An image segmentation method and apparatus based on improved entropy-regularized fuzzy K-means

Abstract

This invention discloses an image segmentation method and apparatus based on an improved entropy-regularized fuzzy K-means algorithm. The method includes: first, preprocessing the original image; then, constructing an equivalent objective function for the entropy-regularized fuzzy K-means algorithm using k×1 intermediate variables; next, solving for the variables using a simple alternating iterative algorithm; then, optimizing the variable solution using a simple and efficient iterative reweighting method to obtain the final membership matrix. Finally, clustering each pixel into the cluster with the highest membership degree yields the segmentation result, thus achieving image segmentation. This invention not only reduces the space complexity of the entropy-regularized fuzzy K-means algorithm but also solves the problem of the algorithm easily converging to poor local minima, while simultaneously improving segmentation accuracy.

Description

Technical Field

[0001] This invention belongs to the technical field of image processing, specifically relating to an image segmentation method and apparatus based on an improved entropy-regularized fuzzy K-means. Background Technology

[0002] Image segmentation refers to dividing an image into several non-overlapping regions based on features such as grayscale, color, spatial texture, and geometric shape. These features should exhibit consistency or similarity within the same region, while showing significant differences between different regions. In recent years, research on image segmentation methods has attracted considerable attention. Image segmentation methods include clustering-based methods, edge-based methods, and threshold-based methods, with clustering-based methods being the most prominent. Clustering is the process of dividing elements in a set into multiple classes, where similar objects are grouped together and different objects are assigned to different classes. Common clustering methods include the K-means algorithm, fuzzy K-means algorithm (FKM), and spectral clustering algorithms, among which FKM has attracted significant research interest.

[0003] The Fuzzy K-means algorithm (FKM) has garnered significant attention in image segmentation due to its flexibility and excellent performance. This type of algorithm introduces the concept of fuzziness into the objective function, making it more tolerant of dataset diversity, noise, and outliers. While FKM has achieved good performance, it still has some drawbacks. For example, its performance depends on initialization; it is easily affected by outliers; and it is prone to getting trapped in undesirable local minima. For instance, the image fuzzy clustering segmentation method based on two-dimensional histograms proposed by Liu Jianzhuang, when applied to image segmentation, suffers from two problems: first, the algorithm is sensitive to initial values ​​and easily gets trapped in local optima. These are inherent issues of FKM itself. Therefore, to address the problem of FKM easily getting trapped in local optima, some researchers have combined FKM with Particle Swarm Optimization (PSO), a global optimization technique, to avoid obtaining local minima. For other problems with FKM, some researchers have introduced regularization into the objective function of FKM, proposing the Entropy Regularized Fuzzy K-means algorithm (ERFKM) to improve its performance.

[0004] As an extension of the Free-form Kernel Method (FKM) to the objective function, the ERFKM inevitably inherits the shortcomings of FKM, such as its tendency to fall into a poor local minimum. Therefore, how to avoid ERFKM from getting trapped in poor local minima in image segmentation is a problem worth studying.

[0005] To address the above problems, this invention proposes an image segmentation method based on an improved entropy-regularized fuzzy K-means algorithm. This method utilizes a simple and efficient iterative reweighting algorithm, enabling ERFKM to obtain better local minima with fewer iterations and improving segmentation accuracy. Summary of the Invention

[0006] The main objective of this invention is to overcome the shortcomings and deficiencies of the prior art and provide an image segmentation method and apparatus based on an improved entropy-regularized fuzzy K-means algorithm. By improving the entropy-regularized fuzzy K-means algorithm, which is prone to getting trapped in poor local optima during convergence, the image segmentation algorithm can improve segmentation accuracy.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] In a first aspect, the present invention provides an image segmentation method based on an improved entropy-regularized fuzzy K-means, characterized by comprising the following steps:

[0009] Preprocess the input raw image;

[0010] An equivalent objective function for the entropy-regularized fuzzy K-means algorithm is constructed using k×1 intermediate variables;

[0011] Solve for the fuzzy radius s and membership matrix U of the equivalent objective function;

[0012] The solution of the variable fuzzy radius s and membership matrix U is optimized by iterative reweighting method, and the final membership matrix is ​​obtained.

[0013] Each pixel is clustered into the cluster with the highest membership degree to obtain the image segmentation result.

[0014] As a preferred technical solution, the preprocessing specifically includes:

[0015] The original image is normalized to [0,1], then a Gaussian filter is used to filter the normalized original image, and finally the difference image between the original image and the filtered image is obtained.

