A new image segmentation method based on hybrid offset field correction

Abstract

The present invention proposes a novel image segmentation method based on mixed offset field correction. The steps are as follows: constructing a mixed offset field image decomposition model based on the input image to obtain the image's multiplicative offset field and additive offset field, coupling the image decomposition theory to a piecewise smooth image segmentation model; adding regularization terms of the multiplicative offset field and additive offset field, as well as constraints of the multiplicative offset field, to construct a novel image segmentation model, and using the Lagrange multiplier method to transform the image segmentation model into an unconstrained optimization problem; and utilizing an alternating minimization algorithm to iteratively solve each subproblem of the unconstrained optimization problem to obtain the final segmentation result. By considering the image's multiplicative offset field and additive offset field, the present invention can not only effectively remove the offset field present in the image, but also accurately segment natural and medical images with uneven intensity, demonstrating robustness to various image segmentation tasks.

Description

Technical Field

[0001] The present invention relates to the technical field of image segmentation, and in particular to a novel image segmentation method based on hybrid offset field correction. The method mainly involves advanced analysis and understanding of intensity non-uniform images and can be used for the diagnosis of diseases and the extraction of pathological sites in medical images, such as the segmentation of lesion areas in tumor images, and further extraction of relevant medical features to assist doctors in diagnosis and achieve precise treatment. Background Art

[0002] Image information is one of the primary ways humans acquire information from the outside world. Image segmentation is a key technology in image processing, serving as the foundation for image recognition, analysis, and understanding, and a research hotspot in the field of digital image processing. Image segmentation is a complex task. Unlike what the human visual system perceives, the structural diversity and complexity of different images make it difficult to use a unified segmentation method to complete different segmentation tasks. For example, spatial variations in illumination and the defects and limitations of imaging equipment often lead to illumination shifts (uneven grayscale and shadows) in the acquired images. Consequently, research in image segmentation technology continues to deepen.

[0003] Grayscale non-uniformity is usually described as a smooth spatial variation function, called an offset field, which changes the grayscale of the original grayscale uniform image. The grayscale non-uniform image can be described as the addition or multiplication of the offset field and the original image. The specific image model decomposition idea is: based on the Retinex theory, the illumination component corresponds to a smooth image, and the reflection component corresponds to a piecewise constant image. The intensity non-uniform image can be decomposed into a smooth offset. and a structural part J1, namely Where I represents the observed image and n is zero-mean Gaussian noise. Different from the multiplicative offset field method, the intensity non-uniform image is decomposed into the sum of the components of the piecewise constant image and the components of the smooth offset field. That is, the intensity non-uniform image decomposition model is expressed as represents the smooth offset, and J2 represents the reflective component of the image structure. Generally speaking, natural and medical images often contain not only a multiplicative offset field but also an additive offset field. Therefore, we express the mixed bias field image decomposition model of the multiplicative and additive offset fields as I = b1J + b2 + n, where b1 and b2 represent the multiplicative and additive offset fields, respectively, and J represents the piecewise constant image to be segmented.

[0004] How to effectively segment an intensity-inhomogeneous image into several meaningful regions from the perspective of human visual perception and ensure that the segmented regions are consistent at different resolutions remains a very challenging task. The invention patent with application number 202010428617.9 discloses a non-uniform image segmentation method based on offset field and global smoothness prior, including: obtaining a noisy grayscale non-uniform image; adding an initial contour line to the grayscale non-uniform image; decomposing the grayscale non-uniform image into a structural part, an illumination offset field part, and a noise part; constructing a corresponding multi-phase variational image segmentation model; using the alternating minimization method and variable splitting technique of convex optimization to solve the optimal solution of the above model; using the constructed multi-phase variational image segmentation model to segment the grayscale non-uniform image and obtain the corresponding image segmentation result; the invention introduces a local constant prior in the CVB model, establishes a non-uniform image multi-phase segmentation model, and designs an effective algorithm to calculate and solve the proposed model; the results show that this method has strong robustness to the initial value, and can obtain more accurate segmentation results for noisy grayscale non-uniform images. However, this invention cannot remove the offset field of the image while maintaining the real information of the image, and effectively describe the area to be segmented in the image. However, the model proposed by this invention still needs to be improved and enhanced. For example, the model involves too many parameters, and it takes a certain amount of time to adjust the parameters to obtain ideal experimental results. Summary of the Invention

