CN113409335B - 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 conventional image segmentation is sensitive to an initial value, is easy to fall into local optimum and is inseparable to low-dimensional data linearity. The scheme is as follows: inputting an image to be segmented, setting initial parameters and manually scribing; performing intuitive fuzzification processing on the image; designing a strong and weak combined semi-supervised strategy to obtain a strong supervision membership degree, a weak supervision membership degree and an initial clustering center; introducing a kernel function, a strong supervision membership degree and a weak supervision membership degree into an intuitive fuzzy clustering target function to obtain a strong and weak combined semi-supervised kernel intuitive fuzzy clustering target function; minimizing a target function by adopting a Lagrange multiplier method to calculate a clustering optimal solution; and obtaining a classification result of the image pixel points according to the maximum membership principle. The method improves the sensitivity to the initial value, prevents the local optimization, improves the segmentation accuracy of linear irreparable data, and can be used for identifying natural images.

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, and in particular relates to an image segmentation method, which can be used for natural image recognition and computer vision preprocessing.

Background Art

Image segmentation, as a key link between image processing and subsequent image understanding, has always been a hot topic for scholars to study, 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 similarity, and the pixel features between different sub-regions also have 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 recognition. In the process of practical application, with the increasing complexity of segmentation scenes, people have more and more stringent requirements on the performance of image segmentation technology, and segmentation algorithms based on thresholds, regions, clustering, edges and artificial neural networks have emerged 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 attracted 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. The fuzzy clustering algorithm is based on the basic idea of fuzzy set theory. It gives the degree of membership of each sample point data to different categories. It can accurately represent the characteristics of both things in the objective world and has attracted widespread attention from scholars.

In 1992, Liu Jianzhuang proposed a fuzzy clustering segmentation method for images based on two-dimensional histograms. This method is an unsupervised clustering method based on local search. In addition to considering the grayscale information of pixels, it also considers the spatial correlation information between pixels and their neighborhoods. The fuzzy C-means clustering objective function is constructed using the classic Euclidean distance. The membership of pixels is iteratively calculated, and image segmentation is achieved based on the membership of each pixel. This method has two problems when implementing image segmentation: first, it does not use a small amount of prior information that can be obtained manually, resulting in blindness in the search for the optimal solution, which is easy to fall into the local optimum, resulting in unsatisfactory performance for image segmentation with uneven background distribution; second, it does not consider more fuzziness and uncertainty in the image, making the segmentation of some fuzzy pixels inaccurate. In response to the first problem, Yasunori et al. proposed in 2009 to introduce supervised membership into the fuzzy C-means clustering algorithm and constructed a semi-supervised fuzzy C-means clustering algorithm, which uses a small amount of supervised information to guide the clustering process and improves the accuracy of clustering segmentation. In response to the second question, Chaira et al. found that introducing intuitionistic fuzzy set theory can take into account more fuzziness of data, making the classification of fuzzy data more accurate, and proposed an intuitionistic fuzzy clustering method based on intuitionistic fuzzy sets.

However, both of the above methods use the classic Euclidean distance to construct the fuzzy clustering objective function, and only consider the case of linearly separable data. In fact, in most image segmentation problems, the data to be processed is often linearly inseparable, so it is unreasonable to use the classic Euclidean distance to construct the fuzzy clustering objective function. In order to deal with the linearly inseparable situation in image segmentation, scholars have proposed the method of introducing kernel functions 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 to achieve data division. In 2012, Li et al. proposed a semi-supervised kernel fuzzy C-means data clustering algorithm based on proximity. This method effectively combines semi-supervision and KFCM algorithms to not only divide linearly inseparable data, but also use the proximity between user input data to guide clustering. Finally, the feasibility and superiority of this method were verified through simulation experiments on synthetic data. However, since this method still does not consider more fuzziness of the data and does not make full use of artificial prior information, it is sensitive to the initial value, easily falls into the local optimal solution, and has unsatisfactory performance for image segmentation with uneven background distribution.

