A fuzzy clustering image segmentation method and system based on Lie group theory

Abstract

The application discloses a fuzzy clustering image segmentation method and system based on Lie group theory, and the method comprises the following steps: extracting image bottom features to obtain image pixel feature vectors; constructing matrix Lie group features of the image based on the image pixel feature vectors; initializing a fuzzy membership matrix and clustering centers; calculating distances from Lie group features of pixels to the clustering centers on a Lie group manifold; updating the clustering centers and the fuzzy membership matrix; terminating iteration and segmenting the image; the application improves sample clustering separability while ensuring stability of the algorithm; optimizes utilization of neighborhood space information, improves anti-noise capability of the algorithm while better preserving image details, and improves convergence speed of the algorithm; compared with the prior art, the method provided by the application has good stability and high operation efficiency while improving segmentation precision.

Description

Technical Field

[0001] The technical field of this invention is image processing and computer vision, and in particular, it relates to a fuzzy clustering image segmentation method and system based on Lie group theory. Background Technology

[0002] Image segmentation, as a crucial step in the transition from image processing to image analysis, has always been a hot topic in the fields of image processing and computer vision. Clustering-based image segmentation methods transfer pixels to their corresponding feature spaces for clustering, and then segment the image based on the clustering results. Because clustering-based image segmentation algorithms can be applied to more segmentation scenarios with limited prior information by optimizing sample processing strategies in the feature space, they have become one of the more commonly used image segmentation methods. Among them, the Fuzzy C-means (FCM) algorithm, with its low learning cost and low algorithmic overhead, has become a commonly used clustering-based image segmentation technique. However, when applied to image segmentation, the traditional fuzzy C-means algorithm only considers the Euclidean distance between pixel features and cluster centers, ignoring the correlation between neighboring pixels and the current pixel, making its segmentation results highly susceptible to noise interference.

[0003] To improve the noise robustness of the fuzzy C-means algorithm in image segmentation tasks, most improved algorithms utilize kernel functions to perform high-dimensional mapping of samples and construct constraint terms regarding pixel neighborhood spatial information. However, the fuzzy C-means algorithm is prone to iterating to local minima in the high-dimensional space mapped by the kernel function, leading to highly unstable results. Furthermore, while these improved algorithms enhance the noise robustness of the fuzzy C-means algorithm, they often lose details of points and lines in the image, resulting in decreased segmentation accuracy. Summary of the Invention

[0004] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0005] In view of the above-mentioned problems, the present invention is proposed.

[0006] Therefore, the technical problem solved by this invention is that although existing improved algorithms improve the noise robustness of the fuzzy C-means algorithm, they often lose the details of points and lines in the image, resulting in a decrease in the accuracy of the segmentation results.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0008] In a first aspect, embodiments of the present invention provide a fuzzy clustering image segmentation method based on Lie group theory, comprising:

[0009] Extract the low-level features of the image to obtain the image pixel feature vector;

[0010] Based on the image pixel feature vectors, construct the matrix Lie group features of the image;

[0011] Initialize the fuzzy membership matrix and cluster centers;

[0012] Calculate the distance from the Lie group feature of a pixel to the cluster center on the Lie group manifold;

[0013] Update the cluster center and fuzzy membership matrix;

[0014] Terminate the iteration and segment the image.

[0015] As a preferred scheme for fuzzy clustering image segmentation methods based on Lie group theory, wherein:

[0016] The extraction of low-level image features includes: extracting low-level features from three types of images: grayscale value, gradient, and texture; and representing each pixel in the image as a 9-dimensional feature vector.

[0017]

[0018] Where I(x,y) represents the gray value of the image at pixel (x,y); and These are the first-order gradients along the X and Y directions, respectively. The second-order gradients are along the X and Y directions; Gabor(x,y) and LBP(x,y) represent the Gabor texture features and LBP texture features of the image, respectively.

[0019] It is the sum of squares of the first-order gradients; It is the inverse cosine function of the ratio of two first-order gradients.

