An image segmentation method based on convex level set and double bias field correction

Abstract

The application discloses an image segmentation method based on convex level set and double bias field correction, and aims at solving the segmentation failure problem caused by the sensitivity of an active contour model to an initial contour. The energy functional provided by the application contains a fidelity term and a constraint term. In the fidelity term, a double bias field image model based on local region information is adopted, and a novel convex level set function is introduced as a member function to guide contour movement. A TV (Total Variation) regular term is adopted as the constraint term to maintain the smoothness of the level set function, so that the segmentation problem is converted into a convex optimization problem. The energy functional provided by the application has global convexity, allows flexible setting of the initial contour, can more effectively and robustly segment non-uniform gray images and noise images, and simultaneously corrects the non-uniform gray.

Description

Technical Field

[0001] This invention belongs to the field of image processing and relates to an image segmentation method based on convex level sets and dual bias field correction. Background Technology

[0002] Real-world images often exhibit artifacts, noise, and uneven grayscale, posing significant challenges to image segmentation. Image segmentation is a crucial stage in digital image processing, and researchers have developed various segmentation methods to address different tasks. In recent years, methods based on active contour models have gained prominence. These methods can model images using prior knowledge, offering strong physical interpretability and robust mathematical theory, thus demonstrating significant advantages in the field of image segmentation.

[0003] In recent years, active contour models based on bias field correction have been increasingly widely used in image segmentation. Patent CN116342630A discloses a level set image segmentation method using a multiplicative model, achieving segmentation of images with uneven grayscale. However, the Heaviside function used in this invention lacks convexity, making the model quite sensitive to initial contours. Patent CN109615617A discloses a convexity-preserving indirect regularized level set image segmentation method, which has good robustness to initial values, but cannot eliminate the bias field that causes uneven grayscale in the image, nor can it correct the image grayscale. The paper Ren Yanjun, Li Dong, Tang Liming, "A variational level set model based on additive decomposition for segmenting noisy images with intensity inhomogeneity," Signal Processing, 2023, 212:109169, discloses a model based on additive bias field correction, which has a relatively fast segmentation speed. However, due to the non-convex nature of the model, it is quite sensitive to initial values. In addition, the model involves many parameters, making the adjustment process relatively complex. In general, most existing models are based on the assumption of a single bias field and rarely discuss the convexity of the energy functional, often leading to local minima in the segmentation results, which limits the practical application of such models. Summary of the Invention

[0004] To address the technical problems of existing segmentation methods based on active contour models being sensitive to initial contours, failing to consider the convexity of energy functionals, and thus unable to obtain global minima, this invention provides an image segmentation method based on convex level sets and dual bias field correction. By introducing convex level set functions and TV (Total Variation) regularization terms into the fidelity term containing dual bias fields, the segmentation problem is transformed into a convex optimization problem, thereby more effectively and robustly solving the segmentation challenges of images with uneven gray levels and noise.

[0005] The technical solution adopted by this invention to solve its technical problem includes the following steps:

[0006] Step 1: Define the dual-bias field image model as I = b1J + b2 + n, where I is the input image, b1 and b2 are the multiplicative and additive bias fields respectively, n is zero-mean Gaussian noise, and J is the real image. The bias fields b1 and b2 change slowly, while the real image J takes different constant values ​​c1 and c2 in the non-overlapping regions Ω1 and Ω2. Define the following energy as the fidelity term:

[0007]

[0008] in Here, α is the normalization constant, and ρ is the region scale parameter.

[0009] Step 2: Introducing novel convex level set functions and TV terms related to convex level set functions into the above fidelity model, the total variational level set framework is constructed using the following method:

[0010] (1) Setting For level set functions, use two convex level set functions (φ+1). 2 and (φ-1) 2 Indicates the background and target regions in an image;

[0011] (2) Introducing a convex level set function into equation (1), the formula for calculating the energy functional is:

[0012]

[0013] Where λ1=λ2=1;

[0014] (3) The TV regularization term is introduced into the energy functional (2), thereby transforming image segmentation into a convex optimization problem. The total variational level set framework is established, and the specific definition is as follows:

[0015]

[0016] in It's a TV regular expression. It is the gradient operator, ν>0.

