A Level Set Image Segmentation Method for Multiplicative-Additive Models

Abstract

The present invention provides a level set image segmentation method for multiplicative-additive models, belonging to the field of image processing. Aiming at the problems of inaccurate and incomplete image segmentation caused by image degradation and gray-scale inhomogeneity, this method provides a multiplicative-additive model to represent an image, uses multiplicative bias fields and additive bias fields to characterize the gray-scale inhomogeneity of the image, and realizes image segmentation by constructing an image gray-scale data fitting term, embedding a level set energy functional, defining a bias field constraint term, establishing a total variation level set equation, obtaining each iterative term, and cross-iteratively numerically solving. This method can more accurately characterize the physical properties of images, has outstanding accuracy, reliability, and versatility in the segmentation of natural images, medical images, and industrial images, and can be applied to the segmentation of two-dimensional and three-dimensional image data simultaneously.

Description

Technical Field

[0001] The present invention belongs to the field of image processing, and relates to a level set image segmentation method for multiplicative-additive models. Background Art

[0002] For a large number of digital images such as natural images, medical images, and industrial images that exist in practice, due to the uneven change of illumination, as well as the non-ideality and defects of imaging devices, it is easy to cause image degradation and deterioration, resulting in the phenomenon of uneven gray levels, which brings many problems to image processing and computer vision. Since the gray levels of the image overlap with each other within a certain area, it is extremely difficult to segment the image with uneven gray levels.

[0003] Image segmentation is the main research content of digital image processing. Based on target segmentation and contour extraction, subsequent operations such as target recognition and geometric measurement can be realized. Practical digital images usually contain noise and various non-ideal factors, and negative phenomena such as uneven gray level distribution and low local contrast are relatively common. The accuracy that can be achieved by traditional segmentation algorithms is relatively low, and even wrong segmentation may occur. The threshold-based segmentation method divides the image into a binary image by selecting an appropriate threshold, which is simple to calculate and has strong adaptability, but this method is sensitive to noise and uneven gray levels. The region-based algorithm is relatively simple and has strong immunity to noise, but its computational efficiency is low, and it depends on specific growth, splitting, and merging methods, with poor adaptability. Neural network-based segmentation can achieve segmentation when the data deviates from the normal situation, but this method has high requirements for the construction and training of the data set and low efficiency. In recent years, segmentation algorithms combining specific theories have gradually emerged. The level set segmentation technology is insensitive to noise based on the theory of partial differential equations, can obtain sub-pixel (sub-voxel) level smooth and closed contour curves, and can better overcome the uneven gray levels of the image by combining prior knowledge, and has advantages in the field of image segmentation.

[0004] Some region-based level set models assume that an image is composed of piecewise constant images with uniform gray-level distributions, so they are unable to segment images with non-uniform gray levels. To handle images with non-uniform gray levels, researchers have proposed a variety of image segmentation methods based on the level set theory. The region scale fitting model constructs two local gray-level fitting functions that approximate the contour inside and outside the zero level set contour, and embeds a kernel function in the fitting term to guide the movement of the contour, thereby achieving the segmentation of images with non-uniform gray levels. However, when the center of the kernel function is far from the zero level set, the model cannot define the fitting function values of the foreground and background, often resulting in segmentation failure. The local gray-level clustering level set segmentation method combines the multiplicative image model with the level set method, obtains the level set energy functional representing the image gray levels according to the image gray-level clustering criterion, and realizes the segmentation of images with non-uniform gray levels. However, the multiplicative model cannot fully represent the non-uniform gray-level property of the image and is prone to failure when segmenting images with severe non-uniform gray levels. In addition, this method cannot handle three-dimensional image data. For the segmentation application of three-dimensional image data, the 3D robust Chan-Vese model introduces the gray-level information of the local region of the image and proposes a segmentation method for noisy CT volume data. However, this model assumes that the gray-level distribution of the three-dimensional image data is uniform, so it cannot segment three-dimensional images with non-uniform gray levels. In view of the above problems, the present invention proposes a level set image segmentation method based on an additive-multiplicative model, which uses the additive-multiplicative model to represent the non-uniform gray levels of the image and combines it with the level set method to effectively solve the segmentation problem of non-uniform gray-level and noisy images. Summary of the Invention

