CN110211126B - Image segmentation method based on intuitive fuzzy C-means clustering - Google Patents

Abstract

The invention discloses an image segmentation method based on intuitive fuzzy C-means clustering. The method mainly solves the problems that the image segmentation is sensitive to noise and easy to fall into local optimum, and the clustering number needs to be set, and has the scheme that: constructing an intuitive fuzzy set robust to noise using a switch mean based strategy

Performing curve fitting on the gray value distribution of the image, screening all peak points of a fitting curve as a cluster center initial value range set, and counting the number of the maximum cluster centers; in that

On the basis, the position information and the gray level information of the pixels are utilized to construct a linear weighting function coefficient in an intuitive fuzzy target function, and a membership degree matrix U is obtained; and evaluating the index evaluation U according to the grading distance index to obtain an optimal membership matrix, and screening the misclassified pixels by using an error detection strategy to carry out correct classification. The invention enhances the robustness to noise, can self-adaptively determine the image clustering number, and can be used for image recognition and computer vision preprocessing.

Description

Image segmentation method based on intuitionistic fuzzy C-means clustering

technical field

The invention belongs to the field of digital image processing, in particular to an image segmentation method, which can be used for image recognition and computer vision preprocessing.

Background technique

Since the 1970s and 1980s, many scholars have continued to pay attention to image segmentation. Image segmentation technology has become a basic technology in many fields. As long as it is related to extracting content from images, image segmentation technology cannot be lacking. The quality and effect of image segmentation work It will directly or indirectly affect subsequent image projects. There are many types of existing image segmentation methods, which can be summarized as threshold-based image segmentation methods, edge-based image segmentation methods, region-based image segmentation methods, and cluster-based image segmentation methods. The image segmentation method based on the image segmentation method and the image segmentation method based on the clustering method are mainly based on the image segmentation method based on the threshold value. However, it is only suitable for images with obvious differences in gray level. In addition, interfering elements such as noise also cause difficulties in the accurate segmentation of images. So far, there is still no unified theoretical system to apply to different fields, and image segmentation is still a hot research field.

The image segmentation method based on clustering divides the image into multiple categories according to the similarity between the pixels in the image. It has the characteristics of good segmentation effect, short time consumption and stable operation of the method, and has become one of the most widely used methods in recent years. . Commonly used clustering segmentation methods are: K-means, fuzzy C-means clustering, hierarchical clustering and spectral clustering), etc. Among them, fuzzy C-means clustering is one of the most widely used methods. The fuzzy C-means method was first proposed by Dunn, see: Dunn. A fuzzy image processing method related to iterative self-organizing analysis algorithm and its application in detecting compact and easily separable clusters. Acta Cybernetics. 1973,3(3) :32-57.(J.C.Dunn.A Fuzzy Relative of the ISODATA Process and ItsUse in Detecting Compact Well-Separated Clusters[J].Journal of Cybernetics,1973,3(3):32-57.), this method has no Considering any spatial information in the image, it is sensitive to the noise in the image, so that the ideal segmentation effect cannot be obtained by segmenting the noisy image. Later, many scholars published improved methods combining image space neighborhood information. Ahmed et al. added the spatial neighborhood information item to the objective function of the fuzzy C-means, and proposed the FCM_S algorithm. Although this algorithm improves the robustness to noise, the computational complexity is high. In order to reduce the cost of the FCM_S algorithm Computational complexity, Chen Songcan and Zhang Daoqiang introduced the neighborhood information into the objective function of the algorithm by means of mean filtering and median filtering, and proposed FCM_S1 and FCM_S2 algorithms, see: Chen Songcan, Zhang Daoqiang. A stable combination based on kernel function Spatial Information Fuzzy C-Means Image Segmentation Algorithm. IEEE Transactions on System Control Processing. Volume 34, 1907–1916, 2004. (S.Chen and D.Zhang, “Robust Image Segmentation Using FCM with Spatial Constraints Based on New Kernel -induced Distance Measure,"IEEETrans.Syst,Man,Cybern,vol.34,pp1907-1916,2004.); Among the two algorithms, the FCM_S1 algorithm has a better effect on Gaussian noise, but has poor robustness to salt and pepper noise. Although the FCM_S2 algorithm has a good effect on salt and pepper noise, it has poor robustness to Gaussian noise, so these two algorithms cannot be robust and universal to various types of noise. Cai Weiling et al. combined the spatial information and grayscale information of the image to construct a linear weighted sum image, and proposed a fast generation FCM algorithm, see: Cai Weiling, Chen Songcan, Zhang Daoqiang. A fast and robust blur for image segmentation that introduces local information C-means Clustering Algorithm. Pattern Recognition. Vol. 40, 825-838, 2007. (W. Cai, S. Chen, and D. Zhang, “Fast and RobustFuzzy C-means Clustering Algorithms Incorporating Local Information for ImageSegmentation,” Pattern Recognit., vol.40, no.3, pp.825-838, Mar.2007.), this method has strong robustness to Gaussian noise and good robustness to salt and pepper noise; but the above algorithms are all Without considering more fuzziness of data, Charger et al. further found that using intuitionistic fuzzy set theory can consider more fuzziness of data and classify data more accurately, and proposed a fuzzy clustering method based on intuitionistic fuzzy data. See: A novel intuitionistic fuzzy C means clustering algorithm and its application to medical images. Applied Soft Computation (T, Chaira. "A novel intuitionistic fuzzy C means clustering algorithm and its application to medical images." Appl.Soft Comput. 11(2):1711-1717, 2011.); since the fuzzy clustering method based on intuitionistic fuzzy data is also sensitive to noise, Verma et al. further introduced local spatial information into the intuitionistic fuzzy C-means algorithm, see: Wei. Verma, Agrawal, Sharan. An Improved Intuitionistic Fuzzy C-Means Algorithm Combining Local Spatial Information for Brain Image Segmentation. Applied Soft Computing. 543-557, 2016. (H.Verma, R.K.Agrawal, A.Sharan , "AnImproved Intuitionistic Fuzzy C-means Clustering Algorithm Incorporating Local Information for Brain Image Segmentation," Appl. Soft Comput., 543–557, 2016).