[0020] As a preferred scheme for fuzzy clustering image segmentation methods based on Lie group theory, wherein:

[0021] The step of constructing the matrix Lie group features of the image based on the image pixel feature vectors includes: based on the image pixel feature vectors, combining the relationship between the feature vector of the center pixel within the neighborhood window and the mean of the feature vectors of pixels within the window, expressing each pixel of the image in matrix form:

[0022]

[0023] Among them, D i f is the feature vector of the i-th pixel.i A 9×9 dimensional diagonal matrix is ​​formed along the diagonal, in order to ensure D i Reversible, for f i Normalize each dimension of f to make f i All dimensions lie within the same interval, and the minimum value of the interval is 1; ξ i The mean filtering of the feature vector of pixel i reflects the relationship between the feature vector of pixel i and the feature vectors of all n pixels in the neighborhood window. ξ i Calculate using the following formula:

[0024]

[0025] Where, N i Let ω represent all n pixels within a neighborhood window centered at pixel i, and ω represent the total number of pixels in the neighborhood. i The weight of pixel i within its neighborhood window is constructed based on local difference coefficients and calculated using the following formula:

[0026]

[0027]

[0028] The Local Difference Coefficient (LVC) reflects the degree of difference between the center pixel within a neighborhood window and its n neighboring pixels. The LVC of pixel i is defined as follows:

[0029]

[0030] As a preferred scheme for fuzzy clustering image segmentation methods based on Lie group theory, wherein:

[0031] The initialization of the fuzzy membership matrix and cluster centers includes: initializing the fuzzy membership matrix, and then initializing the cluster centers; the fuzzy membership matrix is ​​an N x C matrix, where the matrix elements u ij This represents the membership value of each of the N samples to category C;

[0032] Initialize the fuzzy membership matrix with random numbers: First, select a row in the fuzzy membership matrix and fill it with random numbers. Then, divide each element in the selected row by the sum of the elements in the selected row, as shown below:

[0033]

[0034] This yields an initial fuzzy membership matrix that meets the conditions; based on the initialized fuzzy membership matrix, the initialized cluster centers are obtained:

[0035]

[0036] As a preferred scheme for fuzzy clustering image segmentation methods based on Lie group theory, wherein:

[0037] The calculation of the distance from the Lie group feature of a pixel to the cluster center on the Lie group manifold includes: on the Lie group manifold, the matrix Lie group feature LgM of pixel i. i To a cluster center V j The shortest path can be represented as a curve, and the distance from the Lie group feature of a pixel to the cluster center can be measured using geodesic distance:

[0038]

[0039] Among them, ||.|| F Let a be the Frobenius norm. For an m x n matrix element X, let a... ij Let X be the matrix element in the i-th row and j-th column. Then the Frobenius norm is defined as:

[0040]

[0041] Using the mapping relationship between Lie groups and Lie algebras, the above Lie group matrix can be written in Lie algebra form:

[0042]

[0043] The distance from the Lie group features of a pixel to the cluster center can be approximated as:

[0044] D LG (LgM i V j )=||-lgm i +v j || F =||log(V) j )-log(LgM i )|| F .

[0045] As a preferred scheme for fuzzy clustering image segmentation methods based on Lie group theory, wherein:

[0046] The updating of cluster centers and fuzzy membership matrices includes: adding fuzzy membership information constraint terms to the objective function, constructing adaptive weights using local difference coefficients, and setting the objective function for adaptive weighted fuzzy membership constraints, expressed as:

[0047]

[0048] Where, ω i and ω is derived from the local differences between global pixels and the features of each dimension of pixels. i This represents the mean of the local difference coefficients of the underlying features of the current pixel across all dimensions. ω is the sum of all pixels in the current image. i The average value is expressed as:

[0049]

[0050] Sample membership degree u ij The update expression is:

[0051]

[0052] Update the cluster centers and fuzzy membership matrix based on the objective function.

[0053] As a preferred scheme for fuzzy clustering image segmentation methods based on Lie group theory, wherein:

[0054] The termination of iteration and image segmentation includes: the algorithm terminates when the number of iterations reaches the maximum number of iterations T, or when the difference between the objective function value obtained after the algorithm iteration and the objective function value obtained in the previous iteration is less than the clustering iteration termination error ε; after the algorithm terminates, the image segmentation result is obtained by outputting membership information; in the fuzzy membership matrix, the column number corresponding to the maximum value in each row of membership values ​​is taken as the final clustering category of the sample represented by that row. At that time, sample LgM i Pixel i is assigned to class j. After obtaining the class assignment of each pixel, pixels of the same class can be set to the same grayscale value to obtain the visualization result of the original image segmentation. Alternatively, pixels of the same class can be displayed separately in one image.

