CN113409335A - Image segmentation method based on strong and weak joint semi-supervised intuitive fuzzy clustering - Google Patents

Abstract

The invention discloses an image segmentation method based on strong and weak joint semi-supervised intuitionistic fuzzy clustering, which mainly solves the problems that the existing image segmentation is sensitive to initial values, easy to fall into local optimum, and linearly inseparable to low-dimensional data. The scheme is: input the image to be segmented and set the initial parameters and manual scribing; perform intuitive fuzzification on the image; design a strong and weak joint semi-supervised strategy to obtain the strong supervision membership degree, weak supervision membership degree and initial cluster center; The kernel function, strongly supervised membership degree and weakly supervised membership degree are introduced into the objective function of intuitionistic fuzzy clustering, and the objective function of strong and weak joint semi-supervised kernel intuitionistic fuzzy clustering is obtained. Class optimal solution; according to the principle of maximum membership, the classification results of image pixels are obtained. The invention improves the sensitivity to the initial value, prevents falling into local optimum, improves the segmentation accuracy of linear inseparable data, and can be used for natural image recognition.

Description

Image segmentation method based on strong and weak joint semi-supervised intuitionistic fuzzy 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 natural image recognition and computer vision preprocessing.

Background technique

As a pivotal link between image processing and subsequent image understanding, image segmentation has always been a hot research topic by scholars, and it occupies an increasingly important position. The purpose of image segmentation is to divide the image into several sub-regions with different attributes and no intersection according to its own characteristics. Each pixel in each sub-region has different degrees of similar characteristics. There are also significant differences. In recent years, image segmentation technology has provided reliable and effective help in the fields of satellite remote sensing, intelligent security, unmanned driving, medical image processing and biometric identification. In the process of practical application, with the increasing complexity of the segmentation scene, people's performance requirements for image segmentation technology are becoming more and more strict, and segmentation algorithms based on threshold, region, clustering, edge and artificial neural network have appeared one after another. Among them, the image segmentation algorithm based on clustering has the advantages of low computational complexity, good algorithm stability, and fast running speed, and has received widespread attention from scholars. Commonly used clustering methods mainly include hard clustering algorithm, fuzzy clustering algorithm, hierarchical clustering algorithm, density peak clustering algorithm and spectral clustering algorithm. Fuzzy clustering algorithm is based on the basic idea of fuzzy set theory, and gives their membership degrees to different categories for each sample point data. focus on.

Liu Jianzhuang proposed an image fuzzy clustering segmentation method based on two-dimensional histogram in 1992, which is an unsupervised clustering method based on local search. Based on the spatial correlation information of the neighborhood, the fuzzy C-means clustering objective function is constructed by using the classical Euclidean distance, the membership degree of the pixel points is obtained by iterative calculation, and the image segmentation is realized by the membership degree of each pixel point. This method has two problems in realizing image segmentation: First, it does not use a small amount of prior information that can be obtained manually, which leads to blindness in the search for the optimal solution, and it is easy to fall into local optimality, resulting in the distribution of the background. The performance of uneven image segmentation is not ideal; the second is that more ambiguity and uncertainty in the image are not considered, which makes the segmentation of some fuzzy pixels inaccurate. In response to the first problem, Yasunori et al. proposed to introduce supervised membership into the fuzzy C-means clustering algorithm in 2009, and constructed a semi-supervised fuzzy C-means clustering algorithm, which uses a small amount of supervision information to analyze the clustering process. Provide guidance to improve the cluster segmentation accuracy. In response to the second problem, Chaira et al. found that the introduction of intuitionistic fuzzy set theory can take into account more ambiguity of data, making the classification of fuzzy data more accurate, and proposed an intuitionistic fuzzy clustering method based on intuitionistic fuzzy sets.