Although the above improved methods have optimized the performance of the fuzzy clustering algorithm in anti-noise performance to a certain extent, there are still problems that the robustness to noise is not strong enough, the initial value of the cluster center is very sensitive, and the number of image clusters cannot be adaptively analyzed. Wait enough.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide an image segmentation method based on intuitionistic fuzzy C-means clustering in view of the above-mentioned deficiencies of the prior art, so as to enhance the robustness to noise, improve the segmentation accuracy, and reduce the initial value of the cluster center. Sensitivity to adaptively determine the number of image clusters.

To achieve the above object, the technology of the present invention comprises the steps:

(1) Input the image to be divided, if the image to be divided is a color image, first convert it into a grayscale image;

(2) Initialization parameters: set the maximum number of iterations T = 100, the stop threshold ε = 10 ^-5 , the fuzzy weighting index m = 2, the radius of the neighborhood window ω = 3, the initial number of iterations t = 1, the default initial value of the number of clusters y = 2;

其中，1≤i≤n，n表示像素总数目；(3) Construct an intuitionistic fuzzy set robust to noise using a switch-mean-based strategy

Among them, 1≤i≤n, n represents the total number of pixels;

其中，c_Y表示第Y个聚类中心的初始值，1≤Y≤Y_max，Y_max表示聚类数目的最大值，2≤Y_max≤n，T表示转置；(4) For the gray value distribution of the input image, use the least squares method to perform curve fitting, select the gray level corresponding to the peak point of the fitting curve as the initialized cluster center value, and set the range of the estimated number of clusters is {2,...,Y _max }, and the initial value range set C of the cluster center is

Among them, c _Y represents the initial value of the Y-th cluster center, 1≤Y≤Y _max , Y _max represents the maximum number of clusters, 2≤Y _max ≤n, T represents the transposition;

和直觉模糊目标函数J：(5) Iteratively calculate the linear weighting function coefficient H _ir , the intuitionistic fuzzy distance

and the intuitionistic fuzzy objective function J:

(5a) Construct the linear weighting function coefficient H _ir using the position information and grayscale information of the pixel:

Among them, (a _i , b _i ) and (ar , b _r ) represent the spatial coordinate values of the center pixel i and the neighborhood pixel _r , respectively, and _xi and x _r represent the grayscale of the center pixel i and the neighborhood pixel r, respectively value, u _ki represents the membership degree of _xi to the _k -th cluster center ck, 1≤k≤Y, 1≤r≤ω ² ;

其中，

和

分别表示像素x_i与聚类中心c_k的直觉模糊集；(5b) Calculate the intuitionistic fuzzy distance from the pixel x _i to the cluster center _ck under the intuitionistic fuzzy set

in,

and

respectively represent the intuitionistic fuzzy sets of pixel _xi and cluster center _ck ;

计算直觉模糊目标函数J，并求解直觉模糊目标函数J中的隶属度函数u_ki和聚类中心c_k的直觉模糊集

(5c) Combine the linear weighting function coefficient H _ir obtained from (5a) with the intuitionistic fuzzy distance obtained from (5b)

Calculate the intuitionistic fuzzy objective function J, and solve the intuitionistic fuzzy set of the membership function u _ki and the cluster center _ck in the intuitionistic fuzzy objective function J

(6) Determine whether the iteration stop condition ||C ^(t+1) -C ^(t) ||<ε or the number of operation iterations t>T holds:

If it does not hold, set t=t+1 and return to (5);

令初始迭代次数t＝1，返回(5)，若Y＜Y_max不成立，执行(7),其中，

为聚类中心数值集合，

表示第Q个聚类中心迭代第t次的直觉模糊集，

表示第P个聚类中心的初始值，1≤Q≤Y，1≤P≤Y，U＝{u_ki}；If it is true, output the membership degree matrix U and judge whether Y<Y _max is true. If it is true, let Y=Y+1, take the first Y values of the cluster center initial value range set C, and let the cluster center initial value set for