Summary of the invention

The purpose of the present invention is to address the shortcomings of the existing technologies and provide an image segmentation method based on strong and weak joint semi-supervised intuitive fuzzy clustering to reduce the sensitivity to initial values, avoid falling into local optimality, achieve the segmentation of low-dimensional linear inseparable data, and improve the accuracy of image segmentation with uneven background distribution.

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

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

(2) Manually mark the image X to be segmented to obtain artificial prior information;

(3) Perform intuitive fuzzy processing on the image X to be segmented, and calculate 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 in the image;

(4) Using the SLIC algorithm, the image to be segmented X is divided into Q different sub-regions R = {R ₁ , R ₂ , …, R _i , …, R _Q }, where R _i represents the i-th sub-region, and the pixels in each sub-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 artificially labeled prior information to calculate the strong supervised membership of the image

Weakly supervised membership

and initial intuitionistic fuzzy cluster centers

和弱先验隶属度

(5a) The manually labeled pixels are taken as strong labels YS, and all pixels in the superpixel region where the strong labels are located are assigned the same category labels as the strong labels as the weak labels ^YW after regional label propagation. Then, the strong labels ^YS and the weak labels ^YW are respectively converted into strong prior membership

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) Using strong prior membership

and weak prior membership

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

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) respectively

and weakly estimated membership

Their corresponding strong prior membership

and weak prior membership

Merge as strong supervision membership after class label transfer

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) The weak supervision membership

Bring in

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

(6) The kernel function, strong supervision membership and weak supervision membership are introduced into the intuitionistic fuzzy clustering objective function, and the 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 the intuitionistic fuzzy set representation of a color image with N pixels.

is the intuitive fuzzy set representation of the j-th pixel _xj , k is the number of clusters, _uij represents the membership of pixel _xj to the i-th class, satisfying

represents the intuitionistic fuzzy cluster center of the i-th category, μ( _ci ) represents the membership corresponding to the cluster center _ci , v( _ci ) represents the non-membership corresponding to the cluster center _ci , π( _ci ) represents the hesitation corresponding to the cluster center _ci , _η1 is the weight index of the strong supervision item, _η2 is the weight index of the weak supervision item,

represents the strong supervision membership of the j-th pixel to the i-th category,

represents the weakly supervised membership of pixel _xj to the i-th category,

Intuitionistic fuzzy distance metric that introduces 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 find the membership degree u _ij and the intuitionistic fuzzy clustering center

The update formula is used to iteratively calculate the membership degree u _ij and the intuitionistic fuzzy clustering 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) Determine 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, return to the iteration and calculate the membership degree u _ij and the intuitionistic fuzzy cluster center again according to the updated formula

(9) Using the obtained membership matrix U, classify each pixel according to the maximum membership principle, 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 transfer, which makes full use of the artificially obtainable prior information to effectively guide the clustering process, solving the problem that the intuitive fuzzy clustering algorithm is sensitive to initial values and easily falls into local optimality.

Secondly, the present invention introduces the kernel function into the intuitionistic fuzzy clustering algorithm, which effectively handles the situation where the intuitionistic fuzzy clustering algorithm is linearly inseparable when applied to image segmentation.

Third, the present invention uses kernel functions, strong supervised membership and weak supervised membership to construct a strong and weak joint semi-supervised intuitive fuzzy clustering objective function, which improves the search and optimization properties and makes the segmentation effect more ideal.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 is a flow chart of the implementation of the present invention;

FIG2 is a comparison diagram of the results of simulating segmentation of the image No. 124084 in the Berkeley image database using the present invention and the prior art method;

FIG. 3 is a comparison diagram of the results of simulating segmentation of an image numbered “nopeeking” in the Weizmann image database using the present invention and the prior art method.

DETAILED DESCRIPTION

The implementation and effects of the invention are further described in detail below with reference to the accompanying drawings:

Referring to FIG. 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 values and manual markings.

