A Symbolic Pressure Function Segmentation Method Combining Global and Local Image Information

Abstract

This paper discloses a signed pressure function segmentation method that combines global and local image information. This method constructs an active contour model that combines global and local image information. First, a hybrid signed pressure function is constructed by linearly combining newly defined global and local grayscale fitting terms. Second, a balloon force function is redefined using global and local image information. Finally, experiments demonstrate that the model constructed by this invention can accurately segment weak boundary and multi-target images. This method not only accurately segments weak boundary and multi-target images, but also performs quickly and exhibits robustness to noise.

Description

Technical Field

[0001] The present invention belongs to the technical field of image segmentation model construction, and in particular relates to a signed pressure function segmentation method combining global and local information of an image. Background Art

[0002] Image segmentation is a crucial preprocessing method in image recognition and computer vision. It divides an image into several subregions based on specific features, with similarities within the regions and differences between them. Segmentation methods vary widely depending on the application requirements, but a universal image segmentation method has yet to be found [Hu Q, Tian J, He D. Wheat leaf lesion color image segmentation with improved multichannel selection based on the Chan–Vese model [J]. Computers and Electronics in Agriculture, 2017, 135: 260-268.].

[0003] Active contour model is a type of digital image segmentation method that seeks to minimize the energy functional. The algorithm can evolve smooth closed curves and has the advantages of stable calculation method and high segmentation accuracy. Its core idea is to use continuous curves to represent the edge of the target. Based on this, an energy functional is defined, and the image segmentation problem is transformed into a problem of solving the minimum value of the energy functional [Sun L, Meng X, Xu J, et al. An image segmentation method based on improved regularized level set model [J]. Applied Sciences, 2018, 8 (12), Article ID 2393.]. According to the different expressions of the initial contour curve, the active contour model can be divided into two categories: parametric active contour model and geometric active contour model. The parametric active contour model is very dependent on the position of the initial contour curve. Different initial contour curves will obtain different segmentation results, and may even fail to obtain the correct boundary contour; and it is more sensitive to the topological structure changes of the curve [Meng Xinchao. Research on image segmentation method based on level set improvement [D]. Henan Normal University, 2019.]. The geometric active contour model can better handle changes in topological structure and solve problems that are difficult to solve with the parametric active contour model [Wang Xiaofeng. Research on level set method and its application in image segmentation [D]. University of Science and Technology of China, 2009.].