[0055] Secondly, embodiments of the present invention provide a fuzzy clustering image segmentation system based on Lie group theory, characterized in that it includes:

[0056] The extraction module is used to extract low-level features of the image to obtain image pixel feature vectors;

[0057] A construction module is used to construct the matrix Lie group features of the image based on the image pixel feature vectors;

[0058] The initialization module is used to initialize the fuzzy membership matrix and cluster centers.

[0059] The computation module is used to calculate the distance from the Lie group feature of a pixel to the cluster center on the Lie group manifold;

[0060] The update module is used to update the cluster center and fuzzy membership matrix;

[0061] The segmentation module is used to terminate the iteration and segment the image.

[0062] Thirdly, embodiments of the present invention provide a computing device, including:

[0063] Memory and processor;

[0064] The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the one or more programs are executed by the one or more processors, the one or more processors implement the fuzzy clustering image segmentation method based on Lie group theory as described in any embodiment of the present invention.

[0065] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the aforementioned fuzzy clustering image segmentation method based on Lie group theory.

[0066] The beneficial effects of this invention are as follows: This invention constructs a matrix Lie group feature for each pixel from the underlying image features, mapping the image from Euclidean space to Lie group space. Based on the geodesic distance metric, fuzzy C-means clustering is implemented on the Lie group manifold, improving the separability of sample clustering while ensuring the stability of the algorithm. Based on local statistical information, weighted mean filtering information in the matrix Lie group features and adaptive weighted fuzzy membership constraints in the objective function are constructed, optimizing the utilization of neighborhood space information. This improves the algorithm's noise resistance while better preserving image details and increasing the convergence speed. Compared with existing technologies, the method proposed in this invention improves segmentation accuracy while exhibiting good stability and high operating efficiency. Attached Figure Description

[0067] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0068] Figure 1 This is an overall flowchart of the fuzzy clustering image segmentation method based on Lie group theory described in the first embodiment of the present invention;

[0069] Figure 2 This is the optimal image segmentation result obtained by running each algorithm on a brain MR image 100 times in a comparative experiment of the fuzzy clustering image segmentation method based on Lie group theory described in the second embodiment of the present invention.

[0070] Figure 3This is the optimal image segmentation result obtained by running each algorithm 100 times on a noisy brain MR image in a comparative experiment of the fuzzy clustering image segmentation method based on Lie group theory described in the second embodiment of the present invention.

[0071] Figure 4 The average and standard deviation of the SA coefficients of the segmentation results obtained by each algorithm in 100 runs on the original brain MR image and its noisy image in the comparative experiment of the fuzzy clustering image segmentation method based on Lie group theory described in the second embodiment of the present invention.

[0072] Figure 5 This refers to the running time and number of iterations of each algorithm in the comparative experiment of the fuzzy clustering image segmentation method based on Lie group theory described in the second embodiment of the present invention when it achieves the best results on brain MR images. Detailed Implementation

[0073] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0074] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0075] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0076] This invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of this invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not adhering to the usual scale. Furthermore, the schematic diagrams are merely examples and should not be construed as limiting the scope of protection of this invention. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.

[0077] Furthermore, in the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used solely for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In addition, the terms "first," "second," or "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0078] Unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" in this invention should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; similarly, they can refer to mechanical connections, electrical connections, or direct connections, or indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0079] Example 1

[0080] Reference Figure 1 This is the first embodiment of the present invention, which provides a fuzzy clustering image segmentation method based on Lie group theory, comprising:

[0081] S1: Extract the low-level features of the image to obtain the image pixel feature vector;

[0082] Specifically, the extraction of low-level image features includes: extracting low-level features from three types of images: grayscale values, gradients, and textures; and representing each pixel in the image as a 9-dimensional feature vector.