[0005] Aiming at the problems of inaccurate and incomplete image segmentation caused by image degradation and non-uniform gray levels, the present invention provides a level set segmentation method based on an additive-multiplicative model, which uses multiplicative bias fields and additive bias fields to represent the non-uniform gray-level property of the image, and realizes image segmentation by constructing an image gray-level data fitting term, embedding a level set energy functional, defining a bias field constraint term, establishing a total variation level set equation, obtaining each iterative term, and cross-iteratively numerically solving. This method is applicable to the segmentation of both two-dimensional and three-dimensional image data.

[0006] The technical solutions adopted by the present invention to solve its technical problems include the following steps:

[0007] Step 1: Define the additive-multiplicative model as I = b1J + b2 + n, where I is the observed image, b1 and b2 are the multiplicative bias field and additive bias field of non-uniform gray levels respectively, J is the true image, and n is the additive noise. This model uses two bias fields with different properties to represent the non-uniform gray-level property of the image, and constructs an image gray-level data fitting term according to this model. When processing two-dimensional image data, the following method is adopted:

[0008] (1) Assume that the true image J is in non-overlapping regions Ω1,…,Ω NTake N different constant values c1, …, c respectively N ;

[0009] (2) Set the constants c1, …, c N as the vector c = (c1, …, c N ), and rewrite the multiplicative-additive model as I(x) ≈ b1(y)c i + b2(y) + n(x), where x and y are the pixel grayscales in the observed image and the bias field respectively. For the pixels in a two-dimensional image, consider a circular neighborhood centered on it with a radius of ρ, and formulate a fitting term for the two-dimensional image data according to the clustering attributes of the grayscales within the image neighborhood:

[0010]

[0011] In the formula, K(s) is a Gaussian truncation function, and its calculation formula is:

[0012]

[0013] where a is a normalization constant and σ is the standard deviation of the Gaussian function.

[0014] Step 2: Embed two level set functions with opposite signs in the above data fitting term to guide the movement of the contour curve and construct a level set energy functional. When dealing with two-dimensional image data, the following method is adopted:

[0015] (1) Set as the level set function, define two non-overlapping regions Ω1 = {x: φ(x) > 0} and Ω2 = {x: φ(x) < 0} using level set functions with opposite signs, and set that Ω1 and Ω2 are represented by membership functions M1(φ) = H(φ) and M2(φ) = 1 - H(φ) respectively. Here, H is the Heaviside function, which is defined as:

[0016]

[0017] where ζ takes 1, and the derivative δ(x) of H(x) is defined as:

[0018]

[0019] (2) Introduce the level set function in formula (1) and exchange the integration order. The calculation formula for the level set energy functional is:

[0020]

[0021] (3) Set that φ, c, b1, and b2 are all variables of ε, and rewrite ε as where e i is set as:

[0022] ei (x) = ∫K(y - x)|I(x) - b1(y)c i - b2(y)| 2 dy (6),

[0023] e i It is calculated by the following formula:

[0024]

[0025] where * is the convolution operator, 1 K = ∫K(y - x)dy, and this function is equal to the constant 1 everywhere except near the boundary of Ω.

[0026] Step 3: Establish the total variation level set equation, embed the above level set energy functional into it, and define the constraint terms for the multiplicative bias field and the additive bias field respectively. When dealing with two-dimensional image data, the following method is adopted:

[0027] (1) Set the length regularization term and the distance regularization term of the level set function as The specific definitions are as follows:

[0028]

[0029]

[0030] where Calculate the arc length of the zero level set contour to ensure the smoothness of the contour curve, The role of is to keep the level set function stable during evolution, where

[0031] (2) Set the constraint term for constraining b1 outside the target object Its role is to keep b1 approximately equal to the constant 1 outside the target object. The specific definition is as follows:

[0032]

[0033] (3) Set the constraint term for constraining b2 outside the target object Its role is to make the additive bias field b2 equal to the observed image I in the background. The specific definition is as follows:

[0034]

[0035] (4) Establish the total variation level set equation as:

[0036]

[0037] where ν, μ, λ1, λ2 are weight coefficients.

