Image segmentation method and system based on directional weighted model

Abstract

The present invention provides an image segmentation method and system based on a directional weighted model, and relates to the field of image processing. The method comprises: establishing a directional weighted model based on a Chan-Vese model, combining a scaled minimum-maximum concave penalty function of an L2 norm constructed based on a Moreau envelope function and a minimum-maximum concave penalty function; acquiring an image to be segmented; inputting the image to be segmented into the directional weighted model, solving the directional weighted model based on an alternating directional multiplier method, and obtaining a segmented image corresponding to the image to be segmented, which has the advantages of improving the efficiency and accuracy of image segmentation.

Description

Technical Field

[0001] The present invention relates to the field of image processing, and in particular to an image segmentation method and system based on a directional weighted model. Background Art

[0002] Image segmentation has always been a hot research topic in image processing, and its applications include target detection, organ segmentation in medical images, and 3D reconstruction.

[0003] In the prior art, variational image segmentation includes two basic models, namely the Snake model and the Mumford-Shah (MS) model. The Snake model is a typical active contour model based on image edges, also known as an active contour model or a parametric active contour model. It uses energy-minimized spline curves, which are attracted by external constraints and image features, and fit the edges of the image by deformation. The Snake model has the advantages of interactive control, adaptability, and scale sensitivity. It can quickly segment the target contour in the image. However, the Snake model is not effective for images with weak edges, because the blurred edges will cause the curve to easily cross the actual edge when deformed. It is also easily affected by the initial position and may fall into a local minimum. The MS model is a typical region-based model that relies on the global information of homogeneous regions in the image for segmentation. The idea of ​​this model is to perform image segmentation by minimizing an energy function that includes image smoothing terms and contour length terms. The MS model can simultaneously achieve image smoothing and segmentation processing, and has the advantages of fast and accurate segmentation for general images.

[0004] It can also achieve good segmentation results for images with weak edges. However, the energy function solution of the MS model is prone to fall into the local optimum, which may lead to the segmentation result not being globally optimal. When the traditional level set method is applied to the MS model, it requires complex level set reinitialization, which increases the computational complexity.

[0005] Therefore, it is necessary to provide an image segmentation method and system based on a directional weighted model to improve the efficiency and accuracy of image segmentation. Summary of the invention

[0006] The present invention provides an image segmentation method based on a directional weighted model, comprising: establishing a directional weighted model based on a Chan-Vese model, combining a scaled minimum-maximum concave penalty function of an L2 norm constructed based on a Moreau envelope function and a minimum-maximum concave penalty function; acquiring an image to be segmented; inputting the image to be segmented into the directional weighted model, solving the directional weighted model based on an alternating directional multiplier method, and obtaining a segmented image corresponding to the image to be segmented.

[0007] Furthermore, the energy function of the direction weighted model is:

[0008]

[0009] in, is the energy function of the direction-weighted model, For separation area and Region The closed contour of the area and Region They are The outer and inner sub-regions of , and are constants, For Region The average strength of For Region The average strength of , is the level set function, and is the weight coefficient, is the input image to be segmented, is the Heaviside function, is the Dirac function, is the weight function, is the rotation matrix, is the main direction of the image to be segmented, is the scaling matrix, is an adjustable parameter. is the smoothing parameter, and is an auxiliary variable, for The first component of for The second component of for The first component of for The second component of for The gradient vector of When the function takes the maximum value The value of When the function takes the minimum value The value of is the domain of the image to be segmented, is the coordinate of the pixel of the image to be segmented.

[0010] Furthermore, the scaled minimum-maximum concave penalty function of the L2 norm constructed based on the Moreau envelope function and the minimum-maximum concave penalty function is:

[0011]

[0012] in, is a scaled minimum-maximum concave penalty function of the L2 norm constructed based on the Moreau envelope function and the minimum-maximum concave penalty function. For vector x The L2 norm of To scale the Moreau envelope, For a given parameter v, find The minimum value of , For use replace After the scaling of the Moreau envelope.

[0013] Furthermore, the weight function is:

[0014]

[0015] in, is the weight function, is the pixel coordinate, is the weight function, is the weight function, k is a parameter, k is greater than 0, The variance is The Gaussian convolution function of is the gradient of the image to be segmented at (x,y) along the x-axis direction, is the gradient of the image to be segmented at (x,y) along the y-axis.