[0083]

[0084] Where I(x,y) represents the gray value of the image at pixel (x,y); and These are the first-order gradients along the X and Y directions, respectively. The second-order gradients are along the X and Y directions; Gabor(x,y) and LBP(x,y) represent the Gabor texture features and LBP texture features of the image, respectively.

[0085] It is the sum of squares of the first-order gradients; It is the inverse cosine function of the ratio of two first-order gradients.

[0086] It should be noted that features such as image edges and points of interest provide rich information about the image content. Ideally, image features should not change with image rotation, scale (i.e., changes in resolution or magnification), or acquisition angle. Furthermore, image features should be insensitive to lighting conditions and color. Therefore, this invention extracts three types of low-level image features from each image: grayscale value, gradient, and texture. Each pixel in the image is represented as a 9-dimensional feature vector.

[0087] S2: Based on the image pixel feature vectors, construct the matrix Lie group features of the image;

[0088] Specifically, constructing the matrix Lie group features of the image based on the image pixel feature vectors includes: based on the image pixel feature vectors, combining the relationship between the feature vectors of the center pixel within the neighborhood window and the mean of the pixel feature vectors within the window, expressing each pixel of the image in matrix form:

[0089]

[0090] Among them, D i f is the feature vector of the i-th pixel. i A 9×9 dimensional diagonal matrix is ​​formed along the diagonal, in order to ensure D i Reversible, for f i Normalize each dimension of f to make f i All dimensions lie within the same interval, and the minimum value of the interval is 1; ξ i The mean filtering of the feature vector of pixel i reflects the relationship between the feature vector of pixel i and the feature vectors of all n pixels in the neighborhood window. ξ i Calculate using the following formula:

[0091]

[0092] Where, N i Let ω represent all n pixels within a neighborhood window centered at pixel i, and ω represent the total number of pixels in the neighborhood. i The weight of pixel i within its neighborhood window is constructed based on local difference coefficients and calculated using the following formula:

[0093]

[0094]

[0095] The Local Difference Coefficient (LVC) reflects the degree of difference between the center pixel within a neighborhood window and its n neighboring pixels. The LVC of pixel i is defined as follows:

[0096]

[0097] It should be noted that when the difference between the center pixel of the neighborhood window and its neighboring pixels is large, the calculated Local Difference Coefficient (LVC) value will also increase. The obtained LVC result is applied to an exponential function, and its weight within the neighborhood window is derived. This weight reflects the heterogeneity within the neighborhood window centered on pixel i. When the heterogeneity within the neighborhood window is high, the calculated value is closer to the mean within the neighborhood window; conversely, it is closer to the value of the center pixel of the window.

[0098] S3: Initialize the fuzzy membership matrix and cluster centers;

[0099] Specifically, the initialization of the fuzzy membership matrix and cluster centers includes: initializing the fuzzy membership matrix, and then initializing the cluster centers; the fuzzy membership matrix is ​​an N x C matrix, where each matrix element u... ij This represents the membership value of each of the N samples to category C;

[0100] Initialize the fuzzy membership matrix with random numbers: First, select a row in the fuzzy membership matrix and fill it with random numbers. Then, divide each element in the selected row by the sum of the elements in the selected row, as shown below:

[0101]

[0102] This yields an initial fuzzy membership matrix that meets the conditions; based on the initialized fuzzy membership matrix, the initialized cluster centers are obtained:

[0103]

[0104] It should be noted that in the Lie group fuzzy clustering algorithm, the cluster center represents the center of a certain category, located on the Lie group manifold, and is related to the position of the Lie group features on the manifold and the membership value u of each category. ij Related. Therefore, the fuzzy membership matrix needs to be initialized first, and then the cluster centers need to be initialized. The fuzzy membership matrix is ​​an N x C matrix, where each matrix element u... ij This represents the membership degree value of each of the N samples to category C.

[0105] S4: Calculate the distance from the Lie group feature of a pixel to the cluster center on the Lie group manifold;

[0106] Specifically, calculating the distance from the Lie group feature of a pixel to the cluster center on the Lie group manifold includes: on the Lie group manifold, the matrix Lie group feature LgM of pixel i... i To a cluster center V j The shortest path can be represented as a curve, and the distance from the Lie group feature of a pixel to the cluster center can be measured using geodesic distance:

[0107]

[0108] in. F Let aij be the element in the i-th row and j-th column of a matrix X with m rows and n columns. Then the Frobenius norm is defined as follows:

[0109]

[0110] Using the mapping relationship between Lie groups and Lie algebras, the above Lie group matrix can be written in Lie algebra form:

[0111]

[0112] The distance from the Lie group features of a pixel to the cluster center can be approximated as:

[0113] D LG (LgM i V j )=||-lgm i +v j || F =||log(V) j )-log(LgM i )|| F .

