Image segmentation method and system based on LoG operator active contour model

Abstract

The application discloses a LoG operator-based active contour model image segmentation method and system, and belongs to the technical field of computer vision, and the technical points are as follows: firstly, an edge fitting function EFF is used to replace a traditional local data fitting function; secondly, an energy functional model is created; finally, two new functions are introduced to serve as the influence of a distance regularization term and a length term, so as to prevent the level set function from being too flat or too stepped, and to smooth or shorten the curve, thereby realizing image segmentation. The LoG operator-based active contour model image segmentation method and system have the advantages that, compared with a segmentation evaluation database and a model of the prior art, the model has a faster segmentation speed, improved robustness to an initial contour, and strong anti-noise capability.

Description

Technical Field

[0001] This application relates to the field of computer vision, and more specifically, to an active contour model image segmentation method and system based on the LoG operator. Background Technology

[0002] Image processing technology is widely used in many fields such as artificial intelligence, computer vision, and medical clinical diagnosis. Due to the richness of images, there is still no universally applicable image segmentation technique. As an important preprocessing step in digital image processing, the accuracy of image segmentation affects subsequent target recognition and feature analysis. Given the importance of image segmentation, researchers have proposed segmentation algorithms for image targets. Among these algorithms, active contour models, with their mature variational theory and excellent segmentation performance, have become a popular research topic in recent years.

[0003] The development of active contour models has been greatly promoted by the introduction of the level set method. This method, driven by an energy functional that incorporates image information, causes the contour lines to continuously deform and gradually reach the boundary of the target region.

[0004] Image segmentation is an important research topic in the fields of computer vision and image processing. Existing active contour models can be broadly classified into two categories: edge-based models and region-based models.

[0005] In 1988, Osher and Sethian proposed a level set method based on a geometric deformation model. Subsequently, some researchers improved upon this method. Traditional level set methods, in order to maintain the level set function's approximation of the signed distance function during evolution, necessitate periodic re-initialization. This initialization process is not only time-consuming but also prone to numerical errors. Typical improvements include Kimmel's approach, which considers image boundary gradient information and combines the CV (Continuous Vision) and GAC (Growth-Oriented Contour) models to achieve good segmentation of images with weak boundaries; and Li et al.'s approach, addressing the re-initialization problem during level set evolution, proposed the concept of a distance regularization term to avoid level set re-initialization, leading to the Distance Regularized Level Set (DRLSE) model. DRLSE is based on distance regularization combined with gradient information, solving the problem of continuous re-initialization required by traditional geometric contour models, but it lacks the ability to select the direction of motion.

[0006] Region-based active contour models guide curves to converge toward the target contour based on the average gray level of the image, thus achieving better segmentation results in blurry and noisy images. In 1989, Mumford and Shah proposed the MS model, which approximates the image with a piecewise smoothing function and then optimizes the level set energy function. This energy function is non-convex, so gradient descent cannot be used to minimize it. In 2001, Chan and Vese proposed the CV model based on MS (Reference: Chan TF, Vese LA. Active contours without edges[J].IEEE Transactions on image processing,2001,10(2):266-277.), which replaces the piecewise smoothing function in the MS model with a piecewise constant and adds length and area terms to control the evolution of the curve. Since the piecewise function represents the average gray level of the region inside and outside the contour line and does not consider the local gray level variation, the application scope of the CV model is limited to images with uniform gray level. In 2008, Li et al. proposed the Region-Scalable Fitting (RSF) model. In the RSF model (see: Li C, Kao CY, Gore JC, et al. Minimization of region-scalable fitting energy for image segmentation[J]. IEEE Transactions on Image Processing, 2008, 17(10): 1940.), the Gaussian kernel function embedded in the energy function provides a suitable local window that represents the local grayscale information of the image. Therefore, the model can overcome the influence of uneven grayscale and correctly segment the target in the image. However, due to the introduction of the Gaussian kernel function, the curve evolution requires four convolution calculations in each iteration, thus increasing the curve evolution time. In addition, the RSF model has extremely high requirements for the initial contour setting. Small changes in the initial contour can easily cause the RSF energy function to fall into a local minimum, thus affecting the curve evolution result. In 2017, in order to solve the problems existing in the RSF model, Ding et al. proposed the Region-Scalable Fitting and Optimized Laplacian of Gaussian (RSF&LOG) model.In the RSF&LOG model (see: Keyan Ding, Linfang Xiao, Guirong Weng. Active contours driven by region-scalable fitting and optimized Laplacian of Gaussian energy for 0.902. Signal Processing 134(2017)224–233.), LOG energy is embedded into the RSF energy term to drive the contour lines to evolve towards the boundary. The added LOG energy enhances the edge information of the image while reducing the model's sensitivity to the initial contour lines, but the problem of slow RSF segmentation speed remains unresolved. To improve segmentation efficiency, Ding et al. proposed a pre-fitting energy (Local Pre-Fitting, LPF) model in 2018 (see: Ding K, Xiao L, Weng G. Active contours driven by local pre-fitting energy for fast image segmentation[J]. Pattern Recognition Letters, 2018, 104: 29-36). This model calculates the mean gray values ​​of the foreground and background in the local region before iteration, reducing the time spent on iterative updates of the gray mean fitting constant. In 2019, Jin proposed an adaptive function and fuzzy c-means energy (AF&FCME) model, which establishes an energy equation by combining adaptive functions and fuzzy c-means energy. The adaptive function effectively solves the problems of slow iteration convergence speed and edge leakage during curve evolution, improving both the target segmentation speed and the robustness of the initial contour.

