Image segmentation method and system of regional active contour model based on p-Laplacian operator
By introducing the energy functional of the adaptive-Laplacian operator and the gradient descent method, the problem of insufficient segmentation accuracy of traditional active contour models in complex images is solved, and adaptive balance and stability improvement of image segmentation are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING UNIV OF SCI & TECH
- Filing Date
- 2026-02-02
- Publication Date
- 2026-05-22
AI Technical Summary
Existing active contour models based on edges and regions struggle to achieve an adaptive balance between smoothness and edge details when processing complex images, resulting in insufficient segmentation accuracy and robustness.
An energy functional of the adaptive-Laplacian operator is introduced as a regularization term for the level set function. By combining local gradient adaptive regulation, global sparse self-representation, and distance regularization, an energy functional is constructed, and image segmentation is optimized through variational and gradient descent methods.
It achieves smoothing of homogeneous regions and adaptive preservation of edge details in complex images, improving segmentation accuracy and robustness, avoiding the re-initialization problem in traditional methods, and improving computational efficiency.
Smart Images
Figure CN122072965A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of image processing technology, specifically a method based on... - An image segmentation method based on the active contour model of the region using the Laplacian operator. 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. Based on different driving mechanisms, active contour models can be mainly divided into two categories: edge-based models and region-based models.
[0003] Edge-based models rely on image gradient information to guide curve evolution, stopping where the gradient is significant and continuously approaching the target boundary in weak gradient regions. They perform well in images with clear target edges and high contrast. However, these models are sensitive to blurred edges, noise interference, and weak boundaries, and are prone to getting trapped in local optima, leading to segmentation failure.
[0004] Region-based models utilize the statistical features of regions inside and outside the contour (such as mean gray level and distribution differences) to drive curve evolution. Segmentation is achieved by minimizing the differences in statistical features between regions inside and outside the contour, which is effective in uniform gray-level images. However, its segmentation accuracy is still insufficient when faced with common situations in natural images such as uneven gray levels and complex textures. Summary of the Invention
[0005] The purpose of this invention is to address the deficiencies or shortcomings of the existing technology by providing a method based on... - An image segmentation method based on the Laplacian operator's region-active contour model, by introducing adaptive... - The energy functional corresponding to the Laplacian operator, as the length regularization term of the level set function, achieves an adaptive balance between homogeneous region smoothing and edge detail preservation, improving the segmentation accuracy and robustness of the model in complex images.
[0006] The technical solution for achieving the objective of this invention is as follows: On the one hand, a method based on... - An image segmentation method using a region-active contour model with the Laplacian operator, the method comprising the following steps:
[0007] Step 1, build based on - The regional active contour model of the Laplacian operator includes:
[0008] Introducing Adaptive The function, whose value is dynamically adjusted according to the local image gradient, achieves a combination of isotropic and anisotropic diffusion, thereby realizing adaptive control of diffusion behavior.
[0009] Build based on - The adaptive regularization term of the Laplace operator is defined as the geometric length regularization term of the level set function;
[0010] An energy functional is constructed that integrates global features, local features, and sparse self-representation high-level features, and is used as the optimization objective for image segmentation.
[0011] Step 2: Solve for the optimal solutions of each variable in the energy functional using variational methods;
[0012] Step 3: Minimize the energy functional using the gradient descent method to obtain the final evolution result;
[0013] Step 4: Extract the image segmentation results based on the evolution results.
[0014] Furthermore, in step 1, the adaptive The function is defined as follows:
[0015]
[0016] In the formula, Indicates adaptive function, The standard deviation is Gaussian kernel function, For edge maps, Represents the gradient. This represents the gradient of the convolution between the edge map and the Gaussian kernel. Indicates modulo operation, " indicates a definition.
[0017] Furthermore, in step 1, the adaptive The value of the function is dynamically adjusted based on the local image gradient, specifically:
[0018] When the image gradient approaches zero, i.e. When, satisfy ,at this time The Laplacian operator degenerates into the Laplacian operator, whose diffusion behavior is isotropic, effectively smoothing homogeneous regions in an image and suppressing noise; as the image gradient approaches infinity, i.e. When, satisfy ,at this time The Laplacian operator degenerates into a total variational regularization term, whose diffusion behavior is characterized by anisotropic edge-preserving diffusion, thereby effectively suppressing noise while preserving the edge details of the image.
[0019] Furthermore, in step 1 - The energy functional corresponding to the Laplace operator, that is, the regularization term of the constructed level set function, is defined as: :
[0020]
[0021] In the formula, " indicates a definition, For definition Bounded regions in Indicates the integral symbol, Representative on Integral infinitesimal domain, This is the Dirac function for regularization, where z has no actual meaning and is only used to refer to the variable. A constant that is greater than zero. It is a level set function.