[0016] Furthermore, the directional weighted model is solved based on the alternating directional multiplier method to obtain a segmented image corresponding to the image to be segmented, including: introducing initial values ​​of multiple solution parameters; repeatedly updating multiple parameters of the directional weighted model according to preset parameter update rules until a stopping criterion is met.

[0017] Furthermore, the preset parameter update rule includes:

[0018]

[0019] in, is the region of the k+1th iteration The average strength of is the regularized version of the Heaviside function, which is used to divide the image to be segmented into regions according to the value of the level set function at the kth iteration. and Region , is the region of the k+1th iteration The average intensity.

[0020] Furthermore, the preset parameter update rule includes:

[0021]

[0022] in, For Region The characteristic vector of For Region The characteristic vector of To dynamically adjust the function, , is a constant, is the penalty parameter, , For the updated The first component and the updated The second component of To obtain and 0, To obtain and 0.

[0023] Furthermore, the preset parameter update rule includes:

[0024]

[0025]

[0026] in, , is the penalty parameter, is an adjustable constant, is the main direction of the image to be segmented, , is the variable in the iteration process, is the first time variable, is the second time variable, , For the updated The first component and the updated The second component of , is the intermediate variable, is the coordinate of the pixel of the image to be segmented.

[0027] Furthermore, the preset parameter update rule includes:

[0028]

[0029]

[0030] in, , is the variable in the iteration process, and is the Lagrange multiplier, is the level set function Find the gradient, , , , , are variables in the iteration process. To obtain and 0, whichever is greater. To obtain and 0 whichever is greater.

[0031] The present invention provides an image segmentation system based on a directional weighted model, which is used to execute the above-mentioned image segmentation method based on the directional weighted model, including: a model establishment module, which is used to establish a directional weighted model based on the Chan-Vese model, in combination with a scaled minimum-maximum concave penalty function of an L2 norm constructed based on a Moreau envelope function and a minimum-maximum concave penalty function; an image acquisition module, which is used to acquire an image to be segmented; and an image segmentation module, which is used to input the image to be segmented into the directional weighted model, solve the directional weighted model based on an alternating directional multiplier method, and obtain a segmented image corresponding to the image to be segmented.

[0032] Compared with the prior art, the image segmentation method and system based on the directional weighted model provided by the present invention have at least the following beneficial effects:

[0033] Constructed using Moreau envelope and min-max concave penalty function Non-convex regularization of the norm, combined with the gradient operator in the regularization term , adaptive weight matrix and the rotation matrix , so that the directional weighted model maintains the local structure during the image segmentation process and can consider the texture details of the image. In addition, the directional weighted model is solved based on the alternating direction multiplier method, so the convergence of the numerical method can be effectively maintained, which is superior in segmentation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] This specification will be further described in the form of exemplary embodiments, which will be described in detail by the accompanying drawings. These embodiments are not restrictive, and in these embodiments, the same number represents the same structure, wherein:

[0035] Figure 1 is a flowchart of an image segmentation method based on a direction weighted model according to some embodiments of this specification;

[0036] Figure 2a It is a schematic diagram of the L2 norm;

[0037] Figure 2b It is a schematic diagram of the Moreau envelope of the L2 norm;

[0038] Figure 3 It is a schematic diagram of the parameter values ​​of the minimum maximum concave penalty function;

[0039] Figure 4 is a schematic diagram of an ellipse set;

[0040] Figure 5 is a schematic diagram of experimental results shown in some embodiments of this specification;

[0041] Figure 6 It is a module diagram of an image segmentation system based on a directional weighted model according to some embodiments of the present specification. DETAILED DESCRIPTION

[0042] In order to more clearly illustrate the technical solutions of the embodiments of this specification, the following is a brief introduction to the drawings required for the description of the embodiments. Obviously, the drawings described below are only some examples or embodiments of this specification. For ordinary technicians in this field, this specification can also be applied to other similar scenarios based on these drawings without creative work. Unless it is obvious from the language environment or otherwise explained, the same reference numerals in the figures represent the same structure or operation.

[0043] Figure 1 is a flow chart of an image segmentation method based on a directional weighted model according to some embodiments of this specification, such as Figure 1 As shown, the image segmentation method based on the direction weighted model may include the following steps.