[0004] The geometric active contour model is further divided into edge-based models and region-based models. Caselles et al. [Caselles V, Kimmel R, Sapiro G. Geodesic active contours [J]. International Journal of Computer Vision, 1997, 22 (1): 61-79.] studied the geodesic active contour model (GAC). This model provides a new mechanism for edge detection by calculating the shortest path, which is the key point in the development of the parametric active contour model to the geometric active contour model. However, it still uses image gradient information, so it cannot segment weak boundary targets. Chan and Vese [Chan TF, Vese LA. Active contours without edges [J]. IEEE Transactions on Image Processing, 2001, 10 (2): 266-277.] proposed an active contour model (Chan-Vese, CV) without edge detection based on the consideration of global region information. This method uses the regional statistical information of the image to construct the driving force of contour evolution, and has a good segmentation effect on both weak boundary and discretized boundary targets. However, this model is based on the assumption that the image grayscale is evenly distributed, so it is difficult to complete the segmentation task of images with uneven grayscale distribution and rich texture information.In order to process grayscale uneven images, Li et al. [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): 1940-1949.] proposed a local binary fitting (LBF) model based on the local information of the image. The algorithm uses the weighted neighborhood pixels to fit the grayscale value of the central pixel, thereby establishing a local binary fitting energy function and driving the evolution curve to move toward the target boundary. However, due to the use of the Gaussian kernel function, multiple convolution operations are required, and it is very sensitive to the initial contour position and parameters [Tu S, Su Y. Fast and accurate target detection based on multiscale saliency and active contour model for high-resolution SAR images [J]. IEEE Transactions on Geoscience and Remote Sensing, 2016, 54(10): 5729-5744.]. Wang et al. [Wang X, Huang D, Xu H. An Efficient Local Chan-Vese Model for Image Segmentation [J]. Pattern Recognition, 2010, 43 (3): 603-618.] introduced global terms, local terms and regularization terms, and proposed the LCV (Local Chan-Vese) model. This model assumes that the grayscale is uniformly distributed in a small local area, and there is a certain gap between the grayscale values of the target and the background. Based on the above assumptions, the LCV model is difficult to accurately segment weak boundary images and images with severely uneven grayscale [Niu Yuefeng. Research on medical image segmentation algorithm based on regional level set theory [D]. University of Chinese Academy of Sciences (Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences), 2020.].Zhang et al. [Zhang K, Song H, Zhang L. Active contours driven by local image fitting energy [J]. Pattern Recognition, 2010, 43 (4): 1199-1206.] used Gaussian filtering to regularize the level set function and proposed a local image fitting (LIF) model. This model uses the difference between the original image and the image composed of the fitting function to define the energy functional, thereby solving the segmentation problem of grayscale non-uniform images. The segmentation effect is similar to the LBF model, but the efficiency is significantly improved. Wang et al. [WANG L, HE L, MISHRAA, et al. Active contours driven by local Gaussian distribution fitting energy[J]. Signal Processing, 2009, 89(12): 2435-2447.] proposed an image segmentation method based on the LBF model using the local Gaussian distribution fitting energy (LGDF) model. This method describes the local grayscale of the image with a Gaussian distribution, and uses the local mean and variance to characterize the pixel grayscale distribution in the local area. Good segmentation results are obtained, but it is sensitive to the shape, position and noise of the initial contour of the image. Zhang et al. [Zhang K, Zhang L, Song H, et al. Active contours with selective local or global segmentation: a new formulation and level set method [J]. Image and Vision Computing, 2010, 28 (4): 668-676.] constructed a signed pressure function (SPF) based on global grayscale information and proposed a selective binary and Gaussian filtering regularized level set (SBGFRLS) model. This method uses the statistical information of the image region to drive the evolution of the level set function, and the introduction of regional information enables the model to have a stronger ability to capture edge information and avoid edge leakage.However, it is based on the assumption of global grayscale constancy, which makes it difficult to complete the segmentation task of images with uneven grayscale [Zhao Yue. Research on brain image segmentation algorithm based on energy minimization method [D]. Changchun: Doctoral Dissertation of Jilin University, 2017.].

[0005] The following are several common image segmentation models:

[0006] 1.GAC Model

[0007] The GAC model is evolved from the snake model. This model combines the level set method and the active contour model for the first time. By minimizing the energy functional, the contour curve of the image to be segmented can be obtained. Its energy functional is defined as follows:

[0008]

[0009] Where L(c) is the arc length of the curve contour c, g(·) is the monotonically decreasing edge stop function, C(s) is the parametric curve, and ▽I represents the image gradient. Using the variational method and gradient descent method, the corresponding Euler-Lagrange equation is obtained:

[0010]

[0011] Where α is the balloon force, which is used to control the expansion or contraction rate of the contour curve.

[0012] The GAC model constructs an edge stop function based on image gradient information, which can quickly detect target edges. However, it is difficult to segment target images with blurred boundaries and has weak anti-noise performance.

[0013] 2.CV Model

[0014] Chan and Vese [Chan TF, Vese LA. Active contours without edges [J]. IEEE Transactions on Image Processing, 2001, 10 (2): 266-277.] assumed that the image grayscale is uniformly distributed and constructed an energy functional by minimizing the square error between the grayscale values of the pixels inside and outside the curve and the mean, thereby transforming the image segmentation problem into a function extreme value problem. When the function approaches the minimum value, the target contour is segmented. Its energy functional is expressed as:

[0015]