[0005] Aiming at the technical problem that the existing intensity non-uniform image segmentation method cannot remove the image offset field while maintaining the real information of the image and effectively describe the image area to be segmented, this paper proposes a new image segmentation method based on hybrid offset field correction, which takes into account the multiplicative offset field and additive offset field in the image and uses the Sobolev space W 1,2 To describe the multiplicative offset field and the additive offset field, and use a constraint on the multiplicative offset field. By considering the mixed offset field of the image, the mixed offset field image decomposition model can not only effectively remove the offset field existing in the image, but also accurately segment natural images and medical images with uneven intensity. It is robust to different image segmentation tasks, improves the image segmentation accuracy and segmentation effect, and can be used to segment natural images and medical images with uneven intensity.

[0006] In order to achieve the above object, the technical solution of the present invention is implemented as follows: a new image segmentation method based on hybrid offset field correction, the steps of which are as follows:

[0007] Step 1: Construct a mixed offset field image decomposition model, obtain the multiplicative offset field b1 and additive offset field b2 of the image according to the input image, and couple the image decomposition theory to the piecewise smooth image segmentation model;

[0008] Step 2: Add regularization terms of the multiplicative offset field b1 and the additive offset field b2, as well as constraints on the multiplicative offset field b1, so that the multiplicative offset field b1 always fluctuates around a fixed value. A new image segmentation model is constructed, and the Lagrange multiplier method is used to transform the image segmentation model into an unconstrained optimization problem.

[0009] Step 3: Use the alternating minimization algorithm to iteratively solve each sub-problem of the unconstrained optimization problem to obtain the final segmentation result.

[0010] Preferably, the mixed offset field image decomposition model of the multiplicative offset field b1 and the additive offset field b2 is I=b1J+b2+n, where I represents the input image, b1 and b2 represent the multiplicative offset field and the additive offset field respectively, n is Gaussian noise with zero mean, and J represents the piecewise constant image to be segmented.

[0011] Preferably, the multiplicative offset field b1 and the additive offset field b2 are slowly varying and smooth, and the multiplicative offset field b1 and the additive offset field b2 belong to the Sobolev space, that is, b1∈W 1,2 (Ω) and b2∈W 1,2 (Ω); the multiplicative offset field b1 changes slowly around 1.

[0012] Preferably, the method of coupling the image decomposition theory into the piecewise smooth image segmentation model is:

[0013] The piecewise constant image J consists of two parts:

[0014]

[0015] Where Ω1 represents the region of interest (ROI), Ω2 represents the outer area of ​​the ROI, c1 represents the average pixel value of the inner area of ​​the ROI, and c2 represents the average pixel value of the outer area of ​​the ROI.

[0016] Preferably, based on the definition of bounded variation space, the new image segmentation model is:

[0017]

[0018] Where Ω represents the entire observation image domain, x represents a pixel point, ε>0 is an arbitrarily small bias parameter, λ is the parameter of the data fitting term; α and β are the parameters of the mixed offset field smoothing term respectively; represents the gradient of the mixed offset field; D is the weak derivative symbol, and the indicator function u is:

[0019]

[0020] Preferably, the indicator function u is relaxed to a convex set u∈[0,1], and the Lagrange multiplier method is used to add the Lagrange multiplier term v∫ Ω ((b1-1) 2 -ε)dx, where ε is an arbitrarily small positive number, usually abbreviated to v∫ Ω (b1-1) 2 dx; transform the inequality constraint into an unconstrained optimization problem:

[0021]

[0022] Among them, v>0 is the Lagrange multiplier, indicating function Γ δ (u) is:

[0023]

[0024] Preferably, the alternating minimization algorithm converts the unconstrained optimization problem into several sub-problems by introducing auxiliary variables, adopts the alternating direction multiplier method to solve the sub-problems, converts the problem of solving multiple variables at the same time into the process of solving a single variable in sequence, and then fixes the other variables in the process of solving one of the variables.

[0025] Preferably, the alternating minimization algorithm converts the variable b i ,c i , i=1,2 is decoupled from the indicator function u, and an alternating solution is obtained:

[0026]

[0027] Where S = (I - b1c1 - b2) 2 -(I-b1c2-b2) 2 .

