CN111462145B - Active contour image segmentation method based on double-weight symbol pressure function - Google Patents

Abstract

The invention discloses a method for segmenting an active contour image based on a double-weight sign pressure function, comprising the following steps: step S1, inputting the original image to be segmented, initializing the parameters of the active contour model and setting the initial contour; step S2, calculating The global grayscale term and the Legendre polynomial are used to obtain the symbolic pressure function based on double weights; the edge stop function g(|▽I|) is calculated; step S3 is to use the gradient descent algorithm to solve the energy function of the active contour model to obtain the corresponding The gradient flow equation is used to iterate the segmentation curve to obtain the level set function at the new moment; step S4, perform binarization penalty and regularization processing of Gaussian filtering on the level set function at the new moment; step S5, judge whether the curve continues to iterate, If the convergence condition is satisfied, the iteration is stopped and the image segmentation is completed; if the convergence condition is not satisfied, step S2 is executed for the next iteration.

Description

Active contour image segmentation method based on dual-weighted signed pressure function

Technical Field

The invention relates to the field of image segmentation, and in particular to an active contour image segmentation method based on a dual-weighted signed pressure function.

Background Art

Image segmentation plays an important role in image processing, machine learning, computer vision and other fields. Image segmentation technology based on active contour model (ACM) currently occupies a very important position. It is currently widely used in medical images, radar images, synthetic image segmentation and other related fields, and has broad application prospects and application value. Medical images have a variety of image modalities, such as MR, CT, PET, ultrasound imaging, etc. Various images can obtain physiological and physical characteristics of the human body in two-dimensional and three-dimensional regions. When image segmentation technology based on active contour model is applied to the field of medical images, it can segment and extract characteristic areas in medical images, provide a reliable basis for subsequent clinical diagnosis and treatment and pathological research, and assist doctors in making more accurate diagnoses, such as the segmentation of coronary artery CT blood vessels shown in Figure 1, and the segmentation of cerebral hemorrhage CT images shown in Figure 2.

Existing ACMs can be classified into two types: edge-based active contour models and region-based active contour models. The edge-based active contour model uses the edge stop function defined by the image gradient modulus to stop the evolution curve at the edge of the image to be segmented. The region-based active contour model uses the statistical information inside and outside the contour line to control the evolution of the curve. In the image segmentation method based on the active contour model, complex situations such as uneven grayscale, noise, blurred edges, time-consuming calculations, and sensitivity to initial contours pose certain challenges to accurately and efficiently obtaining image segmentation results. Therefore, it is necessary to propose a more accurate and efficient method to ensure that a high segmentation accuracy can be maintained in various complex situations and that time consumption and calculation amount can be effectively controlled.

Summary of the invention

The purpose of the present invention is to overcome the problem of low real-time accuracy of image segmentation methods based on active contour models in the prior art, and to provide an active contour image segmentation method based on a dual-weighted signed pressure function, which improves the segmentation efficiency and accuracy when the image to be segmented has complex situations such as uneven grayscale, noise, and blurred edges.

In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions:

An active contour image segmentation method based on a dual-weighted signed pressure function comprises the following steps:

Step S1, inputting the acquired original image to be segmented; initializing the parameters of the active contour model and setting the initial contour;

Step S2, calculating the global grayscale term and Legendre polynomial to obtain a double-weighted signed pressure function; calculating the edge stop function g(|▽I|);

Step S3, using a gradient descent algorithm to numerically solve the energy function of the active contour model, obtain the corresponding gradient flow equation to iterate the segmentation curve, and obtain the level set function at a new moment;

Step S4, performing binarization penalty and Gaussian filtering regularization processing on the new moment level set function obtained in step S3;

Step S5, determining whether the curve continues to iterate, if the convergence condition is met, stopping the iteration and completing the image segmentation; if the convergence condition is not met, executing step S2 and performing the next iteration.

Preferably, the detailed steps of step S1 are as follows:

Input the original image and calculate the grayscale value of each pixel, denoted as I(x), where x is the pixel in the image domain Ω; initialize the parameters of the active contour model and set the initial contour.

Preferably, in step S2,

The symbolic pressure function based on dual weights is:

为勒让德项，

为全局灰度项，w₁为勒让德项在符号压力函数中所占的权重，w₂为全局灰度项在符号压力函数中所占的权重。Where I(x) is the gray value of the pixel in the image domain,

For Legendre,

is the global grayscale term, _w1 is the weight of the Legendre term in the signed pressure function, and _w2 is the weight of the global grayscale term in the signed pressure function.

