CT image segmentation method based on new threshold formula and adaptive double potential well function

Abstract

The present invention relates to a CT image segmentation method based on a new threshold formula and an adaptive double potential well function, and belongs to the field of image processing. The present invention is divided into two parts: coarse segmentation and fine segmentation. The regional growth model is used as the coarse segmentation, and a threshold formula based on the mean absolute deviation is proposed. The formula can automatically generate a reasonable threshold according to the image features, and can process images with uneven grayscale or low contrast; the LRCV model is used as the fine segmentation, and an adaptive double potential well function is proposed, which dynamically adjusts the coefficient to increase the diffusion rate in the initial stage of segmentation, reduce the diffusion rate in the later stage, and reduce the diffusion rate near the zero potential well, so that the possibility of the zero level set invading the interior of the segmented target is reduced, thereby improving the segmentation accuracy. The problem of initial contour sensitivity of the LRCV model is effectively solved. For CT images with uneven grayscale or low contrast, it has more accurate segmentation results than the traditional active contour model.

Description

Technical Field

[0001] The invention belongs to the field of image processing and relates to a CT image segmentation method based on a novel threshold formula and an adaptive double potential well function. Background Art

[0002] Computed Tomography (CT) obtains projection data by scanning an object with rays, and uses the data to reconstruct a cross-sectional image of the object. Image segmentation is to divide an image into several non-overlapping regions with their own characteristics, and extract and separate the target region of interest based on certain characteristics of the image in these regions. Image segmentation is a key step from image processing to image analysis and understanding. Whether the target of interest can be accurately and efficiently extracted from CT images is crucial for subsequent processing (such as defect detection, dimensional measurement, and reverse manufacturing). Therefore, it is of great practical significance to study how to improve the accuracy of image segmentation.

[0003] In the prior art, the Chan-Vese (CV) model proposed by Chan and Vese is a classic active contour model. The CV model has the advantages of fast segmentation speed and insensitivity to initial contours, but the effect of segmenting images with uneven grayscale is poor. In 2008, Li and Kao et al. proposed an active contour model driven by Region Scalable Fitting (RSF) energy. The RSF model can effectively segment images with uneven grayscale, but the initial contour is relatively sensitive, and four convolution operations need to be performed in each iteration, so the RSF model requires a long segmentation time. In 2010, Li and Xu et al. proposed a distance-preserving level set evolution (DRLSE) model. The DRLSE model uses a penalty term based on a double potential well function to avoid periodic initialization of the level set function and greatly improve the level set evolution speed. However, the evolution speed of its double potential well function reaches the maximum at the zero potential well, which makes the level set evolve rapidly, causing the zero level set to invade the inside of the segmented target, which may eventually lead to the DRLSE model segmentation being not ideal. In 2012, Liu and Peng proposed the Local Region Chan-Vese (LRCV) model. The LRCV model can effectively segment images with uneven grayscale, and only needs to perform two convolution operations in each iteration, so the segmentation speed is slightly faster than the RSF model. However, since it only considers local features, the initial contour is more sensitive, which leads to reduced segmentation accuracy.

[0004] Therefore, in order to improve the segmentation accuracy of the LRCV model for CT images, the present invention proposes a CT image segmentation method based on a new threshold formula and an adaptive double potential well function. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a CT image segmentation method based on a new threshold formula and an adaptive double potential well function. Combining region growing and active contour, the invention is divided into two parts: coarse segmentation and fine segmentation. The region growing model is used as the coarse segmentation, and the LRCV model is used as the fine segmentation, which effectively solves the problem that LRCV is sensitive to the initial contour, thereby improving the segmentation accuracy of the LRCV model for CT images.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A CT image segmentation method based on a novel threshold formula and an adaptive double potential well function comprises the following steps:

[0008] S1: Calculate image statistics and thresholds;

[0009] S2: determine the seed point and growth criteria;

[0010] S3: Use breadth-first search to traverse;

[0011] S4: Use the result of region growing as the initial outline;

[0012] S5: Solve the Euler-Lagrange equation corresponding to the energy functional to obtain the level set function evolution equation;

[0013] S6: Level set function iteration using finite difference method;

[0014] S7: Output the segmentation result.