[0016] In the above formula, I(x) is the segmented image, L is the arc length of curve C, and A is the area enclosed by the contour of curve C. μ, ν >= 0, λ1, λ2 > 0 are weighting coefficients, and c1 and c2 represent the grayscale mean inside and outside curve C, respectively. The contour line can be used to divide the image into two parts, inC and outC. When the contour curve C is located at the boundary of the image object, the energy functional E reaches its minimum value. E is expressed as follows:

[0017]

[0018] Among them, H(Φ) is the Heaviside function, δ(Φ) is the Dirac function, and its smooth form is expressed as:

[0019]

[0020] Here c1 and c2 are calculated as follows:

[0021]

[0022] By minimizing formula (4) using the variational method, we obtain the following level set evolution equation:

[0023]

[0024] The CV model makes full use of the global information of the image, so this method can be applied to both strong-edge and weak-edge image segmentation, and is also suitable for the segmentation of internal target areas with hollows [Sun Lin, Ke Zhengyou, Feng Xiaobo, et al. Active contour image segmentation method based on double-signed pressure function [J]. Computer Engineering and Applications, 2018, 54(20): 213-218.]. However, the segmentation effect of images with blurred boundaries and uneven grayscale distribution is not ideal.

[0025] 3.SBGFRLS Model

[0026] Zhang et al. [Zhang K, Zhang L, Song H, et al. Active contours with selective local or global segmentation: a new formulation and level set method [J]. Image and Vision Computing, 2010, 28 (4): 668-676.] proposed the SBGFRLS model based on global grayscale information. This model fully integrates the advantages of the GAC and CV algorithms and uses the direction-adaptive SPF function to replace the edge stop function g(·) in the GAC model. On this basis, the level set evolution equation is obtained as follows:

[0027]

[0028] The calculation method of spf(I(x)) is as follows:

[0029]

[0030] Where c1 and c2 can be calculated by formulas (7) and (8). According to formula (11), the range of spf(I(x)) function is [-1, 1]. According to the literature [Zhang K, Zhang L, Song H, et al. Active contours with selective local or global segmentation: a new formulation and level set method [J]. Image and Vision Computing, 2010, 28 (4): 668-676.], the value of formula (10) can be obtained. and can be ignored. Therefore, the level set evolution equation of the model can be simplified as:

[0031]

[0032] The SBGFRLS model avoids the expensive time cost of reinitialization in traditional level set methods and can automatically detect image boundaries based on the location of the initial contour in the image, with the property of selective global or local segmentation. However, based on the assumption of uniform image distribution, it cannot accurately segment grayscale heterogeneous images, and the location and size of the initial contour have a significant impact on the image segmentation effect [Sun L, Meng X, Xu J, et al. An image segmentation method using an active contour model based on improved SPF and LIF [J]. Applied Sciences, 2018, 8 (12), Article ID: 2576.].

[0033] 4.LIF Model

[0034] The LIF model proposed by Zhang et al. [Zhang K, Song H, Zhang L. Active contours driven by local image fitting energy [J]. Pattern Recognition, 2010, 43(4): 1199-1206.] is a classic region-based active contour model. This model uses the difference between the fitted image and the original image to define the local image fitting function. Its segmentation effect is similar to the LBF model, but it can ensure sub-pixel accuracy and boundary regularity. The energy functional of this algorithm is defined as follows:

[0035]

[0036] Where I(x) is the original image to be segmented, and the calculation formula of the local image fitting function is as follows:

[0037]

[0038] In the above formula, W k (x) is a rectangular window function using a truncated Gaussian window The standard deviation is The window size is (4k+1)*(4k+1), and k is less than The maximum integer.

[0039] According to the variational method and the steepest descent method, the level set evolution equation corresponding to formula (13) is obtained:

[0040]

[0041] The model uses Gaussian kernel filtering to replace the regularization term in the traditional level set function, avoiding the disadvantage of its periodic initialization operation. From the perspective of segmentation effect, the LIF model can achieve similar segmentation accuracy as the LBF model with lower time complexity. However, due to the lack of global information in the image, the segmentation effect of this model on strong noisy images is not good.