However, the above two methods use the classical Euclidean distance to construct the objective function of fuzzy clustering, and only consider the case of linearly separable data. In fact, in most image segmentation problems, the data to be processed are often linearly inseparable. , so it is unreasonable to use the classical Euclidean distance to construct the objective function of fuzzy clustering. In order to be able to deal with the situation of linear inseparability in image segmentation, scholars have proposed a method of introducing a kernel function to transform the linearly inseparable data in the original space into a higher-dimensional feature space, and find a linear function in the high-dimensional feature space. Implement data partitioning. In 2012, Li et al. proposed a proximity-based semi-supervised kernel fuzzy C-means data clustering algorithm, which effectively combines semi-supervised and KFCM algorithms to not only partition linearly inseparable data, but also utilize user input data. The proximity between them is used to guide the clustering. Finally, the feasibility and superiority of the method are verified by simulation experiments on synthetic data. However, this method still does not consider more ambiguity of data and does not make full use of artificial prior information, so it is sensitive to the initial value, easy to fall into the local optimal solution, and has poor performance for image segmentation with uneven background distribution. ideal question.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide an image segmentation method based on strong and weak joint semi-supervised intuitionistic fuzzy clustering to reduce the sensitivity to the initial value, avoid falling into local optimum, and realize low-dimensional The segmentation of linear inseparable data improves the accuracy of image segmentation with uneven background distribution.

To achieve the above object, the technology of the present invention includes:

(1) Input the image X to be segmented, and set the initial parameter values: the number of clusters k, the maximum number of iterations T=100, and the termination threshold ε=10 ⁻⁵ ;

(2) Manually marking the image X to be segmented to obtain manual prior information;

(3) Perform intuitive fuzzy processing on the image X to be segmented, and obtain the membership degree μ(x _j ), the non-membership degree v(x _j ), and the hesitation degree π(x _j ) corresponding to each pixel point x _j of the image;

(4) Use the SLIC algorithm to divide the image X to be divided into Q different sub-regions R={R ₁ , R ₂ ,...,R _i ,...,R _Q }, where R _i represents the ith sub-region, and each sub-region The pixels in the region have different degrees of similarity;

弱监督隶属度

及初始直觉模糊聚类中心

(5) Design a strong and weak joint semi-supervised strategy for class label transfer, and use the prior information of artificial labels to obtain the strong supervision membership degree of the image

Weakly supervised membership

and the initial intuitionistic fuzzy clustering center

和弱先验隶属度

(5a) Take the artificially labeled pixels as strong labels YS, assign the same category labels as the strong labels to all pixels in the superpixel area where the strong labels are located, and use them as weak labels Y ^W after the regional label propagation, and then assign the strong labels Y ^S and weak labels Y ^W are transformed into strong prior membership degrees, respectively

and weak prior membership

和弱先验隶属度

对无标记像素进行隶属度的估计，计算得到强估计隶属度

和弱估计隶属度

(5b) Use strong prior membership

and weak prior membership

Estimate the membership degree of unlabeled pixels, and calculate the strong estimated membership degree

and weakly estimated membership

和弱估计隶属度

与其各自对应的强先验隶属度

和弱先验隶属度

合并，作为类标签传递后的强监督隶属度

和弱监督隶属度

(5c) separate the strongly estimated membership

and weakly estimated membership

and their respective strong prior memberships

and weak prior membership

Merge, strongly supervised membership after passing as class labels

and weakly supervised membership

带入

计算初始聚类中心c_i(1)，再对其做直觉模糊化处理得到初始直觉模糊聚类中心

(5d) Weakly supervised membership

bring in

Calculate the initial cluster center c _i (1), and then perform intuition fuzzification on it to obtain the initial intuition fuzzy cluster center

(6) The kernel function, strongly supervised membership degree, and weakly supervised membership degree are introduced into the objective function of intuitionistic fuzzy clustering, and a strong and weak joint semi-supervised intuitionistic fuzzy clustering objective function J _{LP-SKIFCM is designed} :

表示一个具有N个像素点的彩色图像的直觉模糊集表示，

为第j个像素x_j的直觉模糊集表示，k是聚类数目，u_ij表示像素x_j对于第i类的隶属度，满足

表示第i类的直觉模糊聚类中心，μ(c_i)表示聚类中心c_i对应的隶属度、v(c_i)表示聚类中心c_i对应的非隶属度、π(c_i)表示聚类中心c_i对应的犹豫度，η₁是强监督项的权重指数，η₂是弱监督项的权重指数，