[0016] As a preferred technical solution, the objective function is as follows:

[0017]

[0018] in, Let d be the original image matrix, and d be the dimension of the sample features. i Let u be the i-th sample, a d×1 dimensional vector, i = 1, 2, ..., n, where n is the number of original data points. ij It is a membership matrix The value in the i-th row and j-th column represents the membership degree of the i-th sample to the j-th class. j Represents the j-th column of the membership matrix U; Let z be the central matrix. j Let U be the j-th center, k denotes dividing the samples into k clusters, and U1 = 1 indicates that the sum of the membership degrees of each sample to each class is 1. x represents i The transpose of , s is a k×1 vector, and λ is the parameter of the penalty term entropy.

[0019] As a preferred technical solution, the process of solving the fuzzy radius s and membership matrix U of the equivalent objective function specifically involves:

[0020] First, fix the membership matrix U and solve for the fuzzy radius s in equation (1). Since U is fixed, i.e., a constant, equation (2) is obtained by deriving equation (1):

[0021]

[0022] Then, solve equation (2) with respect to s. j Taking the derivative of and setting its value to zero, we get equation (3):

[0023]

[0024] Next, with the fuzzy radius s fixed, the membership matrix U in equation (1) is solved. When the fuzzy radius s is fixed, equation (1) is derived into equation (4):

[0025]

[0026] Thus, the variable fuzzy radius s and membership matrix U can be obtained by solving equation (3) and equation (4).

[0027] As a preferred technical solution, the step of optimizing the variable solution through an iterative reweighting method to obtain the final membership matrix is ​​as follows:

[0028] First, calculate About u j The derivative of is shown in equation (5), where

[0029]

[0030] Next, after obtaining α j Then, u is updated by solving for the optimal solution in equation (6). ij :

[0031]

[0032] Next, using constraints And using the Lagrange multiplier method, we derive the Lagrange function of equation (6) as equation (8):

[0033]

[0034] Then, solve equation (7) with respect to u. ij Taking the derivative of and setting it to zero, we get equation (8):

[0035]

[0036] Then, based on the constraint U1 = 1, the membership matrix U is updated according to the following formula:

[0037]

[0038] Finally, by iteratively calculating equations (3), (5), and (9), the final membership matrix U is obtained.

[0039] As a preferred technical solution, the step of clustering each pixel into the cluster with the highest membership degree to obtain the image segmentation result is specifically as follows:

[0040] Find the largest membership value for each pixel and its corresponding cluster, then consider the cluster as the best match for the corresponding pixel; then assign each pixel to its best matching cluster to generate a new labeled image, which is the final image segmentation result, where each pixel is assigned to a cluster.

[0041] Secondly, the present invention provides an image segmentation system based on an improved entropy-regularized fuzzy K-means, which is applied to the image segmentation method based on the improved entropy-regularized fuzzy K-means, including a preprocessing module, an objective function construction module, a variable solving module, a variable optimization module, and an image segmentation module;

[0042] The preprocessing module is used to preprocess the input raw image;

[0043] The objective function construction module is used to construct an equivalent objective function for the entropy-regularized fuzzy K-means algorithm using k×1 intermediate variables;

[0044] The variable solving module is used to solve for the variable fuzzy radius s and membership matrix U of the equivalent objective function;

[0045] The variable optimization module is used to optimize the solution of variable fuzzy radius s and membership matrix U through an iterative reweighting method, and obtain the final membership matrix.

[0046] The image segmentation module is used to cluster each pixel into the cluster with the highest membership degree to obtain the image segmentation result.

[0047] Thirdly, the present invention provides an electronic device, characterized in that the electronic device comprises:

[0048] At least one processor; and,

[0049] A memory communicatively connected to the at least one processor; wherein,

[0050] The memory stores computer program instructions that can be executed by the at least one processor to enable the at least one processor to perform the image segmentation method based on the improved entropy regularized fuzzy K-means.

[0051] Fourthly, the present invention provides a computer-readable storage medium storing a program, characterized in that, when the program is executed by a processor, it implements the image segmentation method based on the improved entropy-regularized fuzzy K-means.

