Image segmentation method based on Finsler infinity-Laplacian parametric active contour model

Abstract

The invention discloses an image segmentation method of a parametric type active contour model based on Finsler-Laplacian. According to the method, an anisotropic Finsler norm is introduced under a static external force field, and a new energy minimization problem is provided and comprises a data fidelity term and a regularization term based on the Finsler norm. A corresponding Euler-Lagrange equation is derived through a variational method and is converted into a time-evolved parabolic partial differential equation for numerical solution. A comparison principle is established under the framework of the viscous solution, and the existence of the understanding, the continuity about the space Lipschitz and the continuity about the time consistency are proved. The model has the advantages of being large in capture range, insensitive to initial contours, high in noise immunity, capable of effectively retaining image edge details and the like, and shows excellent performance in medical image and natural image segmentation.

Description

Technical Field

[0001] This invention belongs to the field of image processing and computer vision technology, specifically a Finsler-based method. - Laplacian is a parametric active contour model for image segmentation. Background Technology

[0002] Image segmentation is a fundamental task in computer vision, aiming to divide an image into semantically meaningful regions based on pixel grayscale, texture, or feature similarity. This method has wide applications in numerous fields such as medical imaging, autonomous driving, and object recognition. Active contour models (also known as "Snake" models) are a classic image segmentation technique. Their core idea is to define an energy functional to drive an initial curve to evolve towards the target boundary under the combined influence of internal and external force fields. Since its inception, this model has spawned many improved variants, continuously driving the development of this technological field.

[0003] However, active contour models still face some challenges in noisy and complex edge images: 1) Although active contour models have made some progress, they still suffer from insufficient capture range and noise sensitivity; 2) Most current methods are based on isotropic Euclidean norms to construct energy functionals, which drive contour evolution in a consistent manner in all directions, thus easily leading to weak edge leakage. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings and deficiencies of the existing technology by providing a Finsler-based solution. - Laplacian is a parametric active contour model for image segmentation.

[0005] The technical solution to achieve the purpose of this invention is: a Finsler-based... - An image segmentation method based on the parametric active contour model of Laplacian, the method comprising the following steps:

[0006] Step 1, Input the image to be segmented Calculate its gradient vector flow external force field ;

[0007] Step 2, construct a data fidelity term containing Finsler norm-based terms and The energy functional of the regularization term;

[0008] Step 3: Apply the variational method to the energy functional to obtain the corresponding Euler-Lagrange equation, and introduce the time variable. Periodic extensions are performed to construct a time-dependent parabolic partial differential equation as the evolution equation, denoted as Finsler-based. -Laplacian parametric active contour model;

[0009] Step 4, Custom Initialization Based on Finsler - The initial contour of the parametric active contour model of Laplacian;

[0010] Step 5: Based on the discrete iterative format, perform the Finsler-based... - The Laplacian parametric active contour model is iteratively solved until convergence to obtain the image segmentation contour.

[0011] Step 1 calculates the image to be segmented Gradient vector flow external force field Specifically, it includes:

[0012] Image to be segmented Perform Gaussian smoothing and calculate the gradient of the edge image. ;

[0013] Based on edge image gradient Using edge detection functions Calculate the external force field of gradient vector flow :

[0014]

[0015] in, satisfy and ;

[0016] In the formula, They are respectively about and directional components, Represents the edge detection function Find the gradient. Represents absolute value. express The value at the origin.

[0017] Furthermore, the energy functional described in step 2 is expressed as: :

[0018]

[0019] In the formula, express A bounded region yes Norm, Represents the edge image. It is an external force field of gradient vector flow; The image to be segmented The component of the external force field, It is the gradient operator. It is Finsler norm. It is a Sobolev space. They represent about Integral infinitesimal element;

[0020] and initialize parameters .

[0021] Furthermore, the periodic extension in step 3 specifically involves: the function Initially defined in a bounded region Above, it is extended to through symmetry. Then, periodically extend it to the entire plane. .

[0022] Furthermore, the parabolic partial differential equation of time evolution described in step 3 is expressed as:

[0023]

[0024] in, It is Finsler Laplacian. It is Finsler -Laplacian; , It is a function exist The value; denoted of for ,Right now Similarly, there are ;

[0025] In the formula, yes exist The value, This represents the inner product operation. yes The original function, This indicates that with respect to the gradient operator, It is a divergence operator; It is time. ; Represents the components of the direction vector. The partial derivative representing the direction of spatial coordinates. yes directional partial derivative, yes directional partial derivative; It is a Sobolev space. It is the entire two-dimensional real space The set of all real-valued continuous functions on the x-axis. It is a constant.