Set the initial number of iterations t=1, return to (5), if Y< _Ymax does not hold, execute (7), where,

is the set of cluster center values,

represents the intuitionistic fuzzy set of the t-th iteration of the Q-th cluster center,

Represents the initial value of the Pth cluster center, 1≤Q≤Y, 1≤P≤Y, U={u _ki };

(7) Output (Y _max -1) membership degree matrices U from (6), and use the hierarchical distance index evaluation index GD to evaluate these membership degree matrices; let the membership degree matrix with the largest GD value be U _max , and U _max corresponds to The number of clusters Y _fin of the input image is taken as the final number of clusters of the input image, where 1≤Y _fin ≤Y _max ;

(8) Perform pixel classification on the membership matrix U _max output in (7), and perform error detection and classification, and output the segmented image:

(8a) According to the maximum membership principle and the final number of clusters Y _fin , classify the pixels of the membership matrix U _max output from (7), and output the label matrix UL , where _UL only contains the category values _{ 1, 2,…,Y _W ,…,Y _fin }, 1≤Y _W ≤Y _fin ;

(8b) Set the label type value of the central pixel i as Li, and in the 5×5 neighborhood of the central pixel _i , determine whether the number of pixels n _L of the label type value _Li satisfies n _L ≤ 25/(Y _fin +1) conditions of:

If it is satisfied, then determine that the central pixel _i is a misclassified pixel, and correct the label type value Li of the misclassified pixel to the label type value with the largest number of the same type of label type value in the neighborhood, and execute (8c);

If it is not satisfied, then determine that the center pixel i is a correctly allocated pixel, and execute (8c);

( _8c ) judge whether the pixels in the label matrix UL are all traversed, if so, output the final label matrix _UF , and execute (8d), if not, return to (8b) to continue traversing;

(8d) Assign different corresponding gray values x _W to the pixels with the label category value Y _W in the final label matrix _UF , and output the matrices with different gray values as a segmented image.

Compared with the prior art, the present invention has the following beneficial technical effects:

First, the present invention constructs an intuitionistic fuzzy set that is robust to noise based on the switching mean strategy, uses the position information and grayscale information of the pixels to construct a linear weighting function coefficient and introduces it into the intuitionistic fuzzy objective function, and solves the problem of the clustering algorithm. sensitive issue.

Second, the present invention uses the least squares method to perform curve fitting on the gray value distribution of the image, and selects the gray levels corresponding to all the peak points of the fitting curve as the initial value range of the cluster center, and evaluates the index according to the hierarchical distance index. The membership matrix is evaluated, the number of clusters suitable for the input image is selected, the adaptive determination of the number of image clusters is realized, and the disadvantage that the traditional clustering algorithm is easy to fall into the local optimum is overcome.

Third, the present invention uses an error detection strategy to screen the wrongly classified pixels, and correctly assigns the wrongly classified elements, which improves the segmentation accuracy and makes the segmentation effect more ideal.

Description of drawings

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

Fig. 2 is the result comparison diagram that the #3096 image in the Berkeley image database is carried out simulation segmentation with the present invention and existing method;

FIG. 3 is a comparison diagram of the simulation segmentation results of the #238011 image in the Berkeley image database using the present invention and the existing method.

Detailed ways

Embodiments and effects of the present invention are further described below in conjunction with the accompanying drawings:

Referring to Fig. 1, the implementation steps of the present invention are as follows:

Step 1: Input the image to be segmented.

Input the image to be divided. If the image to be divided is a color image, first convert it to a grayscale image.

Step 2: Set initial parameter values.

Set the maximum number of iterations T=100, the stop threshold ε=10 ⁻⁵ , the fuzzy weighting index m=2, the radius of the neighborhood window ω=3, the initial iteration number t=1, and the default initial value of the number of clusters Y=2.

Step 3: Construct an intuitionistic fuzzy set robust to noise

Methods for constructing intuitionistic fuzzy sets in the prior art include IFCM algorithm and IIFCM algorithm, both of which use Yager operators to construct intuitionistic fuzzy sets.

In this example, the pixel gray value of the input image is corrected based on the switching mean strategy, and the Yager operator is used to construct an intuitionistic fuzzy set robust to noise. The switching mean strategy is based on the distribution of pixel gray values in the neighborhood of pixel i. Do the gray value correction, which is implemented as follows:

3.1) First, determine whether the pixel gray values in the 3-by-3 neighborhood of the central pixel i are not all 0 or 255:

If it is true, it means that the gray value of the pixel in the neighborhood has other gray values besides 0 or 255. First, take out the pixels with the gray value of 0 and 255 in the neighborhood, and then take the average gray value of the remaining pixels in the neighborhood. , and set it as the correction value of the center pixel, and then execute 3.2);

If not, do not modify the gray value of the center pixel, and directly execute 3.2);

3.2) Determine whether all the pixels in the input image are traversed: if so, output the image after gray value correction, and execute 3.3), if not, return to 3.1) to continue traversing;

3.3) Calculate the pixel gray value of the corrected image output in 3.2) as an intuitionistic fuzzy set