[0052] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0053] This invention provides an image segmentation method based on an improved entropy-regularized fuzzy K-means algorithm. First, the original image is preprocessed. Then, an equivalent objective function for the entropy-regularized fuzzy K-means algorithm (ERFKM) is constructed using k×1 intermediate variables, reducing the algorithm's space complexity. Next, a simple alternating iterative method is proposed to solve the new equivalent objective function, involving a simple and efficient iterative reweighting method. This invention not only solves the problem of the ERFKM algorithm easily converging to a poor local minimum, achieving convergence to a better local minimum with fewer iterations, but also improves segmentation accuracy. Furthermore, on several challenging real-world datasets, the clustering method involved in this invention outperforms the original ERFKM algorithm in terms of objective function value and external evaluation metrics. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1 This is a flowchart of an image segmentation method based on improved entropy-regularized fuzzy K-means according to an embodiment of the present invention;

[0056] Figure 2 (a) is the original image of one embodiment of the present invention;

[0057] Figure 2 (b) is an ERFKM pair in one embodiment of the present invention. Figure 2 (a) segmentation results;

[0058] Figure 2 (c) is an embodiment of the present invention. Figure 2 (a) segmentation results;

[0059] Figure 3 (a) is the original image of another embodiment of the present invention;

[0060] Figure 3 (b) ERFKM is another embodiment of the present invention. Figure 3 (a) segmentation results;

[0061] Figure 3 (c) For another embodiment of the present invention Figure 3 (a) is the segmentation result.

[0062] Figure 4 This is a block diagram of an image segmentation system based on improved entropy-regularized fuzzy K-means, according to an embodiment of the present invention.

[0063] Figure 5 This is a structural diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0064] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present application, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present application without creative effort are within the scope of protection of the present application.

[0065] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments.

[0066] Please see Figure 1The image segmentation method based on improved entropy-regularized fuzzy K-means provided in this embodiment includes the following steps:

[0067] S1. Preprocess the original image.

[0068] Furthermore, the original image is first normalized to [0,1], then a Gaussian filter is used to filter the original image, and finally the difference image between the original image and the filtered image is obtained.

[0069] S2. Construct the equivalent objective function of the entropy-regularized fuzzy K-means algorithm using k×1 intermediate variables.

[0070] Furthermore, the equivalent objective function is shown below:

[0071]

[0072] in, Let d be the original image matrix, and d be the dimension of the sample features. i Let be the i-th sample, and let be a d×1 dimensional vector, i = 1, 2, ..., n, where n is the number of original data points. ij It is a membership matrix The value in the i-th row and j-th column represents the membership degree of the i-th sample to the j-th class. j It represents the j-th column of the membership matrix U. Let z be the central matrix. j Let U be the j-th center, and k represent dividing the samples into k clusters. U1 = 1 means that the sum of the membership degrees of each sample to each class is 1, i.e. x represents i The transpose of . The variable fuzzy radius s is a k×1 vector. λ is the parameter of the penalty term entropy.

[0073] S3. Solve the variable fuzzy radius s and membership matrix U in equation (1) using a simple alternating iterative algorithm.

[0074] Furthermore, the process of using the alternating iterative algorithm to solve for the fuzzy radius s and membership matrix U in the objective function is as follows:

[0075] First, fix the membership matrix U and solve for the variable fuzzy radius s in equation (1). Since the membership matrix U is fixed, i.e., a constant, equation (2) is derived from equation (1) as follows:

[0076]

[0077] Then, solve equation (2) with respect to s. j Taking the derivative and setting its value to zero, we obtain equation (3), as follows:

[0078]

[0079] Next, fix s and solve for the membership matrix U in equation (1); when the fuzzy radius s is fixed, equation (1) can be derived into equation (4):

[0080]

[0081] In this way, the variable fuzzy radius s and the membership matrix U can be solved by equation (3) and solving equation (4).

[0082] S4. Optimize the solution of the variable fuzzy radius s and membership matrix U through a simple and efficient iterative reweighting method, and obtain the final membership matrix.

[0083] Furthermore, since it is difficult to obtain the membership matrix U by directly solving equation (4), and X T X is a positive semi-definite matrix and It's about u j Since the membership matrix U is a convex function, a simple and efficient iterative reweighting method is proposed to optimize the solution of the membership matrix U. Specifically:

[0084] First, calculate About u j The derivative of is shown in equation (5), where

[0085]

[0086] Next, after obtaining α j Then, u can be updated by solving for the optimal solution in equation (6). ij :

[0087]

[0088] According to equation (6), α j It will change with the membership matrix U. Therefore, when calculating the membership matrix U using equation (6), α j This will be updated accordingly. This means that the membership matrix U and α can be computed using an alternating iterative method. j In addition, due to and Equation (6) can be rewritten as the following equation:

[0089]

[0090] Then, using constraints And using the Lagrange multiplier method, we can derive the Lagrange function of equation (6) as equation (8):

[0091]

[0092] in α=[a1,…,a n [] is the vector of Lagrange multipliers. Next, solve equation (7) with respect to u. ij Taking the derivative of and setting it to zero, we get equation (8):

[0093]

[0094] Then, based on the constraint U1 = 1, the membership matrix U can be updated according to the following formula:

[0095]

[0096] Finally, by iteratively calculating equations (3), (5), and (9), the final membership matrix can be obtained.