[0026] Furthermore, in step 5, based on the discrete iterative format, the Finsler-based... - The parametric active contour model of the Laplacian is solved iteratively, specifically including: for the diffusion term, the central difference scheme is used for discretization; for the flow term, the upwind difference scheme is used for discretization.

[0027] On the other hand, an image segmentation system is provided, the system comprising:

[0028] The first module is used to receive the image to be segmented. Calculate its gradient vector flow external force field ;

[0029] The second module is used to construct a data fidelity item containing Finsler norm-based data and The energy functional of the regularization term;

[0030] The third module is used to apply the variational method to the energy functional to obtain the corresponding Euler-Lagrange equation, and to introduce the time variable. Periodic extensions are performed to construct a time-dependent parabolic partial differential equation as the evolution equation, denoted as Finsler-based. -Laplacian parametric active contour model;

[0031] The fourth module is used for custom initialization based on Finsler. - The initial contour of the parametric active contour model of Laplacian;

[0032] The fifth module is used to perform the Finsler-based method based on a discrete iterative format. - The Laplacian parametric active contour model is iteratively solved until convergence to obtain the image segmentation contour.

[0033] On the other hand, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the Finsler-based... - Laplacian is a parametric active contour model for image segmentation.

[0034] On the other hand, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the Finsler-based... - Laplacian is a parametric active contour model for image segmentation.

[0035] Compared with the prior art, the significant advantages of this invention are:

[0036] (1) This invention proposes a novel Finsler-based method. - The Laplacian parametric active contour model, by introducing anisotropic Finsler norms, achieves accurate segmentation of complex edges and effective noise suppression, thereby enabling accurate image segmentation.

[0037] (2) This invention proposes a theoretical proof system for the viscous solution of parabolic problems. By establishing the comparison principle and proving the existence and regularity of the solution, it realizes the rigorous mathematical theoretical support of the model and the reliable convergence of the numerical solution.

[0038] (3) This invention proposes a robust image segmentation method that, through the direction selection characteristics of the Finsler norm, exhibits excellent robustness in the processing of Gaussian noise, speckle noise and salt-and-pepper noise.

[0039] (4) The present invention proposes a more comprehensive experimental verification scheme. By comparing with a variety of mainstream models on medical and natural images, it has achieved superior performance in both subjective visual and objective indicators (such as Dice coefficient, Jaccard index, recall rate).

[0040] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0042] Figure 1 This invention is based on Finsler. -Flowchart of the overall implementation of the parametric active contour image segmentation method of Laplacian.

[0043] Figure 2 This is an example illustrating the experimental effects of the present invention on a set of medical and natural images, wherein... Figure 2 In the image, (a1) to (d1) represent the original ultrasound image to be segmented, the initial contour settings, the curve evolution process, and the final segmentation result, respectively. Figure 2 In the diagram, (a2) to (d2) represent the original image of the fruit to be segmented, the initial contour settings, the curve evolution process, and the final segmentation result, respectively. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0046] It should be noted that if the embodiments of the present invention involve directional indicators (such as up, down, left, right, front, back, etc.), the directional indicators are only used to explain the relative positional relationship and movement of the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.

[0047] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0048] In one embodiment, a Finsler-based approach is provided. - An image segmentation method based on the parametric active contour model of Laplacian, the method comprising the following steps:

[0049] Step 1, Input the image to be segmented Calculate its gradient vector flow external force field ;

[0050] Step 2, construct a data fidelity term containing Finsler norm-based terms and The energy functional of the regularization term;

[0051] Step 3: Apply the variational method to the energy functional to obtain the corresponding Euler-Lagrange equation, and introduce the time variable. Periodic extensions are performed to construct a time-dependent parabolic partial differential equation as the evolution equation, denoted as Finsler-based. -Laplacian parametric active contour model;

[0052] Step 4, Custom Initialization Based on Finsler - The initial contour of the parametric active contour model of Laplacian;

[0053] Step 5: Based on the discrete iterative format, perform the Finsler-based... - The Laplacian parametric active contour model is iteratively solved until convergence to obtain the image segmentation contour.