3.3.1) Let μ( _xi ) denote the membership degree of pixel gray value x _i , v( _xi ) and π( _xi ) are the non-membership degree and hesitation degree of x _i constructed by using Yager operator, μ ( _xi ), v( _xi ) and π( _xi ) are calculated as follows:

π(x _i )=1-μ(x _i )-v(x _i ),

Among them, 0≤μ(x _i )≤1, 0≤v(x _i )≤1, 0≤μ(x _i )+v(x _i )≤1, α=0.8 represents the Yager operator coefficient;

3.3.2) Construct an intuitionistic fuzzy set according to μ( _xi ), v( _xi ) and π( _xi ) calculated in 3.3.1)

Step 4: According to the gray value distribution of the input image, use the least squares method to perform curve fitting, select the gray level corresponding to the peak point of the fitting curve as the initialized cluster center value, and estimate the maximum number of clusters and clusters. Center initial value range.

The existing techniques for selecting the initial value of the cluster center include directly selecting the peak point of the grayscale histogram of the image as the initial cluster center.

This example first uses the least squares method to fit the image gray value distribution, and then selects the peak point in the smooth fitting curve. The implementation is as follows:

4.1) Set the grayscale image to 256 grayscales, the grayscale range is [0,255], and draw the grayscale histogram of the grayscale image;

4.2) Count the number of pixels corresponding to 256 gray levels on the gray histogram, set it as the gray value distribution frequency f(l), and use the seventh-order least squares method to perform curve fitting on f(l), The degree value data points are fitted to a gray value curve, where 0≤l≤255;

4.3) Find the first derivative f'(l) of f(l), and compare the first derivative f'(l-1) and f'(l+ of f'(l) and f(l) before and after the gray level 1);

4.4) Determine whether the gray level l is under the condition of l=0 or l=255:

If under the condition of l=0 or l=255 and l=0, then judge whether f'(l)<0 is established, if so, output the gray level l=0 as the peak point, and then execute 4.5);

If under the condition of l=0 or l=255 and l=255, then judge whether f'(l)>0 is established, if so, output the gray level l=255 as the peak point, and then execute 4.5);

If it is not under the condition of l=0 or l=255, that is, under the condition of 0<l<255, then it is judged that f'(l)=0 and f'(l-1)>0 and f'(l Whether +1)<0 is established, if so, output the gray level l as the peak point, and then execute 4.5);

4.5) Determine whether all 256 gray levels are traversed, if so, output the peak point and execute 4.6), if not, return to 4.4) to continue traversing;

将灰度级对应数值统计为聚类中心初始值，即

设聚类中心初始值范围集合C为

其中：4.6) Sort the peak points outputted in 4.5) in descending order of gray distribution frequency value, count the number of peak points as Y _max , set the number of clusters to range from 2 to Y _max , and count from large to small The gray level l corresponding to the sorted peak points is obtained, and the range of gray level values is

The value corresponding to the gray level is counted as the initial value of the cluster center, that is,

Let the initial value range set C of the cluster center be

in:

l _Y represents the gray level corresponding to the gray distribution frequency value of the Y th peak point in the order from largest to smallest in the gray distribution frequency value of the peak point, c _Y represents the initial value of the Y th cluster center, 1 ≤Y≤Y _max , Y _max represents the maximum number of clusters, 2≤Y _max ≤n, T represents transposition.

和直觉模糊目标函数J。Step 5: Iteratively calculate the linear weighting function coefficient H _ir , the intuitionistic fuzzy distance

and the intuitionistic fuzzy objective function J.

The existing FCM_S1 algorithm and FCM_S2 algorithm introduce the local spatial information of the image into its objective function. The FCM_S1 algorithm considers the mean filtering feature of the image, and the FCM_S2 algorithm considers the median filtering feature of the image.

In this example, the position information and grayscale information of pixels are used to construct the linear weighting function coefficient H _ir , and then the H _ir containing the local spatial information of the image is introduced into the intuitionistic fuzzy objective function J, which is realized as follows:

5.1) Construct the linear weighting function coefficient H _ir using the position information and grayscale information of the pixel:

Among them, (a _i , b _i ) and (ar , b _r ) represent the spatial coordinate values of the center pixel i and the neighborhood pixel _r , respectively, and _xi and x _r represent the grayscale of the center pixel i and the neighborhood pixel r, respectively value, u _ki represents the membership degree of _xi to the _k -th cluster center ck, 1≤k≤Y, 1≤r≤ω ² ;

5.2) Calculate the intuitionistic fuzzy distance from the pixel gray value x _i to the cluster center _ck under the intuitionistic fuzzy set

5.2.1) Let μ( _ck ) represent the membership degree of the cluster center _ck , v( _ck ) and π( _ck ) represent the non-membership degree and hesitation degree of the cluster center _ck constructed by the Yager operator, respectively , the calculation formulas of μ( _ck ), v( _ck ) and π( _ck ) are as follows:

π(c _k )=1-μ(c _k )-v(c _k ),

Wherein, 0≤μ(c _k )≤1, 0≤v(c _k )≤1, 0≤μ(c _k )+v(c _k )≤1;

5.2.2) Calculate the intuitionistic fuzzy distance according to the result obtained in (5.2.1)