[0097] S5. Cluster each pixel into the cluster with the highest membership degree to obtain the segmentation result and realize image segmentation.

[0098] Furthermore, the maximum membership value for each pixel and its corresponding cluster are found, and the cluster is then considered as the best match for the corresponding pixel. Each pixel is then assigned to its best matching cluster to generate a new labeled image, which is the final image segmentation result, where each pixel is assigned to a cluster.

[0099] Please see Figure 2 and Figure 3 The image segmentation effect diagram of an embodiment of the present invention is shown. Figure 2 (a) and Figure 3 (a) both represent the original image; Figure 2 (b) and Figure 3 (b) both represent the segmentation effect of the comparison method ERFKM on the original image; Figure 2 (c) and Figure 3 (c) both represent the segmentation effect of the IRW-ERFKM method of the present invention on the original image. From Figure 2 and Figure 3 As can be seen, for image segmentation, the method of this invention has higher segmentation accuracy than the comparison method, and can segment the edge of the target very well.

[0100] Furthermore, to further verify the effectiveness of the method of this invention, experiments were conducted using MATLAB software on a Windows 10 operating system with an Intel Core i5-7300HQ CPU (2.50GHz) and 24GB of RAM. The method of this invention was used to cluster the USPS, Yale64, ORL64, COIL20, Yale32, and Palm25 datasets, as shown in Table 1. The clustering results for different datasets are shown in Tables 2 and 3, with the standard deviation in parentheses representing the results after 20 runs. Max_obj, Min_obj, and Mean_obj represent the maximum weighted sum, minimum weighted sum, and average weighted sum, respectively, after 20 runs. Mean_iter is the average number of iterations required for convergence between this invention and ERFKM. Fewer iterations result in faster convergence and lower cost. Accuracy (ACC) represents the proportion of clusters with the most samples in the true class, ranging from 0 to 1. A higher ACC value indicates more samples predicted as class A in the true class A. ARI is a function that evaluates the similarity of distributions between two sets, ranging from -1 to 1. A negative ARI indicates poor algorithm performance, suggesting independent label distributions. Higher ARI values ​​indicate better algorithm performance. ARI = 1 represents the best result, indicating perfectly consistent distributions between the two groups. All better results are highlighted in bold. As can be seen from these metrics, the IRW-ERFKM proposed in this invention can find better local minima with fewer iterations. Furthermore, across all datasets, IRW-ERFKM achieves better external clustering performance metrics than ERFKM with a smaller standard deviation. Table 4 shows the computation time required for clustering different datasets. It can be seen that the IRW-ERFKM method of the present invention can complete the clustering task well in a short time.

[0101] Table 1

[0102]

[0103] Table 2

[0104]

[0105] Table 3

[0106]

[0107] Table 4

[0108]

[0109] This invention improves the image segmentation algorithm by addressing the drawback of the entropy-regularized fuzzy K-means algorithm, which is prone to getting trapped in poor local optima during convergence. It not only solves the problem of the ERFKM algorithm easily converging to a poor local minimum, achieving a better local minimum with fewer iterations, but also improves segmentation accuracy. Furthermore, on several challenging real-world datasets, the clustering method involved in this invention outperforms the original ERFKM algorithm in terms of objective function value and external evaluation metrics.

[0110] It should be noted that, for the sake of simplicity, the aforementioned method embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, because according to the present invention, some steps can be performed in other orders or simultaneously.

[0111] Based on the same idea as the image segmentation method based on improved entropy-regularized fuzzy K-means in the above embodiments, this invention also provides an image segmentation system based on improved entropy-regularized fuzzy K-means, which can be used to perform the above-described image segmentation method based on improved entropy-regularized fuzzy K-means. For ease of explanation, the schematic diagram of the embodiment of the image segmentation system based on improved entropy-regularized fuzzy K-means only shows the parts relevant to the embodiments of this invention. Those skilled in the art will understand that the illustrated structure does not constitute a limitation on the device, and it may include more or fewer components, combine certain components, or have different component arrangements.