[0017] Step 3: Use the alternating minimization algorithm to iteratively solve each subproblem of the unconstrained optimization problem to obtain the final segmentation result and bias field correction result. The specific steps are as follows:

[0018] (1) Solving the image segmentation problem in equation (3) is equivalent to solving the following minimization problem:

[0019]

[0020] (2) Minimize each unknown variable in minimization problem (4), transforming it into solving the following 5 minimization problems respectively:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] Where k is the number of iterations;

[0027] (3) Subproblems (5)-(9) are solved by the following equations.

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] Where * is the convolution operator and Δt is the time step;

[0034] (4) The iterative process of the alternating minimization algorithm is as follows:

[0035] 1) Initialize φ, b1, and b2, and set k max And the termination threshold τ, starting the iteration from k=1;

[0036] 2) When the convergence condition is ||φ k+1 -φ k ||1≤τ||φ k ||1 or k≤k maxIf the condition is met, proceed to the next step; otherwise, terminate the loop. The result obtained at this point is φ. k+1 It refers to the segmentation result of two-dimensional image data, and the result of bias field correction is based on... calculate;

[0037] 3) Calculate and update according to equations (10) and (11). and

[0038] 4) Calculate and update φ according to equation (12) k+1 ;

[0039] 5) Calculate and update according to equations (13) and (14). and

[0040] 6) Let k = k + 1, and return to step 2).

[0041] The beneficial effects of this invention are as follows: the dual-bias field image model provided by this invention can more comprehensively characterize gray-level non-uniformity compared with the traditional single-bias field model; the novel convex level set function makes each variable in the energy functional convex, thus allowing for more flexible setting of the initial contour; the introduced TV regularization term further improves the model's robustness to noise; while extracting the target contour more completely, it corrects gray-level non-uniformity, demonstrating outstanding accuracy, reliability, and versatility in the segmentation applications of natural images, medical images, and industrial images.

[0042] The present invention will be further described below with reference to the accompanying drawings and examples. Attached Figure Description

[0043] The attached figure shows the flowchart and results of the image segmentation method based on convex level sets and dual bias field correction. Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 The results of this invention on images with uneven gray levels are as follows, from left to right: original image, segmentation result, multiplicative bias field, additive bias field, and corrected image; from top to bottom: noisy synthetic image, uneven gray level synthetic image, industrial CT image, and cardiac CT image. Detailed Implementation

[0044] The method of this invention processes two-dimensional image data, specifically a CT two-dimensional image I with a resolution of 400×400 and a grayscale level of 256. In this example, the TV regularization coefficient ν = 10. 3 The data fitting coefficients λ1=λ2=1, the region scale parameter σ=8, and the maximum number of iterations k max =20, time step Δt=10 -4 Termination threshold τ = 10 -3Based on this information, perform the following steps:

[0045] Step 1: Define the dual-bias field image model as I = b1J + b2 + n, where I is the input image, b1 and b2 are the multiplicative and additive bias fields respectively, n is zero-mean Gaussian noise, and J is the real image. The bias fields b1 and b2 change slowly, while the real image J takes different constant values ​​c1 and c2 in the non-overlapping regions Ω1 and Ω2. Define the following energy as the fidelity term:

[0046]

[0047] in Here, α is the normalization constant, and ρ is the region scale parameter.

[0048] Step 2: Introducing novel convex level set functions and TV terms related to convex level set functions into the above fidelity model, the total variational level set framework is constructed using the following method:

[0049] (1) Setting For level set functions, use two convex level set functions (φ+1). 2 and (φ-1) 2 Indicates the background and target regions in an image;

[0050] (2) Introducing a convex level set function into equation (1), the formula for calculating the energy functional is:

[0051]

[0052] Where λ1=λ2=1;

[0053] (3) The TV regularization term is introduced into the energy functional (2), thereby transforming image segmentation into a convex optimization problem. The total variational level set framework is established, and the specific definition is as follows:

[0054]

[0055] in It's a TV regular expression. It is the gradient operator, ν>0.