[0007] Edge-based models have low computational complexity and fast target edge localization. Among region-based models, models based on global information are robust and fast, but cannot handle images with uneven grayscale. Models based on local information perform well in handling images with uneven grayscale and are relatively robust to noise, but are slow. Summary of the Invention

[0008] The purpose of this application is to address the shortcomings of the existing technology by proposing an active contour model image segmentation method and system based on the LoG operator. The invention aims to improve upon the deficiencies of region-based active contour models, resulting in improved segmentation efficiency and enhanced initialization robustness, making it more applicable to various image segmentation applications.

[0009] The technical solution of this application is as follows:

[0010] An active contour model image segmentation method based on the LoG operator includes the following steps:

[0011] First, a new edge fitting function (EFF) is proposed to replace the traditional local data fitting function;

[0012] Secondly, a completely new energy functional model is created;

[0013] Finally, two new functions are introduced to influence the distance regularization term and the length term, respectively, to prevent the level set function from being too flat or too stepped, and to smooth or shorten the curve. This model enhances the robustness of initialization, improves segmentation efficiency, and achieves higher segmentation accuracy, making it more suitable for segmenting various images.

[0014] An active contour model image segmentation method based on the LoG operator includes the following steps:

[0015] Step 1, Input image I; Set the following parameters: N, c, α, k, σ, Δt.

[0016] Step 2, set the initial level set φ:

[0017]

[0018] Where x represents a point in the image domain, and t represents the number of iterations.

[0019] Where Ω0 is a subset of the image domain Ω, It is the boundary of Ω0;

[0020] Where c0 = 1;

[0021] Step 3, calculate the boundary fitting function f eff ;

[0022] Step 4, calculate Data;

[0023] Step 5, repeat the calculation:

[0024] Step 5-1, i is initially set to 1;

[0025] Step 5-2, Calculate φ i :

[0026] φ i =φ i-1 +Δt·Data

[0027] Step 5-3, for the level set function φ i Perform regularization processing;

[0028] Step 5-4, use formula (8) to calculate φ L :

[0029] φ L =M L *φ R

[0030] Step 5-5, if |φ i -φ i-1 If |φ ≤ 0.001, proceed to Step 6; if |φ i -φ i-1 If the value is greater than 0.001, proceed to Step 5-6.

[0031] Steps 5-6: Increment the value of i by 1.

[0032] Step 5-7: If i is less than or equal to N, repeat steps 5-2 to 5-7; if i is greater than N, proceed to step 6.

[0033] Step 6, Output the level set function φ = φ L And the segmentation results.

[0034] Furthermore, in Step 3, f eff The calculation method is as follows:

[0035] f eff (x)=Δ(G σ *I(x))

[0036]

[0037] Among them, G σ It is a Gaussian kernel function with a standard deviation of σ, and Δ represents the Laplacian operation;

[0038] This indicates that a second difference calculation is performed in the direction of the row containing x.