1.1) Input the image to be segmented X, set the number of clusters k, the maximum number of iterations T = 100, and the termination threshold ε = 10 ^-5 ;

1.2) On the image to be segmented, manually mark each class according to the number of classes k to be segmented to obtain artificial prior information.

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

2.1) Find the membership degree μ(x _j ) corresponding to each pixel x _j in 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；Wherein, μ ^R (x _j ) is the membership degree of pixel x _j in the color image under the R channel, which is obtained by the maximum and minimum value normalization method.

and

Represent the maximum and minimum values of image X under 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 pixel x _j in the color image under the G channel.

calculate,

and

Represent the maximum and minimum values of image X under 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 pixel x _j in the color image under the B channel.

calculate,

and

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

2.2) Use Segno intuitionistic fuzzy generation operator to find the non-membership v(x _j ) and hesitation π(x _j ) corresponding to each pixel x _j in 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 image X into regions.

The SLIC algorithm is used to divide the image X to be segmented into Q different sub-regions R = {R ₁ , R ₂ , …, R _i , …, R _Q }, where R _i represents the i-th sub-region, and the pixels in each sub-region have different 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 artificially labeled prior information to find the strong supervised membership of the image

Weakly supervised membership

and initial intuitionistic fuzzy cluster centers

和弱先验隶属度

4.1) The manually labeled pixels are taken as strong labels Y ^S , and all pixels in the superpixel region where the strong label Y ^S is located are assigned the same category label as the strong label as the weak label Y ^W after regional label propagation. Then, the strong label Y ^S and the weak label Y ^W are respectively converted into strong prior membership

and weak prior membership

4.1.1) Convert the strong label Y ^S into strong prior membership 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 pixels _xu without strong labels, the corresponding membership is 0, that is,

in,

is the strong prior membership of the pixel x _u without strong label to the i-th category, 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 _xl with a strong label and belonging to the i-th class, then

otherwise,

in,

is the strong prior membership of the strongly labeled pixel _xl to the i-th class,

is the strong prior membership of the strongly labeled pixel _xl to the t-th class, t∈{1,2,…,k,t≠i};

4.1.2) Convert the weak label ^YW 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 a pixel _x′u without a weak label, its corresponding membership is 0, that is,

in,

is the weak prior membership of the pixel _x′u without weak label to the i-th category, 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 a pixel _x′l with a weak label and belonging to the i-th class, then

otherwise,

in,

is the weak prior membership of the weakly labeled pixel x′ _l to the i-th class,

is the weak prior membership of the weakly labeled pixel x′ _l to 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) Using strong prior membership

and weak prior membership

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

and weakly estimated membership

求强估计隶属度

4.2.1) Using strong prior membership

Find the 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 strongly labeled pixel _xl to the i-th class,

The strong estimated membership of the pixel x _u without strong label to the i-th class,

l∈SL, SL represents a set of pixels with strong labels,

represents the Euclidean distance between the strongly labeled pixel x _l and the unlabeled pixel _xu ;

求弱估计隶属度

4.2.2) Using weak prior membership

Find the 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 weakly labeled pixel x′ _l to the i-th class,

is the weakly estimated membership of the pixel _x′u without weak label to the i-th class,

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) The strong estimated membership

and weakly estimated membership

Their corresponding strong prior membership

and weak prior membership

Merge as strong supervision membership after class label transfer

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 intuitive fuzzy processing on the initial cluster center c _i (1) to obtain the initial intuitive fuzzy cluster center

Step 5: Construct the 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 a scale parameter that controls the radial range of action;

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 intuitive fuzzy set representation of pixel _xj , k is the number of clusters, N is the number of data, _uij represents the membership of pixel _xj to the i-th class, m is the fuzzy index,

The intuitive model representing the cluster center _ci of the i-th class

是

和

之间的直觉欧式距离，表示为:Fuzzy said,

yes

and

The intuitive Euclidean distance between is 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) and the strong supervision membership