[0044] Step 110 , based on the Chan-Vese model, a directional weighted model is established in combination with a scaled minimum-maximum concave penalty function of an L2 norm constructed based on the Moreau envelope function and the minimum-maximum concave penalty function.

[0045] Given an image to be segmented , whose size is , is the image domain. The gradient of is:

[0046] (1)

[0047] in, They are exist and They are computed as forward differences as follows:

[0048] (2)

[0049] (3)

[0050] Similarly, the backward difference operator is defined as:

[0051] (4)

[0052] (5)

[0053] The Chan-Vese model is:

[0054] (6)

[0055] in, is the image to be segmented, Defined as separating two regions and The closed contour of and They are The outer and inner subregions. Constant and They are respectively The average intensity of each separated region, The goal of the Chan-Vese model is to find a piecewise smooth image with a minimum contour .

[0056] Defining Lipschitz continuous LSF for:

[0057] (7)

[0058] The Heaviside function is defined as:

[0059] (8)

[0060] Dirac function It is actually the derivative of the Heaviside function in terms of distribution:

[0061] (9)

[0062] In image segmentation, the purpose of the regularization term is mainly to reflect some prior information of the image to be segmented, and sparse regularization that reflects the sparse prior information of the image is the most widely used. Commonly used sparse regularization terms include Regularization, Regularization, Regularization and total variation regularization, etc. The general form of regularization is , which represents the number of non-zero elements in the sparse solution, but the solution with The optimization problem of the norm is an NP-hard problem. Regularization yes Regularized convex relaxation, but The norm is not differentiable, and it underestimates large values ​​in sparse solutions. Regularization It can more effectively estimate the larger value of the sparse solution, but since the objective function itself is non-convex, it may fall into the local optimal value during the solution process. Therefore, the Moreau envelope function and the minimum maximum concave (Minmax-Concave, MC) penalty function are combined to construct A segmentation model based on isotropic nonconvex total variation regularization is constructed. The proposed nonconvex regularization can effectively avoid the underestimation of large non-zero elements in convex regularization, thereby segmenting the target more effectively.

[0063] Given a suitable closed convex function , The Moreau envelope is defined as:

[0064] (10)

[0065] Given a suitable closed convex function , The MC penalty is defined as:

[0066] (11)

[0067] make (12)

[0068] Apparently exist However, according to the definition of subdifferentials, we have:

[0069] (13)

[0070] when hour, The subdifferential of is not a value but a set of infinite values.

[0071] about right The partial derivatives of are:

[0072] (14)

[0073] Substituting formula (13) into (14), we obtain:

[0074] (15)

[0075] From (15), we can see that and have the same direction, i.e. ,so

[0076] (16)

[0077] In summary, we can get:

[0078] (17)

[0079] make , The MC penalty function is given by:

[0080] (18)

[0081] The L2 norm and the Moreau envelope of the L2 norm are as follows Figure 2a and Figure 2b shown.

[0082] In order to better control the non-convexity of the MC penalty, a smoothing parameter is introduced To construct Scaled Moreau envelope and scaled MC penalty for the norm.

[0083] for and , The scaled Moreau envelope can be defined as:

[0084] (19)

[0085] According to equation (10), replace , we can get

[0086] (20)

[0087] Multiply both sides of the above equation by :

[0088] (twenty one)

[0089] make ,have:

[0090] (twenty two)

[0091] make .function satisfy:

[0092] . (twenty three)

[0093] From (19), we can see that for all ,have , in particular, lead to ,at the same time ,because is defined as the minimum value of a non-negative function.

[0094] for and , The scaled MC penalty can be defined as:

[0095] (twenty four)

[0096] in, is a scaled minimum-maximum concave penalty function of the L2 norm constructed based on the Moreau envelope function and the minimum-maximum concave penalty function. For vector x The L2 norm of To scale the Moreau envelope, For a given parameter v, find The minimum value of , For use replace After the scaling of the Moreau envelope.

[0097] The parameter values ​​of the MC penalty function are as follows: Figure 3 As shown, Figure 3 The horizontal axis shown is the variable and the vertical axis is the penalty value.