Among them, μ(x _i ), v( _xi ) and π( _xi ) represent the membership degree, non-membership degree and hesitation degree of the pixel gray value x _i , respectively;

计算直觉模糊目标函数J：5.3) Combine the linear weighting function coefficient H _ir obtained from (5.1) with the intuitionistic fuzzy distance obtained from (5.2)

Calculate the intuitionistic fuzzy objective function J:

Among them, u _ki is the membership function of the pixel _xi to the cluster center _ck , and m represents the fuzzy weighting index;

5.4) Use the Lagrange multiplier method to solve the intuitionistic fuzzy objective function J, and obtain the intuitionistic fuzzy set of the membership function u _ki and the cluster center _ck

5.4.1) Introduce the Lagrangian multiplier λ _i into the intuitionistic fuzzy objective function J, and construct the objective function L with the Lagrangian multiplier:

和拉格朗日乘子λ_i的偏导数

和

5.4.2) Calculate the intuitionistic fuzzy set of the objective function L with Lagrange multipliers for the membership function u _ki and the cluster center _ck respectively

and the partial derivative of the Lagrange multiplier λ _i

and

的条件下，通过如下求得隶属度函数u_ki与聚类中心c_k的直觉模糊集

5.4.3) In partial derivatives

Under the condition of , the intuitionistic fuzzy set of the membership function u _ki and the cluster center _ck is obtained by the following

Wherein, k=1,2,...,Y, i=1,2,...,n, r=1,2,...,ω ² .

Step 6: Determine whether the iteration stop condition is satisfied.

为聚类中心数值集合，

表示第Q个聚类中心迭代第t次的直觉模糊集；If the iteration stop condition ||C ^(t+1) -C ^(t) ||<ε or the number of operation iterations t>T is satisfied, output the membership matrix U, and execute 7), where,

is the set of cluster center values,

represents the intuitionistic fuzzy set of the t-th iteration of the Q-th cluster center;

If the iteration stop condition is not satisfied, then let t=t+1, and return to 5.1).

Step 7: Determine whether the current number of clusters Y satisfies the condition.

令初始迭代次数t＝1，返回5.1)，其中，

表示第P个聚类中心的初始值，1≤P≤Y；If it is satisfied that the current number of clusters Y is less than the maximum number of clusters Y _max , that is, Y < Y _max , then let Y=Y+1, then take the first Y values of the cluster center initial value range set C, and output to the cluster center Initial value set, and let the cluster center initial value set C ⁽¹⁾ be

Let the initial iteration number t=1, return to 5.1), where,

Represents the initial value of the P-th cluster center, 1≤P≤Y;

If Y< _Ymax is not satisfied, execute (8).

Step 8: Use the grading distance index evaluation index GD to evaluate the membership degree matrix.

The existing evaluation indexes for the membership degree matrix include the partition coefficient V _pc and the partition entropy V _pe , both of which can reflect the _fuzziness of the membership degree matrix _. The smaller it is, the more accurate the pixel classification is.

This example uses the hierarchical distance index evaluation index GD to evaluate the membership degree matrix, that is, input (Y _max -1) membership degree matrices U from 7), use the hierarchical distance index evaluation index GD to evaluate these membership degree matrices, and output the one with the largest GD value. The membership matrix, and the membership matrix with the largest GD value is U _max , and the number of clusters Y _fin corresponding to U _max is taken as the final number of clusters of the input image, where: the hierarchical distance index evaluation index GD formula is as follows:

Among them, u _i1 represents the maximum membership value of the i-th pixel, and u _i2 represents the second-largest membership value of the i-th pixel, 1≤Y _fin ≤Y _max .

Step 9: Perform pixel classification on the membership matrix _Umax .

According to the maximum membership principle and the final number of clusters Y _fin , classify the pixels of the membership matrix U _max output in 8), and output the label matrix UL , where the maximum membership principle is based on V _{k =} arg _k {max( u _ki )} divides the pixel i into the category V _k with the largest membership degree, and U _L only contains category values {1,2,…,Y _W ,…,Y _fin }, 1≤Y _W ≤Y _fin .

Step 10: _Perform error detection and classification on the label matrix UL.

10.1) Suppose 9) The label class value of the central pixel i of the output label matrix UL is _{L i} , in the 5×5 neighborhood of the central pixel _i , determine whether the number of pixels n _L of the label class value Li satisfies n _L ≤ 25(Y _fin +1) condition:

If it is satisfied, the central pixel _i is determined to be a misclassified pixel, and the label category value Li of the misclassified pixel is corrected to the label category value with the largest number of the same type of label category value in the neighborhood, and execute 10.2);

If it is not satisfied, then determine that the center pixel i is a correctly allocated pixel, and execute 10.2);

10.2) Determine whether all the pixels in the label matrix _UL are traversed. If so, output the final label matrix _UF , and execute 11). If not, return to 10.1) to continue traversing.

Step 11: Assign value to the final label matrix _UF and output the image.