Weakly supervised membership

Introduced into the intuitive fuzzy clustering objective function J _IFCM , the strong and weak joint semi-supervised intuitive 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 the intuitionistic fuzzy set representation of a color image with N pixels.

is the intuitive fuzzy set representation of the j-th pixel _xj , k is the number of clusters, _uij represents the membership of pixel _xj to the i-th class, satisfying

represents the intuitionistic fuzzy cluster center of the i-th category, μ( _ci ) represents the membership corresponding to the cluster center _ci , v( _ci ) represents the non-membership corresponding to the cluster center _ci , π( _ci ) represents the hesitation corresponding to the cluster center _ci , _η1 is the weight index of the strong supervision item, _η2 is the weight index of the weak supervision item,

represents the strong supervision membership of the j-th pixel to the i-th category,

represents the weakly supervised membership of the j-th pixel to the i-th category,

It represents the intuitionistic fuzzy distance metric with the kernel function, which is 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 u _ij and the intuitionistic fuzzy cluster center.

The update style.

6.1) The partial derivative of the objective function J _LP-SKIFCM with respect to the membership u _ij is obtained to obtain the update formula of the membership, 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) Find the cluster center of the objective function J _LP-SKIFCM

The partial derivative of , we get the intuitionistic fuzzy cluster center

The update formula is 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 measure of the membership of pixel _xj to cluster center _ci ,

为像素x_j对聚类中心c_i非隶属度下的核度量，

is the kernel measure of pixel _xj under non-membership of cluster center _ci ,

为像素x_j对聚类中心c_i犹豫度下的核度量。

is the kernel measure of the hesitation of pixel _xj to cluster center _ci .

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 membership matrix U and intuitionistic fuzzy clustering centers

7.1) Initialize the number of iterations 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 u _ij and intuitionistic fuzzy clustering center

The update formula is used to iteratively calculate the membership degree u _ij and the intuitionistic fuzzy clustering center at 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

The difference:

in

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

represents the intuitive 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 to determine 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, set t=t+1 and return to 7.2).

Step 8: Output the result of image X segmentation.

The obtained membership matrix U is classified according to the maximum membership principle for each pixel point, that is, the category label corresponding to the maximum membership value in each column of the membership matrix U is used as the category of the pixel at that position, the clustering label of the entire image is obtained, and the segmentation result of the image X is output.

The following is a further description of the technical effects of the present invention in combination with simulation experiments:

1. Simulation conditions:

The simulation experiments were carried out on a computer with Intel(R) Core(TM) i5-4258U CPU@2.40GHz 2.10GHz, 8G memory, and 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, and eSFCM method to segment the image numbered 124084 in the Berkeley image database, the results are shown in FIG2, where:

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

2(b) is the manually labeled image of 124084 images;

2(c) is the region label expansion diagram of 124084 images;

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

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 the 124084 image using 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 insensitive to the initial clustering center. Its segmentation effect is significantly better than the existing KFCM method, IFCM method, sSFCM 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, and eSFCM method, the image numbered nopeeking in the Weizmann image database is segmented respectively, and the results are shown in FIG3, where:

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 noisy image of the nopeeking image, with a noise intensity of 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 using 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 using 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 insensitive to the initial clustering center. Its segmentation effect is significantly better than the existing KFCM method, IFCM method, sSFCM method, SSFC-SC method and eSFCM method.