[0054] Furthermore, in one embodiment, step 1 calculates the image to be segmented. Gradient vector flow external force field Specifically, it includes:

[0055] Image to be segmented Perform Gaussian smoothing and calculate the gradient of the edge image. ;

[0056] Based on edge image gradient Using edge detection functions Calculate the external force field of gradient vector flow :

[0057]

[0058] in, satisfy and ;

[0059] In the formula, They are respectively about and directional components, Represents the edge detection function Find the gradient. Represents absolute value. express The value at the origin.

[0060] Furthermore, in one embodiment, the Finsler norm of the anisotropic aspect in step 2 is specifically:

[0061]

[0062] In the formula, It's a transpose operation. They are Two components;

[0063] The energy functional is expressed as :

[0064]

[0065] In the formula, express A bounded region yes Norm, Represents the edge image. It is an external force field of gradient vector flow; The image to be segmented The component of the external force field, It is the gradient operator. It is Finsler norm. It is a Sobolev space. They represent about Integral infinitesimal element;

[0066] and initialize parameters .

[0067] Furthermore, in one embodiment, the periodic extension in step 3 specifically involves: function Initially defined in a bounded region Above, it is extended to through symmetry. Then, periodically extend it to the entire plane. .

[0068] Furthermore, in one embodiment, the parabolic partial differential equation of time evolution described in step 3 is expressed as:

[0069]

[0070] in, It is Finsler Laplacian. It is Finsler -Laplacian; , It is a function exist The value; denoted of for ,Right now Similarly, there are ;

[0071] In the formula, yes exist The value, This represents the inner product operation. yes The original function, This indicates that with respect to the gradient operator, It is a divergence operator; It is time. ; Represents the components of the direction vector. The partial derivative representing the direction of spatial coordinates. yes directional partial derivative, yes directional partial derivative; It is a Sobolev space. It is the entire two-dimensional real space The set of all real-valued continuous functions on the x-axis. It is a constant.

[0072] Here, we focus on the anisotropic operator in the evolution equation. To address the singularity at zero gradient, this invention employs a viscous solution framework, providing relevant definitions and notation for viscous solutions. By doubling the variables, a comparison principle for parabolic equations is established, successfully overcoming the challenge of non-differentiability at the origin. Using the Perron method, the existence of viscous solutions to the equations is proven. The Lipschitz continuity of the viscous solutions in space is proven using the continuous mode method, and the uniform temporal continuity of the viscous solutions is proven using the micro-ground photon method. Although the model of this invention is two-dimensional, these results are relevant to... The rules still apply.

[0073] Furthermore, based on the convergence criteria of Barles and Souganidis, this invention proves the convergence of the approximate solution of the numerical discrete scheme.

[0074] Furthermore, in one embodiment, step 5 is based on a discrete iterative format, applying the Finsler-based... - The parametric active profile model of the Laplacian is solved iteratively, specifically including: for the diffusion term, a central difference scheme is used for discretization to ensure the stability and accuracy of the numerical calculation; for the flow term, an upwind difference scheme is used for discretization to adapt to the directional characteristics of the external force field and avoid non-physical oscillations.

[0075] In each iteration step, update the numerical solution for the next time step based on the current solution. Check the convergence condition. If convergence is achieved, the iteration stops.

[0076] In one embodiment, an image segmentation system is provided, the system comprising:

[0077] The first module is used to receive the image to be segmented. Calculate its gradient vector flow external force field ;

[0078] The second module is used to construct a data fidelity item containing Finsler norm-based data and The energy functional of the regularization term;

[0079] The third module is used to apply the variational method to the energy functional to obtain the corresponding Euler-Lagrange equation, and to introduce the time variable. Periodic extensions are performed to construct a time-dependent parabolic partial differential equation as the evolution equation, denoted as Finsler-based. -Laplacian parametric active contour model;

[0080] The fourth module is used for custom initialization based on Finsler. - The initial contour of the parametric active contour model of Laplacian;

[0081] The fifth module is used to perform the Finsler-based method based on a discrete iterative format. - The Laplacian parametric active contour model is iteratively solved until convergence to obtain the image segmentation contour.