[0028] Preferably, for subproblem b i ,c i , two auxiliary variables p1 and p2 are introduced, and the problem is transformed into optimization problem I:

[0029]

[0030] Based on the augmented Lagrangian method, the following saddle point problem I is obtained:

[0031]

[0032] Where L(c1,c2,b1,b2,p1,p2;ξ1,ξ2) is the augmented Lagrangian function, ξ1 and ξ2 can be regarded as Lagrangian multiplier variables of the dual variables, and r represents the penalty parameter;

[0033] The saddle point problem I is solved by the alternating direction multiplier method, and the iterative framework is:

[0034]

[0035] Use the alternating direction multiplier method to decompose the subproblem of the indicator function u into smaller subproblems and introduce auxiliary variables The optimization problem of the indicator function u is:

[0036]

[0037] Its augmented Lagrangian function is expressed as L τ (q,u;ξ3), where ξ3 is the Lagrange multiplier and τ is the penalty parameter. Based on the augmented Lagrangian method, the following saddle point problem II is obtained:

[0038]

[0039] Saddle point problem II is solved by the alternating direction multiplier method, and the iterative framework is:

[0040]

[0041] Preferably, the solving steps of the alternating minimization algorithm are:

[0042] (1) Initial value selection: Select parameters based on image characteristics Parameters λ, α, β> 0; k = 1 and start the kth iteration, where Represents an identity matrix of the same size as the input image;

[0043] (2) External iteration: subproblem b i ,c i The solution:

[0044]

[0045] (3) Inner iteration: The subproblem of the indicator function u is an inner iteration process:

[0046]

[0047] Let k = k + 1 and return to step (2) until convergence;

[0048] The termination condition of the outer iteration is k≤K max , where K max Indicates the maximum number of iterations;

[0049] The inner iteration uses relative error as the termination condition; the relative error is:

[0050] Where θ is the error value that satisfies the termination condition.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] 1. Based on the intensity non-uniform image decomposition model, the present invention simultaneously considers the multiplicative offset field b1 and the additive offset field b2 in the image to form a mixed offset field image decomposition model. The image decomposition theory is coupled to the piecewise smooth image segmentation model. It is assumed that the components of the mixed offset field are slowly varying and smooth, so that the model can effectively remove the offset field during segmentation, thereby improving the quality of image segmentation.

[0053] 2. The present invention adopts a regularization-based approach, adding regularization terms of the offset fields b1 and b2 and constraints of the multiplicative offset field, so that the offset field b1 always fluctuates around a fixed value, and a fixed initial value is selected. Subsequent experiments are conducted so that the image segmentation model not only has the advantage of capturing image details, but also is more robust to different initial contour segmentations.

[0054] 3. The present invention uses an alternating minimization algorithm to transform the original problem into several easily solvable subproblems. The present invention uses the alternating direction method of multipliers (ADMM) to solve the subproblems. That is, by introducing auxiliary variables, the original problem is transformed into several subproblems, and then each subproblem is solved alternately and iteratively.

[0055] 4. The present invention can be used to segment different types of images, such as real natural images, medical images, etc. The present invention can be widely used in subsequent computer image analysis fields, such as image enhancement, image recognition, etc.

[0056] Aiming at the problem of image segmentation with non-uniform intensity, this paper analyzes and studies the existing segmentation models for non-uniform intensity. Based on the assumption of image decomposition model, this paper combines the multiplicative offset field with the additive offset field to form a hybrid offset field correction model. This is a variational model that realizes both image segmentation and offset correction. At the same time, it uses the Sobolev space W 1 ,2 To describe the multiplicative and additive offset fields, a constraint is applied to the multiplicative offset field. By combining the multiplicative and additive offset fields, weak edge information and intensity inhomogeneity information can be captured, effectively describing the segmented regions in the image domain. Based on the alternating minima algorithm and the operator splitting algorithm, an efficient numerical algorithm is employed to solve the proposed variational model. By considering the mixed offset field of the image, the present invention not only effectively removes the offset field present in the image, but also accurately segments natural and medical images with inhomogeneous intensities, demonstrating robustness to various image segmentation tasks. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0058] Figure 1 It is a schematic diagram of the process of the present invention.

[0059] Figure 2 This is the result of the present invention on a general natural image, where (a) is the original input image, (b) is the multiplicative offset field image decomposed from (a), and (c) is the additive offset field image decomposed from (a).