Claims (9)

1. An image segmentation method based on strong and weak union semi-supervised intuitionistic fuzzy clustering is characterized by comprising the following steps:

(1) Inputting an image X to be segmented, and setting initial parameter values: the number of clusters k, the maximum number of iterations T =100, and the termination threshold e =10 ^-5 ；

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

(3) The image X to be divided is subjected to intuitive fuzzification processing to solve each pixel point X of the image _j Corresponding degree of membership mu (x) _j ) Degree of non-membership v (x) _j ) Angle of hesitation pi (x) _j )；

(4) Dividing an image X to be segmented into Q different sub-regions R = { R ] by using SLIC algorithm ₁ ,R ₂ ,…,R _i ,…,R _Q In which R is _i Representing the ith sub-region, wherein the pixels in each sub-region have different degrees of similarity;

(5) Designing a strong and weak combined semi-supervised strategy for class label transmission, and solving the strong supervision membership degree of an image by using the prior information of artificial markers

Degree of membership in weak supervision>

And an initial intuitive fuzzy cluster center>

(5a) Using artificially marked pixels as strong labels Y ^S Assigning the same class label as the strong label to all pixels in the super-pixel region where the strong label is located, and using the class label as the weak label Y after the region label propagation ^W Then, the strong label Y is added ^S And weak label Y ^W Respectively converted into strong prior membership

And weak a priori membership->

(5b) Using strong a priori membership

And weak a priori membership degree>

Evaluating the membership degree of the unmarked pixel, and calculating to obtain the strong evaluation membership degree->

And weak estimate membership &' s>

(5c) Respectively estimating the strong degree of membership

And weak estimate membership>

Strong prior affiliation with their respective counterpartsGenus degree->

And weak a priori membership->

Merging as strong supervision membership degree after class label transmission>

And weak supervision membership degree->

(5d) Degree of membership of weak supervision

Brings in and/or holds>

Calculating an initial clustering center c _i (1) Then, the initial intuitive fuzzy clustering center is obtained by performing intuitive fuzzification processing on the cluster to obtain the initial intuitive fuzzy clustering center->

(6) Introducing kernel function, strong supervision membership degree and weak supervision membership degree into intuitive fuzzy clustering target function, and designing strong and weak combined semi-supervised intuitive fuzzy clustering target function J _LP-SKIFCM ：

Wherein,

intuitive fuzzy set representation representing a color image having N pixels, based on the intensity of the image signal>

Is the jth pixel x _j K is the number of clusters, u _ij Representing a pixel x _j For membership of the i-th class, satisfy +>

Intuitive fuzzy cluster center, μ (c), representing class i _i ) Representing the center of the cluster c _i Corresponding degree of membership, v (c) _i ) Representing the center of the cluster c _i Corresponding non-membership, π (c) _i ) Representing the center of the cluster c _i Corresponding degree of hesitation, η ₁ Is a weight index, η, of a strong supervision term ₂ Is a weight index of the weakly supervised term,. Sup.,>

represents the strong supervision membership degree of the jth pixel point to the ith class and is combined with the ith class>

Representing a pixel x _j For weak supervision membership of class i, <' > based on>

An intuitive fuzzy distance metric representing the introduction of a kernel function;

the strong and weak combined semi-supervised intuitive fuzzy clustering objective function J _LP-SKIFCM In (1), introducing an intuitive fuzzy distance metric of kernel function

The definition is as follows:

wherein,

is a gaussian radial basis function, the formula is as follows:

wherein σ represents a scale parameter of the kernel function, and the calculation formula is:

denotes the jth pixel x _j To the ith cluster center c _i The formula is as follows:

(7) Minimizing an objective function J using a Lagrange multiplier method _LP-SKIFCM To find out the degree of membership u _ij And intuitive fuzzy clustering center

And iteratively calculating the membership u according to the updated formula _ij And intuitive fuzzy cluster center>

(8) Judging an iteration termination condition: if it is

Or the iteration times T is more than T, the membership matrix U and the intuitive fuzzy clustering center are obtained>

Executing (9); otherwise, let t = t +1, return iteration and calculate membership u again according to the updated formula _ij And intuitive fuzzy cluster center>

(9) And classifying the obtained membership matrix U according to a maximum membership principle to obtain a clustering label of the image pixel, and outputting a segmentation result of the image X.