Preferably, the calculation formulas of the Legendre term and the global grayscale term are as follows:

为轮廓线内部区域勒让德多项式系数向量的闭式解，

为轮廓线外部区域勒让德多项式系数向量的闭式解，c₁为轮廓线内部的平均灰度值，c₂为轮廓线外部的平均灰度值；上述4个变量c₁，c₂与

的计算公式如下所示：Where P(x) is the Legendre polynomial vector, and η is used to adjust the weights of the internal and external parts;

is the closed-form solution of the Legendre polynomial coefficient vector for the interior region of the contour,

is the closed-form solution of the Legendre polynomial coefficient vector outside the contour line, c ₁ is the average gray value inside the contour line, and c ₂ is the average gray value outside the contour line; the above four variables c ₁ , c ₂ and

The calculation formula is as follows:

Among them, n ₁ (x) = H _ε (φ (x)), n ₂ (x) = 1-H _ε (φ (x));

Where M represents the k×k identity matrix, K and L represent the k×k Grimm matrices, λ ₁ and λ ₂ are two constants with default values; ε is a preset parameter.

Preferably, the edge stop function is a monotonically decreasing non-negative function.

Preferably, the edge stop function is composed of fractional and exponential forms, and the calculation formula is as follows:

表示标准差为δ的高斯核函数G_δ与待分割图像I的卷积运算，

为梯度算子。Where x and y represent pixel points.

represents the convolution operation of the Gaussian kernel function G _δ with the image to be segmented I,

is the gradient operator.

Preferably, the numerical solution process of the energy function in step S3 is to first calculate the gradient flow equation and then perform numerical iteration operation on the gradient flow equation, and the gradient flow equation is as follows:

表示曲率。Among them, α, μ are preset constants, t is time,

Represents curvature.

Preferably, step S4 comprises the following steps:

Step S41, when the level set function φ ⁱ⁺¹ at the new moment is >0, φ ⁱ⁺¹ =1; when φ ⁱ⁺¹ ≤0, φ ⁱ⁺¹ =-1;

Step S42: Regularize the level set function φ ⁱ⁺¹ using Gaussian filtering, φ ⁱ⁺¹ = φ ⁱ⁺¹ *G _δ .

Preferably, the convergence condition of the numerical iteration operation in step S5 is:

的长度，i+1为迭代次数。Where Γ is the preset pixel number threshold, length(·) is used to calculate

The length of i+1 is the number of iterations.

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

(1) The Legendre term and the global grayscale term are integrated into the signed pressure function. The improved signed pressure function can adapt to more complex application environments and has good robustness to grayscale unevenness, noise, edge blur, multi-target images and different initial contours.

(2) A weight coefficient is used to control the influence of the Legendre term and the global grayscale term, and another weight coefficient is introduced to adjust the ratio coefficient between the inner and outer fitting centers of the contour line, so that the curve can better evolve and shrink into the interior of the region.

(3) A new edge stop function is proposed, which is incorporated into the gradient flow equation and introduces edge information. The edge information is combined with the regional information provided by the signed pressure function to drive the evolution of the contour line, so that the curve can better converge to the edge of the target and complete image segmentation.

Description of the drawings:

FIG1 is an example diagram of ACM used for segmentation of coronary CT vascular images;

FIG2 is an example diagram of ACM used for CT image segmentation of cerebral hemorrhage;

FIG3 is a flowchart 1 of an active contour image segmentation method based on a dual-weighted signed pressure function according to an exemplary embodiment 1 of the present invention;

FIG. 4 is a second flowchart of the active contour image segmentation method based on a dual-weighted signed pressure function according to exemplary embodiment 1 of the present invention.

DETAILED DESCRIPTION

The present invention is further described in detail below in conjunction with test examples and specific implementation methods. However, this should not be understood as the scope of the above subject matter of the present invention being limited to the following embodiments, and all technologies realized based on the content of the present invention belong to the scope of the present invention.

Example 1

As shown in FIG. 3 or FIG. 4 , this embodiment provides an active contour image segmentation method based on a dual-weighted signed pressure function, comprising the following steps:

Step S1, inputting the acquired original image to be segmented; initializing the parameters of the active contour model and setting the initial contour;

Step S2, calculating the global grayscale term and Legendre polynomial to obtain a double-weighted signed pressure function; calculating the edge stop function g(|▽I|);

Step S3, using a gradient descent algorithm to numerically solve the energy function of the active contour model, obtain the corresponding gradient flow equation to iterate the segmentation curve, and obtain the level set function at a new moment;

Step S4, performing binarization penalty and Gaussian filtering regularization processing on the new moment level set function obtained in step S3;

Step S5, determining whether the curve continues to iterate, if it meets the convergence condition, stopping the iteration and completing the image segmentation; if it does not meet the convergence condition, executing step S2 and performing the next iteration.

