CN110751662B - Image segmentation method and system for quantum-behaved particle swarm optimization fuzzy C-means - Google Patents

Abstract

The invention discloses an image segmentation method and system for a fuzzy C mean value optimized by quantum-behaved particle swarm, comprising the following steps: an acquisition step: acquiring an image to be processed, and converting the image to be processed into a Zhongzhi image; an image preprocessing step: denoising the intermediate intelligent image, and then performing image enhancement operation on a denoised result; and (3) information entropy calculation: calculating the element information entropy of the image set I for the result after image enhancement; an image segmentation step: if the ratio of the information entropies of the adjacent elements is smaller than a set threshold, carrying out segmentation on the mesology image by using a fuzzy C-means algorithm optimized by quantum-behaved particle swarm to obtain an image segmentation result; otherwise, returning to the image preprocessing step.

Description

Image Segmentation Method and System Based on Quantum Behavior Particle Swarm Optimization Fuzzy C-Means

technical field

The present disclosure relates to the technical field of image segmentation, and in particular, to an image segmentation method and system for optimizing fuzzy C-means by quantum behavior particle swarm.

Background technique

The statements in this section merely mention background related to the present disclosure and do not necessarily constitute prior art.

Images carry vivid and rich information and play an extremely important role in the era of multimedia information. Images can directly imitate or truly describe the objective existence of things. Image segmentation is an important preprocessing for image recognition and computer vision. Without proper segmentation, there is no proper identification. This is a critical step from image processing to image analysis. Image segmentation is in increasing demand in military, remote sensing, meteorology, communications, transportation, and medical image applications.

In the process of realizing the present disclosure, the inventor found that the following technical problems exist in the prior art:

Generally, image segmentation decomposes a complete image into several regions with the same or different features, and extracts objects of interest and technical processes from these regions. When a computer handles segmentation automatically, it encounters various difficulties. For example, segmentation errors often occur due to uneven lighting, the effect of noise, the presence of unclear parts in the image, and shadows. Therefore, image segmentation is a technique that requires further research.

SUMMARY OF THE INVENTION

In order to solve the deficiencies of the prior art, the present disclosure provides an image segmentation method and system for optimizing fuzzy C-means by quantum behavior particle swarm;

In a first aspect, the present disclosure provides an image segmentation method for quantum behavior particle swarm optimization fuzzy C-means;

Quantum behavioral particle swarm optimization fuzzy C-means image segmentation method, including:

Obtaining step: obtaining the image to be processed, and converting the image to be processed into a neutrosophic image;

Image preprocessing step: denoise the neutrosophic image, and then perform image enhancement on the denoised result;

Information entropy calculation step: to the result after image enhancement, calculate the element information entropy of image set I;

Image segmentation step: If the ratio of the information entropy of adjacent elements is less than the set threshold, use the fuzzy C-means algorithm of quantum behavior particle swarm optimization to segment the neutrosophic image to obtain the image segmentation result; otherwise, return to the image preprocessing step.

In a second aspect, the present disclosure also provides an image segmentation system for quantum behavior particle swarm optimization fuzzy C-means;

A quantum-behavioral particle swarm-optimized fuzzy C-means image segmentation system, including:

an acquisition module, which is configured to: acquire the to-be-processed image, and convert the to-be-processed image into a neutrosophic image;

an image preprocessing module, which is configured to: perform denoising processing on the neutrosophic image, and then perform an image enhancement operation on the denoised result;

an information entropy calculation module, which is configured to: calculate the element information entropy of the image set I for the result after image enhancement;

The image segmentation module is configured to: if the ratio of the information entropy of adjacent elements is less than the set threshold, use the fuzzy C-means algorithm of quantum behavior particle swarm optimization to segment the neutrosophic image, and obtain the image segmentation result; otherwise, return the image preprocessing module.

In a third aspect, the present disclosure also provides an electronic device, including a memory, a processor, and computer instructions stored in the memory and executed on the processor, and when the computer instructions are executed by the processor, the first aspect is completed. steps of the method.

In a fourth aspect, the present disclosure further provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps of the method in the first aspect.

Compared with the prior art, the beneficial effects of the present disclosure are:

The invention proposes a neutrosophic image segmentation method based on quantum behavior particle swarm optimization fuzzy C-mean algorithm. The fuzzy control algorithm is optimized by the simplicity and effectiveness of the fuzzy control algorithm and the global optimization ability of QPSO. Experiments show that the algorithm is feasible and has good anti-noise ability. The overall effect of this method is better than that of FCM, the boundary of the segmentation is clearer, and it does not require multiple experiments to select the optimal result. The algorithm effectively solves the problem that FCM has strong dependence on the initial value and is easy to fall into local optimum. The algorithm has strong global search ability and good image segmentation effect. Although a good segmentation effect can be accurately obtained, the single time of the program running is not significantly shortened.

Description of drawings

The accompanying drawings that form a part of the present application are used to provide further understanding of the present application, and the schematic embodiments and descriptions of the present application are used to explain the present application and do not constitute improper limitations on the present application.

FIG. 1 is a flow chart of the method of Embodiment 1 of the present disclosure;

FIG. 2( a ) is an image of a warship (240×320) according to Embodiment 1 of the present disclosure;

FIG. 2(b) is an effect diagram of a neutrosophic image using α-mean operation and image enhancement operation according to Embodiment 1 of the present disclosure;

FIG. 2(c) is an effect diagram of the fuzzy C-means segmentation based on FIG. 2(b) according to the first embodiment of the present disclosure;

Fig. 2(d) is an effect diagram of the improved particle swarm optimization fuzzy C-mean segmentation based on Fig. 2(b) according to the first embodiment of the present disclosure.