[0082] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements:

[0083] Step 1, Input the image to be segmented Calculate its gradient vector flow external force field ;

[0084] Step 2, construct a data fidelity term containing Finsler norm-based terms and The energy functional of the regularization term;

[0085] Step 3: Apply the variational method to the energy functional to obtain the corresponding Euler-Lagrange equation, and introduce the time variable. Periodic extensions are performed to construct a time-dependent parabolic partial differential equation as the evolution equation, denoted as Finsler-based. -Laplacian parametric active contour model;

[0086] Step 4, Custom Initialization Based on Finsler - The initial contour of the parametric active contour model of Laplacian;

[0087] Step 5: Based on the discrete iterative format, perform the Finsler-based... - The Laplacian parametric active contour model is iteratively solved until convergence to obtain the image segmentation contour.

[0088] For specific limitations on each step, please refer to the section above regarding Finsler-based approaches. The limitations of the Laplacian parametric active contour model for image segmentation are not elaborated here.

[0089] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program being implemented when executed by a processor:

[0090] Step 1, Input the image to be segmented Calculate its gradient vector flow external force field ;

[0091] Step 2, construct a data fidelity term containing Finsler norm-based terms and The energy functional of the regularization term;

[0092] Step 3: Apply the variational method to the energy functional to obtain the corresponding Euler-Lagrange equation, and introduce the time variable. Periodic extensions are performed to construct a time-dependent parabolic partial differential equation as the evolution equation, denoted as Finsler-based. -Laplacian parametric active contour model;

[0093] Step 4, Custom Initialization Based on Finsler - The initial contour of the parametric active contour model of Laplacian;

[0094] Step 5: Based on the discrete iterative format, perform the Finsler-based... - The Laplacian parametric active contour model is iteratively solved until convergence to obtain the image segmentation contour.

[0095] For specific limitations on each step, please refer to the section above regarding Finsler-based approaches. The limitations of the Laplacian parametric active contour model for image segmentation are not elaborated here.

[0096] In some embodiments, the present invention has been further verified and described.

[0097] (1) For the input chest CT image, the obtained external force field The output is visualized and compared with the external force field of the traditional GVF model. The results show that the model of this invention can effectively extrapolate the gradient vector field, forming a larger-scale and more directional driving force field around the target boundary, thereby significantly expanding the capture range and reducing the sensitivity to the initial contour position.

[0098] (2) To verify the robustness of the proposed model in noisy environments, different types and intensities of noise, including Gaussian noise, speckle noise, and salt-and-pepper noise, were added to the original chest CT images. The segmentation process was performed under each noise interference, and the contour evolution behavior and final convergence results were observed. The experiments showed that the model could stably converge to the target boundary in the three typical noisy images without obvious boundary leakage or contour divergence, demonstrating good noise adaptability and convergence robustness.

[0099] (3) On the same chest CT image, the performance of the model of the present invention was compared with that of six existing mainstream active contour models (including GVF, GGVF, NGVF, ADF, ILGVF, and GVFOM models). The segmentation results show that the model of the present invention performs better in capturing the edge features of the shape to be segmented, preserving weak edges, and suppressing noise, thus capturing the edge structural features of chest tissue more accurately. Furthermore, by generating a binary segmentation mask and using the Dice coefficient, Jaccard index, and recall rate as quantitative evaluation indicators, statistical analysis was performed on the segmentation results of each model. Experimental data show that the model of the present invention outperforms the comparison methods in all evaluation indicators, confirming its significant advantages in segmentation accuracy and stability, and demonstrating better performance in edge detail.

[0100] Here, the Dice coefficient, Jaccard index, and recall rate are respectively:

[0101]

[0102]

[0103] ,

[0104] in, : The segmented region predicted by the model (binary mask). : The actual labeled area (binary mask). : Total number of pixels in the prediction region : Total number of pixels in the real area : The number of pixels correctly predicted as foreground pixels : The number of pixels correctly predicted as foreground pixels : Number of pixels incorrectly predicted as background.

[0105] (4) To evaluate the convergence behavior of the proposed energy functional during the numerical iteration process, an energy tracking experiment was conducted on the same thoracic CT image. The value of the energy functional was recorded in each iteration, and the energy change curve with time step was plotted. The results show that as the iteration proceeds, the energy value shows a monotonically decreasing trend and eventually tends to stabilize, without obvious oscillation or divergence, verifying that the proposed model has good reliability in both theoretical convergence and numerical implementation.

[0106] Figure 2 The images show the segmentation results of this invention on a set of medical images and physical images. It can be seen that the method of this invention maintains strong detail preservation capabilities even in chest CT medical images requiring precise segmentation. For physical images with blurred edges, the method of this invention can still successfully preserve weak edges and performs even better in edge detail processing.