[0060] Figure 3 This is the result of removing the offset field from the natural image tested by the present invention, where (a1) is the original input image, (a2) is the pixel distribution diagram of the row represented by the straight line in (a1), and (a3) ​​is the grayscale histogram of (a1). Similarly, (b1) is the corrected image, (b2) is the pixel distribution diagram of the row represented by the straight line in (b1), and (b3) is the grayscale histogram of (b1).

[0061] Figure 4 This figure compares the results of segmenting the target in the natural image "fish" by the present invention and the existing image segmentation method, where (a) is the original input image, (b1), (b2) and (b3) are different initial contours, (c1), (c2) and (c3) are the experimental results of the weighted bounded Hessian total variation (WBHMS) model, (d1), (d2) and (d3) are the segmentation results of the local intensity clustering (LIC) model, and (e1), (e2) and (e3) are the segmentation results of the model proposed in the present invention.

[0062] Figure 5 This is a comparison diagram of the results of decomposition of brain glioma images by the present invention and the existing image segmentation and decomposition method, wherein (a1) is the original input medical image, (a2) is the true value image of (a1), (b1), (b2) and (b3) are different initial contours, (c1), (c2) and (c3) are the experimental results of the iterative threshold method (ICTM) model, (d1), (d2) and (d3) are the segmentation results of the Euler elasticity (CVE) model based on the Chan-Vese segmentation model, and (e1), (e2) and (e3) are the segmentation results of the model proposed in the present invention.

[0063] Figure 6 This is a comparison diagram of the results of the decomposition of real MRI medical images by the present invention, wherein (a1), (a2) and (a3) ​​are the original input medical images, (b1), (c1) and (d1) are the segmentation results of (a1), (a2) and (a3) ​​by the model proposed in the present invention, (b2), (c2) and (d2) are the local enlarged images of the segmentation results, (b3), (c3) and (d3) are the true value images of (b2), (c2) and (d2), and (b4), (c4) and (d4) are the local enlarged images of the true value images. DETAILED DESCRIPTION

[0064] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0065] like Figure 1 As shown in the figure, an image segmentation method based on mixed offset field correction is used to segment natural images and medical images with uneven intensity. The multiplicative offset field b1 and additive offset field b2 in the image are considered, and the Sobolev space W is used to calculate the image segmentation method. 1,2 To describe the multiplicative offset field b1 and the additive offset field b2, and use a constraint on the multiplicative offset field b1 to improve the image segmentation accuracy and segmentation effect, and finally obtain a high-quality segmentation result. The specific steps are as follows:

[0066] Step 1: Construct a mixed offset field image decomposition model, obtain the multiplicative offset field b1 and additive offset field b2 of the image according to the observed image, and couple the image decomposition theory into the piecewise smooth image segmentation model.

[0067] Generally speaking, natural and medical images usually contain not only a multiplicative offset field but also an additive offset field. Therefore, the mixed offset field image decomposition model of the multiplicative and additive offset fields is expressed as I = b1J + b2 + n, where I represents the observed image, b1 and b2 represent the multiplicative and additive offset fields, respectively, n is zero-mean Gaussian noise, and J represents the piecewise constant image to be segmented.

[0068] In order to propose the segmentation model of the present invention, some assumptions need to be made about the multiplicative offset field b1 and the additive offset field b2. The specific description is as follows:

[0069] (1) For the multiplicative offset field b1 and the additive offset field b2, it is assumed that they are slowly varying and smooth. Therefore, it is assumed that the multiplicative offset field b1 and the additive offset field b2 belong to the Sobolev space, that is, b1∈W 1,2 (Ω) and b2∈W 1,2 In addition, it is assumed that the grayscale value of the multiplicative offset field b1 changes slowly around 1, which is achieved by adding an inequality constraint.

[0070] (2) Assume that the piecewise constant image J consists of two parts:

[0071]

[0072] Where Ω1 represents the region of interest (ROI), Ω2 represents the area outside the ROI, c1 represents the average pixel value inside the ROI, and c2 represents the average pixel value outside the ROI.

[0073] Step 2: Add regularization terms of the multiplicative offset field b1 and the additive offset field b2, as well as constraint terms of the multiplicative offset field b1, so that the multiplicative offset field b1 always fluctuates around a constant value, and construct a new image segmentation model, namely the mixed offset field image decomposition model. The Lagrange multiplier method is used to transform the mixed offset field image decomposition model into an unconstrained optimization problem.