[0039] This indicates that a second difference calculation is performed along the column direction containing y.

[0040] I(x,y) represents the intensity at the image point (x,y).

[0041] * indicates convolution calculation

[0042] Furthermore, in Step 4, the method for calculating Data is as follows:

[0043] Data = -α·c·softsgn(f eff / τ)

[0044]

[0045] τ=std2(I)

[0046] Furthermore, in Step 5-3, the level set function φ i The calculation method for regularization is as follows:

[0047]

[0048]

[0049] Furthermore, the parameters in Step 1 are: α = 5, k = 7, σ = 1.75, Δt = 1.

[0050] An active contour model image segmentation calculation system based on the LoG operator, the calculation system being capable of running the aforementioned calculation method.

[0051] A storage medium storing the execution steps of the computational method as described above.

[0052] The beneficial effects of this application are as follows: Active contour models generally suffer from the following two problems: (a) slow calculation speed; (b) sensitivity to initial contour lines. The principle of this invention can solve these two problems by employing the following technology:

[0053] 1) This paper proposes for the first time to use the Laplacian-of-Gaussian operator as the data-driven kernel of the active contour model, which is fast and simple;

[0054] 2) This invention mainly introduces an innovative method, which introduces a level set function into the energy function. Unlike existing methods, the data terms are independent of the level set function during iteration, making the iteration process the simplest and fastest. Since the data terms are calculated before iteration, the initial contour line has high robustness. Attached Figure Description

[0055] The present application will be further described in detail below with reference to the embodiments in the accompanying drawings, but this does not constitute any limitation on the present application.

[0056] Figure 1 These are fitting plots of different models (the first row from left to right is: CV model, RSF model, LIF model, LPF model; the second row from left to right is: LoG & RSF model, BC model, PBC & FCM model, ABC model).

[0057] Figure 2 Example image of the LoG operator for image I.

[0058] Figure 3 This is an example image of the second-order differential of the LoG boundary of an image.

[0059] Figure 4 This is a schematic diagram of the gradient descent flow direction in the LoG model.

[0060] Figure 5 The diagram shows the evolution process and segmentation results obtained by selecting different initial contours.

[0061] Figure 6 This is a model comparison experiment (categorized by column, from left to right: original image, AF&FCM model, PBC model, LDJD model, ABC model, EFF model). Detailed Implementation

[0062] The present invention will be further described below with reference to the accompanying drawings and embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention. The implementation of the present invention will be described in detail below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the following embodiments.

[0063] First and second order differential data terms

[0064] The analysis region and bias field model, the data fitting term in the model, in fact reflects the information of the image edge below the current contour line. The data fitting term in the CV model is -(λ1|I(y)-c1(x)| 2 )-λ2|I(y)-c2(x)| 2 The data fitting term (λ2e2-λ1e1) in the RSF model, and the data fitting term (II) in the LIF model (see reference: K. Zhang, H. Song, L. Zhang, Activecontours driven by local image fitting energy, Pattern Recognition 43(4)(2010)1199–1206.) f (m1(x)-m2(x)), the data fitting term in the LPF model -(λ1e) s -λ2e l In the LoG&RSF model, the data fitting terms (λ2e2-λ1e1)+ωL, etc., all express the edge information under the current contour state and are called second-order differential data terms.

[0065] like Figure 1As shown, there are five regional models (CV, RSF, LIF, LPF, LoG & RSF) and three bias correction models (BC model, see reference: Li C, Huang R, Ding Z, et al. A level set method for imagesegmentation in the presence of intensity inhomogeneities with application to MRI[J]. IEEE Transactions on Image Processing, 2011, 20(7): 2007-2016); PBC & FCM model, see reference: R. Jin, G. Weng. A robust active contour model driven by pre-fitting bias correction and optimized fuzzy c-means algorithm for fast imagesegmentation[J]. Neurocomputing, 2019, 359: 408-419; ABC model, see reference: Guirong Weng, Bin Dong, Yu Lei. A level set method based on additive bias correction for image segmentation. Expert Systems With Information on data fitting terms in Applications.185(2021)115633.