[0098] Combining model (6) and MC penalty function (24), we can get the CV model based on non-convex total variation (MCTV) as follows:

[0099] (25)

[0100] Gradient information can be associated with the structure of objects in an image, directly identifying features of interest for recognition and classification, or providing a basis for further processing of various computer vision tasks, but this setting of setting the same weights for the two sub-variables in the gradient operator cannot effectively handle local features. To handle this situation and improve the segmentation effect while maintaining the image structure, different weights are added to each component of the gradient operator, and a weight function is added to the regularization term. , which is defined based on the image gradient and only depends on the given image itself, without requiring additional parameters. In addition, the weight parameter Depends on and The edge indicator function in the direction of the axis, so this matrix can rotate the direction of the gradient operator to a larger weight. The nonlinear expression of can more effectively maintain the structure and texture of the image. When coupling the local structural information at and , which can effectively describe local features and provide more robust segmentation results.

[0101] The weight function is:

[0102] (26)

[0103] in, is the weight function, is the pixel coordinate, is the weight function, is the weight function, As parameters, greater than 0, The variance is The Gaussian convolution function of is the gradient of the image to be segmented at (x,y) along the x-axis direction, is the gradient of the image to be segmented at (x,y) along the y-axis.

[0104] Based on (25), a model with more flexible anisotropy (WMCTV) is proposed by adding different weights in the gradient operator:

[0105] (27)

[0106] In actual image segmentation, the texture details of the image are also an issue that cannot be ignored. This section continues to consider the image texture based on the previous section and proposes a technique for identifying the main texture direction. The segmentation model based on isotropic total variation is an isotropic functional and is not suitable for images with dominant directions; in addition, the segmentation model based on isotropic total variation is rotation invariant. In order to adapt it to the texture information of the image, it is changed into a rotation variable.

[0107] The definition is centered at the origin, the major semi-axis is 1, and the minor semi-axis is and Ellipse Set for:

[0108] (28)

[0109] Among them, the angle Measurements relative to a Cartesian coordinate system from The ellipse set is a counterclockwise rotation from the axis to the major semi-axis. Figure 4 shown.

[0110] Based on the definition of the ellipse set, define the rotation matrix and the scaling matrix as follows

[0111]

[0112] in, , The above formula will give , for the scaling parameter , the form of the discrete directional gradient operator is:

[0113]

[0114] in, Respectively indicate along and Directed forward finite difference operator, denote the forward finite difference operators along the horizontal and vertical directions, respectively.

[0115] By fixing and , we have and .

[0116] The direction is estimated according to the following process:

[0117] Determine the edges of the image using the Sobel filter to determine the edges of the image;

[0118] Apply a mask to the edge image, considering only the pixels within the largest circle in the center of the image;

[0119] Apply Hough transform to edge image to detect straight lines;

[0120] Calculate the square of the L2 norm of each column of the transformation result matrix to determine the score for each angle from 0° to 180°;

[0121] Estimating the direction Set to:

[0122] (29)

[0123] Based on (27), by adding direction information to the gradient operator, i.e., the rotation matrix and the scaling matrix , a model (DWMCTV) that adapts to local feature structures and considers texture structures is proposed:

[0124] (30)

[0125] Step 120: Obtain the image to be segmented.

[0126] Step 130 , input the image to be segmented into a directional weighted model, solve the directional weighted model based on an alternating directional multiplier method, and obtain a segmented image corresponding to the image to be segmented.

[0127] Specifically include:

[0128] Introducing initial values ​​of multiple solution parameters;

[0129] Repeatedly update multiple parameters of the directional weighted model according to preset parameter update rules until a stopping criterion is met.

[0130] Alternating Direction Method of Multipliers (ADMM) is a simple and effective convex optimization algorithm. Its main idea is to transform the unconstrained optimization problem into a constrained problem by splitting the variables, and then solve it by alternating iterations.

[0131] First, the original problem is decomposed into several easily solvable sub-problems by introducing some auxiliary variables, and then each sub-problem is solved separately by some effective numerical methods. Two auxiliary variables W and Z, then problem (30) is transformed into:

[0132] (31)

[0133] in, is the energy function of the direction-weighted model, For separation area and Region The closed contour of the area and Region They are The outer and inner sub-regions of , and are constants, For Region The average strength of For Region The average strength of , is the level set function, and is the weight coefficient, is the input image to be segmented, is the Heaviside function, is the Dirac function, is the weight function, is the rotation matrix, is the main direction of the image to be segmented, is the scaling matrix, is an adjustable parameter. is the smoothing parameter, and is an auxiliary variable, for The first component of for The second component of for The first component of for The second component of for The gradient vector of When the function takes the maximum value The value of When the function takes the minimum value The value of is the domain of the image to be segmented, is the coordinate of the pixel of the image to be segmented.