[0015] Optionally, the S1 specifically comprises the following steps:

[0016] S11: Calculate the image grayscale mean, standard deviation and mean absolute deviation:

[0017]

[0018] Among them I avr Represents the grayscale mean of the image, I std Represents the grayscale standard deviation of the image, I MD Represents the grayscale mean absolute deviation of the image, R represents the number of rows of the matrix corresponding to the image, C represents the number of columns of the matrix corresponding to the image, (x, y) represents the pixel coordinates, and I(x, y) represents the grayscale value of the pixel at the coordinate (x, y);

[0019] S12: Calculate the corresponding threshold. The proposed threshold formula is as follows:

[0020]

[0021] Where T 1 Indicates the threshold used for grayscale uneven images, T 2 Indicates the threshold used for low contrast images.

[0022] Optionally, S2 specifically includes the following steps:

[0023] S21: taking the pixel whose gray value is greater than or equal to the maximum value multiplied by 0.9 as the seed point;

[0024] S22: Determine a growth criterion, the growth criterion is determined as follows:

[0025]

[0026] Where Q 1 represents the growth criterion used for the grayscale uneven image, Q 2 Indicates the growth criterion used for low-contrast images. TRUE indicates that the coordinates in the image at (x n ,y n ) points are added to the seed area, FALSE means not to add, I(x n ,y n ) represents the grayscale value of the pixel adjacent to I(x,y).

[0027] Optionally, S5 specifically includes the following steps:

[0028] S51: Add a penalty regularization term to the energy functional. The penalty regularization term R p for:

[0029]

[0030] Where μ is the penalty coefficient, is the modulus of the level set function gradient, denoted as s, and p is the double potential well function;

[0031] S52: The original potential well function is changed to the adaptive double potential well function proposed in the present invention. The adaptive double potential well function and the diffusion rate function are as follows:

[0032]

[0033]

[0034] Where s represents the modulus of the level set function gradient, K(i) represents the adaptive coefficient, which is defined as follows:

[0035]

[0036] Where α represents the diffusion coefficient, which controls the range of the diffusion rate, i is the current iteration number, and imax is the maximum number of iterations;

[0037] S53: Use the gradient descent method to obtain the level set function evolution equation:

[0038]

[0039] where c 1 and c 2 Respectively represent the local grayscale mean of the internal and external images of the evolution curve, K σ represents the Gaussian kernel function with standard deviation σ, I(y) is the gray value of the points in the neighborhood of point x, is the level set function, M i is the membership function, a is the regularization constant, r is the radius of the neighborhood of point x, H ε is the regularized form of the Heaviside function, δ ε is the regularized form of the one-dimensional Dirac measure, ε is a positive constant, For function The gradient of , div(·) represents the divergence operator, μ, ν, λ 1 ,λ 2 is the weight coefficient of each item.

[0040] Optionally, the S6 specifically comprises the following steps:

[0041] S61: Using the finite difference method for the gradient descent flow of the energy function, the discrete iterative format is as follows:

[0042]

[0043] Where n is the number of iterations, Δt is the time step, is the level set function;

[0044] S62: Select the maximum number of iterations i max , until convergence.

[0045] The beneficial effects of the present invention are:

[0046] The present invention is divided into two parts: coarse segmentation and fine segmentation. The regional growth model is used as the coarse segmentation, and a threshold formula based on the mean absolute deviation is proposed. The formula can automatically generate a reasonable threshold according to the image features, and can process images with uneven grayscale or low contrast; the LRCV model is used as the fine segmentation, and an adaptive double potential well function is proposed, which dynamically adjusts the coefficients to increase the diffusion rate in the initial stage of segmentation, reduce the diffusion rate in the later stage, and reduce the diffusion rate near the zero potential well, so that the possibility of the zero level set invading the interior of the segmented target is reduced, thereby improving the segmentation accuracy. The problem of initial contour sensitivity of the LRCV model is effectively solved. For CT images with uneven grayscale or low contrast, it has more accurate segmentation results than the traditional active contour model.

[0047] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0049] Figure 1 is the graph of the diffusion rate function of the classic double potential well function;

[0050] Figure 2 It is the diffusion rate function image of the adaptive double potential well function proposed by the present invention;

[0051] Figure 3 The present invention is a flow chart of the CT image segmentation method based on a novel threshold formula and an adaptive double potential well function. DETAILED DESCRIPTION

[0052] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0053] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0054] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0055] Figure 1 It is a classic double potential well function, but the evolution speed of the double potential well function near the zero potential well is close to 1, reaching the maximum value of the evolution speed, causing the level set to evolve rapidly forward, resulting in the zero level set invading the interior of the segmented target, and ultimately leading to segmentation failure.