[0038] Step 4: Fix each variable respectively, and use the gradient descent method to minimize and solve the total variation level set equation to obtain each iteration term. When processing two-dimensional image data, the following method is adopted:

[0039] (1) Fix c, b1, and b2 in formula (12), and use the gradient descent method to obtain the minimization equation of φ:

[0040]

[0041] where div(·) is the divergence symbol, and the function d p is defined as

[0042] (2) Fix φ, b1, and b2, and use the gradient descent method to obtain the optimal constant estimates and

[0043]

[0044]

[0045] where u i (y) = M i (φ(y));

[0046] (3) Fix φ and c, and use the gradient descent method to obtain the optimal bias field estimates and

[0047]

[0048]

[0049] Step 5: Use the finite difference method and the continuation strategy of the increasing sequence to perform cross-iteration numerical solution on each iteration term to achieve image segmentation. When processing two-dimensional image data, the following method is adopted:

[0050] (1) Numerically discretize formula (13) using the finite difference method, and the calculation formula is:

[0051]

[0052] where △t is the time step and m is the number of iterations;

[0053] (2) Adopt the cross-iteration method and the continuation strategy of the increasing sequence to numerically solve each variable to achieve image segmentation. The specific steps are as follows:

[0054] 1) Initialize φ, b1, and b2, and set λ 2max ;

[0055] 2) Calculate λ2. If λ2 < λ, 2max continue to the next step; otherwise, exit the loop. The latest φ obtained is the segmentation result of the two-dimensional image data.

[0056] 3) Calculate and update and

[0057] 4) Calculate and update φ according to Equation (18);

[0058] 5) Calculate and update and

[0059] 6) Return to step 2).

[0060] The above-described multiplicative-additive model level set image segmentation method mainly describes the technical solution for processing two-dimensional image data. It should be noted that the above method can be extended to the segmentation of three-dimensional image data. When processing three-dimensional image data, the two-dimensional objects involved in the above method are replaced or extended to three-dimensional objects, and for the sake of consistency in method description, the three-dimensional objects are not marked with additional symbols. The specific method is as follows:

[0061] (1) The multiplicative-additive model is still expressed as I(x) ≈ b1(y)c i + b2(y) + n(x), where x and y are the pixel grayscales in the three-dimensional observed image and the three-dimensional bias field respectively. For the pixels in the three-dimensional image, considering a spherical neighborhood with a radius of ρ centered on it, according to the clustering property of the grayscales within the image neighborhood, the fitting term for the three-dimensional image data is formulated as:

[0062]

[0063] (2) Embed two level set functions with opposite signs in the fitting term of the three-dimensional image data, and at the same time impose the length regularization term and the distance regularization term of the level set function. Additionally, considering that the information of the three-dimensional image data is more sufficient and reliable, no constraint is set on the bias field, thus forming the total variation level set equation as:

[0064]

[0065] (3) Use the gradient descent method to minimize and solve each variable of the total variation level set equation. The calculation formula is:

[0066]

[0067]

[0068]

[0069]

[0070]

[0071] (4) Solve Equation (21) using the finite difference method, and the calculation formula is:

[0072]

[0073] (5) Numerically solve each variable using the cross-iteration method to achieve three-dimensional image data segmentation. The specific steps are as follows:

[0074] 1) Initialize φ, b1, and b2, and set the maximum number of iterations m max ;

[0075] 2) When the number of iterations m < m max continue to execute the next step, otherwise exit the loop, and the latest φ obtained is the segmentation result of the three-dimensional image data;

[0076] 3) Calculate and update and

[0077] 4) Calculate and update φ according to Equation (26);

[0078] 5) Calculate and update and

[0079] 6) Increment the number of iterations m by 1, and return to step 2).