Detailed ways

It should be noted that the following detailed description is exemplary and intended to provide further explanation of the application. Unless otherwise defined, all technical and scientific terms used in this disclosure have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

It should be noted that the terminology used herein is for the purpose of describing specific embodiments only, and is not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly dictates otherwise, the singular is intended to include the plural as well, furthermore, it is to be understood that when the terms "comprising" and/or "including" are used in this specification, it indicates that There are features, steps, operations, devices, components and/or combinations thereof.

Embodiment 1, this embodiment provides an image segmentation method for quantum behavior particle swarm optimization of fuzzy C-means;

As shown in Figure 1, the image segmentation method of quantum behavior particle swarm optimization fuzzy C-means, including:

Obtaining step: obtaining the image to be processed, and converting the image to be processed into a neutrosophic image;

Image preprocessing step: denoise the neutrosophic image, and then perform image enhancement on the denoised result;

Information entropy calculation step: to the result after image enhancement, calculate the element information entropy of image set I;

Image segmentation step: If the ratio of the information entropy of adjacent elements is less than the set threshold, use the fuzzy C-means algorithm of quantum behavior particle swarm optimization to segment the neutrosophic image to obtain the image segmentation result; otherwise, return to the image preprocessing step.

As one or more embodiments, the fuzzy C-means algorithm using quantum behavior particle swarm optimization is used to segment a neutrosophic image to obtain an image segmentation result; the specific steps include:

S41: the initial number of clusters C, the ambiguity parameter m, the particle swarm size N, and the maximum number of iterations MaxIt; the number of cluster centers is the dimension of each particle;

S42: Initialize and encode N cluster centers to form N first-generation particles; the number of cluster centers is equivalent to the particle dimension; the pbest of each particle is its current position, and gbest is all particles in the current population the best location;

S43: Calculate the center vector U(k) of each cluster center C(k) and membership degree;

S44: Calculate the fitness of each particle; if the fitness of the particle is better than the fitness of the current optimal position of the particle, update the optimal position of a single particle. If the fitness of the current global best position is better than the fitness of the best position in all particles, update the global best position;

S45: Update the position of each particle to generate a new particle swarm;

S46: If the current number of iterations reaches the previously set maximum number, stop the iteration; find the best solution in the last generation, otherwise repeat S43.

Further, in the step S45, the position of each particle is updated with equations (30)-(33) to generate a new particle swarm:

X _i,j (t+1)=pi _,j (t)±α·|C _j (t)-X _i,j (t)|·ln[1/u _i,j (t)]; u _i,j (t)～U(0,1)(31)

The parameter C in formula (31) is called the average optimal position, which can be denoted as mbest, which is the center point of the individual optimal positions of all particles:

Among them, p _i,j (t) is the potential well (local attraction point) of the j-th dimension of the i-th particle at the t-th iteration, and its position is actually located at the individual optimal position pbest _j (t) and the group The optimal position gbest(t) is in the hyperrectangle of the vertices, and changes with the changes of pbest and gbest. φ _j (t) and ui _,j (t) are both the t-th iteration, the j-th dimension is a random number uniformly distributed on [0,1], and X _i,j (t+1) is the t-th iteration , the position of the i-th particle in the j-th dimension, C _j (t) is a vector in C(t), α is the contraction and expansion coefficient of QPSO, and the value of α is determined by formula (33):

α=(α ₁ -α ₂ )*(MaxIt-t)/MaxIt+α ₂ (33)

Among them, α ₁ and α ₂ are the initial and final values of the parameter α, respectively, t is the current number of iterations, and MaxIt is the maximum number of iterations allowed. By changing the value of α, from 1.0 at the beginning of the search to 0.5 at the end of the search.

As one or more embodiments, the neutrosophic images include a neutrosophic set image T, a neutrosophonic set image I, and a neutrosophic set image F:

The neutropen set image T is represented as the authenticity representation of the original image;

The neutrosophon set image I is represented as the uncertainty representation of the original image;

The neutropen set image F is represented as a non-authentic representation of the original image.

As one or more embodiments, converting the to-be-processed image into a neutrosophic image; the specific steps include:

According to the average value of the pixel value area of the original image, calculate the neutropen set image T;

According to the absolute value of the difference between the original image pixel value and the regional pixel mean value, calculate the neutropen set image I;

From the neutropen set image T, the neutropen set image F is calculated.

As one or more embodiments, converting the to-be-processed image into a neutrosophic image; the specific steps include:

P _NS = {T,I,F} (1)

F(i,j)=1-T(i,j) (6)

Among them, P _NS is the pixel point of the image in the NS domain;

T(i,j) is the value of the neutron set image T at point (i,j);

I(i,j) is the value of the neutron set image I at point (i,j);

F(i,j) is the value of the neutropen set image F at point (i,j);

是g(i,j)在w×w区域内的均值；

is the mean of g(i,j) in the w×w region;

表示

的最小值，

表示

的最大值；

express

the minimum value of ,

express

the maximum value of ;

g(m,n) is the value of the neutropen set image T at point (m,n);

之差的绝对值。δ(i,j) is the mean of pixels g(i,j) and g(i,j) in the w×w area

The absolute value of the difference.