[0114] S5: Update the cluster centers and fuzzy membership matrix;

[0115] Specifically, updating the cluster centers and fuzzy membership matrix includes: adding fuzzy membership information constraint terms to the objective function, constructing adaptive weights using local difference coefficients, and setting the objective function for the adaptive weighted fuzzy membership constraint as follows:

[0116]

[0117] Where, ω i and ω is derived from the local differences between global pixels and the features of each dimension of pixels. i This represents the mean of the local difference coefficients of the underlying features of the current pixel across all dimensions. ω is the sum of all pixels in the current image. i The average value is expressed as:

[0118]

[0119] Sample membership degree u ij The update expression is:

[0120]

[0121] Update the cluster centers and fuzzy membership matrix based on the objective function.

[0122] It should be noted that utilizing the clustering membership information of each pixel within the neighborhood window is an important approach to improve the noise resistance of fuzzy clustering algorithms. This method adds a fuzzy membership information constraint term to the objective function and constructs adaptive weights using local difference coefficients. Then, based on this objective function, it updates the cluster centers and the fuzzy membership matrix, proposing an adaptive weighted fuzzy membership constraint objective function.

[0123] It should also be noted that the membership information constraint term associates the cluster membership degree of each pixel with the cluster membership degrees of its n neighboring pixels. When the membership degree values ​​of the center pixel and its neighboring pixels with respect to a certain category are both small or large, it indicates that the difference between the center pixel and its neighboring pixels is small, and the center pixel is less likely to be noise; conversely, it indicates that the difference between the center pixel and its neighboring pixels is large, and the center pixel is more likely to be noise. However, the membership information constraint term is also related to the signal-to-noise ratio of the image. When the image noise level is high, the probability of multiple noisy pixels appearing in the neighborhood window is also greater, and the weight of the membership information constraint term should be reduced in this case. The membership information constraint term proposed in this invention does not require manual determination of weights based on prior information, but rather uses local difference coefficient information to achieve adaptive weighting. Furthermore, it includes not only global information of the pixel but also information of each dimension of the feature, making it applicable to the clustering of multi-dimensional feature pixels.

[0124] S6: Terminate the iteration and segment the image.

[0125] Specifically, the termination of iteration and image segmentation includes: terminating the iteration when the algorithm reaches the maximum iteration count T, or when the difference between the objective function value obtained after the algorithm iteration and the objective function value obtained in the previous iteration is less than the clustering iteration termination error ε; after the algorithm terminates, the image segmentation result is obtained by outputting membership information; in the fuzzy membership matrix, the column number corresponding to the maximum value in each row of membership values ​​is taken as the final clustering category of the sample represented by that row, when... At that time, sample LgM i Pixel i is assigned to class j. After obtaining the class assignment of each pixel, pixels of the same class can be set to the same grayscale value to obtain the visualization result of the original image segmentation. Alternatively, pixels of the same class can be displayed separately in one image.

[0126] It should be noted that the Lie group fuzzy clustering image segmentation algorithm is as follows:

[0127]

[0128]

[0129] Example 2

[0130] Reference Figure 2-5 As an embodiment of the present invention, a fuzzy clustering image segmentation method based on Lie group theory is provided. To verify the beneficial effects of the present invention, scientific demonstration is carried out through simulation and control experiments.

[0131] To verify the performance of the proposed algorithm in image segmentation, the experiment compared the segmentation results of the traditional Fuzzy C-means (FCM) algorithm with those of four improved algorithms: KFCM, SKFCM, KWFLICM, and ARKFCM. The common parameters for each algorithm are as follows: fuzziness factor m = 2, clustering iteration termination error ε = 0.001, and maximum number of clustering iterations T = 200. For algorithms using neighborhood windows, the neighborhood window size was set to 3×3. Since all algorithms use random initialization, the best result (referring to the optimal SA coefficient mentioned below) was compared after running each algorithm 100 times on each image.