[0066] Figure 1 This reflects that when the model has converged and completed segmentation, its data fitting terms all express the same second-order differential property. This indicates that the active contour model is searching for the second-order differential feature values ​​of the image.

[0067] II. Boundary Fitting Function (EFF)

[0068] Taking the second derivative of an image will create a zero-crossing point, and generate a peak (positive) and a trough (negative) on both sides of the zero point. The second derivative is concerned with abrupt changes in image grayscale rather than emphasizing regions where grayscale changes slowly, and has a stronger ability to locate edges.

[0069] from Figure 1Among the data fitting terms, it can be found that they all have second-order differential features for image edges. Functions with such characteristics are called edge fitting functions (EFF) in this paper. The idea of ​​this application is to replace the traditional local data fitting terms with edge fitting functions (EFF) to improve the robustness of the initial contour and the speed of image segmentation.

[0070] The LoG (Laplacian-of-Gaussian) operator is a well-known edge detection operator based on second-order differentiation (see: Marr D, Hildreth E. Theory of edge detection[J]. Proceedings of the Royal Society of London, 1980, 207(1167):187.). Its principle is to first smooth the image using a Gaussian filter, and then use the Laplacian operator to detect the image edges. Its mathematical definition is:

[0071]

[0072] Among them G σ It is a Gaussian kernel function with a standard deviation of σ, and Δ represents the Laplacian operation. For example... Figure 2 As shown, the zero-crossing point is the area where grayscale values ​​jump. On the bright side, the image's LoG value is negative, and on the dark side, the image's LoG value is positive.

[0073] Figure 3 Given a composite image, and images with added uniformity, non-uniformity, and Gaussian noise, edge locations are obtained by detecting the zeros of the second derivative of the image.

[0074] The LoG data above shows that near the target boundary, the LoG data outside the target area is positive; inside the target boundary area, the LoG data is negative; and far from the boundary area, the second-order derivative data represents a small range of positive and negative values. According to the definition of the level set function and the gradient descent method, the level set function φ takes positive and negative values ​​outside and inside the contour C, respectively. If there is a point 'a' on the contour line near the outer region of the white target, Figure 3 The second-order differential value of point a is positive. According to the gradient descent flow equation, it should move towards the region of lower energy. The region within the contour line is the negative energy region. Therefore, the direction of motion of point a is inward contraction (the normal to the tangent at this point on the contour line), and the velocity is... Δt is the step size. For example... Figure 4 The diagram shows the gradient descent flow direction of the LoG model. The green line is the initial outline, and the red line is the result of the first iteration.

[0075] If point b on the contour line is located near the interior region of the white target, its LoG data is negative. According to the gradient descent flow equation, it should move towards the higher energy region. The region outside the contour line is the positive energy region. Therefore, the direction of movement of point b is outward expansion (the normal to the tangent at this point on the contour line), and its velocity is... If a point on the contour line falls on the target boundary, the LoG data value of this point is zero. The points on the contour line are zero, therefore the movement stops.

[0076] Due to the nature of second-order derivatives, the LoG operator is sensitive to image edges. Therefore, the LoG operator can replace the traditional local data fitting term or gradient indicator function to construct an external energy function of the contour line C based on the boundary fitting function (EFF):

[0077]

[0078]

[0079] f eff (x)=Δ(G σ *I(x)) (4)

[0080] In formula (2), f eff This is called the boundary fitting function, and the LoG (Laplacian-of-Gaussian) operator is used directly. c represents the segmentation object symbol, and α is used to adjust the model's running speed to prevent undersegmentation and oversegmentation. τ = std2(I) (The standard f) eff The region and slope, std2() is the standard deviation of the image, softsgn(·) is the normalization function with a range of (-1, 1). 1+φ represents the outer region of the zero level set (contour line C), G σ It is a Gaussian kernel function with a standard deviation of σ, Δ represents the Laplacian operation, and * represents the convolution calculation.

[0081] By using the gradient descent method to minimize the energy functional in equation (2), we obtain the gradient flow equation as shown below:

[0082]

[0083] The evolution equation of the contour line of the level set is:

[0084] φ n =φ n-1 +Δt·Data (6)

[0085] Specifically, the data-driven term here is Data = -α·c·softsgn(f eff / τ) is a fixed value, calculated before iteration. Therefore, the EFF model significantly reduces computational overhead and greatly improves the robustness of the initial profile.