As one or more embodiments, the denoising process is performed on the neutrosophic image; the specific steps include:

图像在NS域中的像素经过点α-均值的集合，

中智子集合图像T的α-均值子集合，

为中智子集合图像I的α-均值子集合，

为中智子集合图像F的α-均值子集合，T为原图像真实值的集合，

为待进行α-均值集合，I为原图像不确定值的集合，α取值0.85，w*w为限制区域大小，(i,j)为原始图像的像素点，(m，n)为w*w区域内领域像素信息点，T(m,n)为中智子集合图像T在点(m，n)的取值，

为中智子集合图像T进行α-均值的灰度平均强度值，

需要进行α-均值集合，F(m,n)为中智子集合图像F在点(m，n)的取值，

为中智子集合图像F进行α-均值的灰度平均强度值。

为中智子集合图像I的平均强度值,

是像素点(i,j)进行过α均值运算后的T_α(i,j)与

之差的绝对值，

和

是

的最小值和最大值。in,

The pixels of the image in the NS domain pass through the set of point α-means,

the α-means subset of the neutrosophonic set image T,

is the α-mean subset of the neutropen set image I,

is the α-mean subset of the neutrosophonic set image F, T is the set of true values of the original image,

For the α-mean set to be performed, I is the set of uncertain values of the original image, α is 0.85, w*w is the size of the restricted area, (i, j) is the pixel point of the original image, (m, n) is w *The domain pixel information points in the w area, T(m,n) is the value of the neutrosophon set image T at point (m,n),

The gray-scale mean intensity value of the α-mean for the neutrosophore set image T,

It is necessary to perform α-mean set, and F(m,n) is the value of the neutrosophon set image F at point (m,n),

Gray-scale mean intensity values for alpha-means for the neutropen ensemble image F.

is the average intensity value of the neutropen set image I,

is the T _α (i, j) and the

The absolute value of the difference,

and

Yes

the minimum and maximum values.

It should be understood that the purpose of the denoising step is to reduce noise points and pixel points with high uncertainty in the image, and the distribution of image pixel information is also more reasonable and facilitates the subsequent processing of the image.

As one or more embodiments, the image enhancement operation is performed on the denoised result; the specific steps include:

为中智集合经过β增强运算的真实性集合，

为当

中智集合经过β增强运算的真实性子集合，

为表示中智集合的不确定性智的子集合,β为取值0.85，

为

进行β增强运算的真实值，

为集合T经过均值运算后的值,

为中智集合经过β增强运算的非真实性集合，

为当

中智集合经过β增强运算的非真实性子集合，

为

进行β增强运算的非真实值，

为经过均值运算后的非真实像素点,

是

的不确定性的像素点子集合，δ'(i,j)是像素点(i,j)进行过图像增强操作后的值

与均值

之差的绝对值，δ'_min为像素点(i,j)进行过图像增强操作后的值

与均值

之差的绝对值的最小值，δ'_max为像素点(i,j)进行过图像增强操作后的值

与均值

之差的绝对值的最大值,

为子集合

在w*w区域内的平均强度,

为子集合

在w*w区域内经过β增强运算后的真实性集合。δ'(i,j)是像素点(i,j)进行过图像增强操作后的

与

之差的绝对值。in:

is the authenticity set of the neutrosophic set after β-enhanced operation,

for when

The reality subset of the neutrosophic set after β-enhanced operation,

is a subset representing the uncertainty intelligence of the neutrosophic set, β is 0.85,

for

the true value of the beta enhancement operation,

is the value of the set T after the mean operation,

is the unreal set of the neutrosophic set after β-enhanced operation,

for when

The unreal subset of the neutrosophic set after β-enhancing operation,

for

untrue values for beta enhancement operations,

is the unreal pixel point after mean operation,

Yes

The uncertainty subset of pixel points, δ'(i, j) is the value of pixel point (i, j) after image enhancement operation

with mean

The absolute value of the difference, δ' _min is the value of the pixel point (i, j) after image enhancement operation

with mean

The minimum value of the absolute value of the difference, δ' _max is the value of the pixel point (i, j) after image enhancement operation

with mean

The maximum value of the absolute value of the difference,

as a sub-collection

The average intensity in the w*w region,

as a sub-collection

The authenticity set after beta enhancement operation in the w*w region. δ'(i,j) is the pixel point (i,j) after image enhancement operation

and

The absolute value of the difference.

It should be understood that the purpose of the enhancement processing step is to enhance the visual effect of the image, enlarge the feature difference between different objects (such as the target and the background) in the image, and improve the recognition effect of the image.

As one or more embodiments, for the result after image enhancement, the element information entropy of image set I is calculated; the specific steps include:

where En _I is the entropy of the neutropen set image I, and p _I (i) is the probability of element i in the neutropen set image I.

In order to overcome the limitations of general image segmentation methods and improve the expression and processing ability of image uncertainty information, interval-valued fuzzy sets, intuitionistic fuzzy sets and extended fuzzy theory of interval-valued intuitionistic fuzzy sets are proposed. Fuzzy theory uses membership function to describe the degree to which an element belongs to a certain class, so it can well express and deal with ambiguity and uncertainty in the segmentation process. Among them, neutrosophic theory is a new extended fuzzy theory, which summarizes classical fuzzy theory and related extended fuzzy theory.