2. The method according to claim 1, wherein the step (3) of determining each pixel point x of the image _j Corresponding degree of membership mu (x) _j ) The formula is as follows:

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

wherein, mu ^R (x _j ) For pixel point x in a colour image _j The membership degree under the R channel is calculated by using a maximum and minimum normalization method,

and &>

Respectively representing the maximum value and the minimum value of the image X under the R component;

μ ^G (x _j ) For pixel point x in a colour image _j Degree of membership under G channel, use thereof

The calculation is carried out according to the calculation,

and &>

Respectively representing the maximum value and the minimum value of the image X under the G component;

μ ^B (x _j ) For pixel point x in a colour image _j Degree of membership under B channel, use thereof

The calculation is carried out in such a way that,

and &>

Respectively representing the maximum and minimum values of image X under the B component.

3. The method according to claim 1, wherein in the step (3), each pixel point x of the image is obtained _j Corresponding non-membership degree v (x) _j ) And a degree of hesitation pi (x) _j ) The method is solved by utilizing a Segno intuitive fuzzy generation operator, and the formulas are respectively as follows:

π(x _j )＝1-μ(x _j )-v(x _j )，

wherein, delta is a variable parameter, and the value range thereof is (-1, infinity).

4. The method according to claim 1, wherein the strong label Y is used in (5 a) ^S Conversion to strong prior membership

Two different pixel transformations were included:

for pixels x without strong labels _u With a corresponding degree of membership of 0, i.e.

Wherein it is present>

Is a pixel x without a strong label _u For strong prior membership of class i, i ∈ {1,2, \8230;, k };

for strongly labeled pixels x _l And belong to the i-th class, then

Otherwise, is greater or less>

Wherein it is present>

For strongly labelled pixels x _l For strong a priori membership of class i->

For strongly labelled pixels x _l For strong prior membership of the t-th class, t belongs to {1,2, \8230 ≠ i }.

5. The method according to claim 1, wherein the weak label Y in (5 a) ^W Conversion to weak prior membership

Two different pixel transformations were included:

for pixels x without weak labels _u ', with a corresponding degree of membership of 0, i.e.

Wherein it is present>

As a pixel x without a weak label _u ' for weak prior membership of class i, i ∈ {1,2, \8230;, k };

for weakly labeled pixel x _l And belong to the i-th class, then

Otherwise, is greater or less>

Wherein it is present>

As weakly labeled pixel x _l ' for weak a priori membership of class i `, `>

As weakly labeled pixel x _l ' for weak prior membership of class t, t ∈ {1,2, \ 8230;, k, t ≠ i }.

6. The method according to claim 1, wherein (5 b) uses strong a priori membership

Evaluating a strength estimate membership degree->

The formula is as follows:

wherein,

for strongly labelled pixels x _l For the firstStrong prior membership in class i,. Sup.,>

pixel x without strong mark _u For a strong evaluation membership of the i-th class, a degree of membership>

SL represents a set of pixels with a strong label, <' > or>

Indicating a strongly marked pixel x _l And pixels x without strong marks _u The euclidean distance between.

7. The method of claim 1, wherein weak a priori membership is used in (5 b)

Evaluating the degree of membership of the weak estimate>

The formula is as follows:

wherein,

as weakly labeled pixel x _l ' for weak a priori membership of class i `, `>

Weak Mark free Pixel x _u ' Weak estimate membership for class i `>

WL denotes the set of pixels with a weak label, <' >>

Indicating a pixel x with a weak mark _l ' with pixels without weak marks x _u The euclidean distance between'.

8. The method according to claim 1, wherein the degree of membership u in (7) _ij Is represented as follows:

9. the method of claim 1, wherein the intuitive fuzzy clustering center in (7)

Respectively, as follows:

wherein,

is a pixel x _j To the clustering center c _i A measure of the membership degree->

Is a pixel x _j To the clustering center c _i The kernel metric at the non-membership level, device for selecting or keeping>

Is a pixel x _j To the clustering center c _i Nuclear metric at hesitation. />

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