[0086] III. Regularization of the level set function Φ

[0087] The literature “K.Zhang,H.Song,L.Zhang,Active contours driven by local imagefitting energy,Pattern Recognition 43(4)(2010)1199–1206” applies Gaussian smoothing filter to make the contour lines smooth and regularized. As a result, the level set function φ is too flat, which is not conducive to regularization and boundary determination.

[0088] This application argues that a function should be used to prevent the level set function φ from being too steep or too flat, to implement the distance rule on both sides of the level set, i.e., to increase the slope of the zero-crossing region of the level set, and then to smooth and regularize φ. In order to effectively and robustly regularize the level set function, this paper defines the following function:

[0089] φ R =softsgn(9·φ) (7)

[0090] Formula (7) is the φ regularization function, which aims to increase the slope of the zero-crossing region, ensure that φ has strong regularization characteristics, suppress the slope at the two high points, and achieve the regularization of the horizontal set function φ.

[0091] φ L =M k *φ R (8)

[0092] Among them, the kernel function M k It is a neighborhood mean filter template with a size of w1×w1, and the mask size is w1=round(2×k)×2+1.

[0093] In E EFF When minimized, the contour line will include all the boundary lines located on the edges, but there will also be some extra curves on the non-edges. Therefore, it is necessary to add formula (8), which acts like the length constraint term L(φ), to smooth and shorten the curves.

[0094] IV. Experimental Analysis

[0095] The main steps of the algorithm in this paper are as follows:

[0096] Input: The observed image I; Settings: Maximum number of iterations N, sign c, coefficients α, k, and σ.

[0097]

[0098] The reference values ​​for the parameters in the experiment are: α=5, k=7, σ=1.75, and the fixed parameters are: Δt=1, c0=1.

[0099] The Matlab code for the above solution is as follows:

[0100]

[0101] V. Robustness Experiment Regarding Initial Contour Setting

[0102] Traditionally, active contour models have been sensitive to the boundary settings of initial contour lines. The main problem is that during iterative computation, the level set function participates in the calculation of the model's fitting function, thus the position of the initial contour line affects the fitting function value. In this invention, the fitting function of the model is completed before iteration, and during iteration, the data term (Data=-α·c·softsgn(f)) is used. eff / τ)) is a fixed value, therefore, it has good robustness in initial contour setting, as demonstrated in experiments. Figure 5 As shown.

[0103] VI. Segmentation Effect Experiment

[0104] The accuracy of the calculation is achieved using the intersection-union ratio (IOU), also known as the Jaccard Similarity Coefficient (JSC), as follows:

[0105]

[0106] In formula (9), A s B represents the area of ​​the model segmentation. s This represents the area of ​​the evaluation database, calculated for the target intersection-union ratio of the segmented objects, with JSC=1 indicating a perfect segmentation.

[0107] To illustrate the speed and accuracy of our model, we used images from a standard database (commonly used in comparative experiments of active contour models) for segmentation. The model was run on the same computer in the same environment and compared with models published in top SCI journals over the past three years. The model description is as follows:

[0108] AF&FCM (see reference: Ri Jin, Guirong Weng. Active contours driven by adaptive functions and fuzzy c-means energy for fast imagesegmentation. Signal Processing, 163:1-10, 2019.) is an edge level set model. The characteristic of the model is that before iteration, it uses the principle of fuzzy C-means clustering based on local regions to fit two fuzzy center points inside and outside the contour line, and constructs an adaptive edge indicator function, which solves the unidirectional motion problem of the edge level set model.

[0109] The PBC model (see reference: Jin R, Weng GA, Robust Active Contour Model Driven by Pre-fitting Bias Correction and Optimized Fuzzy C-Means Algorithm for Fast Image Segmentation. Neurocomputing, 359:408-419, 2019.) is a non-uniform bias correction model that utilizes the principle of fuzzy C-means clustering based on local regions to pre-calculate the fitting function for the non-uniform bias of the model. This model exhibits high segmentation accuracy and stable robustness.