Active contour image segmentation methods are widely used in medical images, radar images, synthetic image segmentation and other related fields, so the collected original images can be medical images or radar images. Taking medical images as an example, the original images collected in this embodiment can be medical images of various image modalities (such as MR, CT, PET, ultrasound imaging, etc.), such as the coronary artery CT image shown in Figure 1 and the brain CT image shown in Figure 2. The active contour image segmentation method based on the dual-weighted signed pressure function described in this embodiment is used to extract the characteristic area of the medical image to achieve image segmentation, such as extracting the blood vessel part of the coronary artery CT image shown in Figure 1 and extracting the brain hemorrhage position of the brain CT image shown in Figure 2. In this embodiment, the Legendre term and the global grayscale term are integrated into the signed pressure function, so that the improved signed pressure function can adapt to more complex application environments and has good robustness to grayscale unevenness, noise, blurred edges, multi-target images and different initial contours.

Step S1, inputting the acquired original image to be segmented; initializing the parameters of the active contour model and setting the initial contour;

The detailed steps of step S1 are as follows:

Input the original image and calculate the grayscale value of each pixel, recorded as I(x), where x is the pixel in the image domain Ω, and in the original image I:Ω→R.

Initialize the parameters of the active contour model and set the initial contour. Initialize the parameters of the active contour model, including the signed pressure function, edge stop function, gradient flow equation, and preset parameter values in the convergence condition. The initial contour is an initialized contour curve. The energy of the initial contour is not necessarily the minimum, and the target contour edge needs to be obtained through iterative evolution. The target contour edge can extract the feature area in the image and realize image segmentation. The initial contour, the curve generated by the intermediate iterative process, and the final target contour can all be called active contours.

The zero level set function is set as:

Φ ⁰ = x:Φ(x) = 0

Where Φ is the level set function, and x is the pixel point in the image domain Ω to be segmented; the zero level set function Φ ⁰ divides the region Ω into two non-adjacent regions Ω ₁ ={x:Φ(x)>0} and Ω ₂ ={x:Φ(x)<0}, representing the foreground and background regions respectively.

Step S2, calculating the global grayscale term and Legendre polynomial to obtain a double-weighted signed pressure function; calculating the edge stop function g(|▽I|);

Wherein, the double-weighted sign pressure function is:

为勒让德项，

为全局灰度项，w₁为勒让德项在符号压力函数中所占的权重，w₂为全局灰度项在符号压力函数中所占的权重。将勒让德项以及全局灰度项融合到符号压力函数中，并分别使用一个权重系数来控制勒让德项以及全局灰度项的影响程度,引入另一个权重系数来调节轮廓线内部与外部拟合中心的比例系数，使曲线能够更好地演化收缩到区域内部。勒让德项占主导地位时有利于分割灰度不均匀图像，而全局灰度项占主导地位时有利于分割噪声图像。根据具体的图像特征调整勒让德项以及全局灰度项的权重，控制勒让德项以及全局灰度项的影响程度，使得改进后的符号压力函数能够适应更加复杂的应用环境，对灰度不均匀、噪声、边缘模糊、多目标图像以及不同的初始轮廓都有较好的鲁棒性。Where I(x) is the gray value of the pixel in the image domain,

For Legendre,

is the global grayscale term, _w1 is the weight of the Legendre term in the sign pressure function, and _w2 is the weight of the global grayscale term in the sign pressure function. The Legendre term and the global grayscale term are integrated into the sign pressure function, and a weight coefficient is used to control the influence of the Legendre term and the global grayscale term respectively. Another weight coefficient is introduced to adjust the ratio coefficient of the inner and outer fitting centers of the contour line, so that the curve can better evolve and shrink to the inside of the region. When the Legendre term is dominant, it is beneficial to segment grayscale uneven images, while when the global grayscale term is dominant, it is beneficial to segment noisy images. According to the specific image features, the weights of the Legendre term and the global grayscale term are adjusted to control the influence of the Legendre term and the global grayscale term, so that the improved sign pressure function can adapt to more complex application environments and has good robustness to grayscale unevenness, noise, edge blur, multi-target images and different initial contours.