Neutrosophy studies actual things, theories, propositions, concepts, or entities "A" and its opposite "Anti-A", its negation "Non-A" and "Netu-A" (neither "A" nor "Netu-A". Not "Anti-A") the relationship between the three. Neutrosophy is the basis of neutrosophic logic, neutrosophic probability, neutrosophic ensemble, and neutrosophic statistics.

The basic idea of neutron physics is that any opinion has t% true value, i% uncertainty and f% false value.

The fuzzy segmentation technology based on fuzzy theory can effectively describe the ambiguity of images, and is very suitable for dealing with the uncertainty of medical images that require accurate segmentation. With the continuous improvement of fuzzy theory, its application in image segmentation has become increasingly active and has become a research hotspot.

The main basis of image segmentation is the similarity and discontinuity of gray level. Image segmentation algorithms can be divided into region-based segmentation algorithms and boundary-based segmentation algorithms and segmentation methods combined with specific theoretical tools. Region-based image segmentation algorithms separate objects from the background in the image by choosing an appropriate threshold. This method is simple and intuitive, but it only considers the grayscale information of the image, not the spatial information of the image, and is very sensitive to noise and grayscale inhomogeneity. Edge-based image segmentation algorithms complete the segmentation of regions by detecting edges between different uniform regions. The difficulty of edge detection methods lies in the contradiction between anti-noise and detection accuracy. At this stage, many improved multi-scale edge detection methods have been proposed, but the effect is still not ideal. The segmentation method combined with specific theoretical tools is to use many theoretical methods at this stage for image segmentation, such as the FCM method based on cluster analysis. The fuzzy C-means algorithm (FCM) based on cluster analysis has attracted more and more attention and has been widely used in various fields due to its simple design, wide solution range, and easy computer implementation. In addition, traditional FCM algorithms do not consider spatial information during image segmentation and are sensitive to noise and grayscale inhomogeneity.

Fuzzy C-means algorithm has been widely used because of its simple implementation; however, fuzzy C-means algorithm is very sensitive to initial parameters, sometimes even very sensitive to initial parameters. Human intervention parameters are required to approximate the global optimal solution and improve the segmentation speed. However, it is limited by the selection of the initial cluster center, which is easy to fall into the local optimum and is more sensitive to noise. The classical improvement of FCM mainly has two aspects: one is the improvement of the objective function in FCM; the other is the introduction of other intelligent algorithms in the iterative solution process. In recent years, many scholars have tried various methods to solve the problem that fuzzy C-means algorithm falls into local extreme value due to improper selection of initial value. For example, the combination of FCM and particle swarm optimization algorithm can improve the quality of image segmentation to a certain extent.

The particle swarm (PSO) algorithm was proposed by Kennedy and Eberhar in 1995. The calculation of PSO is simple and easy to implement. However, due to the inability to effectively control the flying speed of particles in the later stage of evolution, the algorithm easily leaps over the optimal solution, which in turn leads to a decrease in the convergence speed and accuracy of the algorithm. In view of the above shortcomings, Sun Jun et al., from the perspective of quantum mechanics, used the quantum uncertainty principle to describe the motion state of particles, and established a new PSO algorithm model, namely quantum behavioral particle swarm optimization (Quantum-behaved PSO, QPSO) algorithm model. In the QPSO algorithm, QPSO regards each individual as a particle without weight and volume in the D-dimensional search space, which can randomly appear at any position in the space with a certain probability, thereby realizing the algorithm global convergence. The algorithm not only has a small number of parameters, but also outperforms the developed PSO algorithm in search ability.

In order to solve the problems of FCM algorithm, quantum behavior particle swarm optimization (QPSO) is applied to fuzzy C-means clustering.

FCM obtains the membership degree of each data sample point to all class centers by optimizing the objective function, so as to determine the attribution of sample points to achieve the purpose of automatically classifying data samples. Since the FCM algorithm essentially uses the gradient descent method to find the optimal solution, there is a problem of falling into the local optimal solution. In view of the above situation, the present disclosure introduces a particle swarm algorithm that can ensure global convergence, that is, the quantum behavior particle swarm algorithm forms a fuzzy clustering algorithm based on evolutionary computation.

(1) Neutrosophy images

Because the classical fuzzy segmentation algorithm is difficult to obtain better results when dealing with more complex and high uncertainty problems. Therefore, the neutrosophic theory is introduced into the image, and the neutrosophic image is generated to enhance the expression ability of the uncertain information in the image.

The neutrosophic image is the representation of an image in the field of neutrosophy. The basic method is to use the theory of neutrosophy to convert the original digital image and image-related features to the neutrosophic area, so as to obtain a neutrosophic image. Neutrophil images can better express and describe the ambiguity and uncertainty of images, not only can use gray information, but also use edge and spatial information to solve problems that cannot be solved by fuzzy segmentation algorithms.

Definition 1 (neutrosophic image): Given that the image is P, suppose the universe of universe is U, the complete set of image pixels is W, and W is a non-empty subset of U. _PNS images have three membership sets T, I and F.

P _NS = {T,I,F} (1)

Among them, the subset image T represents the authenticity representation of the original image, the subset image I represents the uncertainty representation of the original image, and the subset image F represents the non-authenticity representation of the original image.

The feature information used in the neutrosophic image is the gray value of the image pixel. A pixel P in the image is described as P(t,i,f) and belongs to W for the element P(t,i,f) in the following way: t% true, i% indeterminate, and f% false, where , t∈T, i∈I, f∈F. Pixels P(i,j) in the image domain are transformed into neutrosophic regions.