[0132] When evaluating the segmentation results of various algorithms, the Jaccard similarity coefficient (JS) and segmentation accuracy (SA) are used. The JS coefficient is used to determine the segmentation accuracy for each category, while the SA coefficient is used to determine the overall segmentation accuracy across multiple categories. The JS coefficient is the ratio of the number of elements in the intersection of the algorithm's segmentation result S1 and the number of elements in the union of the standard segmentation result S2.

[0133]

[0134] A larger JS coefficient indicates that the segmentation result obtained by the algorithm is closer to the standard segmentation result, meaning the algorithm has better segmentation performance; conversely, a smaller JS coefficient indicates worse segmentation performance. The maximum value of the JS coefficient is 1, and the minimum value is 0. The SA coefficient represents the segmentation result S for each category. i Compared with the standard segmentation result S i The SA coefficient is the ratio of the sum of the number of elements in the intersection of the segments to the total number of samples. If the total number of categories is C and the total number of samples is N, then the SA coefficient is:

[0135]

[0136] A higher SA coefficient indicates that the segmentation results obtained by the algorithm for multiple categories are more similar to the overall standard segmentation results, meaning the algorithm has better segmentation performance; conversely, a lower SA coefficient indicates worse segmentation performance. The SA coefficient also has a maximum value of 1 and a minimum value of 0. Additionally, the background segmentation results obtained in the experiment are not shown separately, but they are still included in the calculation of the SA coefficient.

[0137] All experiments were conducted on a personal desktop computer equipped with an Intel(R) Core(TM) i5-11400H CPU, 16GB of RAM, a 2TB hard drive, Windows 11 operating system, and MATLAB 2021b as the programming environment.

[0138] Table 1 shows the specific segmentation accuracy of the optimal image segmentation results obtained by each algorithm after running it 100 times on brain MR images.

[0139] Table 1. Segmentation accuracy of each algorithm on brain MR images.

[0140]

[0141] Table 2 shows the specific segmentation accuracy of the optimal image segmentation results obtained by each algorithm after running it 100 times on noisy brain MR images.

[0142] Table 2. Segmentation accuracy of each algorithm on noisy brain MR images.

[0143]

[0144] Depend on Figure 2 and Figure 3 As can be seen, regardless of whether the image is in low-noise or high-noise mode, the image segmentation method proposed in this invention achieves better segmentation integrity, less noise, and richer image details. The specific segmentation accuracy in Tables 1 and 2 shows that the segmentation accuracy of the method proposed in this invention is higher than that of the traditional Fuzzy C-means (FCM) algorithm and other improved algorithms. Figure 4 It can be seen that, in multiple runs, the segmentation results of other improved algorithms are highly unstable with large standard deviations, while the method proposed in this invention maintains the same stability as the traditional fuzzy C-means (FCM) algorithm, while improving the segmentation accuracy. Figure 5 It can be seen that the running time and number of iterations of the method proposed in this invention are much smaller than those of other improved algorithms. Although the running time and number of iterations of the proposed method are slightly higher than those of the traditional fuzzy C-means (FCM) algorithm due to its complexity, the overall efficiency is still within an acceptable range.

[0145] It can be seen that the method proposed in this invention improves the image segmentation accuracy while ensuring the stability of the algorithm and increasing the algorithm's running efficiency.