[0074] Based on the above assumptions and the definition of bounded variation (BV) space, the following new image segmentation model is proposed. The specific description is as follows:

[0075]

[0076] Where Ω represents the entire observation image domain, x represents the pixel point, ε>0 is an arbitrarily small bias parameter, λ is the parameter of the data fitting term, and the specific value range is: λ∈[6,100]; α, β are the parameters of the offset field smoothing term, and the specific value range is: α∈[50,300], β∈[50,400]; Represents the gradient of the mixed offset field, ensuring that the offset field changes slowly; D is the weak derivative symbol, and the indicator function u is defined as

[0077]

[0078] In model (2), the first term is a data fitting term, forcing b1c i +b2 is close to the input image, where i=1,2. The second and third terms are smoothing terms of the offset, requiring the offset field to be slowly changing and smooth. The last term is the length term of the regularization term contour. The goal of this invention is to recover b from the observed image. i ,c i, i = 1, 2. Then the segmentation result is obtained. In addition, it is usually assumed that the multiplicative offset field b1 changes slowly around 1, so a constraint term is used to describe it. For the new image segmentation model (2), it is difficult to solve numerically due to the binary constraint u∈{0, 1}. To overcome this shortcoming, an effective method is to relax it into a convex set of u∈[0, 1]. For the inequality constraint, the Lagrange multiplier method is used to rewrite the new image segmentation model (2) as the following unconstrained optimization problem:

[0079]

[0080] Among them, v>0 is the Lagrange multiplier, usually v is 0.1, indicating function Γ δ (u) is defined as

[0081]

[0082] The Lagrange multiplier method is used to obtain the unconstrained optimization problem, that is, the problem of finding the extreme value under the constraints is transformed into the problem of finding the extreme value of the Lagrangian function. Regardless of whether the original problem is convex or not, the dual problem is a convex optimization problem, and the dual problem can give a lower bound for the original problem; when certain conditions are met, the solutions of the original problem and the dual problem are completely equivalent.

[0083] Step 3: Use the alternating minimization algorithm to iteratively solve each sub-problem of the unconstrained optimization problem to obtain the final segmentation result.

[0084] The present invention employs the alternating direction method of multipliers (ADMM) to solve this subproblem. By introducing auxiliary variables, the original unconstrained optimization problem is transformed into several subproblems, making each subproblem easier to solve. The alternating minimization algorithm is employed to solve the decomposed subproblems sequentially in each iteration, yielding the final segmentation result. Since the proposed model is a multivariable optimization problem, the alternating minimization algorithm is employed. This algorithm transforms the simultaneous solution of multiple variables into a sequential solution of a single variable, fixing the remaining variables while solving one variable.

[0085] The unconstrained optimization problem proposed in the present invention, namely model (4), is a multivariable optimization problem, in which the variable b i ,c i , i=1,2. is coupled with the indicator function u. If it is solved directly, it will require solving a large-scale problem, which will make numerical solution difficult. In order to overcome this problem, the present invention uses the alternating minimization algorithm to solve, that is, to convert the problem of solving multiple variables at the same time into the process of solving a single variable in sequence. To this end, the alternating minimization algorithm is first applied to b i ,c i, i=1,2. Decoupled from u, the following alternating solution is obtained:

[0086]

[0087] Where S = (I - b1c1 - b2) 2 -(I-b1c2-b2) 2 .

[0088] For subproblem b i ,c i ,i=1,2.,In order to decouple the multiplicative offset field b1 and the additive offset field b2 from their optimization conditions, two auxiliary variables p1 and p2 are introduced, which are then transformed into the following optimization problem:

[0089]

[0090] Based on the augmented Lagrangian method, the following saddle point problem is obtained:

[0091]

[0092] Among them, L(c1,c2,b1,b2,p1,p2;ξ1,ξ2) is the augmented Lagrangian function, ξ1 and ξ2 can be regarded as Lagrangian multiplier variables of the dual variables, and ξ1 is taken as 0 =ξ2 0 = 0, and then update using Equation (9), where r represents the penalty parameter, and its value range is: r∈[0.05,0.9]. Using the alternating direction multiplier method, while solving for one variable, the other variables are fixed, that is, the classic alternating minimization algorithm is used to solve the above problem, and the Gauss-Seidel iteration scheme is used to solve the above problem. Therefore, the saddle point problem (8) can be solved by the alternating direction multiplier method, and the iterative framework is as follows:

[0093]

[0094] Now consider solving the non-smooth and convex subproblem u. The main question is how to effectively overcome the non-smoothness of the proposed numerical method. To this end, we use the ADMM method to decompose the subproblem of the indicator function u into smaller subproblems, making them more tractable. The specific method is to introduce auxiliary variables The corresponding optimization problem can be written as:

[0095]

[0096] Its augmented Lagrangian function is expressed as L τ (q,u;ξ3), where ξ3 is the Lagrange multiplier, and the initial value is ξ3 0= 0, and then update using formula (11); τ represents the penalty parameter, and its value range is τ∈[0.001,11]. The augmented Lagrangian function is specifically described as follows:

[0097]

[0098] The corresponding optimization sub-problem using the ADMM method can be written as:

[0099]

[0100] In the following, we will consider the details of solving the subproblems. After obtaining the expression of each subproblem, the overall solution and iteration framework of the proposed model are described below. i ,c i ,i=1,2. When solving the sub-problem with u, each sub-problem needs to be solved independently. i ,c i , i=1,2. The sub-problem is used as the outer loop, and the sub-problem of solving u is used as the inner loop. After multiple iterations, the optimal value is obtained to obtain the segmentation result. The solution steps of the alternating minimization algorithm are:

[0101] (1) Initial value selection: Select appropriate parameters based on image characteristics Parameters λ, α, β> 0, let k = 1 and start the kth iteration, let k = k + 1 and return to the k + 1th iteration until convergence, where Represents an identity matrix of the same size as the input image.

[0102] (2) External iteration: subproblem b i ,c i ,i=1,2. The outer iteration uses the number of iterations as the termination condition k≤K max , K max Indicates the maximum number of iterations, usually the maximum number of iterations K max Take it as 300.

[0103]

[0104] (3) Inner iteration: The subproblem of finding the indicator function u is an inner iteration process, and the inner iteration uses the relative error as the termination condition;

[0105]

[0106] (4) The iteration is terminated when the termination condition is met. The specific expression of relative error is:

[0107]

[0108] Among them, θ is the error value that meets the termination condition, usually taken as θ = 10 -4 ,Through the above steps, the optimal segmentation result is obtained after multiple iterations.

[0109] The experimental platform of the present invention is: Intel Core processor 5e i7 3.20GHz, 16G memory personal desktop computer, and Matlab2021 is used for program design.

[0110] Specific experiment 1

[0111] The experimental results of this invention on natural image buildings are shown in Figure 2 , where (a) is the original input image, (b) is the image of the multiplicative offset field b1 decomposed from (a), and (c) is the image of the additive offset field b2 decomposed from (a). By selecting the pixel values ​​of any row or column to draw a curve graph, it can be observed that the decomposed offset field image is slowly changing and smooth.

[0112] Depend on Figure 3 The result of removing the offset field from the natural image tested by the present invention can be intuitively found. (a1) is the original input image, (a2) is the pixel distribution diagram of the row represented by the straight line in the image, and (a3) ​​is the grayscale histogram of (a1). Similarly, (b1) is the corrected image obtained after removing the mixed offset field, (b2) is the pixel distribution diagram of the row represented by the straight line in the image, and (b3) is the grayscale histogram of (b1). It can be observed that the image after removing the mixed offset field is more inclined to piecewise constant. By comparing (a2) and (b2), it can be obtained that the image after correction is more inclined to piecewise constant. In order to obtain a more detailed observation, the histogram of the drawn images (a1) and (b1) is observed. The histogram has two peaks, which means that the two-phase segmentation is reasonable, and the histogram of the segmentation scheme proposed by the present invention has the largest inter-class variance.