In general, we use the standard deviation to express the uncertainty of the data. Since the uncertainty of the target area and the background area is much smaller than that of the edge, this section defines I according to the standard deviation and discontinuity of the image gray level. The standard deviation represents the difference in the local area of the image, and the discontinuity represents the sudden change of gray level. The standard deviation reflects the difference in the local area of the image. The background and target area in the image are uniform, while the blurred edge is a gradual change from the target to the background, then, we use the mean, standard deviation, and range of the pixel value area to describe T, I, F.

In the process of image transformation, we limit the pixel (i, j) to a small area, and take the size of this area as w×w. The transformation process of neutrosophic images is the acquisition process of the three sets T, I, F. This process is calculated by the following formula:

F(i,j)=1-T(i,j) (6)

是图像的局部平均值，δ(i,j)是像素点g(i,j)与其局部平均值

之差的绝对值。in:

is the local average of the image, δ(i,j) is the pixel g(i,j) and its local average

The absolute value of the difference.

(2) Information entropy of neutrosophic images

The information entropy of the image is used to describe the aggregation characteristics of the grayscale distribution of image pixels. In the neutrosophic image, we use the information entropy of the image to describe the aggregation characteristics of the gray distribution of image pixels.

Definition 2 (Information Entropy of Neutrosophic Image) The information entropy of a neutrosophic image is defined as the sum of the entropy of the three sets T, I and F, which is used to evaluate the distribution of elements in the neutrosophic region:

En _NS =En _T +En _I +En _F (7)

where: En _T , En _I , En _F are the entropy of sets T, I and F, respectively, and the probability of element i in the three sets T, I, and F, respectively. And En _T and En _F are used to describe the distribution of elements in the neutrosophic set; En _I is used to describe the distribution of element uncertainty.

According to the concept of neutrosophy, the change of elements in sets T and F can affect the uncertainty distribution of set I. The larger the entropy of the set T and the smaller the entropy of the set I, the more uniform the gray distribution of the image is, and the more reasonable the distribution of gray values is. In order to increase the entropy of the set T and reduce the entropy of the set I, a new operation-α-mean operation is proposed in the neutrosophic image denoising. to judge and update the current pixel value.

When there is noise in the image, image segmentation is easily disturbed by noise, and the segmentation effect is poor, which affects image analysis and understanding. In order to solve this problem, the present disclosure adopts the method of alpha mean filtering to eliminate image noise, which is convenient for subsequent image segmentation.

定义为：Definition 3 (α-mean operation): perform α-mean operation on P _NS ,

defined as:

和

分别是T(i,j)和F(i,j)在w×w区域内的均值；δ_α(i,j)是像素点(i,j)进行过α均值运算后的T_α(i,j)与

之差的绝对值。in:

and

are the mean values of T(i,j) and F(i,j) in the w×w area respectively; δ _α (i, j) is the T _α (i ,j) with

The absolute value of the difference.

After the α-mean operation, the entropy of the uncertain subset I decreases, and the distribution of elements in I becomes more uneven. This unevenness reduces the uncertainty of the neutrosophic set PNS. The noise points and pixels with high uncertainty in the image are reduced, and the distribution of image pixel information is more reasonable, which is beneficial to the subsequent processing of the image.

(4) Image enhancement operation

使模糊的图像轮廓变得更加清晰，其增强公式为In the process of neutrosophic image segmentation, transforming the image into a neutrosophic image and performing α-mean operation will make the image contour blurred, so image enhancement is used to solve this problem in the processing process. The main purpose of image enhancement is to improve the contrast of the image and highlight the information of interest. Image enhancement can improve image blur and image quality. It can further enhance the edge information of the object and weaken the non-edge information, thereby reducing the blurring of the image. Using the principle of fuzzy set enhancement operation on set elements, the β-enhancement operation is performed on the T image in the neutrosophic image P _NS to obtain

Make the blurred image outlines clearer, and the enhancement formula is

与

之差的绝对值。Among them: δ'(i,j) is the pixel point (i,j) after image enhancement operation

and

The absolute value of the difference.

(5) Fuzzy C-means algorithm

The key to image segmentation based on FCM clustering algorithm is how to unify the mathematical form of the image with that of the FCM clustering algorithm. To this end, the image can be regarded as a sample set, each pixel in the image can be regarded as a clustering sample, the feature of the pixel can be regarded as the feature vector of the sample, and the pixels are clustered in the feature space. Divide the pixels with the same or similar features into one category as much as possible; then mark the category of each pixel to complete the image segmentation.

即α均值和图像增强操作后的中智子集。For neutrosophic subsets, a new clustering method is defined to deal with

That is, the neutrosophic subset after alpha-means and image enhancement operations.

Considering the effect of uncertainty, we combine the two sets T and I into a new cluster value.

An improved fuzzy c-means algorithm for neutrosophic sets is proposed. The objective function is defined as:

The FCM algorithm obtains the fuzzy classification of the sample set by iterative optimization of the objective function.

The algorithm is sensitive to the initial value and largely depends on the choice of initial cluster centers. When the initial cluster center is seriously deviated from the global optimal cluster center, FCM is prone to fall into a local minimum. When the number of clusters is large, the disadvantage is more obvious.