表示第j个像素点对于第i类的强监督隶属度，

表示像素x_j对于第i类的弱监督隶属度，

表示引入核函数的直觉模糊距离度量；in,

represents an intuitionistic fuzzy set representation of a color image with N pixels,

is the intuitionistic fuzzy set representation of the j-th pixel x _j , k is the number of clusters, and u _ij represents the membership degree of the pixel x _j to the i-th class, satisfying

represents the intuitionistic fuzzy clustering center of the _i -th class, μ(ci) represents the degree of membership corresponding to the cluster center _ci , v( _ci ) represents the degree of non-membership corresponding to the cluster center ci, and π( _ci ) represents the degree of non-membership corresponding to the cluster center _ci The hesitation degree corresponding to the cluster center c _i , η ₁ is the weight index of the strong supervision item, η ₂ is the weight index of the weak supervision item,

represents the strong supervised membership of the jth pixel to the ith class,

represents the weakly supervised membership of pixel x _j for the i-th class,

represents the intuitionistic fuzzy distance metric introduced into the kernel function;

的更新式，并根据更新式迭代计算隶属度u_ij和直觉模糊聚类中心

(7) Use the Lagrange multiplier method to minimize the objective function J _LP-SKIFCM , and obtain the membership degree u _ij and the intuitionistic fuzzy clustering center

The update formula of , and iteratively calculate the membership degree u _ij and the intuitionistic fuzzy cluster center according to the update formula

或迭代次数t＞T，则获得隶属度矩阵U和直觉模糊聚类中心

执行(9)；否则，令t＝t+1，返回迭代再次根据更新式计算隶属度u_ij和直觉模糊聚类中心

(8) Judging the iteration termination condition: if

Or the number of iterations t>T, then the membership matrix U and the intuitionistic fuzzy clustering center are obtained

Execute (9); otherwise, set t=t+1, and return to iteration to calculate the membership degree u _ij and the intuitionistic fuzzy cluster center again according to the update formula

(9) Use the obtained membership degree matrix U to classify each pixel point according to the principle of maximum membership degree, obtain the clustering label of the image pixel, and output the segmentation result of the image X.

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

First, the present invention designs a strong and weak joint semi-supervised strategy for class label transmission, which makes full use of manually available prior information to effectively guide the clustering process, and solves the problem of intuitionistic fuzzy clustering algorithm for initial Value-sensitive and prone to falling into local optima.

Second, the present invention introduces the kernel function into the intuitionistic fuzzy clustering algorithm, which effectively handles the linear inseparability when the intuitionistic fuzzy clustering algorithm is applied to image segmentation.

Third, the present invention constructs an objective function based on strong and weak joint semi-supervised intuitionistic fuzzy clustering by using kernel function, strong supervision membership degree and weak supervision membership degree, which improves the searchability and optimization, 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 image numbered 124084 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 results of the simulation segmentation of the image numbered nopeeking in the Weizmann image database using the present invention and the existing method.

Detailed ways

The implementation and effect of the invention are described in further detail below in conjunction with the accompanying drawings:

Referring to Figure 1, the implementation steps of the present invention include the following:

Step 1: Input the image to be segmented X and set the initial parameter value and manual marking.

1.1) input the image X to be divided, set the number of clusters k, the maximum number of iterations T=100, the termination threshold ε=10 ⁻⁵ ;

1.2) On the image to be segmented, according to the number of categories k to be segmented, each category is manually marked with a line to obtain artificial prior information.

Step 2: Perform intuitive fuzzy processing on the image X to be segmented, and obtain the membership degree μ(x _j ), non-membership degree v(x _j ), and hesitation degree π(x _j ) corresponding to each pixel point x _j of the image.

2.1) Find the membership degree μ(x _j ) corresponding to each pixel point x _j of the image, the formula is as follows:

μ(x _j )=(μ ^R (x _j ), μ ^G (x _j ), μ ^B (x _j )),

和

分别代表图像X在R分量下的最大值和最小值；Among them, μ ^R (x _j ) is the membership degree of the pixel point x _j in the color image under the R channel, which is calculated by the maximum and minimum normalization method,

and

Represent the maximum and minimum values of the image X under the R component, respectively;

计算，

和

分别代表图像X在G分量下的最大值和最小值；μ ^G (x _j ) is the membership degree of the pixel point x _j in the color image under the G channel, which uses

calculate,

and

Represent the maximum and minimum values of the image X under the G component, respectively;

计算，

和

分别代表图像X在B分量下的最大值和最小值；μ ^B (x _j ) is the membership degree of the pixel point x _j in the color image under the B channel, which uses

calculate,

and

Represent the maximum and minimum values of the image X under the B component, respectively;

2.2) Use the Segno intuitionistic fuzzy generation operator to obtain the non-membership degree v(x _j ) and hesitation degree π(x _j ) corresponding to each pixel x _j of the image:

π(x _j )=1-μ(x _j )-v(x _j ),

Among them, δ is a variable parameter, and its value range is (-1, ∞).