[0056] Step 3: Use the alternating minimization algorithm to iteratively solve each subproblem of the unconstrained optimization problem to obtain the final segmentation result and bias field correction result. The specific steps are as follows:

[0057] (1) Solving the image segmentation problem in equation (3) is equivalent to solving the following minimization problem:

[0058]

[0059] (2) Minimize each unknown variable in minimization problem (4), transforming it into solving the following 5 minimization problems respectively:

[0060]

[0061]

[0062]

[0063]

[0064]

[0065] Where k is the number of iterations;

[0066] (3) Subproblems (5)-(9) are solved by the following equations.

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] Where * is the convolution operator and Δt is the time step;

[0073] (4) The iterative process of the alternating minimization algorithm is as follows:

[0074] 1) Initialize φ, b1, and b2, and set k max And the termination threshold τ, starting the iteration from k=1;

[0075] 2) When the convergence condition is ||φ k+1 -φ k ||1≤τ||φ k ||1 or k≤k max If the condition is met, proceed to the next step; otherwise, terminate the loop. The result obtained at this point is φ. k+1 It refers to the segmentation result of two-dimensional image data, and the result of bias field correction is based on... calculate;

[0076] 3) Calculate and update according to equations (10) and (11). and

[0077] 4) Calculate and update φ according to equation (12) k+1 ;

[0078] 5) Calculate and update according to equations (13) and (14). and

[0079] 6) Let k = k + 1, and return to step 2).

Claims

1. An image segmentation method based on convex level sets and dual bias field correction, characterized in that... Includes the following steps: Step 1: Define the dual-bias field image model as follows ,in I It is the input image. and These are the multiplicative bias field and the additive bias field, respectively, for grayscale non-uniformity. n It is zero-mean Gaussian noise. J It is a real image, in which the bias field and It changes slowly, while the real image J In non-intersecting regions and Take different constant values and The following energy is defined as the fidelity term: (1)， in , here It is a normalization constant. It is a regional scale parameter; Step 2: Introduce a novel convex level set function and a TV (Total Variation) term for the convex level set function into the above fidelity term, and construct the total variational level set framework using the following method: (1) Setting For level set functions, use two convex level set functions. and Indicates the background and target regions in an image; (2) Introducing a convex level set function into equation (1), the formula for calculating the energy functional is: (2)， in ; (3) The TV regularization term is introduced into the energy functional (2), thereby transforming image segmentation into a convex optimization problem. The total variational level set framework is established, and the specific definition is as follows: (3)， in It's a TV regular expression. It is the gradient operator. ; Step 3: Use the alternating minimization algorithm to iteratively solve each subproblem of the unconstrained optimization problem to obtain the final segmentation result and bias field correction result.

2. The image segmentation method based on convex level sets and dual bias field correction according to claim 1, characterized in that, Step 3 uses the alternating minimization algorithm to iteratively solve each subproblem of the unconstrained optimization problem, obtaining the final segmentation result and bias field correction result. The specific steps are as follows: (1) Solving the image segmentation problem in equation (3) is equivalent to solving the following minimization problem: (4)； (2) Minimize each unknown variable in minimization problem (4), transforming it into solving the following 5 minimization problems respectively: (5)， (6)， (7)， (8)， (9)， in It is the number of iterations; (3) The iterative process of the alternating minimization algorithm is as follows: 1) Initialization , and ,set up and termination threshold ,from Start iterating; 2) When the convergence condition or If the condition is met, proceed to the next step; otherwise, terminate the loop. The result obtained at this point... It refers to the segmentation result of two-dimensional image data, and the result of bias field correction is based on... calculate; 3) Calculate and update according to equations (5) and (6). and ; 4) Calculate and update according to equation (7) ; 5) Calculate and update according to equations (8) and (9). and ; 6) Let And return to step 2).

Images