[0056] Figure 2 The image of the adaptive double potential well diffusion rate function of the present invention reduces the evolution rate of the zero potential well compared with the classical model, so that the possibility of the zero level set invading the interior of the segmented target is reduced, thereby improving the segmentation accuracy. Then, an adaptive coefficient is added to increase the diffusion rate in the early stage of evolution to better utilize the global information; in the later stage of evolution, the diffusion rate is reduced to achieve more accurate segmentation.

[0057] The present invention discloses a CT image segmentation method based on a new threshold formula and an adaptive double potential well function. The present invention is divided into two steps: coarse segmentation and fine segmentation. For coarse segmentation: firstly, the image grayscale mean, standard deviation and mean absolute deviation are calculated, and then the corresponding threshold is calculated, and then the pixel points with grayscale values ​​greater than or equal to the maximum value multiplied by 0.9 are used as seed points, and then the growth law is determined, and the traversal is realized by using the breadth-first search algorithm. For fine segmentation: the result of the coarse segmentation is used as the initial contour of the level set, and then a penalty regularization term is added to the LRCV model. The potential well function adopts the adaptive double potential well function proposed by the present invention to construct an energy functional, and then the Euler-Lagrange equation corresponding to the energy functional is solved to obtain the level set function evolution equation, and then the finite difference method is used to iterate the level set function until the segmentation result is converged and output. The present invention effectively solves the problem that the LRCV model is sensitive to the initial contour. In CT images with uneven grayscale or low contrast, it has more accurate segmentation results than the traditional active contour model.

[0058] Figure 3 The flowchart of the CT image segmentation method based on the novel threshold formula and the adaptive double potential well function of the present invention comprises the following steps:

[0059] S1. Calculate image statistics and thresholds. Step S1 specifically includes the following sub-steps:

[0060] S11. Calculate the image grayscale mean, standard deviation and mean absolute deviation:

[0061]

[0062] Among them I avr Represents the grayscale mean of the image, I std Represents the grayscale standard deviation of the image, I MD Represents the grayscale mean absolute deviation of the image, R represents the number of rows of the matrix corresponding to the image, C represents the number of columns of the matrix corresponding to the image, (x, y) represents the pixel coordinates, and I(x, y) represents the grayscale value of the pixel at the coordinate (x, y);

[0063] S12. Calculate the corresponding threshold. The proposed threshold formula is as follows:

[0064]

[0065] Where T 1 Indicates the threshold used for grayscale uneven images, T 2 Indicates the threshold used for low-contrast images;

[0066] S2. Determine the seed point and growth criteria, the step S2 specifically comprises the following sub-steps:

[0067] S21. Taking the pixel whose gray value is greater than or equal to the maximum value multiplied by 0.9 as the seed point;

[0068] S22. Determine the growth criteria, the growth criteria are determined as follows:

[0069]

[0070] Where Q 1 represents the growth criterion used for the grayscale uneven image, Q 2 Indicates the growth criterion used for low-contrast images. TRUE indicates that the coordinates in the image at (x n ,y n ) points are added to the seed area, FALSE means not to add, I(x n ,y n ) represents the gray value of the pixel adjacent to I(x,y);

[0071] S3. Use breadth-first search to traverse;

[0072] S4. Using the result of region growing as the initial outline;

[0073] S5. Solve the Euler-Lagrange equation corresponding to the energy functional to obtain the level set function evolution equation, wherein step S5 specifically comprises the following sub-steps:

[0074] S51. Add a penalty regularization term to the energy functional. The penalty regularization term R p for:

[0075]

[0076] Where μ is the penalty coefficient, is the modulus of the level set function gradient, denoted as s, and p is the double potential well function;

[0077] S52. The original potential well function is changed to the adaptive double potential well function proposed in the present invention. The adaptive double potential well function and the diffusion rate function are as follows:

[0078]

[0079]

[0080] Where s represents the modulus of the level set function gradient, K(i) represents the adaptive coefficient, which is defined as follows:

[0081]

[0082] Where α represents the diffusion coefficient, which controls the range of the diffusion rate, i is the current iteration number, and i max is the maximum number of iterations;