[0146] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A fuzzy clustering image segmentation method based on Lie group theory, characterized in that, include: Extract the low-level features of the image to obtain the image pixel feature vector; Based on the image pixel feature vectors, construct the matrix Lie group features of the image; The step of constructing the matrix Lie group features of the image based on the image pixel feature vectors includes: based on the image pixel feature vectors, combining the relationship between the feature vector of the center pixel within the neighborhood window and the mean of the feature vectors of pixels within the window, expressing each pixel of the image in matrix form: in, For the first pixel feature vector To ensure that the 9×9 dimensional diagonal matrix is ​​formed on the diagonal, Reversible, for Normalize each dimension to make All dimensions are within the same interval and the minimum value of the interval is 1; Represents pixels i Mean filtering of the feature vectors reflects the pixel i The feature vectors and all features within the neighborhood window n The relationship between the feature vectors of each pixel Calculate using the following formula: in, Represented in pixels i All within the centered neighborhood window n 1 pixel, and Represents pixels i The weights within its neighborhood window are constructed based on local difference coefficients and calculated using the following formula: Local difference coefficient (LVC) reflects the difference between the center pixel and its neighbors within a neighborhood window. n The degree of difference between individual pixels, pixels i The local difference coefficient is defined as: ； Initialize the fuzzy membership matrix and cluster centers; The initialization of the fuzzy membership matrix and cluster centers includes: initializing the fuzzy membership matrix, and then initializing the cluster centers; the fuzzy membership matrix is ​​a... N OK C Column matrix, matrix elements u ij express N Each sample is for C Membership value of category; Initialize the fuzzy membership matrix with random numbers: First, select a row in the fuzzy membership matrix and fill it with random numbers. Then, divide each element in the selected row by the sum of the elements in the selected row, as shown below: This yields an initial fuzzy membership matrix that meets the conditions; based on the initialized fuzzy membership matrix, the initialized cluster centers are obtained: ； Calculate the distance from the Lie group feature of a pixel to the cluster center on the Lie group manifold; The step of calculating the distance from the Lie group feature of a pixel to the cluster center on the Lie group manifold includes: on the Lie group manifold, dividing the pixel... i Matrix Lie group characteristics LgM i To a cluster center V j The shortest path is represented by a curve, and the distance from the Lie group feature of a pixel to the cluster center is measured using geodesic distance: in For Frobenius norm, for m OK n Column matrix elements ,set up for The Middle i Line number j For the matrix elements of columns, the Frobenius norm is defined as: Using the mapping relationship between Lie groups and Lie algebras, the above Lie group matrix can be written in Lie algebra form: The distance from the Lie group features of a pixel to the cluster center can be approximated as: ； Update the cluster center and fuzzy membership matrix; The updating of cluster centers and fuzzy membership matrices includes: adding fuzzy membership information constraint terms to the objective function, constructing adaptive weights using local difference coefficients, and setting the objective function for adaptive weighted fuzzy membership constraints, expressed as: in, and This was derived from the local differences in global pixel data and pixel features across different dimensions. This represents the mean of the local difference coefficients of the underlying features of the current pixel across all dimensions. For all pixels in the current image The average value is expressed as: Sample membership The update expression is: Update the cluster centers and fuzzy membership matrix based on the objective function; Terminating the iteration and segmenting the image; The termination of iteration and image segmentation includes: when the algorithm's iteration count reaches the maximum iteration count. T This occurs when the difference between the objective function value obtained after the algorithm iteration and the objective function value obtained in the previous iteration is less than the clustering iteration termination error. When the algorithm terminates its iteration, the image segmentation result is obtained by outputting membership information. In the fuzzy membership matrix, the column number corresponding to the maximum value of the membership values ​​in each row is taken as the final clustering category of the sample represented by that row. At that time, the sample Representing pixels i Belongs to the first j Classification; after obtaining the category of each pixel, pixels of the same category are set with the same grayscale value, thereby obtaining the visualization result of the original image segmentation, or displaying pixels of the same category separately in one image.

2. The fuzzy clustering image segmentation method based on Lie group theory as described in claim 1, characterized in that, The extraction of low-level image features includes: extracting low-level features from three types of images: grayscale value, gradient, and texture; and representing each pixel in the image as a 9-dimensional feature vector. in, This indicates the image at pixel points ( x, y The grayscale value at () and These are the first-order gradients along the X and Y directions, respectively. The second-order gradients are along the X and Y directions; Gabor(x,y) and LBP (x,y) These represent the Gabor texture features and LBP texture features of the image, respectively. It is the sum of squares of the first-order gradients; It is the inverse cosine function of the ratio of two first-order gradients.