(6) Improved PSO-FCM

The FCM algorithm based on gradient descent is essentially a local search algorithm, which is easy to fall into a local minimum value and is sensitive to the initial value, that is, different initial values may lead to different clustering results. The QPSO algorithm has a global search ability and is not easy to fall into a local area. Therefore, the present disclosure proposes a new neutrosophic image segmentation hybrid clustering algorithm (QPSO-FCM), which combines the QPSO algorithm and FCM and applies it to neutrosophic images. to split.

QPSO operates on the fitness of individuals (particles) using the concepts of "population" and "evolution". Assuming that in a multi-objective search space, m is the particle number of particles, the position of the first particle is represented as a vector Xi = (xi1,xi2,...xiD) In each iteration, the particle is obtained by tracking the two best positions. update itself. One is the optimal solution found by the particle itself, called a single optimal position pi=(pi1, pi2, ... pid); the other is the optimal solution found by the entire particle swarm optimization at present, called the global optimal position pg . After finding the above two extremes, take the average best position (mbest) or C(t) as the average of the best positions of all particles. Move according to the formula below to search for the best solution to the problem.

X _i,j (t+1)=pi _,j (t)±α·|C _j (t)-X _i,j (t)|·ln[1/u _i,j (t)] u _{i ,j} (t)～U(0,1)(31)

p _i,j (t) is the individual optimal position of the i-th particle at the t-th iteration (1<=j<=D). α is the contraction expansion coefficient of QPSO. It is an important parameter for QPSO convergence, and the value of α is determined by the following formula:

α=(α ₁ -α ₂ )*(MaxIt-t)/MaxIt+α ₂ (33)

In the formula, α ₁ and α ₂ are the initial and final values of the parameters, respectively, t is the current number of iterations, and MaxIt is the maximum number of iterations allowed, by changing the value from 1.0 at the beginning of the search to 0.5 at the end of the search.

In the application of QPSO-FCM algorithm, the fitness function of each individual in QPSO is defined as follows:

where J _m (U, C) is the fitness function of the image. k is the grayscale, k=0-C, C is the maximum value of the grayscale.

The QPSO-based FCM algorithm randomly generates next-generation solutions, so it is easy to search for the global optimum. Moreover, each generation of the solution has the dual advantages of self-improvement and learning from others; therefore, it has a fast convergence rate.

(7) Neutrosopic Image Segmentation Based on QPSO-FCM Algorithm

A new neutrosophic image segmentation algorithm—QPSO-FCM algorithm is proposed, which includes the following steps:

Step 1: Input image;

Step 2: Transform the image into the NS domain using equations (1)-(6);

Step 3: Perform an alpha mean operation using equations (11)-(17);

Step 4: Perform an image enhancement operation using equations (18)-(24);

Step 5: Calculate the entropy of the indeterminate subset I using equation (9);

进入步骤7；否则进入步骤3；Step 6: If

Go to step 7; otherwise go to step 3;

Step 7: Apply the improved FCM algorithm to the neutrosophic set:

初始聚类类数C，模糊度参数m，粒子群大小N和最大迭代次数MaxIt。聚类中心的数量是每个粒子的维数。

The initial clustering class number C, the ambiguity parameter m, the particle swarm size N and the maximum number of iterations MaxIt. The number of cluster centers is the dimension of each particle.

对N个簇中心进行初始化编码，形成N个第一代粒子。聚类中心的个数相当于粒子的维度。每个粒子的pbest是它的当前位置，而gbest是当前总体中所有粒子的最佳位置。

Initialize the N cluster centers to form N first-generation particles. The number of cluster centers is equivalent to the dimension of the particle. The pbest of each particle is its current position, and the gbest is the best position of all particles in the current population.

利用等式(28)-(29)在k步计算每个聚类中心C(k)以及隶属度的中心向量U(k)；

Calculate each cluster center C(k) and the membership center vector U(k) in k steps using equations (28)-(29);

根据等式(34)计算各粒子的适应度。如果粒子的适应度优于粒子当前最佳位置的适应度，则更新单个粒子的最佳位置。如果当前全局最佳位置的适应度都优于所有粒子中的最佳位置的适应度，则更新全局最佳位置。

The fitness of each particle is calculated according to equation (34). If the fitness of the particle is better than the fitness of the particle's current best position, the best position of a single particle is updated. If the fitness of the current global best position is better than the fitness of the best position among all particles, update the global best position.

用等式(30)-(33)来更新每个粒子的位置以生成新的粒子群。

Equations (30)-(33) are used to update the position of each particle to generate a new particle swarm.

如果当前迭代次数达到先前设置的最大次数，则停止迭代。在最后一代中找到最佳解决方案，否则重复步骤(3)。

Stops iterating if the current iteration count reaches the previously set maximum. Find the best solution in the last generation, otherwise repeat step (3).

Step 8: Get the image segmentation result.

The QPSO-FCM segmentation algorithm is applied to denoised neutrosophic images of various real images, and compared with the neutrosophic denoising image segmentation method based on fuzzy C-means.

In the FCM image segmentation method and the QPSO-FCM image segmentation method, the cluster centers set in the present invention are both 5, so as to compare with each other.

It can be seen from Fig. 2(a)-Fig. 2(d) that the warship boundary is clearer in Fig. 2(d) compared with Fig. 2(c). Especially at the front of the boat, the boundary of the segment in Fig. 2(d) is clearer. The warship boundary in Fig. 2(c) is blurred.

From the experimental data in Figure 2(a)-Figure 2(d), it can be seen that the combination of QPSO and FCM applied to neutrosophic images has a clearer segmentation effect than the combination of FCM applied to neutrosophic images.