[0083] S53. Using the gradient descent flow method, the level set function evolution equation is obtained:

[0084]

[0085] where c 1 and c 2 Respectively represent the local grayscale mean of the internal and external images of the evolution curve, K σ represents the Gaussian kernel function with standard deviation σ, I(y) is the gray value of the points in the neighborhood of point x, is the level set function, M i is the membership function, a is the regularization constant, r is the radius of the neighborhood of point x, H ε is the regularized form of the Heaviside function, δ ε is the regularized form of the one-dimensional Dirac measure, ε is a positive constant, For function The gradient of , div(·) represents the divergence operator, μ, ν, λ 1 ,λ 2 is the weight coefficient of each item;

[0086] S6. Performing level set function iteration using finite difference method, wherein step S6 specifically comprises the following sub-steps:

[0087] S61. Using the finite difference method for the gradient descent flow of the energy function, the discrete iterative format is as follows:

[0088]

[0089] Where n is the number of iterations, Δt is the time step, is the level set function;

[0090] S62. Select the maximum number of iterations i max , until convergence;

[0091] S7. Output the segmentation result.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A CT image segmentation method based on a novel threshold formula and an adaptive double potential well function, characterized in that: The method comprises the following steps: S1: Calculate image statistics and thresholds; S2: determine the seed point and growth criteria; S3: Use breadth-first search to traverse; S4: Use the result of region growing as the initial outline; S5: Solve the Euler-Lagrange equation corresponding to the energy functional to obtain the level set function evolution equation; S6: Level set function iteration using finite difference method; S7: Output segmentation result; The S1 specifically comprises the following steps: S11: Calculate the image grayscale mean, standard deviation and mean absolute deviation: Among them I avr Represents the grayscale mean of the image, I std Represents the grayscale standard deviation of the image, I MD Represents the grayscale mean absolute deviation of the image, R represents the number of rows of the matrix corresponding to the image, C represents the number of columns of the matrix corresponding to the image, (x, y) represents the pixel coordinates, and I(x, y) represents the grayscale value of the pixel at the coordinate (x, y); S12: Calculate the corresponding threshold. The proposed threshold formula is as follows: Where T1 represents the threshold used for grayscale uneven images, and T2 represents the threshold used for low-contrast images; The S2 specifically comprises the following steps: S21: taking the pixel whose gray value is greater than or equal to the maximum value multiplied by 0.9 as the seed point; S22: Determine a growth criterion, the growth criterion is determined as follows: Where Q1 represents the growth criterion used for grayscale uneven images, Q2 represents the growth criterion used for low-contrast images, and TRUE represents the growth criterion used for the image with coordinates at (x n ,y n ) points are added to the seed area, FALSE means not to add, I(x n ,y n ) represents the gray value of the pixel adjacent to I(x,y); The S5 specifically comprises the following steps: S51: Add a penalty regularization term to the energy functional. The penalty regularization term R p for: Where μ is the penalty coefficient, is the modulus of the level set function gradient, denoted as s, and p is the double potential well function; S52: The double potential well function is changed to an adaptive double potential well function. The adaptive double potential well function and the diffusion rate function are as follows: Where s represents the modulus of the level set function gradient, K(i) represents the adaptive coefficient, which is defined as follows: Where α represents the diffusion coefficient, which controls the range of the diffusion rate, i is the current iteration number, and i max is the maximum number of iterations; S53: Use the gradient descent method to obtain the level set function evolution equation: Where c1(x, y) and c2(x, y) represent the local grayscale mean of the internal and external images of the evolution curve, respectively, and K σ represents the Gaussian kernel function with standard deviation σ, I(x,y) represents the grayscale value of the pixel at the coordinate (x,y), is the level set function, M i is the membership function, a is the regularization constant, r represents the neighborhood radius of the point at (x, y), H ε is the regularized form of the Heaviside function, δ ε is the regularized form of the one-dimensional Dirac measure, ε is a positive constant, For function The gradient of , div(·) represents the divergence operator, μ, ν, λ1, λ2 are the weight coefficients of each item; The S6 specifically comprises the following steps: S61: Using the finite difference method for the gradient descent flow of the energy function, the discrete iterative format is as follows: Where n is the number of iterations, Δt is the time step, is the evolution equation of the level set function; S62: Select the maximum number of iterations i max , until convergence.

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