[0134] By introducing two Lagrange multipliers for the two constraints, problem (31) can be written as a saddle point problem:

[0135] (32)

[0136] Among them, the augmented Lagrangian function is defined as:

[0137] (33)

[0138] in, and is the penalty parameter, and is the Lagrange multiplier.

[0139] The preset parameter update rule can be:

[0140] (34)

[0141] in, and is the acceleration weight parameter.

[0142] for , , through simple calculation, we can get:

[0143] (35)

[0144] in, is the region of the k+1th iteration The average strength of It is a regularized version of the Heaviside function, which is used to divide the image to be segmented into regions according to the value of the level set function at the kth iteration. and Region , is the region of the k+1th iteration The average intensity.

[0145] To avoid singularities in numerical implementation, Heaviside and Dirac functions are often used with small regularization parameters. The regularized version of is approximately:

[0146] (36)

[0147] (37)

[0148] Formula (35) is transformed into:

[0149] (38)

[0150] for , using the Gauss-Seidel method to solve:

[0151] (39)

[0152] The updating of is done by introducing an artificial time variable t and moving in the direction of steepest descent:

[0153] (40)

[0154] (41)

[0155] in:

[0156] make

[0157]

[0158] have:

[0159] (42)

[0160] So the optimal solution of (39) is:

[0161] (43)

[0162] for :

[0163] (44)

[0164] Rewrite it as:

[0165] (45)

[0166] in, For Region The characteristic vector of For Region The characteristic vector of To dynamically adjust the function, , is a constant, is the penalty parameter, , For the updated The first component and the updated The second component of To obtain and the maximum value of 0, To obtain and the maximum value of 0,

[0167] (46)

[0168] and,

[0169]

[0170] (46) can be rewritten as

[0171] (47)

[0172] The closed-form solution is obtained by the following soft threshold operator:

[0173] (48)

[0174] in, For Region The characteristic vector of For Region The characteristic vector of , is a constant, is the penalty parameter, , is the variable in the iteration process.

[0175] for:

[0176] (49)

[0177] The optimization conditions are:

[0178] (50)

[0179] Right now:

[0180] (51)

[0181] in:

[0182] (52)

[0183] Then the optimal solution of (49) can be written as

[0184] (53)

[0185] in,

[0186] (54)

[0187] in, , is the penalty parameter, is an adjustable constant, is the main direction of the image to be segmented, , is the variable in the iteration process, is the first time variable, is the second time variable, , For the updated The first component and the updated The second component of , is the intermediate variable, is the coordinate of the pixel of the image to be segmented.

[0188] for :

[0189] (55)

[0190] The solution is obtained by the soft threshold operator:

[0191] (56)

[0192] for ,

[0193] (57)

[0194] (58)

[0195] for :

[0196] (59)

[0197] (60)

[0198] in, , is the variable in the iteration process, and is the Lagrange multiplier, is the level set function Find the gradient, , , , , are all variables in the iteration process. As the segmented image, To obtain and 0, whichever is greater. To obtain and 0 whichever is greater.

[0199] The beneficial effects of the image segmentation method based on the direction weighted model are explained below in combination with experimental data.

[0200] In Algorithm 1, the acceleration weight parameter and Set to 1.01, the penalty parameter and is set to 1, and the standard deviation of the Gaussian filter in the weight parameter is set to 0.5. and Adjust according to different images. For numerical implementation, the stopping criterion is met when the following conditions are met:

[0201]

[0202] Quantitatively, in order to verify the effectiveness of the proposed model, Dice Similarity Coefficient (DSC), specificity, precision, recall, Jaccard Similarity Coefficient (JS) and segmentation accuracy (SA) are used as quantitative metrics. These six quantitative indicators can be expressed by the following formula:

[0203]

[0204]

[0205] The closer the values ​​of DSC, specificity, precision, recall, Jaccard similarity coefficient and segmentation accuracy are to 1, the better the segmentation result. In our method, true positives (TP) correspond to voxels that are correctly labeled as belonging to the analyzed category. False positives (FP) correspond to voxels that are incorrectly labeled as belonging to the analyzed category. True negatives (TN) are those voxels that are correctly classified as not belonging to the corresponding category, and false negatives (FN) are those voxels that are incorrectly classified as not belonging to the category. See the table below for details.