10.2) The pixels with the label category value Y _W in the final label matrix _UF output in 10.2) are assigned different corresponding gray values x _W , and the matrices with different gray values are output as the segmented image. In the final label matrix _UF , only Contains category values {1,2,…,Y _W ,…,Y _fin }, the assignment formula is as follows:

x _W = [255/Y _W ],

Among them, [·] means to take an internal integer.

The technical effects of the present invention are further described below in conjunction with simulation experiments;

1. Simulation conditions:

The simulation experiment was carried out in the computer Inter(R)Core(TM)i5-3210M 2.50GHZ CPU, 8G memory, MATLABR2014a software environment.

2. Simulation content:

Simulation 1, select the image numbered 3096 in the Berkeley image database, and segment it with the present invention and the existing FCM method, FCM_S1 method, FCM_S2 method, FGFCM method, IFCM method and IIFCM method respectively, the results are shown in Figure 2 ,in:

2(a) is the original image of the 3096 image;

2(b) is the standard segmentation map of 3096 images;

2(c) is a Gaussian noisy image of 3096 images, and the noise intensity is 0.006;

2(d) is the segmentation result of the Gaussian noisy image of 3096 images using the existing FCM method;

2(e) is the segmentation result of the Gaussian noisy image of 3096 images using the existing FCM_S1 method;

2(f) is the segmentation result of the Gaussian noisy image of 3096 images using the existing FCM_S2 method;

2(g) is the segmentation result of the Gaussian noisy image of 3096 images using the existing FGFCM method;

2(h) is the segmentation result of the Gaussian noisy image of 3096 images using the existing IFCM method;

2(i) is the segmentation result of the Gaussian noisy image of 3096 images using the existing IIFCM method;

2(j) is the segmentation result of the Gaussian noisy image of 3096 images by the present invention;

2(k) is the salt and pepper noise image of the 3096 image, and the noise intensity is 0.01;

2(1) is the segmentation result of the salt and pepper noise image of 3096 images using the existing FCM method;

2(m) is the segmentation result of the salt and pepper noise image of 3096 images using the existing FCM_S1 method;

2(n) is the segmentation result of the salt and pepper noise image of 3096 images using the existing FCM_S2 method;

2(o) is the segmentation result of the salt-and-pepper noise image of 3096 images using the existing FGFCM method;

2(p) is the segmentation result of the salt and pepper noise image of 3096 images using the existing IFCM method;

2(q) is the segmentation result of the salt-and-pepper noisy image of 3096 images using the existing IIFCM method;

2(r) is the segmentation result of the salt and pepper noise image of the 3096 image by the present invention;

It can be seen from FIG. 2 that the present invention can separate the background and the target on the basis of suppressing noise, the number of image clusters can be determined adaptively, and is not sensitive to the initial value of the cluster center, so the present invention is suitable for noisy images. The segmentation effect is better than the existing FCM method, FCM_S1 method, FCM_S2 method, FGFCM method, IFCM method and IIFCM method.

Simulation 2, select the image numbered 238011 in the Berkeley image database, and segment it with the present invention and the existing FCM method, FCM_S1 method, FCM_S2 method, FGFCM method, IFCM method and IIFCM method respectively, the results are shown in Figure 3 ,in:

3(a) is the original image of the 238011 image;

3(b) is the standard segmentation map of the 238011 image;

3(c) is a Gaussian noisy image of the 238011 image with a noise intensity of 0.006;

3(d) is the segmentation result of the Gaussian noisy image of the 238011 image using the existing FCM method;

3(e) is the segmentation result of the Gaussian noisy image of the 238011 image using the existing FCM_S1 method;

3(f) is the segmentation result of the Gaussian noisy image of the 238011 image using the existing FCM_S2 method;

3(g) is the segmentation result of the Gaussian noisy image of the 238011 image using the existing FGFCM method;

3(h) is the segmentation result of the Gaussian noisy image of the 238011 image using the existing IFCM method;

3(i) is the segmentation result of the Gaussian noisy image of 238011 images using the existing IIFCM method;

3(j) is the segmentation result of the Gaussian noisy image of the 238011 image by the present invention;

3(k) is the salt and pepper noise image of the 238011 image, and the noise intensity is 0.01;

3(1) is the segmentation result of the salt and pepper noise image of the 238011 image using the existing FCM method;

3(m) is the segmentation result of the salt-and-pepper noise image of 238011 images using the existing FCM_S1 method;

3(n) is the segmentation result of the salt and pepper noise image of 238011 images using the existing FCM_S2 method;

3(o) is the segmentation result of the salt-and-pepper noisy image of the 238011 image using the existing FGFCM method;

3(p) is the segmentation result of the salt-and-pepper noisy image of 238011 images using the existing IFCM method;

3(q) is the segmentation result of the salt-and-pepper noise image of 238011 images using the existing IIFCM method;

3(r) is the segmentation result of the salt and pepper noise image of the 238011 image using the present invention;

As can be seen from Figure 3, the present invention can separate the background and the target on the basis of suppressing noise, the number of image clusters can be determined adaptively, and is insensitive to the initial value of the cluster center, which is not sensitive to the segmentation of noisy images. The effect is better than the existing FCM method, FCM_S1 method, FCM_S2 method, FGFCM method, IFCM method and IIFCM method.