[0113] Depend on Figure 4It can be intuitively found that the comparison diagram of the results of the segmentation of the target in the natural image "fish" by the present invention and the existing image segmentation method is obtained from the public dataset on the Internet. Among them, (a) is the original input image, (b1), (b2) and (b3) are different initial contours, and three representative initial contours are selected. The initial contour is inside the target, intersecting with the target and the initial contour is outside the target. (c1), (c2) and (c3) are the segmentation results of the WBHMS model for (b1), (b2) and (b3), which failed to accurately segment the weak boundary area. (d1), (d2) and (d3) are local intensity clustering (Local Intensity Clustering) Clustering, LIC) model for (b1), (b2) and (b3). From the experimental results, it can be seen that the LIC model has a slightly better segmentation effect than the WBHMS model, but its segmentation ability is poor and it is difficult to accurately segment weak boundary areas. (e1), (e2) and (e3) are the segmentation results of the image segmentation model proposed in the present invention. It can be observed that for different initial contours, the model proposed in the present invention is robust to different initial contours.

[0114] Specific experiment 2:

[0115] The present invention, the CVE model, and the ICTM method were used to segment and compare a medical image of brain glioma. The experimental data were obtained from a public dataset on the Internet. The results are shown in Figure 2. Figure 5 As shown, Figure (a1) is the input original grayscale image, (a2) is the annotated true value image, and different initial contours (b1), (b2) and (b3) are selected for segmentation. (c1), (c2) and (c3) are the segmentation results of the CVE model for (b1), (b2) and (b3), respectively. It can be observed that the CVE model has over-segmentation and incorrectly segments areas with higher pixel values. (d1), (d2) and (d3) are the segmentation results of the ICTM model for (b1), (b2) and (b3), respectively. The ICTM model fails to well depict the edge details of the ROI. (e1), (e2) and (e3) are the segmentation results of the model proposed in the present invention, respectively. The present invention can not only effectively segment the lesion area, but also overcome some weak boundary effects and achieve good segmentation effect.

[0116] In order to further demonstrate the effectiveness of the present invention, relevant experiments are conducted on another set of real MRI datasets, namely Figure 6 (a1)-6(d4). The enlarged images of the local details can well demonstrate that the method of the present invention is more robust. Figure 6The comparison diagram of the results after the decomposition of the real MRI medical image by the present invention, wherein (a1), (a2) and (a3) ​​are the original input medical images. It can be observed from the images that the segmentation tasks of these three lesions have different challenges. The lesion area is small, the boundary is not clear, the image itself has the problem of uneven grayscale, and the grayscale of the lesion area is also inconsistent. (b1), (c1) and (d1) are the segmentation results of the model proposed by the present invention, (b2), (c2) and (d2) are the local enlarged images of the segmentation results, (b3), (c3) and (d3) are the true values, and (b4), (c4) and (d4) are the local enlarged images of the true values. It can be observed that the method proposed by the present invention achieves a good segmentation effect, and the boundaries of the segmented lesion area are continuous and smooth.

[0117] Overall experimental summary: In order to verify the effectiveness of the method of the present invention, relevant experiments were conducted on different types of images, such as natural images and medical images. At the same time, different initial contours were used to verify the robustness of the method proposed in the present invention. In specific experiment 1, the model proposed in the present invention was compared with two different types of segmentation models, namely the WBHMS model and the LIC model. The advanced nature of the proposed model can be observed. In specific experiment 2, in order to add different types of comparative experiments, the model proposed in the present invention was compared with two other different types of segmentation models, namely the CVE model and the ICTM model. It can be observed that the method proposed in the present invention achieved a better segmentation effect, which is better than these latest models. After experimental analysis and discussion, the present invention can be widely used in subsequent computer image analysis fields, such as image enhancement and image recognition.

[0118] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A novel image segmentation method based on hybrid offset field correction, characterized in that: The steps are as follows: Step 1: Construct a mixed offset field image decomposition model, obtain the multiplicative offset field b1 and additive offset field b2 of the image according to the input image, and couple the image decomposition theory to the piecewise smooth image segmentation model; The mixed offset field image decomposition model of the multiplicative offset field b1 and the additive offset field b2 is I = b1J + b2 + n, where I represents the input image, b1 and b2 represent the multiplicative offset field and the additive offset field, respectively, n is zero-mean Gaussian noise, and J represents the piecewise constant image to be segmented. The method of coupling the image decomposition theory into the piecewise smooth image segmentation model is: Piecewise Constant Image J consists of two parts: Where Ω1 represents the region of interest (ROI), Ω2 represents the area outside the ROI; c1 represents the average pixel value inside the ROI, and c2 represents the average pixel value outside the ROI. Step 2: Add regularization terms of the multiplicative offset field b1 and the additive offset field b2, as well as constraints on the multiplicative offset field b1, so that the multiplicative offset field b1 always fluctuates around a fixed value. A new image segmentation model is constructed, and the Lagrange multiplier method is used to transform the image segmentation model into an unconstrained optimization problem. Based on the definition of bounded variation space, the new image segmentation model is: Where Ω represents the entire observation image domain, x represents a pixel point, ε>0 is an arbitrarily small bias parameter, λ is the parameter of the data fitting term; α and β are the parameters of the mixed offset field smoothing term respectively; represents the gradient of the mixed offset field; D is the weak derivative symbol, and u is the indicator function; Step 3: Use the alternating minimization algorithm to iteratively solve each sub-problem of the unconstrained optimization problem to obtain the final segmentation result.