[0042] In summary, the global information of the image can reduce the influence of the initial contour and noise, and the local information can enhance the model's processing ability for grayscale heterogeneous images. However, there is currently no report on the active contour model that combines the global and local information of the image. Summary of the Invention

[0043] The technical problem solved by the present invention is to provide a signed pressure function segmentation method that combines global and local image information. This method constructs an active contour model that combines global and local image information. First, a hybrid signed pressure function is constructed by linearly combining newly defined global grayscale fitting terms and local grayscale fitting terms. Second, a balloon force function is redefined using global and local image information. Finally, experiments demonstrate that the model constructed by the present invention can accurately segment weak boundary and multi-target images. The method not only accurately segments weak boundary and multi-target images, but also has a high segmentation speed and a certain degree of robustness to noise.

[0044] In order to solve the above technical problems, the present invention adopts the following technical solution, which is a signed pressure function segmentation method that combines global and local information of the image. The method is characterized by the following specific process: first, the global and local area information of the image are used to construct global and local grayscale fitting terms respectively; second, the defined global fitting terms are linearly combined with the local fitting terms to construct a mixed signed pressure function; finally, the balloon force function is redefined to achieve the purpose of adaptively changing the level set evolution rate.

[0045] The method for segmenting a signed pressure function by combining global and local image information of the present invention is characterized by the following specific steps:

[0046] First, based on the global regional statistical information of the image, the global regional grayscale mean weighted combination function Gspf of the image is given by combining c1 and c2, where c1 and c2 can be calculated by formulas (7) and (8):

[0047] Gspf=(I-c1H-c2(1-H)) (16)

[0048] Secondly, the local area information f1 and f2 of the image are used to construct the local grayscale fitting term Lspf:

[0049] Lspf=(I-f1H-f2(1-H)) (17)

[0050] Where: f1 and f2 are given by m1 and m2 in formula (14);

[0051] Finally, the global area grayscale mean weighted combination function Gspf and the local grayscale fitting term Lspf of the image are combined to construct the function spf:

[0052]

[0053] Among them, a is a variable with a value range of [0,1]. The function spf combines the local grayscale information of the image with the global information of the image, which not only speeds up the image segmentation speed, but also improves the robustness of the algorithm.

[0054] In summary, the spf function in equation (12) can be replaced by equation (18) to obtain the level set evolution equation corresponding to the signed pressure function segmentation model that combines global and local information of the image:

[0055]

[0056] Considering that the model uses a fixed balloon force to control the evolution rate of the level set function, different balloon force parameters need to be set for different images. Based on the construction method of the balloon force function, this paper uses the global and local information of the image to redefine the balloon force function in order to achieve the purpose of adaptively changing the evolution rate of the level set function. Its definition is as follows:

[0057] α=(I-(c1+c2)-(f1+f2)) 2 (20)

[0058] Compared with existing technologies, this invention offers the following advantages and benefits: It proposes a signed pressure function segmentation method that combines global and local image information. First, a hybrid signed pressure function is constructed using both global and local image information. Then, a new balloon force function is defined, which automatically contracts and expands, ultimately completing the image segmentation task. Simulation results demonstrate that this method can effectively address the segmentation of weak-boundary and multi-target images while exhibiting a certain degree of noise immunity. Furthermore, the proposed method demonstrates both segmentation accuracy and efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is the weak boundary image segmentation result image.

[0060] Figure 2 It is the multi-target image segmentation result map.

[0061] Figure 3 It is the natural image segmentation result map. DETAILED DESCRIPTION

[0062] The above contents of the present invention are further described in detail below through examples, but this should not be understood as limiting the scope of the above subject matter of the present invention to the following examples. All technologies implemented based on the above contents of the present invention fall within the scope of the present invention.