[0080] The beneficial effects of the present invention are as follows: The multiplicative-additive model provided by the present invention can more accurately characterize the physical properties of images compared with other image models. Moreover, imposing reasonable constraints on the multiplicative bias field and the additive bias field respectively can ensure the stability of the segmentation algorithm, and can more completely extract the target contour for the segmentation of images with uneven gray levels. It has outstanding accuracy, reliability, and versatility in the segmentation applications of natural images, medical images, and industrial images. In addition, when applying the multiplicative-additive model level set segmentation method to three-dimensional image data, the continuity between adjacent images can be effectively utilized, the robustness to image noise and uneven gray levels can be enhanced, and the segmentation accuracy and reliability of three-dimensional image data can be improved.

[0081] The following further describes the present invention with reference to the accompanying drawings and embodiments. Description of the Drawings

[0082] Attached Figure 1 is a flow chart of the multiplicative-additive model level set segmentation method. Detailed Embodiments

[0083] Example 1: The multiplicative-additive model level set segmentation method is used to process two-dimensional image data. The specific data is a CT two-dimensional image I with a resolution of 400×400 and 256 gray levels. In this example, the length regularization term coefficient ν of the level set function is 0.001×255×255, the distance regularization term coefficient μ is 1.5, The coefficient is taken as λ1 = 512, λ 2max = 4, The initial value of the coefficient is taken as and where m is the number of iterations, the standard deviation σ of the Gaussian function is 10, the time step Δt is 0.1, and ζ = 1.0. The following steps are performed according to this information:

[0084] Step 1: Define the multiplicative-additive model as I = b1J + b2 + n, where I is the observed image, b1 and b2 are the multiplicative bias field and additive bias field of gray level inhomogeneity respectively, J is the true image, and n is the additive noise. According to this model, construct an image gray data fitting term by the following method:

[0085] (1) Assume that the true image J takes two different constant values c1 and c2 in two non-overlapping regions Ω1 and Ω2 respectively;

[0086] (2) Set the constants c1 and c2 as the vector c = (c1, c2), and rewrite the multiplicative-additive model as I(x) ≈ b1(y)c i + b2(y) + n(x), where x and y are the pixel gray levels in the observed image and the bias field respectively. For the pixels in the two-dimensional image, consider a circular neighborhood with radius ρ centered on it, and formulate the fitting term of the two-dimensional image data according to the clustering attribute of the gray level in the image neighborhood:

[0087]

[0088] In the formula, K(s) is the Gaussian truncation function, and the calculation formula is:

[0089]

[0090] where a is the normalization constant.

[0091] Step 2: Embed two level set functions with opposite signs in the above data fitting term, and construct a level set energy functional by the following method:

[0092] (1) Set Let \(\varphi\) be the level set function. Two non - overlapping regions \(\Omega_1=\{x:\varphi(x)>0\}\) and \(\Omega_2 = \{x:\varphi(x)<0\}\) are defined by level set functions with opposite signs. Suppose \(\Omega_1\) and \(\Omega_2\) are represented by membership functions \(M_1(\varphi)=H(\varphi)\) and \(M_2(\varphi)=1 - H(\varphi)\) respectively, where \(H\) is the Heaviside function, defined as:

[0093]

[0094] The derivative \(\delta(x)\) of \(H(x)\) is defined as:

[0095]

[0096] (2) Introduce the level set function into equation (1) and exchange the order of integration. The calculation formula for the level set energy functional is:

[0097]

[0098] (3) Suppose \(\varphi\), \(c\), \(b_1\) and \(b_2\) are all variables of \(\varepsilon\). Rewrite \(\varepsilon\) as where \(e\) i is set as:

[0099] e i (x)=\(\int K(y - x)|I(x)-b_1(y)c\) i -b_2(y)| 2 dy (6),

[0100] e i is calculated by the following formula:

[0101]

[0102] where \(*\) is the convolution operator, \(1\) K =\(\int K(y - x)dy\), and this function is equal to the constant \(1\) everywhere except near the boundary of \(\Omega\).