2. The novel image segmentation method based on hybrid offset field correction according to claim 1, characterized in that: The multiplicative offset field b1 and the additive offset field b2 are slowly changing and smooth, and the multiplicative offset field b1 and the additive offset field b2 belong to the Sobolev space, that is, b1∈W 1,2 (Ω) and b2∈W 1,2 (Ω); the multiplicative offset field b1 changes slowly around 1.

3. The novel image segmentation method based on hybrid offset field correction according to claim 1, characterized in that: The indicator function u is:

4. The novel image segmentation method based on hybrid offset field correction according to claim 3, characterized in that: Relax the indicator function u to a convex set u∈[0,1], use the Lagrange multiplier method, and add the Lagrange multiplier term v∫ Ω ((b1-1) 2 -ε)dx, where ε is an arbitrarily small positive number, usually abbreviated to v∫ Ω (b1-1) 2 dx; transform the inequality constraints into an unconstrained optimization problem: Among them, v>0 is the Lagrange multiplier, indicating function Γ δ (u) is:

5. The novel image segmentation method based on hybrid offset field correction according to claim 3 or 4, characterized in that: The alternating minimization algorithm converts the unconstrained optimization problem into several sub-problems by introducing auxiliary variables, and adopts the alternating direction multiplier method to solve the sub-problems. The problem of solving multiple variables at the same time is converted into the process of solving a single variable in sequence, and then the other variables are fixed while solving one of the variables.

6. The novel image segmentation method based on hybrid offset field correction according to claim 5, characterized in that: The alternating minimization algorithm changes the variable b i ,c i , i=1,2 is decoupled from the indicator function u, and an alternating solution is obtained: Where S = (I - b1c1 - b2) 2 -(I-b1c2-b2) 2 .

7. The novel image segmentation method based on hybrid offset field correction according to claim 6, characterized in that: For subproblem b i ,c i , two auxiliary variables p1 and p2 are introduced, and the problem is transformed into optimization problem I: Based on the augmented Lagrangian method, we get the following saddle point problem I: Where L(c1,c2,b1,b2,p1,p2;ξ1,ξ2) is the augmented Lagrangian function, ξ1 and ξ2 can be regarded as Lagrangian multiplier variables of the dual variables, and r represents the penalty parameter; The saddle point problem I is solved by the alternating direction multiplier method, and the iterative framework is: Use the alternating direction multiplier method to decompose the subproblem of the indicator function u into smaller subproblems and introduce auxiliary variables The optimization problem of the indicator function u is: Its augmented Lagrangian function is expressed as L τ (q,u;ξ3), where ξ3 is the Lagrange multiplier and τ represents the penalty parameter. Based on the augmented Lagrangian method, the following saddle point problem II is obtained: Saddle point problem II is solved by the alternating direction multiplier method, and the iterative framework is:

8. The novel image segmentation method based on hybrid offset field correction according to claim 7, characterized in that: The solution steps of the alternating minimization algorithm are: (1) Initial value selection: Select parameters based on image characteristics Parameters λ, α, β> 0; k = 1 and start the kth iteration, where Represents an identity matrix of the same size as the input image; (2) External iteration: subproblem b i ,c i The solution: (3) Inner iteration: The subproblem of the indicator function u is an inner iteration process: Let k = k + 1 and return to step (2) until convergence; The termination condition of the outer iteration is k≤K max , where K max Indicates the maximum number of iterations; The inner iteration uses relative error as the termination condition; the relative error is: Where θ is the error value that satisfies the termination condition.

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