[0107] The foregoing has shown and described 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 embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention without departing from its spirit and scope should be included within the protection scope of the present invention.

Claims

1. An image segmentation method based on a Finsler -Laplacian parametric active contour model, characterized in that, The method comprises the steps of: Step 1, input the image to be segmented , calculate its gradient vector flow external force field ; Step 2, construct an energy functional containing a data fidelity term based on the Finsler norm and a regularizing term. Step 3, apply the variational method to the energy functional, obtain the corresponding Euler-Lagrange equation, and introduce the time variable , periodic continuation, construct a time-dependent parabolic partial differential equation as the evolution equation, denoted as the parameterized active contour model based on Finsler -Laplacian; Step 4, Custom initialization based on Finsler Initial contours for parametric active contour model of Laplacian; Step 5, iteratively solve the parametric active contour model based on Finsler -Laplacian until convergence is obtained, to obtain the image segmentation contour.

2. The Finsler-based image segmentation method of claim 1, wherein the Finsler metric is defined as An image segmentation method using a parametric active contour model of Laplacian, characterized in that, The image to be segmented is calculated in step 1 Gradient vector flow external force field Specifically, the method comprises: To segment an image Gaussian smoothing and computing edge image gradients ; Based on edge image gradients , using edge detection function Compute gradient vector flow external force field : ； wherein satisfies and ; wherein are respectively about and components of the direction, denotes the gradient of the edge detection function denotes the gradient, denotes the absolute value, denotes the value at the origin.

3. The Finsler based An image segmentation method of a parametric active contour model of Laplacian, characterized by, The energy functional described in step 2 is represented as : ； wherein denotes a bounded region, is a norm, denotes the edge image, is the gradient vector flow external force field; is the image to be segmented a component of the external force field, is the gradient operator, is the Finsler norm, is the Sobolev space, denotes the integral element with respect to respectively. and initializing parameters .

4. The Finsler-based image segmentation method of claim 3, wherein the Finsler metric is defined as An image segmentation method of a parametric active contour model of Laplacian, characterized in that, The periodic continuation in step 3 is specified as follows: the function is initially defined on a bounded region , which is extended by symmetry to , and then periodically to the entire plane .

5. The Finsler-based image segmentation method of claim 4, wherein the Finsler metric is defined as An image segmentation method using a parametric active contour model of Laplacian, characterized in that The time-evolving parabolic partial differential equation in step 3 is expressed as: ； wherein is the Finsler Laplacian, is the Finsler -Laplacian; , is a function In the value of is is , i.e. , and the same has ; In the formula, yes exist The value, This represents the inner product operation. yes The original function, This indicates that with respect to the gradient operator, It is a divergence operator; It is time. ; Represents the components of the direction vector. The partial derivative representing the direction of spatial coordinates. yes directional partial derivative, yes directional partial derivative; It is a Sobolev space. It is the entire two-dimensional real space The set of all real-valued continuous functions on the x-axis. It is a constant.

6. The Finsler-based image segmentation method of claim 5, wherein the Finsler metric is defined as An image segmentation method of a parametric active contour model of Laplacian, characterized in that, In step 5, the Finsler-based The iterative solution of the parametric active contour model based on Laplacian includes: for the diffusion term, a central difference format is adopted for discretization; and for the flow term, an upwind difference format is adopted for discretization.

7. An image segmentation system based on the method of any one of claims 1 to 6, characterized in that, The system comprises: A first module for receiving an image to be segmented , computing its gradient vector flow external force field ; a second module for constructing an energy functional comprising a data fidelity term based on a Finsler norm and a regularization term; A third module is configured to apply a variational method to the energy functional, obtain a corresponding Euler-Lagrange equation, and introduce a time variable , perform periodic continuation, and construct a time-dependent parabolic partial differential equation as an evolution equation, denoted as a parameterized active contour model based on Finsler -Laplacian a fourth module for customizing initialization of the Finsler initial contours of a parametric active contour model of Laplacian; The fifth module is used to perform the Finsler-based method based on a discrete iterative format. - The Laplacian parametric active contour model is iteratively solved until convergence to obtain the image segmentation contour.

8. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor implements the method of any one of claims 1 to 6 when executing the computer program.

9. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program implements the method of any one of claims 1 to 6 when executed by a processor.

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