[0206]

[0207] The performance of the used methods is evaluated using a segmentation evaluation dataset which contains 200 grayscale images along with the ground-truth segmented images.

[0208] First, four most representative natural grayscale images are selected, involving the size of the segmented target object and the grayscale value difference between the segmented target object and the background. The experimental results of DSC, accuracy, and JSC are shown in the following table, where S1, T1, U1, V1, W1, X1, and Y1 are 7 images respectively.

[0209]

[0210]

[0211] From the above table, we can see that MCTV, WMCTV and DWMCTV recorded in this specification are superior to CV in terms of DSC, accuracy and Jaccard similarity coefficient (JS). Their real segmented images are used as test images, and the segmentation results are shown in Figure 2. Figure 5 As shown in the figure, the first and second columns represent the original grayscale images and the true segmentation results of S1, T1, U1, V1, W1, X1 and Y1 respectively, and the third to sixth columns represent the segmentation results of S1, T1, U1, V1, W1, X1 and Y1 after segmentation using CV, MCTV, WMCTV and DMCTV methods respectively. Figure 5 It can be seen that MCTV, WMCTV and DWMCTV achieve good segmentation in the comparison. Compared with CV, MCTV, WMCTV and DWMCTV are less disturbed by parts other than the segmentation target.

[0212] Figure 6 is a schematic diagram of a module of an image segmentation system based on a directional weighted model according to some embodiments of this specification, such as Figure 6 As shown, the image segmentation system based on the direction weighted model may include a model building module, an image acquisition module and an image segmentation module.

[0213] The model building module can be used to build a directional weighted model based on the Chan-Vese model, combined with a scaled minimum-maximum concave penalty function of an L2 norm built based on a Moreau envelope function and a minimum-maximum concave penalty function.

[0214] The image acquisition module can be used to acquire the image to be segmented.

[0215] The image segmentation module can be used to input the image to be segmented into a directional weighted model, solve the directional weighted model based on an alternating directional multiplier method, and obtain a segmented image corresponding to the image to be segmented.

[0216] The image segmentation system based on the directional weighted model can be used to execute the image segmentation method based on the directional weighted model. For more descriptions of the image segmentation system based on the directional weighted model, please refer to the relevant descriptions of the image segmentation method based on the directional weighted model, which will not be repeated here.

[0217] Finally, it should be understood that the embodiments described in this specification are only used to illustrate the principles of the embodiments of this specification. Other variations may also fall within the scope of this specification. Therefore, as an example and not a limitation, alternative configurations of the embodiments of this specification may be considered consistent with the teachings of this specification. Accordingly, the embodiments of this specification are not limited to the embodiments explicitly introduced and described in this specification.

Claims

1. An image segmentation method based on a directional weighted model, characterized in that: include: Based on the Chan-Vese model, a directional weighted model is established by combining the scaled minimum-maximum concave penalty function of the L2 norm based on the Moreau envelope function and the minimum-maximum concave penalty function. Obtain the image to be segmented; Inputting the image to be segmented into the directional weighted model, solving the directional weighted model based on an alternating directional multiplier method, and obtaining a segmented image corresponding to the image to be segmented; Among them, based on the Chan-Vese model, combined with the scaled minimum-maximum concave penalty function of the L2 norm constructed based on the Moreau envelope function and the minimum-maximum concave penalty function, a directional weighted model is established, including: Based on the Moreau envelope function and the minimum-maximum concave penalty function, a scaled minimum-maximum concave penalty function of the L2 norm is constructed; Based on the Chan-Vese model and the scaled minimum-maximum concave penalty function of the L2 norm, a CV model based on non-convex total variation is established; Establish weight function; On the basis of the CV model based on non-convex total variation, different weights are added to the gradient operator based on the weight function to establish an intermediate model; Based on the intermediate model, by adding direction information to the gradient operator, that is, the rotation matrix R θ and the scaling matrix Λ a , establish a direction weighted model; The energy function of the direction weighted model is: Wherein, F(Γ, C1, C2) is the energy function of the directional weighted model, Γ is the closed contour separating region Ω1 and region Ω2, region Ω1 and region Ω2 are the outer subregion and inner subregion of Γ respectively, Ω=Ω1∪Ω2, C1 and C2 are both constants, C1 is the average intensity of region Ω1, C2 is the average intensity of region Ω2, φ is the level set function, η1, η2 and γ are weight coefficients, I is the input image to be segmented, H() is the Heaviside function, δ() is the Dirac function, T is the weight function, is the rotation matrix, θ is the main direction of the image to be segmented, is the scaling matrix, a is an adjustable parameter, b is the smoothing parameter, w and z are auxiliary variables, w1 is the first component of w, w2 is the second component of w, z1 is the first component of z, and z2 is the second component of z. is the gradient vector of φ, is the value of v when the function reaches its maximum value, is the value of φ, C1, C2 when the function takes the minimum value, Ω is the domain of the image to be segmented, and x is the coordinate of the pixel of the image to be segmented; The weight function is: Among them, T(x,y) is the weight function, (x,y) is the pixel coordinate, t1(x,y) is the weight function, t2(x,y) is the weight function, k is the parameter, k is greater than 0, The variance is The Gaussian convolution function of is the gradient of the image to be segmented at (x, y) along the x-axis direction, is the gradient of the image to be segmented at (x, y) along the y-axis.