Claims (7)

1. An image segmentation method based on intuitionistic fuzzy C-means clustering, characterized in that it includes the following: (1) Input the image to be divided, if the image to be divided is a color image, first convert it into a grayscale image; (2) Initialization parameters: set the maximum number of iterations T = 100, the stop threshold ε = 10 ^-5 , the fuzzy weighting index m = 2, the radius of the neighborhood window ω = 3, the initial number of iterations t = 1, the default initial value of the number of clusters y = 2; (3) Construct an intuitionistic fuzzy set robust to noise using a switch-mean-based strategy

Among them, 1≤i≤n, n represents the total number of pixels; its implementation is as follows: (3a) First, determine whether the pixel gray values in the 3-by-3 neighborhood of the i-th pixel are not all 0 or 255: If it is true, take out the pixels with gray values of 0 and 255, then take the average value of the gray values of the remaining pixels, and set it as the corrected value of the center pixel, and execute (3b); If not, do not modify the gray value of the center pixel, and execute (3b); (3b) Determine whether all the pixels in the input image are traversed: if so, output the corrected image, and execute (3c), if not, return to (3a) to continue traversing; (3c) Calculate the pixel gray value of the corrected image as an intuitionistic fuzzy set

(3c1) Let μ(x _i ) represent the membership degree of pixel gray value _xi , v( _xi ) and π( _xi ) are the non-membership degree and hesitation degree of _xi constructed by Yager operator, respectively, the calculation formula They are as follows:

π(x _i )=1-μ(x _i )-v(x _i ), Among them, 0≤μ(x _i )≤1, 0≤v(x _i )≤1, 0≤μ(x _i )+v(x _i )≤1, α=0.8 represents the Yager operator coefficient; (3c2) Construct an intuitionistic fuzzy set according to the result obtained in (3c1)

(4) For the gray value distribution of the input image, use the least squares method to perform curve fitting, select the gray level corresponding to the peak point of the fitting curve as the initialized cluster center value, and set the range of the estimated number of clusters is {2,...,Y _max }, and the initial value range set C of the cluster center is

Among them, c _Y represents the initial value of the Y-th cluster center, 1≤Y≤Y _max , Y _max represents the maximum number of clusters, 2≤Y _max ≤n, T represents the transposition; (5) Iteratively calculate the linear weighting function coefficient H _ir , the intuitionistic fuzzy distance

and the intuitionistic fuzzy objective function J: (5a) Construct the linear weighting function coefficient H _ir using the position information and grayscale information of the pixel:

Among them, (a _i , b _i ) and (ar , b _r ) represent the spatial coordinate values of the center pixel i and the neighborhood pixel _r , respectively, and _xi and x _r represent the grayscale of the center pixel i and the neighborhood pixel r, respectively value, u _ki represents the membership degree of _xi to the _k -th cluster center ck, 1≤k≤Y, 1≤r≤ω ² ; (5b) Calculate the intuitionistic fuzzy distance from the pixel x _i to the cluster center _ck under the intuitionistic fuzzy set

in,

and

respectively represent the intuitionistic fuzzy sets of pixel _xi and cluster center _ck ; (5c) Combine the linear weighting function coefficient H _ir obtained from (5a) with the intuitionistic fuzzy distance obtained from (5b)

Calculate the intuitionistic fuzzy objective function J, and solve the intuitionistic fuzzy set of the membership function u _ki and the cluster center _ck in the intuitionistic fuzzy objective function J

(6) Determine whether the iteration stop condition ||C ^(t+1) -C ^(t) ||<ε or the number of operation iterations t>T holds: If it does not hold, set t=t+1 and return to (5); If it is true, output the membership degree matrix U and judge whether Y<Y _max is true. If it is true, let Y=Y+1, take the first Y values of the cluster center initial value range set C, and let the cluster center initial value set for

Set the initial number of iterations t=1, return to (5), if Y< _Ymax does not hold, execute (7), where,

is the set of cluster center values,

represents the intuitionistic fuzzy set of the t-th iteration of the Q-th cluster center,

Represents the initial value of the Pth cluster center, 1≤Q≤Y, 1≤P≤Y, U={u _ki }; (7) Output (Y _max -1) membership degree matrices U from (6), and use the hierarchical distance index evaluation index GD to evaluate these membership degree matrices; let the membership degree matrix with the largest GD value be U _max , and U _max corresponds to The number of clusters Y _fin of the input image is taken as the final number of clusters of the input image, where 1≤Y _fin ≤Y _max ; the formula of the hierarchical distance index evaluation index GD is expressed as follows:

Among them, u _i1 represents the maximum membership value of the ith pixel, and u _i2 represents the second largest membership value of the ith pixel; (8) Perform pixel classification on the membership matrix _Umax output in (7), and perform error detection and classification, and output the segmented image: (8a) According to the maximum membership principle and the final number of clusters Y _fin , classify the pixels of the membership matrix U _max output from (7), and output the label matrix UL , where _UL only contains the category values _{ 1, 2,…,Y _W ,…,Y _fin }, 1≤Y _W ≤Y _fin ; (8b) Set the label type value of the central pixel i as Li, and in the 5×5 neighborhood of the central pixel _i , determine whether the number of pixels n _L of the label type value _Li satisfies n _L ≤ 25/(Y _fin +1) conditions of: If it is satisfied, then determine that the central pixel _i is a misclassified pixel, and correct the label type value Li of the misclassified pixel to the label type value with the largest number of the same type of label type value in the neighborhood, and execute (8c); If not satisfied, then determine that the center pixel i is a correctly allocated pixel, and execute (8c); ( _8c ) judge whether the pixels in the label matrix UL are all traversed, if so, output the final label matrix _UF , and execute (8d), if not, return to (8b) to continue traversing; (8d) Assign different corresponding gray values x _W to the pixels with the label category value Y _W in the final label matrix _UF , and output the matrices with different gray values as a segmented image. 2. The method according to claim 1, wherein, in (4), for the gray value distribution of the input image, curve fitting is performed using the least squares method, and the corresponding gray level is selected as the initialized cluster center value, which is implemented as follows: (4a) Set the grayscale image to 256 grayscales, the grayscale range is [0, 255], and draw the grayscale histogram of the grayscale image; (4b) Count the gray value distribution frequency f(l) of the gray level l on the grayscale histogram, and perform a seventh-order least squares curve fitting, where 0≤l≤255; (4c) Find the first-order derivative f'(l) of f(l), and compare the first-order derivatives f'(l-1) and f'(l+ of the gray level before and after f'(l) and f(l). 1), when l=0 or l=255, only judge whether f'(l) is less than or greater than 0: When l=0, judge whether f'(l)<0 is established, if so, output the gray level l=0 as the peak point; When 0<l<255, judge whether f'(l)=0 and f'(l-1)>0 and f'(l+1)<0, if so, take the gray level l as the peak point output; When l=255, judge whether f'(l)>0 is established, if so, output the gray level l=255 as the peak point; (4d) Determine whether all 256 gray levels are traversed: If it is, output the peak point and execute (4e), if not, return to (4c) to continue traversing; (4e) Sort the peak points output from (4d) in descending order of gray distribution frequency value, count the number of peak points as Y _max , and count the gray level l corresponding to the peak points sorted from large to small , the gray scale value range is

The corresponding value of the gray level is counted as the initial value of the cluster center, such as

Let the initial value range set C of the cluster center be

Among them, l _Y represents the gray level corresponding to the Y-th peak point gray distribution frequency value in the order of the peak point gray distribution frequency value in descending order. 3. method according to claim 1, is characterized in that, in (5b), calculate the intuitionistic fuzzy distance of pixel gray value x _i to cluster center _ck under intuitionistic fuzzy set

It is implemented as follows: (5b1) Let μ( _ck ) represent the membership degree of the cluster center _ck , v( _ck ) and π( _ck ) represent the non-membership degree and hesitation degree of the cluster center _ck constructed by the Yager operator, respectively, The calculation formulas are as follows:

π(c _k )=1-μ(c _k )-v(c _k ), Wherein, 0≤μ(c _k )≤1, 0≤v(c _k )≤1, 0≤μ(c _k )+v(c _k )≤1; (5b2) Calculate the intuitionistic fuzzy distance based on the result obtained in (5b1)

Among them, μ(x _i ), v( _xi ) and π( _xi ) represent the membership degree, non-membership degree and hesitation degree of the pixel gray value _xi , respectively. 4. method according to claim 1, is characterized in that, in (5c) utilizes the local spatial information of pixel and combines the linear weighting function coefficient H _ir that (5a) obtains and the intuitive fuzzy distance that (5b) obtains

Calculate the intuitionistic fuzzy objective function J, and its formula is as follows:

Among them, u _ki is the membership function of the pixel _xi to the cluster center _ck , and m represents the fuzzy weighting index. 5. method according to claim 4 is characterized in that, obtains the intuitionistic fuzzy set of membership function u _ki and cluster center _ck from intuitionistic fuzzy objective function J using Lagrange multiplier method

It is implemented as follows: (5c1) Introduce the Lagrangian multiplier λ _i into the intuitionistic fuzzy objective function J, and construct the objective function L with the Lagrangian multiplier:

(5c2) Calculate the intuitionistic fuzzy set of L for the membership function u _ki and the cluster center _ck respectively

and the partial derivative of the Lagrange multiplier λ _i

and

and in the partial derivative

Under the condition of , obtain u _ki and

Wherein, k=1,2,...,Y, i=1,2,...,n, r=1,2,...,ω ² . 6. The method according to claim 1, wherein the maximum membership degree principle in (8a) is to divide the pixel i into the category V with the largest membership degree according to V _k =arg _k {max(u _ki )} _k . 7. method according to claim 1 is characterized in that, in (8d), to the pixel whose label class value is Y _W in the final label matrix _UF is given different corresponding gray value x _W , and its formula is as follows: _xW =[255/ _YW ] Among them, [·] means to take an internal integer, and the final label matrix UF only contains the category values _{ 1,2,…,Y _W ,…,Y _fin }.

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