Step 3: Use the SLIC algorithm to divide the area of the image X to be segmented.

Use the SLIC algorithm to divide the image X to be divided into Q different sub-regions R={R ₁ , R ₂ ,...,R _i ,...,R _Q }, where R _i represents the ith sub-region, and the pixels in each sub-region have varying degrees of similarity.

弱监督隶属度

及初始直觉模糊聚类中心

Step 4: Design a strong and weak joint semi-supervised strategy for class label transfer, and use the manually labeled prior information to obtain the strong supervision membership of the image

Weakly supervised membership

and the initial intuitionistic fuzzy clustering center

和弱先验隶属度

4.1) Take the artificially labeled pixels as the strong label Y ^S , assign the same category label as the strong label to all the pixels in the superpixel region where the strong label Y ^S is located, as the weak label Y ^W after the regional label propagation, and then assign the strong label Y W . Label Y ^S and weak label Y ^W are transformed into strong prior membership degrees, respectively

and weak prior membership

4.1.1) Convert the strong label Y ^S into a strong prior membership degree according to two different pixels

其中，

为无强标签的像素x_u对于第i类的强先验隶属度，i∈{1,2,…,k}；For the pixel x _u without strong label, its corresponding membership is 0, namely

in,

is the strong prior membership degree of the pixel x _u without strong label for the i-th class, i∈{1,2,…,k};

否则，

其中，

为有强标签的像素x_l对于第i类的强先验隶属度，

为有强标签的像素x_l对于第t类的强先验隶属度，t∈{1,2,…,k,t≠i}；For a pixel x _l with a strong label and belonging to the i-th class, then

otherwise,

in,

is the strong prior membership of the pixel x _l with a strong label for the i-th class,

is the strong prior membership of the pixel x _l with a strong label to the t-th class, t∈{1,2,…,k,t≠i};

4.1.2) Convert the weak label Y ^W into weak prior membership according to the following two different pixels

其中，

为无弱标签的像素x′_u对于第i类的弱先验隶属度，i∈{1,2,…,k}；For the pixel x' _u without weak label, its corresponding membership is 0, that is,

in,

is the weak prior membership of the pixel x′ _u without weak label for the i-th class, i∈{1,2,…,k};

否则，

其中，

为有弱标签的像素x′_l对于第i类的弱先验隶属度，

为有弱标签的像素x′_l对于第t类的弱先验隶属度，t∈{1,2,…,k,t≠i}；For the pixel x′ _l with weak label and belonging to the i-th class, then

otherwise,

in,

is the weak prior membership of the pixel x′ _l with weak label for the i-th class,

is the weak prior membership of the pixel x′ _l with weak label for the t-th class, t∈{1,2,…,k,t≠i};

和弱先验隶属度

对无标记像素进行隶属度的估计，计算得到强估计隶属度

和弱估计隶属度

4.2) Use strong prior membership

and weak prior membership

Estimate the membership degree of unlabeled pixels, and calculate the strong estimated membership degree

and weakly estimated membership

求强估计隶属度

4.2.1) Using strong prior membership

Seek Strong Estimated Membership

为有强标签的像素x_l对于第i类的强先验隶属度，

无强标记的像素x_u对于第i类的强估计隶属度，

l∈SL,SL表示有强标签的像素集合，

表示有强标记的像素x_l与无强标记的像素x_u之间的欧氏距离；in,

is the strong prior membership of the pixel x _l with a strong label for the i-th class,

Strongly estimated membership for the i-th class of pixels x _u without strong labels,

l∈SL,SL denotes the set of pixels with strong labels,

represents the Euclidean distance between the pixel x _l with strong label and the pixel x _u without strong label;

求弱估计隶属度

4.2.2) Using weak prior membership

Find Weak Estimated Membership

为有弱标签的像素x′_l对于第i类的弱先验隶属度，

为无弱标记的像素x′_u对于第i类的弱估计隶属度，

l∈WL,WL表示有弱标签的像素集合，

表示有弱标记的像素x′_l与无弱标记的像素x′_u之间的欧氏距离；in,

is the weak prior membership of the pixel x′ _l with weak label for the i-th class,

is the weakly estimated membership degree of the i-th class for the pixel x' _u without weak label,

l∈WL, WL represents the set of pixels with weak labels,

represents the Euclidean distance between the pixel x' _l with weak label and the pixel x' _u without weak label;