The calculation formulas of the Legendre term and the global grayscale term are as follows:

为轮廓线内部区域(即为前景区域)勒让德多项式系数向量的闭式解，

为轮廓线外部区域(即为背景区域)勒让德多项式系数向量的闭式解，c₁为轮廓线内部的平均灰度值，c₂为轮廓线外部的平均灰度值，上述4个变量c₁，c₂与

的计算公式如下所示：Where P(x) is the Legendre polynomial vector, and η is used to adjust the weights of the internal and external parts;

is the closed-form solution of the Legendre polynomial coefficient vector in the inner area of the contour (i.e., the foreground area),

is the closed-form solution of the Legendre polynomial coefficient vector of the area outside the contour (i.e., the background area), c ₁ is the average grayscale value inside the contour, and c ₂ is the average grayscale value outside the contour. The above four variables c ₁ , c ₂ are related to

The calculation formula is as follows:

Among them, n ₁ (x) = H _ε (φ (x)), n ₂ (x) = 1-H _ε (φ (x));

Where M represents the k×k identity matrix, K and L represent the k×k Grimm matrices, λ ₁ and λ ₂ are two constants, and the default values are usually used; H _ε (φ) is the Hyatt function.

The calculation formula of H _ε (φ(x)) is as follows:

Where ε is one of the initial parameters in step S1.

和

在目标边缘有

趋于无穷大且

即背景区域与前景区域的差别较大，若活动轮廓划分的区域满足该条件，则认为已识别出待分割的区域，可以停止活动轮廓的演化。在基于区域信息的能量函数中引入一个边缘停止函数来约束曲率，将区域信息与边缘信息相结合，以停止活动轮廓的演化，进一步得到目标边缘轮廓。The edge stop function in step S2 can be any monotonically decreasing non-negative function.

and

At the edge of the target

tends to infinity and

That is, the difference between the background area and the foreground area is large. If the area divided by the active contour meets this condition, it is considered that the area to be segmented has been identified and the evolution of the active contour can be stopped. An edge stop function is introduced into the energy function based on region information to constrain the curvature, and the region information is combined with the edge information to stop the evolution of the active contour and further obtain the target edge contour.

Preferably, in order to robustly capture the edge of the target and speed up the segmentation of the multi-target image, two monotonically decreasing non-negative functions are introduced into the edge stop function g(|▽I|), which are respectively composed of fractional and exponential forms. The edge stop function is as follows:

表示标准差为δ的高斯核函数G_δ与待分割图像I的卷积运算，

为梯度算子。其中标准差δ，根据具体情况设定，本实施例中，该值为步骤S1中初始的参数之一。Where x and y represent pixel points, x is the center pixel point, and y is the pixel points around x's neighborhood;

represents the convolution operation of the Gaussian kernel function G _δ with the image to be segmented I,

is the gradient operator. The standard deviation δ is set according to the specific situation. In this embodiment, this value is one of the initial parameters in step S1.

This embodiment proposes a new edge stop function, incorporates the edge stop function into the gradient flow equation, and introduces edge information. The edge information is combined with the regional information provided by the signed pressure function to drive the evolution of the contour line, so that the curve can better converge to the edge of the target and complete image segmentation.

Step S3, using the gradient descent algorithm to numerically solve the energy function of the active contour model, obtain the corresponding gradient flow equation to iterate the segmentation curve, calculate the partial differential equation to obtain the new moment level set function φ ⁱ⁺¹ ; where i+1 represents the number of iterations, if it is the first iteration, i is 0; φ ⁰ represents the initialized level set function, and φ ¹ represents the new moment level set function obtained after the first iteration.

In another preferred embodiment of the present invention, the numerical solution process of the energy function is to first calculate the gradient flow equation and then perform numerical iteration operation on the gradient flow equation, and the gradient flow equation is as follows:

表示曲率。常数项α和μ，可根据具体情况设定，本实施例中，该值为步骤S1中初始的参数之一。Among them, α, μ are constant terms, t is time,

The constant terms α and μ can be set according to the specific situation. In this embodiment, the value is one of the initial parameters in step S1.

Step S4, performing binarization penalty and Gaussian filtering regularization processing on the new level set function φ ⁱ⁺¹ obtained in step S3.

Specifically, step S4 includes the following steps:

Step S41, when φ ⁱ⁺¹ >0, φ ⁱ⁺¹ =1; when φ ⁱ⁺¹ ≤0, φ ⁱ⁺¹ =-1;

Step S42: Regularize the level set function φ ⁱ⁺¹ using Gaussian filtering, such as φ ⁱ⁺¹ = φ ⁱ⁺¹ *G _δ .

