index and comprise:

According to original tag with carry out the label that Iamge Segmentation obtains according to clustering method and carry out performance evaluation according to two class indexs.The present invention selects following two large indexs, evaluates, can be evaluated the performance of this algorithm by two standards intuitively to the result of cluster, and two classes refer to target value, and larger to represent performance better.RandIndex evaluation index:

$\mathrm{RI}=\frac{f_{00}+f_{11}}{N(N-1)/2}$

Wherein: f ₀₀represent that data point has different class labels, and belong to inhomogeneous data point number; f ₁₁represent that there is identical class label, and belong to other data point number of same class; N represents the amount of capacity of sample.

NMI evaluation index:

$\mathrm{NMI}=\frac{\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{c}{\mathrm{\&Sigma;}}}{N}_{i,j}\log \frac{N\&times;N_{i,j}}{N_i\&times;N_j}}{\sqrt{(\underset{i=1}{\overset{c}{\mathrm{\&Sigma;}}}{N}_i\log N_i/N)\&times;(\underset{j=1}{\overset{c}{\mathrm{\&Sigma;}}}{N}_j\log N_j/N)}}$

Wherein: N _{i, j}represent i-th compatible degree between cluster and class j; N represents the size of sample capacity; N _irepresent the number of samples of i-th cluster; N _jrepresent the number of samples of a jth cluster.