和弱估计隶属度

与其各自对应的强先验隶属度

和弱先验隶属度

合并，作为类标签传递后的强监督隶属度

和弱监督隶属度

4.3) Separate strong estimates of membership

and weakly estimated membership

and their respective strong prior memberships

and weak prior membership

Merge, strongly supervised membership after passing as class labels

and weakly supervised membership

计算初始聚类中心c_i(1)：4.4) Using Weakly Supervised Membership

Calculate the initial cluster center c _i (1):

4.5) Perform intuitionistic fuzzification processing on the initial cluster center c _i (1) to obtain the initial intuitionistic fuzzy cluster center

Step 5: Construct strong and weak joint semi-supervised intuitionistic fuzzy clustering objective function J _LP-SKIFCM .

5.1) Define the kernel function k(x,y) as a Gaussian kernel, which is expressed as:

σ是尺度参数，控制径向作用范围；in,

σ is the scale parameter, which controls the radial action range;

5.2) Define the intuitionistic fuzzy clustering objective function J _IFCM as:

为像素x_j的直觉模糊集表示，k为聚类数目，N为数据个数，u_ij表示像素x_j对于第i类的隶属度，m为模糊指数，

表示第i类的聚类中心c_i的直觉模in,

is the intuitionistic fuzzy set representation of pixel x _j , k is the number of clusters, N is the number of data, u _ij represents the membership degree of pixel x _j to the i-th class, m is the fuzzy index,

Intuitive modulus representing the cluster center c _i of the i-th class

是

和

之间的直觉欧式距离，表示为:The fuzzy set says,

Yes

and

The intuitive Euclidean distance between , expressed as:

弱监督隶属度

引入到直觉模糊聚类目标函数J_IFCM中，得到强弱联合半监督直觉模糊聚类目标函数J_LP-SKIFCM：5.3) The kernel function k(x,y), strong supervision membership degree

Weakly supervised membership

It is introduced into the intuitionistic fuzzy clustering objective function J _IFCM , and the strong and weak joint semi-supervised intuitionistic fuzzy clustering objective function J _{LP-SKIFCM is obtained} :

表示一个具有N个像素点的彩色图像的直觉模糊集表示，

为第j个像素x_j的直觉模糊集表示，k是聚类数目，u_ij表示像素x_j对于第i类的隶属度，满足

表示第i类的直觉模糊聚类中心，μ(c_i)表示聚类中心c_i对应的隶属度、v(c_i)表示聚类中心c_i对应的非隶属度、π(c_i)表示聚类中心c_i对应的犹豫度，η₁是强监督项的权重指数，η₂是弱监督项的权重指数，

表示第j个像素点对于第i类的强监督隶属度，

表示第j个像素点对于第i类的弱监督隶属度，

表示引入核函数的直觉模糊距离度量，定义如下：

是高斯径向基函数，

表示核函数的尺度参数。in,

represents an intuitionistic fuzzy set representation of a color image with N pixels,

is the intuitionistic fuzzy set representation of the j-th pixel x _j , k is the number of clusters, and u _ij represents the membership degree of the pixel x _j to the i-th class, satisfying

represents the intuitionistic fuzzy clustering center of the _i -th class, μ(ci) represents the degree of membership corresponding to the cluster center _ci , v( _ci ) represents the degree of non-membership corresponding to the cluster center ci, and π( _ci ) represents the degree of non-membership corresponding to the cluster center _ci The hesitation degree corresponding to the cluster center c _i , η ₁ is the weight index of the strong supervision item, η ₂ is the weight index of the weak supervision item,

represents the strong supervised membership of the jth pixel to the ith class,

represents the weakly supervised membership of the jth pixel to the ith class,

Represents an intuitionistic fuzzy distance metric that introduces a kernel function, defined as follows:

is the Gaussian radial basis function,

Represents the scale parameter of the kernel function.

的更新式。Step 6: Use the Lagrange multiplier method to minimize the objective function J _LP-SKIFCM , and find the membership degree u _ij and the intuitionistic fuzzy clustering center

update.