[0103] Step 3: Set up the total variation level set equation, embed the above - mentioned level set energy functional into it, and define constraint terms for the multiplicative bias field and the additive bias field respectively. The following method is adopted:

[0104] (1) Suppose the length regularization term and the distance regularization term of the level set function are respectively Specifically defined as follows:

[0105]

[0106]

[0107] where

[0108] (2) Set the constraint terms for constraining b1 outside the target object The specific definitions are as follows:

[0109]

[0110] (3) Set the constraint terms for constraining b2 outside the target object The specific definitions are as follows:

[0111]

[0112] (4) Establish the total variation level set equation as:

[0113]

[0114] where ν, μ, λ1, and λ2 are weight coefficients.

[0115] Step 4: Fix each variable separately and use the gradient descent method to minimize and solve the total variation level set equation to obtain each iteration term. The following method is used:

[0116] (1) Fix c, b1, and b2 in Equation (12), and use the gradient descent method to obtain the minimization solution equation for φ:

[0117]

[0118] where div(·) is the divergence symbol, and the function d p is defined as

[0119] (2) Fix φ, b1, and b2, and use the gradient descent method to obtain the optimal constant estimation values and

[0120]

[0121]

[0122] Here, u i (y) = M i (φ(y));

[0123] (3) Fix φ and c, and use the gradient descent method to obtain the optimal bias field estimation values and

[0124]

[0125]

[0126] Step 5: Use the finite difference method and the continuation strategy of the increasing sequence to perform cross-iteration numerical solution on each iteration term to achieve image segmentation, and the following method is adopted:

[0127] (1) Numerically discretize Equation (13) using the finite difference method, and the calculation formula is:

[0128]

[0129] where △t is the time step and m is the number of iterations;

[0130] (2) Adopt the cross-iteration method and the continuation strategy of the increasing sequence to perform numerical solution on each variable to achieve image segmentation. The specific steps are as follows:

[0131] 1) Initialize φ, b1, and b2, and set λ 2max ;

[0132] 2) Calculate λ2. When λ2 < λ 2max continue to execute the next step, otherwise exit the loop, and the latest φ obtained is the segmentation result of the two-dimensional image data;

[0133] 3) Calculate and update and

[0134] 4) Calculate and update φ according to Equation (18);

[0135] 5) Calculate and update and

[0136] 6) Return to step 2).

[0137] Example 2: Use the multiplicative-additive model level set segmentation method to process three-dimensional image data. The specific data is: a cone-beam CT three-dimensional image I with a size of 400×400×100 and a gray level of 256. In this example, the length regularization term coefficient ν of the level set function is 0.001×255×255, the regularization term coefficient μ is 1.5, the standard deviation σ of the Gaussian function is 10, the time step △t is 0.1, the maximum number of iterations m max = 50, and ζ = 1.0. Perform the following steps according to this information:

[0138] Step 1: The multiplicative-additive model is still expressed as I(x)≈b1(y)c i +b2(y)+n(x), where x and y are the pixel grayscales in the three-dimensional observed image and the three-dimensional bias field respectively. For the pixels in the three-dimensional image, consider a spherical neighborhood with a radius of ρ centered on it, and formulate the fitting term of the three-dimensional image data according to the clustering attribute of the grayscales in the image neighborhood:

[0139]

[0140] Step 2: Embed two level set functions with opposite signs in the fitting terms of the 3D image data. At the same time, impose the length regularization term and the distance regularization term of the level set function. Additionally, considering that the information of the 3D image data is more sufficient and reliable, no constraint is set on the bias field, thus forming the total variation level set equation as follows:

[0141]