[0063] Example

[0064] Signed pressure function segmentation method combining global and local image information

[0065] As discussed above, the SPF proposed by the SBGFRLS model, which uses global grayscale information, can effectively address image contours with blurred edges. However, its assumption of a constant global grayscale makes it difficult to segment images with uneven grayscale. Furthermore, the LIF model, lacking global image information, is highly sensitive to the position and size of the initial contour curve. Based on this discussion, this paper proposes a signed pressure function segmentation method that combines both global and local image information.

[0066] First, based on the global regional statistical information of the image, the global regional grayscale mean weighted combination function Gspf of the image is given by combining c1 and c2, where c1 and c2 can be calculated by formulas (7) and (8):

[0067] Gspf=(I-c1H-c2(1-H)) (16)

[0068] Secondly, the local area information f1 and f2 of the image are used to construct the local grayscale fitting term Lspf:

[0069] Lspf=(I-f1H-f2(1-H)) (17)

[0070] Where: f1 and f2 are given by m1 and m2 in formula (14);

[0071] Finally, referring to the construction method of the SBGFRLS model in the literature [Zhang K, Zhang L, Song H, et al. Active contours with selective local or global segmentation: a new formulation and level set method [J]. Image and Vision Computing, 2010, 28 (4): 668-676.], a new function SPF is constructed by combining the image global information Gspf and the image local information Lspf. This function SPF combines the local grayscale information of the image with the global information, which not only speeds up the image segmentation speed but also improves the robustness of the algorithm.

[0072]

[0073] Here, a is a variable whose value range is [0,1].

[0074] In summary, the spf function in equation (12) can be replaced by equation (18) to obtain the level set evolution equation corresponding to the model in this paper:

[0075]

[0076] Considering that the model in the literature [Zhang K, Zhang L, Song H, et al. Active contours with selective local or global segmentation: a new formulation and level set method [J]. Image and Vision Computing, 2010, 28 (4): 668-676.] uses a fixed balloon force to control the evolution rate of the level set function, different balloon force parameters need to be set for different images. Based on the construction method of the balloon force function in the literature [Abdelsamea MM, Tsaftris S A. Active contours model globally signed regionpressure force [C] / / 2013 18th International Conference on Digital SignalProcessing (DSP), Santorini, Greece, 2013, 1: 512-517.], this paper redefines the balloon force function using the global and local information of the image in order to achieve the purpose of adaptively changing the evolution rate of the level set function. Its definition is as follows:

[0077] α=(I-(c1+c2)-(f1+f2)) 2 (20)

[0078] Simulation Experiment Results and Analysis

[0079] The experimental environment: Intel(R) Core(TM) i5-7500M CPU @ 3.40GHz, 16.00GB RAM, 64-bit Windows 10, using MATLAB R2014a toolbox for coding. In this paper, three sets of comparative experiments were conducted. To enhance the credibility of the experimental results, the segmentation results were compared with those of the CV model, the LIF model, and the SBGFRLS model. The parameter selection of the comparative models can be found in the respective literature and will not be detailed here.

[0080] Figure 1 The first column is the original image, and the second to fifth columns are the segmentation results of the CV model, LIF model, SBGFRLS model and the model constructed by the present invention. Figure 1In (e), the values of a are 0.6 and 0.1, respectively. As can be seen from the segmentation results, the LIF model is unable to complete the segmentation of weak-boundary images. The CV model and the SBGFRLS model, due to their excessive reliance on global image information, result in over-segmentation and incomplete segmentation results. The method proposed in the present invention combines global and local information, thereby rapidly completing image segmentation. This demonstrates that the model constructed in the present invention is capable of processing weak-boundary images well.

[0081] Figure 2 is the segmentation result of the multi-target image, where Figure 2 The value of a in (e) is 0.2. Experimental results show that the LIF model cannot complete the multi-target image segmentation task, and the CV model is Figure 2 The first image shows over-segmentation. The SBGFRLS model and the proposed model can successfully complete the segmentation of the multi-target image. Table 1 shows that the segmentation efficiency of the proposed model is better than that of the SBGFRLS model. In summary, the model constructed by the present invention can efficiently complete the segmentation task of multi-target images.