6.1) Calculate the partial derivative of the membership degree u _ij for the objective function J _LP-SKIFCM , and obtain the update formula of the membership degree, which is expressed as follows:

的偏导数，得到直觉模糊聚类中心

的更新公式，其表示如下：6.2) For the objective function J _LP-SKIFCM, find about the cluster center

The partial derivative of , get the intuitionistic fuzzy cluster center

The update formula of , which is expressed as follows:

为像素x_j对聚类中心c_i隶属度下的核度量，in,

is the kernel metric under the membership degree of the pixel x _j to the cluster center c _i ,

为像素x_j对聚类中心c_i非隶属度下的核度量，

is the kernel metric under the non-membership degree of the pixel x _j to the cluster center c _i ,

为像素x_j对聚类中心c_i犹豫度下的核度量。

is the kernel measure under the hesitancy of pixel x _j to cluster center c _i .

获得隶属度矩阵U和直觉模糊聚类中心

Step 7: Iteratively calculate the membership degree u _ij and the intuitionistic fuzzy cluster center

Obtain the membership matrix U and the intuitionistic fuzzy cluster centers

7.1) Initialization iteration number t=1

的更新公式，迭代计算每次迭代下的隶属度u_ij和直觉模糊聚类中心

7.2) According to 6.2) membership degree u _ij and intuitionistic fuzzy cluster center

The update formula of , iteratively calculates the membership degree u _ij and the intuitionistic fuzzy cluster center under each iteration

与

的差值:

其中

表示第t次迭代下的直觉模糊聚类中心，

表示第t-1次迭代下的直觉模糊聚类中心；7.3) Calculation

and

difference:

in

represents the intuitionistic fuzzy cluster center at the t-th iteration,

represents the intuitionistic fuzzy cluster center at the t-1th iteration;

7.4) Compare the difference Z in 7.3) with the termination threshold ε, or compare the number of iterations t with the maximum number of iterations T, and judge the termination condition:

执行步骤8；If Z<ε or t>T is satisfied, the membership matrix U and the intuitionistic fuzzy clustering center are obtained

Go to step 8;

Otherwise, let t=t+1, return to 7.2).

Step 8: Output the result of image X segmentation.

The obtained membership degree matrix U is classified according to the principle of maximum membership degree, that is, in the membership degree matrix U, the category label corresponding to the maximum membership degree of each column is regarded as the category of the position pixel, and the clustering of the whole image is obtained. label, output the segmentation result of image X.

Below in conjunction with the simulation experiment, the technical effect of the present invention is further described:

1. Simulation conditions:

The simulation experiment was carried out in the computer Intel(R) Core(TM) i5-4258U CPU@2.40GHz 2.10GHz, 8G memory, MATLAB R2019a software environment.

2. Simulation content:

Simulation 1, using the present invention and the existing KFCM method, IFCM method, sSFCM method, SSFC-SC method, eSFCM method to segment the image numbered 124084 in the Berkeley image database, the results are shown in Figure 2, wherein:

2(a) is the original image of the 124084 image;

2(b) is the artificially labeled map of 124084 images;

2(c) is the region label extension map of 124084 images;

2(d) is the standard segmentation map of 124084 images;

2(e) is the segmentation result of 124084 images using the existing KFCM method;

2(f) is the segmentation result of 124084 images using the existing sSFCM method;

2(g) is the segmentation result of 124084 images using the existing SSFC-SC method;

2(h) is the segmentation result of 124084 images using the existing eSFCM method;

2(i) is the segmentation result of 124084 images by the method of the present invention.

As can be seen from Figure 2, the present invention can completely separate the target and the background for images with uneven background distribution, and is not sensitive to the initial cluster center, and its segmentation effect is obviously better than the existing KFCM method, IFCM method, sSFCM method method, SSFC-SC method and eSFCM method.

Simulation 2, using the present invention and the existing KFCM method, IFCM method, sSFCM method, SSFC-SC method, eSFCM method, respectively, the image numbered nopeeking in the Weizmann image database is segmented, the result is shown in Figure 3, wherein:

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

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

3(c) is the salt and pepper noise image of the nopeeking image, and the noise intensity is 0.05;

3(d) is the segmentation result of the nopeeking image using the existing KFCM method;

3(e) is the segmentation result of the nopeeking image by the existing IFCM method;

3(f) is the segmentation result of the nopeeking image using the existing sSFCM method;

3(g) is the segmentation result of the nopeeking image using the existing SSFC-SC method;

3(h) is the segmentation result of the nopeeking image using the existing eSFCM method;

3(i) is the segmentation result of the nopeeking image by the method of the present invention.