The ultimate goal of image segmentation is to obtain the target image precisely in one run. Therefore, we need to constantly find new ways to test whether this method is good or bad. It can be seen from the data obtained in a large number of experiments that the FCM is greatly affected by the initial value, so we can only test whether the global optimal value can be found. In many experiments, we can find the best performing images (with sharper borders). Applying the QPSO-FCM method to neutrosophic images, the global optimum can be found in one run, the segmentation boundaries are clearer, the handling of blurred regions is greatly improved, and the global optimum remains the same even if the experiment is repeated.

However, since the data of this method needs to be repeatedly calculated, the running time of the program is not significantly shortened. According to the no-free lunch theorem, we get good and accurate segmentation at the cost of more running time.

Embodiment 2, this embodiment also provides an image segmentation system for quantum behavior particle swarm optimization of fuzzy C-means;

A quantum-behavioral particle swarm-optimized fuzzy C-means image segmentation system, including:

an acquisition module, which is configured to: acquire the to-be-processed image, and convert the to-be-processed image into a neutrosophic image;

an image preprocessing module, which is configured to: perform denoising processing on the neutrosophic image, and then perform an image enhancement operation on the denoised result;

an information entropy calculation module, which is configured to: calculate the element information entropy of the image set I for the result after image enhancement;

The image segmentation module is configured to: if the ratio of the information entropy of adjacent elements is less than the set threshold, use the fuzzy C-means algorithm of quantum behavior particle swarm optimization to segment the neutrosophic image, and obtain the image segmentation result; otherwise, return the image preprocessing module.

Embodiment 3, this embodiment also provides an electronic device, including a memory, a processor, and computer instructions stored in the memory and run on the processor, and when the computer instructions are run by the processor, the first embodiment is completed. steps of the method described.

In Embodiment 4, this embodiment further provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the steps of the method in Embodiment 1 are completed.

The above descriptions are only preferred embodiments of the present application, and are not intended to limit the present application. For those skilled in the art, the present application may have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of this application shall be included within the protection scope of this application.

Claims (4)

1. The image segmentation method for the fuzzy C mean value by quantum-behaved particle swarm optimization is characterized by comprising the following steps of:

an acquisition step: acquiring an image to be processed, and converting the image to be processed into a Zhongzhi image;

converting the image to be processed into a mesology image; the method comprises the following specific steps:

P _NS ＝{T,I,F} (1)

F(i,j)＝1-T(i,j) (6)

wherein, P _NS Is a pixel point of the image in the NS domain;

t (i, j) is the value of the point (i, j) of the Zhongzhi subset image T;

i (I, j) is the value of the point (I, j) of the image I of the Zhongzhi subset;

f (i, j) is the value of the point (i, j) of the Zhongzhi subset image F;

is the mean of g (i, j) over the w × w region;

to represent

The minimum value of (a) is calculated,

to represent

The maximum value of (a);

g (m, n) is the value of the point (m, n) of the Zhongzhi subset image T;

δ (i, j) is the mean value of pixel points g (i, j) and g (i, j) in the region w × w

The absolute value of the difference;

an image preprocessing step: denoising the intermediate intelligent image, and then performing image enhancement operation on a denoised result;

denoising the mesology image; the method comprises the following specific steps:

wherein,

the pixels of the image in the NS domain pass through a set of point alpha-means,

is the alpha-mean of the image T of the wisdom subset,

is an alpha-means subset of the image I of the wisdom subset,

for the noon-child set image FT is the set of real values of the original image,

for the alpha-mean set to be performed, I is the set of the uncertain values of the original image, alpha takes a value of 0.85, w W is the size of the limited region, (I, j) is the pixel point of the original image, (m, n) is the leading region pixel information point in the w W region, T (m, n) is the value of the point (m, n) of the image T of the Zhongzhi subset,

a gray-scale average intensity value of alpha-means is performed for the image T of the wisdom subset,

alpha-mean value set is needed, F (m, n) is the value of the point (m, n) of the image F of the mesogen-junction set,

carrying out alpha-mean gray level average intensity value on the Zhongzhi subset image F;

for the average intensity value of the image I of the wisdom subset,

is T after alpha mean operation of pixel point (i, j) _α (i, j) and

the absolute value of the difference between the two values,

and

is that

Minimum and maximum values of;

performing image enhancement operation on the denoised result; the method comprises the following specific steps:

wherein:

for the set of realisms of the wisdom set subjected to the beta enhancement operation,

is that when

The authenticity subset of the noon set after beta enhancement operation,

is a subset of uncertainty values representing the medium intelligence set, beta is a value of 0.85,

is composed of

The true value of the beta-enhancement operation is performed,

is the value of the set T after the mean operation,

for the non-authentic set of the wisdom set subjected to the beta enhancement operation,

is as follows

The non-reality subset of the noon set is subjected to beta enhancement operation,

is composed of

A non-true value of the beta boost operation is performed,

the non-real pixel points after the mean value operation,

is that

Of uncertainty of pixel point subset, δ' _min Value after image enhancement operation for pixel point (i, j)

And mean value

Minimum value of absolute value of the difference, δ' _max Value of pixel point (i, j) after image enhancement operation

And mean value

The maximum value of the absolute value of the difference between,

as a subset

The average intensity in the region w x w,

as a subset

Performing beta enhancement operation on the authenticity set in the w x w region; delta' (i, j) is the pixel (i, j) after the image enhancement operation