[0022] Furthermore, the energy functional in step 1 is defined as follows:
[0023]
[0024]
[0025]
[0026] In the formula, Represents the energy functional. It is a bias field for a local region, used to adjust the offset of the local fit. This represents the average intensity value inside and outside the evolution profile. This represents the gray-level variance inside and outside the evolutionary profile. It is the mean of the sparse self-representation coefficients inside and outside the contour. For weight parameters, Parameters for balancing local and global information. , For the region any point in, for Points within the neighborhood, For threshold parameters, This represents the grayscale value at position y. For symbolic distance regularization parameters, This is the length regularization parameter; Representatives respectively on Integral infinitesimal domain, , , Refers to respectively according to the specific location or ; This is the regularization heaviside function, where z has no actual meaning and is only used to refer to the variable. It is the defined adaptive function. The sparse self-representation coefficients are defined as follows:
[0027]
[0028] In the formula, yes Norm, It is the Frobenius norm. This represents taking the minimum value. For weighted parameters, Represents the entire sample set. This indicates that the diagonal elements are extracted.
[0029] here, and These are the mean values of the sparse self-representation coefficients inside and outside the contour, expressed as:
[0030]
[0031] In the formula, Indicates double integral;
[0032] and These are the bias fields that change slowly inside and outside the contour, expressed as:
[0033]
[0034] In the formula, The symbol is for convolution, and I represents the input image;
[0035] and The average intensity values inside and outside the evolution profile are represented by the following expressions:
[0036]
[0037] and The gray-level variances inside and outside the evolutionary contour are represented by the following expressions:
[0038] .
[0039] Furthermore, in step 3, the energy functional is minimized using the gradient descent method, and the corresponding variational level set evolution formula is obtained:
[0040]
[0041] In the formula, Called -Laplace operator, For divergence operators, It is a logarithmic function. The definition of is:
[0042] .
[0043] Furthermore, in step 3, an explicit time discretization method is used to numerically solve the gradient descent equation, gradually updating the level set function until convergence, specifically as follows:
[0044]
[0045] in, Terminate iteration. As a stopping criterion, For time step, They represent the first Sublevel set functions.
[0046] On the other hand, an image segmentation system is provided, the system comprising:
[0047] The first module is used to build based on - A regional active profile model of the Laplace operator;
[0048] The second module is used to solve for the optimal solutions of each variable in the energy functional using variational methods;
[0049] The third module is used to minimize the energy functional using the gradient descent method to obtain the final evolution result;
[0050] The fourth module is used to extract image segmentation results based on the evolution results.
[0051] 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 executes the computer program to implement the [specific implementation / feature]. - An image segmentation method based on the active contour model of the region using the Laplacian operator.
[0052] On the other hand, a computer-readable storage medium is provided, on which a computer program is stored, which, when executed by a processor, implements the aforementioned... - An image segmentation method based on the active contour model of the region using the Laplacian operator.
[0053] Compared with the prior art, the significant advantages of this invention are:
[0054] (1) This invention introduces an adaptive control method based on local image gradients. - The energy functional corresponding to the Laplace operator, as the regularization term of the level set function, achieves adaptive control of diffusion behavior, that is, in homogeneous regions ( Isotropic diffusion is performed to effectively suppress noise, especially in the edge region. This approach tends to anisotropic diffusion to accurately preserve details, thus solving the technical problem in traditional methods where fixed regularization terms cannot adaptively balance smoothing and edge preservation effects.
[0055] (2) This invention constructs an energy functional by fusing local gray-level fitting terms and global sparse self-representation terms, thereby realizing the synergistic utilization of local statistical features and global structural information of the image. This enables the model to effectively cope with interference from uneven gray levels, background noise and weak edges, thus achieving higher accuracy and robustness in natural image segmentation.
[0056] (3) This invention achieves the stability and regularity of the level set function by combining the penalty term of the level set function with the explicit time discretization method, avoids the re-initialization process of the level set function in the traditional method, and significantly improves the computational efficiency and the stability of the segmentation effect.
[0057] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description
[0058] Figure 1 One embodiment is based on - Flowchart of the overall implementation of the image segmentation method using the Laplacian operator's region active contour model.
[0059] Figure 2 This is a partial experimental effect diagram of the present invention and existing methods on complex natural images in one embodiment, specifically including: LIF, LBF, LSACM, FeaACM methods and the method of the present invention. Detailed Implementation
[0060] 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.
[0061] It should be noted that if the embodiments of the present invention involve descriptions such as "first" and "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" and "second" may explicitly or implicitly include at least one of those features. Furthermore, 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. When 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 the present invention.
[0062] In one embodiment, a method based on - An image segmentation method using a region-active contour model with the Laplacian operator, the method comprising the following steps:
[0063] Step 1: Input an image to be segmented Initialize level set function Weight parameters Gaussian kernel parameters Time step Stopping Criteria ;
[0064] Step 2, process the image Perform edge detection to obtain gradient map and using Gaussian kernel Smooth it to obtain the smoothed gradient. ;
[0065] Step 3: Define adaptive gradient information function:
[0066]
[0067] In the formula, Indicates adaptive function, The standard deviation is Gaussian kernel function, For edge maps, Represents the gradient. This represents the gradient of the convolution between the edge map and the Gaussian kernel. Indicates modulo operation, "" indicates a definition. In homogeneous regions (small gradients), a larger value is used. The values are isotropically diffused to achieve smoothing and noise reduction; while in the edge regions (where the gradient is large), smaller values are diffused... Anisotropic diffusion of values enhances the ability to preserve edges and improves segmentation performance.