As can be seen from Figure 3, the present invention can completely separate the target and the background for images with uneven background distribution, and is not sensitive to the initial cluster center, and its segmentation effect is obviously better than the existing KFCM method, IFCM method, sSFCM method method, SSFC-SC method and eSFCM method.

Claims (10)

1. an image segmentation method based on strong and weak joint semi-supervised intuition fuzzy clustering, is characterized in that, comprises: (1) Input the image X to be segmented, and set the initial parameter values: the number of clusters k, the maximum number of iterations T=100, and the termination threshold ε=10 ⁻⁵ ; (2) Manually marking the image X to be segmented to obtain manual prior information; (3) Perform intuitive fuzzy processing on the image X to be segmented, and obtain the membership degree μ(x _j ), the non-membership degree v(x _j ), and the hesitation degree π(x _j ) corresponding to each pixel point x _j of the image; (4) Use the SLIC algorithm to divide the image X to be divided into Q different sub-regions R={R ₁ , R ₂ ,...,R _i ,...,R _Q }, where R _i represents the ith sub-region, and each sub-region The pixels in the region have different degrees of similarity; (5) Design a strong and weak joint semi-supervised strategy for class label transfer, and use the prior information of artificial labels to obtain the strong supervision membership degree of the image

Weakly supervised membership

and the initial intuitionistic fuzzy clustering center

(5a) Take the artificially labeled pixels as the strong label Y ^S , assign the same category label as the strong label to all the pixels in the superpixel area where the strong label is located, as the weak label Y ^W after the regional label propagation, and then assign the strong label to the strong label Y W . Y ^S and weak labels Y ^W are transformed into strong prior membership degrees, respectively

and weak prior membership

(5b) Use strong prior membership

and weak prior membership

Estimate the membership degree of unlabeled pixels, and calculate the strong estimated membership degree

and weakly estimated membership

(5c) separate the strongly estimated membership

and weakly estimated membership

and their respective strong prior memberships

and weak prior membership

Merge, strongly supervised membership after passing as class labels

and weakly supervised membership

(5d) Weakly supervised membership

bring in

Calculate the initial cluster center c _i (1), and then perform intuition fuzzification on it to obtain the initial intuition fuzzy cluster center

(6) The kernel function, strongly supervised membership degree, and weakly supervised membership degree are introduced into the objective function of intuitionistic fuzzy clustering, and a strong and weak joint semi-supervised intuitionistic fuzzy clustering objective function J _{LP-SKIFCM is designed} :

in,

represents an intuitionistic fuzzy set representation of a color image with N pixels,

is the intuitionistic fuzzy set representation of the j-th pixel x _j , the k-th is the number of clusters, and u _ij represents the membership degree of the pixel x _j to the i-th class, satisfying

represents the intuitionistic fuzzy clustering center of the _i -th class, μ(ci) represents the degree of membership corresponding to the cluster center _ci , v( _ci ) represents the degree of non-membership corresponding to the cluster center ci, and π( _ci ) represents the degree of non-membership corresponding to the cluster center _ci The hesitation degree corresponding to the cluster center c _i , η ₁ is the weight index of the strong supervision item, η ₂ is the weight index of the weak supervision item,

represents the strong supervised membership of the jth pixel to the ith class,

represents the weakly supervised membership of pixel x _j for the i-th class,

represents the intuitionistic fuzzy distance metric introduced into the kernel function; (7) Use the Lagrange multiplier method to minimize the objective function J _LP-SKIFCM , and obtain the membership degree u _ij and the intuitionistic fuzzy clustering center

The update formula of , and iteratively calculate the membership degree u _ij and the intuitionistic fuzzy cluster center according to the update formula

(8) Judging the iteration termination condition: if

Or the number of iterations t>T, then the membership matrix U and the intuitionistic fuzzy clustering center are obtained

Execute (9); otherwise, set t=t+1, and return to iteration to calculate the membership degree u _ij and the intuitionistic fuzzy cluster center again according to the update formula