[0112] Please see Figure 4 In another embodiment of this application, an image segmentation system 100 based on improved entropy regularized fuzzy K-means is provided. The system includes a preprocessing module 101, an objective function construction module 102, a variable solving module 103, a variable optimization module 104, and an image segmentation module 105.

[0113] The preprocessing module 101 is used to preprocess the input raw image;

[0114] The objective function construction module 102 is used to construct an equivalent objective function for the entropy-regularized fuzzy K-means algorithm using k×1 intermediate variables;

[0115] The variable solving module 103 is used to solve the variable fuzzy radius s and membership matrix U of the equivalent objective function;

[0116] The variable optimization module 104 is used to optimize the solution of the variable fuzzy radius s and the membership matrix U through an iterative reweighting method, and obtain the final membership matrix.

[0117] The image segmentation module 105 is used to cluster each pixel into the cluster with the highest membership degree to obtain the image segmentation result.

[0118] It should be noted that the image segmentation system based on improved entropy regularized fuzzy K-means of the present invention corresponds one-to-one with the image segmentation method based on improved entropy regularized fuzzy K-means of the present invention. The technical features and beneficial effects described in the embodiments of the image segmentation method based on improved entropy regularized fuzzy K-means described above are applicable to the embodiments of image segmentation based on improved entropy regularized fuzzy K-means. For details, please refer to the description in the embodiments of the method of the present invention, which will not be repeated here.

[0119] Furthermore, in the implementation of the image segmentation system based on improved entropy regularized fuzzy K-means in the above embodiments, the logical division of each program module is only an example. In actual applications, the above functions can be assigned to different program modules as needed, for example, for the sake of corresponding hardware configuration requirements or software implementation convenience. That is, the internal structure of the image segmentation system based on improved entropy regularized fuzzy K-means is divided into different program modules to complete all or part of the functions described above.

[0120] Please see Figure 5 In one embodiment, an electronic device is provided for implementing an image segmentation method based on an improved entropy-regularized fuzzy K-means. The electronic device 200 may include a first processor 201, a first memory 202, and a bus. It may also include a computer program stored in the first memory 202 and executable on the first processor 201, such as an entropy-regularized fuzzy K-means image segmentation program 203.

[0121] The first memory 202 includes at least one type of readable storage medium, including flash memory, portable hard drive, multimedia card, card-type memory (e.g., SD or DX memory), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the first memory 202 can be an internal storage unit of the electronic device 200, such as the portable hard drive of the electronic device 200. In other embodiments, the first memory 202 can also be an external storage device of the electronic device 200, such as a plug-in portable hard drive, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on the electronic device 200. Furthermore, the first memory 202 can include both internal storage units and external storage devices of the electronic device 200. The first memory 202 can be used not only to store application software and various types of data installed on the electronic device 200, such as the code of the entropy-normalized fuzzy K-means image segmentation program 203, but also to temporarily store data that has been output or will be output.

[0122] In some embodiments, the first processor 201 may be composed of integrated circuits, such as a single packaged integrated circuit or multiple integrated circuits with the same or different functions, including combinations of one or more central processing units (CPUs), microprocessors, digital processing chips, graphics processors, and various control chips. The first processor 201 is the control unit of the electronic device, connecting various components of the entire electronic device through various interfaces and lines. It executes programs or modules stored in the first memory 202 and calls data stored in the first memory 202 to perform various functions of the electronic device 200 and process data.

[0123] Figure 5 Only electronic devices with components are shown; it will be understood by those skilled in the art that... Figure 5 The structure shown does not constitute a limitation on the electronic device 200, and may include fewer or more components than shown, or combine certain components, or have different component arrangements.

[0124] The entropy-regularized fuzzy K-means image segmentation program 203 stored in the first memory 202 of the electronic device 200 is a combination of multiple instructions, which, when run in the first processor 201, can achieve the following:

[0125] Preprocess the input raw image;

[0126] An equivalent objective function for the entropy-regularized fuzzy K-means algorithm is constructed using k×1 intermediate variables;

[0127] Solve for the fuzzy radius s and membership matrix U of the equivalent objective function;

[0128] The solution of the variable fuzzy radius s and membership matrix U is optimized by iterative reweighting method, and the final membership matrix is ​​obtained.

[0129] Each pixel is clustered into the cluster with the highest membership degree to obtain the image segmentation result.