[0142] Step 3: Use the gradient descent method to minimize and solve each variable of the total variation level set equation. The calculation formula is:

[0143]

[0144]

[0145]

[0146]

[0147]

[0148] Step 4: Use the finite difference method to solve Equation (21). The calculation formula is:

[0149]

[0150] Step 5: Use the cross-iteration method to numerically solve each variable to achieve the segmentation of the 3D image data. The specific steps are as follows:

[0151] (1) Initialize φ, b1, and b2, and set the maximum number of iterations m max ;

[0152] (2) When the number of iterations m < m max , continue to execute the next step; otherwise, exit the loop. The latest φ obtained is the segmentation result of the 3D image data;

[0153] (3) Calculate and update and

[0154] (4) Calculate and update φ according to Equation (26);

[0155] (5) Calculate and update and

[0156] (6) The iteration number m + 1, return to step 2).

Claims

1. A multiplicative-additive model level set image segmentation method, characterized in that It includes the following steps: Step 1: Define the multiplicative-additive model as I = b1J + b2 + n, where I is the observed image, b1 and b2 are the multiplicative bias field and additive bias field of gray-scale inhomogeneity respectively, J is the true image, and n is the additive noise. This model represents the gray-scale inhomogeneity property of the image with two bias fields of different natures, and constructs an image gray-scale data fitting term according to this model. Step 2: Embed two level set functions with opposite signs in the above data fitting term to guide the movement of the contour curve, and construct a level set energy functional. Step 3: Establish a total variation level set equation, embed the above level set energy functional into it, and define constraint terms for the multiplicative bias field and additive bias field respectively. Step 4: Fix each variable respectively, and use the gradient descent method to minimize and solve the total variation level set equation to obtain each iteration term. Step 5: Use the finite difference method and the continuation strategy of the increasing sequence to perform cross-iteration numerical solution for each iteration term to achieve image segmentation.

2. The multiplicative-additive model level set image segmentation method according to claim 1, wherein, In Step 1, an image gray-scale fitting term is established according to the multiplicative-additive model. When processing two-dimensional image data, the following method is adopted: (1) Suppose the real image J is in non - overlapping regions Ω1, …, Ω N Take N different constants c1, …, c respectively N ; (2) Set constants c1, …, c N as vector c = (c1, …, c N ), rewrite the multiplicative-additive model as I(x) ≈ b1(y)c i + b2(y) + n(x), where x and y are the pixel grayscales in the observed image and the bias field respectively. For the pixels in a two-dimensional image, consider a circular neighborhood centered on it with a radius of ρ, and formulate a fitting term for the two-dimensional image data according to the clustering attributes of the grayscales within the image neighborhood: In the formula, K(s) is a Gaussian truncation function, and its calculation formula is: where a is the normalization constant and σ is the standard deviation of the Gaussian function.

3. A multiplicative-additive model level set image segmentation method according to claim 1, characterized in that In Step 2, two level set functions with opposite signs are embedded in the data fitting term, and a level set energy functional is constructed. When processing two-dimensional image data, the following method is adopted: (1) Set φ: Ω → R as the level set function, and define two non-overlapping regions Ω1 = {x: φ(x) > 0} and Ω2 = {x: φ(x) < 0} with level set functions of opposite signs. Set Ω1 and Ω2 are represented by membership functions M1(φ) = H(φ) and M2(φ) = 1 - H(φ) respectively, where H is the Heaviside function, and is defined as: where ζ takes 1, and the derivative δ(x) of H(x) is defined as: (2) Introduce the level set function in formula (1) and exchange the integration order. The calculation formula of the level set energy functional is: (3) Assume that φ, c, b1, and b2 are all variables of ε, and rewrite ε as where e i is set to: e i (x) = ∫K(y - x)|I(x) - b1(y)c i -b2(y| 2 dy (6) e i It is calculated by the following formula: where * is the convolution operator, 1 K = ∫K(y - x)dy, and this function is equal to the constant 1 everywhere except near the boundary of Ω.