[0110] The LGJD model (see reference: Bin Han, Yiquan Wu. Active contour model for inhomogenous image segmentation based on Jeffreys divergence. PatternRecognition, 107, 107520, 2020.) is a hybrid computational method that initially uses a CV model and later switches to an RSF model. It uses the Jeffreys divergence principle to measure the difference between the model's fitted function and the image, and drives the zero-level set function to reach the target boundary to complete the segmentation.

[0111] The ABC model (see reference: Guirong Weng, Bin Dong, Yu Lei. A level set method based on additive bias correction for image segmentation. Expert Systems With Applications. 185(2021)115633.) is an active contour model with bias correction. It has strong theoretical derivation, high system robustness, low runtime overhead, and high segmentation accuracy. Comparison results are as follows: Figure 6 As shown in Table 1, the analysis demonstrates that the segmentation accuracy proposed in this invention is high, and the segmentation speed is significantly improved.

[0112] Table 1: Image segmentation accuracy and running time (JSC / sec)

[0113]

[0114] It should also be noted that:

[0115] Parameter description: The observed image I, i = logI, φ is the level set function, f eff This is called the boundary fitting function, τ = std2(I) (standard f) eff The region and slope, std2() is the standard deviation of the image, softsgn(·) is the normalization function with a range of (-1,1), 1+φ represents the outer region of the zero level set (contour line C), G σ Here, is the Gaussian kernel function, σ is the standard deviation, the radius is ω = j × σ + 1, j is a positive integer, Δ represents the Laplacian operation, and * represents the convolution calculation. α is the coefficient controlling the speed of the evolution curve, and c is the sign function; when the target object is white, c = -1, otherwise c = 1.

[0116] The above-described embodiments are preferred embodiments of this application and are only used to facilitate the illustration of this application. They are not intended to limit this application in any way. Any person with ordinary knowledge in the art can make equivalent embodiments by making partial modifications or alterations to the technical content disclosed in this application without departing from the scope of the technical features of this application. Such equivalent embodiments are still within the scope of the technical features of this application.

Claims

1. An active contour model image segmentation method based on the LoG operator, characterized in that, Includes the following steps: Step 1, Input image I; Set the following parameters: maximum number of iterations N, sign function c, α = 5, k = 7, σ = 1.75, Δt = 1; When the target object is white, c = -1; otherwise, c = 1. Step 2, set the initial level set φ: Where x represents a point in the image domain, and t represents the number of iterations; Where Ω0 is a subset of the image domain Ω, It is the boundary of Ω0; Where c0 = 1; Step 3, calculate the boundary fitting function f eff : f eff (x)=Δ(G σ *I(x)) Among them, G σ It is a Gaussian kernel function with a standard deviation of σ, and Δ represents the Laplacian operation; This indicates that a second difference calculation is performed in the direction of the row containing x. This indicates that a second difference calculation is performed in the column direction containing y. I(x,y) represents the intensity at the image point (x,y). * indicates convolution calculation; Step 4, Calculate the data-driven item Data: Where std2(I) is the standard deviation of the image; Step 5, repeat the calculation: Step 5-1, i is initially set to 1; Step 5-2, Calculate φ i : f i =φ i-1 +Δt·Data Step 5-3, for the level set function φ i Perform regularization: Step 5-4, calculate φ using the following formula. L : Kernel function M k It is a template with a neighborhood mean filter of size w1×w1; Step 5-5, if |φ i -φ i-1 If |φ ≤ 0.001, proceed to Step 6; if |φ i -φ i-1 If the value is greater than 0.001, proceed to Step 5-6. Steps 5-6: Increment the value of i by 1. Step 5-7: If i is less than or equal to N, repeat steps 5-2 to 5-7; if i is greater than N, proceed to step 6. Step 6, Output the level set function φ = φ L And the segmentation results.

2. An active contour model image segmentation calculation system based on the LoG operator, characterized in that, The computing system includes a processor and a memory storing processor-executable instructions, which, when executed by the processor, implement the image segmentation method as described in claim 1.

3. A storage medium, characterized in that, It stores a program that, when executed by a processor, implements the image segmentation method as described in claim 1.

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