3. A fuzzy clustering image segmentation system based on Lie group theory, characterized in that, include: The extraction module is used to extract low-level features of the image to obtain image pixel feature vectors; A construction module is used to construct the matrix Lie group features of the image based on the image pixel feature vectors; The step of constructing the matrix Lie group features of the image based on the image pixel feature vectors includes: based on the image pixel feature vectors, combining the relationship between the feature vector of the center pixel within the neighborhood window and the mean of the feature vectors of pixels within the window, expressing each pixel of the image in matrix form: in, For the first pixel feature vector To ensure that the 9×9 dimensional diagonal matrix is ​​formed on the diagonal, Reversible, for Normalize each dimension to make All dimensions are within the same interval and the minimum value of the interval is 1; Represents pixels i Mean filtering of the feature vectors reflects the pixel i The feature vectors and all features within the neighborhood window n The relationship between the feature vectors of each pixel Calculate using the following formula: in, Represented in pixels i All within the centered neighborhood window n 1 pixel, and Represents pixels i The weights within its neighborhood window are constructed based on local difference coefficients and calculated using the following formula: Local difference coefficient (LVC) reflects the difference between the center pixel and its neighbors within a neighborhood window. n The degree of difference between individual pixels, pixels i The local difference coefficient is defined as: ； The initialization module is used to initialize the fuzzy membership matrix and cluster centers. The initialization of the fuzzy membership matrix and cluster centers includes: initializing the fuzzy membership matrix, and then initializing the cluster centers; the fuzzy membership matrix is ​​a... N OK C Column matrix, matrix elements u ij express N Each sample is for C Membership value of category; Initialize the fuzzy membership matrix with random numbers: First, select a row in the fuzzy membership matrix and fill it with random numbers. Then, divide each element in the selected row by the sum of the elements in the selected row, as shown below: This yields an initial fuzzy membership matrix that meets the conditions; based on the initialized fuzzy membership matrix, the initialized cluster centers are obtained: ； Calculate the distance from the Lie group feature of a pixel to the cluster center on the Lie group manifold; The computation module is used to calculate the distance from the Lie group feature of a pixel to the cluster center on the Lie group manifold; The step of calculating the distance from the Lie group feature of a pixel to the cluster center on the Lie group manifold includes: on the Lie group manifold, dividing the pixel... i Matrix Lie group characteristics LgM i To a cluster center V j The shortest path is represented by a curve, and the distance from the Lie group feature of a pixel to the cluster center is measured using geodesic distance: in For Frobenius norm, for m OK n Column matrix elements ,set up for The Middle i Line number j For the matrix elements of columns, the Frobenius norm is defined as: Using the mapping relationship between Lie groups and Lie algebras, the above Lie group matrix can be written in Lie algebra form: The distance from the Lie group features of a pixel to the cluster center can be approximated as: ； The update module is used to update the cluster center and fuzzy membership matrix; The updating of cluster centers and fuzzy membership matrices includes: adding fuzzy membership information constraint terms to the objective function, constructing adaptive weights using local difference coefficients, and setting the objective function for adaptive weighted fuzzy membership constraints, expressed as: in, and This was derived from the local differences in global pixel data and pixel features across different dimensions. This represents the mean of the local difference coefficients of the underlying features of the current pixel across all dimensions. For all pixels in the current image The average value is expressed as: Sample membership The update expression is: ； Update the cluster centers and fuzzy membership matrix based on the objective function; The segmentation module is used to terminate the iteration and segment the image. The termination of iteration and image segmentation includes: when the algorithm's iteration count reaches the maximum iteration count. T This occurs when the difference between the objective function value obtained after the algorithm iteration and the objective function value obtained in the previous iteration is less than the clustering iteration termination error. When the algorithm terminates its iteration, the image segmentation result is obtained by outputting membership information. In the fuzzy membership matrix, the column number corresponding to the maximum value of the membership values ​​in each row is taken as the final clustering category of the sample represented by that row. At that time, the sample Representing pixels i Belongs to the first j Classification; after obtaining the category of each pixel, pixels of the same category are set with the same grayscale value, thereby obtaining the visualization result of the original image segmentation, or displaying pixels of the same category separately in one image.

4. A computing device, comprising: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, they implement the steps of the fuzzy clustering image segmentation method based on Lie group theory as described in any one of claims 1 to 2.

5. A computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the steps of the fuzzy clustering image segmentation method based on Lie group theory as described in any one of claims 1 to 2.

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