4. A multiplicative-additive model level set image segmentation method according to claim 1, wherein In Step 3, a total variation level set equation is established. When processing two-dimensional image data, the following method is adopted: (1) Set the length regularization term and the distance regularization term of the level set function as The specific definitions are as follows: In formula (9) (2) Set the constraint item that constrains b1 outside the target object The specific definition is as follows: (3) Set a constraint term for constraining b2 outside the target object The specific definition is as follows: (4) Establish the total variation level set equation as: where ν, μ, λ1, and λ2 are weight coefficients.

5. A multiplicative-additive model level set image segmentation method according to claim 1, characterized in that In Step 4, the gradient descent method is used to minimize and solve the total variation level set equation to obtain each iteration term. When processing two-dimensional image data, the following method is adopted: (1) Fix c, b1, and b2 in formula (12), and use the gradient descent method to obtain the minimization solution equation of φ: where div(·) is the divergence symbol, and the function d p is defined as (2) Fix φ, b1, and b2, and use the gradient descent method to obtain the optimal constant estimate value and Here, u i (y) = M i (φ(y)); (3) Fix φ and c, and use the gradient descent method to obtain the optimal bias field estimate value and 6. The multiplicative-additive model level set image segmentation method according to claim 1, characterized in that In Step 5, the finite difference method and the continuation strategy of the increasing sequence are used to perform cross-iteration numerical solution for each variable. When processing two-dimensional image data, the following method is adopted: (1) Numerically discretize formula (13) using the finite difference method. The calculation formula is: where △t is the time step and m is the number of iterations; (2) Use the cross-iteration method and the continuation strategy of the increasing sequence to perform numerical solution for each variable to achieve image segmentation. The specific steps are as follows: 1) Initialize φ, b1, and b2, and set λ 2max ; 2) Calculate λ2. When λ2 < λ 2max continue with the next step, otherwise exit the loop. The latest φ obtained is the segmentation result of the two-dimensional image data; 3) Calculate and update according to Equation (14) and Equation (15) and 4) Calculate and update φ according to formula (18); 5) Calculate and update according to Formula (16) and Formula (17) and 6) Return to Step 2).

7. A multiplicative-additive model level set image segmentation method according to any one of claims 1 to 6, characterized in that, The method can be extended and applied to 3D image data segmentation. When processing 3D image data, the 2D objects involved in the method are replaced or extended to 3D objects. To maintain the consistency of the method description, no other symbols are used to label the 3D objects. The specific method is as follows: (1) The multiplicative-additive model is still expressed as I(x)≈b1(y)c i +b2(y)+n(x), where x and y are the pixel grayscales in the three-dimensional observed image and the three-dimensional bias field respectively. For the pixels in the three-dimensional image, a spherical neighborhood with a radius of ρ centered on it is considered. According to the clustering property of the grayscales within the image neighborhood, the fitting term for the three-dimensional image data is formulated as follows: (2) Embed two level set functions with opposite signs in the fitting term of the 3D image data, and at the same time impose the length regularization term and the distance regularization term of the level set function. In addition, considering that the information of the 3D image data is more sufficient and reliable, no constraint is set on the bias field, thus forming the total variation level set equation as: (3) Use the gradient descent method to sequentially minimize and solve each variable of the total variation level set equation. The calculation formula is: (4) Use the finite difference method to numerically discretize Equation (21). The calculation formula is: (5) Use the cross-iteration method to numerically solve each variable to achieve 3D image data segmentation. The specific steps are as follows: 1) Initialize φ, b1, and b2, and set the maximum number of iterations m max ; 2) Continue to execute the next step when the number of iterations m < m max , otherwise exit the loop, and the latest φ obtained is the segmentation result of the three-dimensional image data; 3) Calculate and update according to Equation (22) and Equation (23) and 4) Calculate and update φ according to Equation (26); 5) Calculate and update according to Formula (24) and Formula (25) and 6) Increment the iteration number m by 1, and return to step 2).

Images