[0130] Furthermore, if the modules / units integrated in the electronic device 200 are implemented as software functional units and sold or used as independent products, they can be stored in a non-volatile computer-readable storage medium. The computer-readable medium may include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, or a read-only memory (ROM).

[0131] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.

[0132] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0133] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. An image segmentation method based on improved entropy-regularized fuzzy K-means, characterized in that, Includes the following steps: Preprocess the input raw image; use The equivalent objective function of the entropy-regularized fuzzy K-means algorithm is constructed using several intermediate variables. Find the fuzzy radius of the variable in the equivalent objective function. and membership matrix ; Optimize the variable fuzzy radius using an iterative reweighting method. and membership matrix Solve for the membership matrix and obtain the final membership matrix; Each pixel is clustered into the cluster with the highest membership degree to obtain the image segmentation result; The objective function is as follows: in, The original image matrix, The dimension of the sample features. For the first One sample, for dimensional vector, , The number of original data points. It is a membership matrix No. Line number The value of the column represents the first column. The sample belongs to the first Membership degree of a class Membership matrix The List; This indicates that the samples are divided into cluster, This means that the sum of the membership degrees of each sample to each class is 1, i.e. , express transpose, It is The vector, The parameter is the entropy of the penalty term; The variable solution is optimized using an iterative reweighting method, and the final membership matrix is ​​obtained as follows: First, calculate about The derivative of is shown in equation (5), where : Then, after obtaining Then, the optimal solution in equation (6) is used to update the equation. : Next, using constraints And using the Lagrange multiplier method, we derive the Lagrange function of equation (6) as equation (7): in Then, solve equation (7) about Taking the derivative of and setting it to zero, we get equation (8): Then, according to Constraints, membership matrix The following formula is updated to obtain: Finally, the membership matrix is ​​obtained through iterative calculation. .

2. The image segmentation method based on improved entropy-regularized fuzzy K-means according to claim 1, characterized in that, The preprocessing specifically includes: Normalize the original image to Then, a Gaussian filter is used to filter the normalized original image, and finally the difference image between the original image and the filtered image is obtained.

3. The image segmentation method based on improved entropy-regularized fuzzy K-means according to claim 1, characterized in that, The fuzzy radius of the variable used to solve the equivalent objective function and membership matrix Specifically: First, fix the membership matrix. Solve for the fuzzy radius of the variable in equation (1). Due to the membership matrix Since it is fixed, that is, a constant, we can derive equation (2) from equation (1): Then, solve equation (2) about Taking the derivative of and setting its value to zero, we get equation (3): Next, the fixed variable fuzzy radius Solve for the membership matrix in equation (1) When the fuzzy radius of the fixed variable is Equation (1) is derived into equation (4): Thus, the variable fuzzy radius can be obtained by solving equation (3) and equation (4). and membership matrix .

4. The image segmentation method based on improved entropy-regularized fuzzy K-means according to claim 1, characterized in that, The process of clustering each pixel into the cluster with the highest membership degree to obtain the image segmentation result is as follows: Find the largest membership value for each pixel and its corresponding cluster, then consider the cluster as the best match for the corresponding pixel; then assign each pixel to its best matching cluster to generate a new labeled image, which is the final image segmentation result, where each pixel is assigned to a cluster.

5. An image segmentation system based on improved entropy-regularized fuzzy K-means, characterized in that, The image segmentation method based on improved entropy regularized fuzzy K-means, applied to any one of claims 1-4, includes a preprocessing module, an objective function construction module, a variable solving module, a variable optimization module, and an image segmentation module; The preprocessing module is used to preprocess the input raw image; The objective function construction module is used to utilize The equivalent objective function of the entropy-regularized fuzzy K-means algorithm is constructed using several intermediate variables. The variable solving module is used to solve for the variable fuzzy radius of the equivalent objective function. and membership matrix ; The variable optimization module is used to optimize the variable fuzzy radius through an iterative reweighting method. and membership matrix Solve for the membership matrix and obtain the final membership matrix; The image segmentation module is used to cluster each pixel into the cluster with the highest membership degree to obtain the image segmentation result.

6. An electronic device, characterized in that, The electronic device includes: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores computer program instructions that can be executed by the at least one processor to enable the at least one processor to perform the image segmentation method based on improved entropy regularized fuzzy K-means as described in any one of claims 1-4.

7. A computer-readable storage medium storing a program, characterized in that, When the program is executed by the processor, it implements the image segmentation method based on improved entropy regularized fuzzy K-means as described in any one of claims 1-4.

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