(9) The obtained membership degree matrix U is used to classify each pixel point according to the principle of maximum membership degree, to obtain the clustering label of the image pixel, and output the segmentation result of the image X. 2. The method according to claim 1, characterized in that, in (3), the degree of membership μ(x _j ) corresponding to each pixel point x _j of the image is obtained, and the formula is as follows: μ(x _j )=(μ ^R (x _j ), μ ^G (x _j ), μ ^B (x _j )), Among them, μ ^R (x _j ) is the membership degree of the pixel point x _j in the color image under the R channel, which is calculated by the maximum and minimum normalization method,

and

Represent the maximum and minimum values of the image X under the R component, respectively; μ ^G (x _j ) is the membership degree of the pixel point x _j in the color image under the G channel, which uses

calculate,

and

Represent the maximum and minimum values of the image X under the G component, respectively; μ ^B (x _j ) is the membership degree of the pixel point x _j in the color image under the B channel, which uses

calculate,

and

represent the maximum and minimum values of the image X under the B component, respectively. 3. The method according to claim 1, wherein in (3), the non-membership degree v(x _j ) and hesitation degree π(x _j ) corresponding to each pixel point x _j of the image are obtained, which are Using the Segno intuition fuzzy generating operator, the formulas are as follows:

π(x _j )=1-μ(x _j )-v(x _j ), Among them, δ is a variable parameter, and its value range is (-1, ∞). 4. method according to claim 1, is characterized in that, in described (5a), strong label Y ^S is transformed into strong a priori degree of membership

Include two different pixel conversions: For the pixel x _u without strong label, its corresponding membership is 0, namely

in,

is the strong prior membership degree of the pixel x _u without strong label for the i-th class, i∈{1,2,…,k}; For a pixel x _l with a strong label and belonging to the i-th class, then

otherwise,

in,

is the strong prior membership of the pixel x _l with a strong label for the i-th class,

is the strong prior membership of a pixel x _l with a strong label to the t-th class, t∈{1,2,…,k,t≠i}. 5. The method according to claim 1, wherein the weak label Y ^W is converted into a weak prior membership in the (5a)

Include two different pixel conversions: For the pixel x' _u without weak label, its corresponding membership is 0, that is,

in,

is the weak prior membership of the pixel x′ _u without weak label for the i-th class, i∈{1,2,…,k}; For the pixel x′ _l with weak label and belonging to the i-th class, then

otherwise,

in,

is the weak prior membership of the pixel x′ _l with weak label for the i-th class,

is the weak prior membership of the pixel x′ _l with weak label to the t-th class, t∈{1,2,…,k,t≠i}. 6. The method according to claim 1, wherein a strong prior membership is used in the (5b)

Seek Strong Estimated Membership

The formula is as follows:

in,

is the strong prior membership of the pixel x _l with a strong label for the i-th class,

Strongly estimated membership for the i-th class of pixels x _u without strong labels,

SL represents the set of pixels with strong labels,

represents the Euclidean distance between the strongly marked pixel _xl and the non _- strongly marked pixel xu. 7. The method according to claim 1, wherein a weak prior membership is used in the (5b)

Find Weak Estimated Membership

The formula is as follows:

in,

is the weak prior membership of the pixel x′ _l with weak label for the i-th class,

The weakly estimated membership of the pixel x' _u without weak label for the i-th class,

WL represents the set of pixels with weak labels,

represents the Euclidean distance between the pixel x' _l with weak label and the pixel x' _u without weak label. 8. method according to claim 1 is characterized in that, in the strong and weak joint semi-supervised intuitionistic fuzzy clustering objective function J _LP-SKIFCM of described (6), the intuitionistic fuzzy distance metric of kernel function is introduced

Defined as follows:

in,

is the Gaussian radial basis function, the formula is as follows:

Among them, σ represents the scale parameter of the kernel function, and the calculation formula is:

Represents the intuitionistic fuzzy distance from the jth pixel x _j to the ith cluster center c _i , and the formula is as follows:

9. The method according to claim 1, wherein the degree of membership u _ij in (7) is expressed as follows:

10. The method according to claim 1, wherein the intuitionistic fuzzy clustering center in (7)

The iterative update formulas of , respectively, are expressed as follows:

in,

is the kernel metric under the membership degree of the pixel x _j to the cluster center c _i ,

is the kernel metric under the non-membership degree of the pixel x _j to the cluster center c _i ,

is the kernel measure under the hesitancy of pixel x _j to cluster center c _i .

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