2. The image segmentation method based on the direction weighted model according to claim 1, characterized in that: The scaled minimum-maximum concave penalty function of the L2 norm constructed based on the Moreau envelope function and the minimum-maximum concave penalty function is: Among them, φ b (x) is the scaled minimum-maximum concave penalty function of the L2 norm constructed based on the Moreau envelope function and the minimum-maximum concave penalty function, ‖x‖2 is the L2 norm of the vector x, S b () is the scaled Moreau envelope, min v For a given parameter v, find The minimum value of S() is used for 2 The scaled Moreau envelope after x is replaced by x.

3. The image segmentation method based on the direction weighted model according to claim 1 or 2, characterized in that: Solving the directional weighted model based on an alternating directional multiplier method to obtain a segmented image corresponding to the image to be segmented includes: Introducing initial values ​​of multiple solution parameters; Repeating the updating of multiple parameters of the directional weighted model according to a preset parameter updating rule until a stopping criterion is met.

4. The image segmentation method based on the direction weighted model according to claim 3, characterized in that: The preset parameter update rules include: in, is the average intensity of region Ω1 at the k+1th iteration, H ε (φ k ) is the regularized version of the Heaviside function, which is used to segment the image to be segmented into regions Ω1 and Ω2 according to the value of the level set function at the kth iteration. is the average intensity of region Ω2 at the k+1th iteration.

5. The image segmentation method based on the direction weighted model according to claim 3, characterized in that: The preset parameter update rules include: Among them, g1 is the eigenvector of region Ω1, g2 is the eigenvector of region Ω2, δ ε () is a dynamic adjustment function, ε is a constant, β1 is a penalty parameter, is the first component of the updated w and the second component of the updated w, To obtain and the maximum value of 0, To obtain and 0.

6. The image segmentation method based on the direction weighted model according to claim 4, characterized in that: The preset parameter update rules include: Among them, β1 and β2 are penalty parameters, a is an adjustable constant, and θ is the main direction of the image to be segmented. is the variable in the iteration process, t1 is the first time variable, t2 is the second time variable, is the first component of the updated z and the second component of the updated z, q1 and q2 are intermediate variables, and x is the coordinate of the pixel of the image to be segmented.

7. The image segmentation method based on the direction weighted model according to claim 6, characterized in that: The preset parameter update rules include: in, is the variable in the iteration process, ρ1 and ρ2 are Lagrange multipliers, To find the gradient of the level set function φ, are variables in the iteration process. To obtain and 0, whichever is greater. To obtain and 0 whichever is greater.

8. An image segmentation system based on a directional weighted model, characterized in that: The method for image segmentation based on a directional weighted model according to any one of claims 1 to 7 comprises: A model building module, for building a directional weighted model based on the Chan-Vese model, combined with a scaled minimum-maximum concave penalty function of an L2 norm built based on a Moreau envelope function and a minimum-maximum concave penalty function; An image acquisition module, used for acquiring an image to be segmented; The image segmentation module is used to input the image to be segmented into the directional weighted model, solve the directional weighted model based on the alternating direction multiplier method, and obtain a segmented image corresponding to the image to be segmented.

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