And

the absolute value of the difference;

and (3) information entropy calculation: calculating the element information entropy of the image set I for the result after image enhancement;

calculating the element information entropy of the image set I for the result after image enhancement; the method comprises the following specific steps:

wherein, en _I Is the entropy, p, of the image of the Zhongzhi subset I _I (i) Is the probability of element I in the wisdom subset image I;

an image segmentation step: if the ratio of the information entropies of the adjacent elements is smaller than a set threshold, carrying out segmentation on the mesology image by using a fuzzy C-means algorithm optimized by quantum-behaved particle swarm to obtain an image segmentation result; otherwise, returning to the image preprocessing step;

the objective function is defined as:

the fuzzy C-means algorithm optimized by quantum-behaved particle swarm is used for segmenting the mesology image to obtain an image segmentation result; the method comprises the following specific steps:

s41: the method comprises the steps of firstly, obtaining an initial clustering class number C, an ambiguity parameter m, a particle swarm size N and a maximum iteration number MaxIt; the number of cluster centers is the dimension of each particle;

s42: carrying out initialization coding on the N cluster centers to form N first-generation particles; the number of the clustering centers is equivalent to the dimension of the particles; pbest for each particle is its current location, and gbest is the best location for all particles in the current population;

s43: calculating each clustering center C (k) and a center vector U (k) of the membership degree;

s44: calculating the fitness of each particle; if the fitness of the particle is better than the fitness of the current optimal position of the particle, updating the optimal position of a single particle; if the fitness of the current global optimal position is better than the fitness of the optimal positions in all the particles, updating the global optimal position;

s45: updating the location of each particle to generate a new population of particles;

the step S45, updating the position of each particle with equations (30) - (33) to generate a new particle population:

X _i,j (t+1)＝p _i,j (t)±α·|C _j (t)-X _i,j (t)|·ln[1/u _i,j (t)]；u _i,j (t)～U(0,1) (31)

wherein p is _i,j (t) is the potential well in the jth dimension of the ith particle at the tth iteration, whose location is actually at the individual optimal location pbest _j (t) and the group optimal position gbest (t) are in the hyper-rectangle of the vertex and vary with the variation of pbest and gbest; phi is a _j (t) and u _i,j (t) are all t iterations, j dimension is [0,1]Random numbers uniformly distributed, X _i,j (t + 1) is the position of the ith particle in the jth dimension, C, at the tth iteration _j (t) is a vector in C (t), α is the contraction-expansion coefficient of QPSO, and α has a value defined byEquation (33) determines:

α＝(α ₁ -α ₂ )*(MaxIt-t)/MaxIt+α ₂ (33)

wherein alpha is ₁ And alpha ₂ Respectively an initial value and a final value of the parameter alpha, t is the current iteration time, maxIt is the maximum time allowed to iterate, and the value of alpha is changed from 1.0 at the beginning of searching to 0.5 at the end of searching;

the fitness function for each individual is defined as follows:

wherein, J _m (U, C) is the fitness function of the image; k is the gray scale, k =0-C, C is the maximum value of the gray scale;

s46: stopping iteration if the current iteration times reach the maximum times set previously; the best solution is found in the last generation, otherwise S43 is repeated.

2. The image segmentation system of the fuzzy C-means with the quantum-behaved particle swarm optimization, which adopts the image segmentation method of the fuzzy C-means with the quantum-behaved particle swarm optimization as claimed in claim 1, is characterized by comprising:

an acquisition module configured to: acquiring an image to be processed, and converting the image to be processed into a Zhongzhi image;

an image pre-processing module configured to: denoising the intermediate intelligent image, and then performing image enhancement operation on a denoised result;

an information entropy calculation module configured to: calculating the element information entropy of the image set I for the result after image enhancement;

an image segmentation module configured to: if the ratio of the information entropies of the adjacent elements is smaller than a set threshold, carrying out segmentation on the mesology image by using a fuzzy C-means algorithm optimized by quantum-behaved particle swarm to obtain an image segmentation result; otherwise, returning to the image preprocessing module;

the fuzzy C-means algorithm optimized by quantum-behaved particle swarm is used for segmenting the mesology image to obtain an image segmentation result; the method comprises the following specific steps:

s41: the method comprises the steps of firstly, obtaining an initial clustering class number C, an ambiguity parameter m, a particle swarm size N and a maximum iteration number MaxIt; the number of cluster centers is the dimension of each particle;

s42: carrying out initialization coding on the N cluster centers to form N first-generation particles; the number of the clustering centers is equivalent to the dimension of the particles; pbest for each particle is its current location, and gbest is the best location for all particles in the current population;

s43: calculating each clustering center C (k) and a center vector U (k) of the membership degree;

s44: calculating the fitness of each particle; if the fitness of the particle is better than the fitness of the current optimal position of the particle, updating the optimal position of a single particle; if the fitness of the current global optimal position is better than the fitness of the optimal positions in all the particles, updating the global optimal position;

s45: updating the location of each particle to generate a new population of particles;

s46: stopping iteration if the current iteration times reach the maximum times set previously; the best solution is found in the last generation, otherwise S43 is repeated.

3. An electronic device comprising a memory and a processor and computer instructions stored on the memory and executed on the processor, wherein the computer instructions, when executed by the processor, perform the steps of the method of claim 1.

4. A computer-readable storage medium storing computer instructions which, when executed by a processor, perform the steps of the method of claim 1.

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