In step S42, the standard deviation δ of the Gaussian kernel function is a key parameter and should be appropriately selected according to the specific image. If it is too small, the model will be sensitive to noise and the evolution will be unstable; on the other hand, if it is too large, edge leakage may occur and the detected boundary may be inaccurate.

Step S5, determining whether the curve continues to iterate, if the convergence condition is met, stopping the iteration and completing the image segmentation; if the convergence condition is not met, executing step S2 and performing the next iteration.

Specifically, the convergence condition of the numerical iteration operation in step S5 is:

的长度，i+1为迭代次数，第一次迭代时，i为0。Where Γ is the pixel number threshold, length(·) is used to calculate

, i+1 is the number of iterations, and i is 0 for the first iteration.

The active contour model uses a continuous curve to express the target contour and defines an energy functional, which transforms the segmentation process into a process of solving the minimum value of the energy functional. When numerically implemented, the gradient flow equation of the energy functional can be obtained by solving the Euler-Lagrange equation corresponding to the function. When the energy reaches the minimum, the final curve is the target contour. The target contour is used to distinguish the foreground area from the background area to achieve image segmentation.

The above is only a detailed description of the specific implementation of the present invention, rather than a limitation of the present invention. Various substitutions, modifications and improvements made by those skilled in the relevant art without departing from the principle and scope of the present invention should be included in the protection scope of the present invention.

Claims (2)

1. An active contour image segmentation method based on a dual-weighted signed pressure function, characterized in that it comprises the following steps: Step S1, inputting the acquired original image to be segmented; initializing the parameters of the active contour model and setting the initial contour; Input the original image and calculate the grayscale value of each pixel, denoted as I(x), where x is the pixel in the image domain Ω; initialize the parameters of the active contour model and set the initial contour; Step S2, calculate the global grayscale term and Legendre polynomial to obtain a double-weighted signed pressure function; calculate the edge stop function

The symbolic pressure function based on dual weights is:

Where I(x) is the gray value of the pixel in the image domain,

For Legendre,

is the global grayscale term, _w1 is the weight of the Legendre term in the signed pressure function, and _w2 is the weight of the global grayscale term in the signed pressure function; The calculation formulas of the Legendre term and the global grayscale term are as follows:

Where P(x) is the Legendre polynomial vector, and η is used to adjust the weights of the internal and external parts;

is the closed-form solution of the Legendre polynomial coefficient vector for the interior region of the contour,

is the closed-form solution of the Legendre polynomial coefficient vector outside the contour line, c ₁ is the average gray value inside the contour line, and c ₂ is the average gray value outside the contour line; the above four variables c ₁ , c ₂ and

The calculation formula is as follows:

Where n ₁ (x) = H _ε (

(x)), n ₂ (x) = 1-H _ε (

(x));

Where M represents the k×k identity matrix, K and L represent the k×k Grimm matrices, λ ₁ and λ ₂ are two constants, using the default values; ε is a preset parameter; H _ε (

) is the Hyatt function; The edge stop function is composed of fractional and exponential forms, and the calculation formula is as follows:

Where x and y represent pixel points.

represents the convolution operation of the Gaussian kernel function G _δ with the image to be segmented I,

is the gradient operator; Step S3, using a gradient descent algorithm to numerically solve the energy function of the active contour model, obtain the corresponding gradient flow equation to iterate the segmentation curve, and obtain the level set function at a new moment; The numerical solution process of the energy function is to first calculate the gradient flow equation and then perform numerical iteration operation on the gradient flow equation. The gradient flow equation is as follows:

Among them, α, μ are preset constants, t is time,

represents curvature; Step S4, performing binarization penalty and Gaussian filtering regularization processing on the new moment level set function obtained in step S3; Step S41, when the level set function at the new moment

When ⁱ⁺¹ > 0,

ⁱ⁺¹ = 1;

When ⁱ⁺¹ ≤ 0,

ⁱ⁺¹ = -1; Step S42, regularize the level set function using Gaussian filtering

ⁱ⁺¹ ,

ⁱ⁺¹ =

ⁱ⁺¹ *G _δ ; Step S5, determining whether the curve continues to iterate, if it meets the convergence condition, stopping the iteration and completing the image segmentation; if it does not meet the convergence condition, executing step S2 and performing the next iteration; The convergence condition of numerical iteration operation is:

Where Γ is the preset pixel number threshold, length(·) is used to calculate

The length of i+1 is the number of iterations. 2. The active contour image segmentation method based on dual-weighted signed pressure function according to claim 1 is characterized in that the edge stop function is a monotonically decreasing non-negative function.

Images