[0082] In order to fully demonstrate the effectiveness of the method proposed in this invention, Figure 3 Two natural images were selected for segmentation experiments. Figure 3 (e) The parameter a is set to 0.1 and 0.15 respectively. It can be clearly seen from the segmentation results that the LIF model only considers local information of the image, and the segmentation results are easily disturbed by detailed information, resulting in incorrect segmentation. The CV model and SBGFRLS model can obtain most of the correct edge contours based on the global information of the image, but they are not very accurate. Figure 3 The second image shows the inner details of the finger, but the processing effect is not satisfactory. However, the model constructed by the present invention can well segment this part of connected pixels, further proving the accuracy of the new model.

[0083] To further verify the performance of the algorithm in this paper, Table 1 shows the performance of the four models. Figures 1 to 3 The number of iterations and convergence time during the segmentation experiment. As can be seen in Table 1, the SBGFRLS model and the model constructed in this paper have similar efficiency, but the processing of some image details needs to be improved. The experimental results in Table 1 once again confirm the stability and effectiveness of the model constructed in this paper.

[0084] Table 1 Four models Figures 1 to 3 The number of iterations and convergence time results when performing segmentation

[0085]

[0086] In summary, the present invention proposes a signed pressure function segmentation method that combines global and local image information. This method constructs a hybrid signed pressure function active contour model that combines global and local image information. First, a hybrid signed pressure function is constructed using both global and local image information. Then, a new balloon force function is defined that can automatically contract and expand, ultimately completing the image segmentation task. Simulation experimental results demonstrate that this method can effectively solve the segmentation problems of weak-boundary and multi-target images while also exhibiting a certain degree of noise immunity. Furthermore, the segmentation accuracy and efficiency of the present method have been effectively demonstrated.

[0087] The above embodiments describe the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for illustrating the principles of the present invention. Without departing from the scope of the principles of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of protection of the present invention.

Claims

1. A signed pressure function segmentation method combining global and local image information, characterized by The specific process is as follows: first, the global and local region information of the image are used to construct global and local grayscale fitting terms respectively; second, the defined global fitting term is linearly combined with the local fitting term to construct a mixed-sign pressure function; finally, the balloon force function is redefined to achieve the purpose of adaptively changing the level set evolution rate; The specific steps are: First, based on the global regional statistical information of the image, the global regional grayscale mean weighted combination function Gspf of the image is given by combining c1 and c2, where c1 and c2 can be calculated by formulas (7) and (8): Gspf=(I-c1H(Φ(x))-c2(1-H(Φ(x)))) (16) Where I is the target image to be segmented, H(Φ) is the Heaviside function; Secondly, the local area information f1 and f2 of the image are used to construct the local grayscale fitting term Lspf: Lspf=(I-f1H-f2(1-H)) (17) Where: f1 and f2 are given by m1 and m2 in formula (14); W k (x) is a rectangular window function using a truncated Gaussian window The standard deviation is The window size is (4k+1)*(4k+1), and k is less than The largest integer; Finally, the global area grayscale mean weighted combination function Gspf and the local grayscale fitting term Lspf of the image are combined to construct the function spf: Among them, a is a variable with a value range of [0,1]. The function spf combines the local grayscale information of the image with the global information of the image, which not only speeds up the image segmentation speed but also improves the robustness of the algorithm. Where: spf(I(x)) represents the symbolic pressure function, I is the target image to be segmented, α is the balloon force function, Refers to the gradient norm of the level set function; Using Equation (18) to replace the spf function in Equation (12), we can obtain the level set evolution equation corresponding to the signed pressure function segmentation model that combines global and local information of the image: Considering that the model uses a fixed balloon force to control the evolution rate of the level set function, different balloon force parameters need to be set for different images. Based on the construction method of the balloon force function, this paper uses the global and local information of the image to redefine the balloon force function in order to achieve the purpose of adaptively changing the evolution rate of the level set function. Its definition is as follows: α=(I-(c1+c2)-(f1+f2)) 2 (20)。

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