[0068] here, The value is dynamically adjusted based on the local gradient; when the gradient is small... The diffusion behavior tends to be isotropic, effectively smoothing homogeneous regions; when the gradient is large, The diffusion behavior tends to be anisotropic, preserving edge details.
[0069] Step 4: An adaptive-based approach is introduced into the energy functional. - The energy functional corresponding to the Laplace operator, as the length regularization term of the level set function, is defined as:
[0070]
[0071] Suppressing false contours and preserving edge details during evolution;
[0072] Step 5: Calculate the self-representation coefficient matrix of the image using the sparse self-representation method. That is, to solve:
[0073]
[0074] Step 6: Introduce a local gray-level weighted fitting function and define a local energy fitting term. This local fitting term, by combining image features within the neighborhood, captures the gray-level distribution characteristics of local regions, thereby improving the segmentation ability for edge regions and local details. It is defined as follows:
[0075]
[0076] In the formula, It is a bias field for a local region, used to adjust the offset of the local fit. This represents the average intensity value inside and outside the evolution profile. This represents the gray-level variance inside and outside the evolutionary profile. Local neighborhood indicator function, defined with radius as The neighborhood, , , This is the regularization Heaviside function.
[0077] Step 7: By introducing a global sparse self-representation term, the robustness of the model in recognizing weak edge regions is enhanced by utilizing the global consistency information of the image structure. This term is defined as:
[0078] ,
[0079] in, Let be the sparse self-representation coefficient matrix of the image. It is the mean of the sparse self-representation coefficients inside and outside the contour. , and These represent the mean of the sparse self-representation coefficients inside and outside the contour, respectively;
[0080] Step 8 introduces a distance regularization term, designed to maintain the signed distance property of the level set function, thereby avoiding the re-initialization process and improving the numerical stability of the evolution process. It is defined as:
[0081]
[0082] Step 9: Construct the energy functional for segmentation, including a global fitting term, a local fitting term, a penalty term for the level set function, and a length regularization term, the expression of which is:
[0083]
[0084]
[0085]
[0086] Step 10: Employ an alternating optimization strategy, keeping other variables fixed, and update each parameter separately, including:
[0087] Update the average intensity value inside and outside the contour. The expression is:
[0088]
[0089] Update the slowly varying bias field inside and outside the contour, expressed as:
[0090]
[0091] The expression for updating the grayscale variance inside and outside the outline is:
[0092]
[0093] Update the mean of the sparse self-representation coefficients inside and outside the contour, as expressed by:
[0094]
[0095] Step 11: Minimize the energy functional using the gradient descent flow method to obtain the evolution equation of the level set function:
[0096]
[0097] in, ;
[0098] Step 12: Numerically solve the gradient descent equation using an explicit time discretization method. Iterate the level set function until convergence. The update formula is as follows:
[0099]
[0100] Until the convergence condition is met The iteration is terminated.
[0101] Step 13: Extract the image segmentation results based on the evolution results.
[0102] In one embodiment, a method based on - An image segmentation system based on a region-active contour model using the Laplacian operator, the system comprising:
[0103] The first module is used to build based on - A regional active profile model of the Laplace operator;
[0104] The second module is used to solve for the optimal solutions of each variable in the energy functional using variational methods;
[0105] The third module is used to minimize the energy functional using the gradient descent method to obtain the final evolution result;
[0106] The fourth module is used to extract image segmentation results based on the evolution results.
[0107] Regarding For specific limitations of image segmentation systems based on the Laplacian operator's region active contour model, please refer to the above section on the Laplacian operator-based region active contour model. The limitations of the Laplacian operator-based region active contour model for image segmentation are not elaborated here. In an image segmentation system based on the Laplacian operator's region active contour model, each module can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independent of the processor in a computer device, or stored in software within the computer device's memory, allowing the processor to invoke and execute the corresponding operations.
[0108] 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:
[0109] Step 1, build based on - The regional active contour model of the Laplacian operator includes:
[0110] Introducing Adaptive The function, whose value is dynamically adjusted according to the local image gradient, achieves a combination of isotropic and anisotropic diffusion, thereby realizing adaptive control of diffusion behavior.
[0111] Build based on - The adaptive regularization term of the Laplace operator is defined as the geometric length regularization term of the level set function;
[0112] An energy functional is constructed that integrates global features, local features, and sparse self-representation high-level features, and is used as the optimization objective for image segmentation.
[0113] Step 2: Solve for the optimal solutions of each variable in the energy functional using variational methods;
[0114] Step 3: Minimize the energy functional using the gradient descent method to obtain the final evolution result;
[0115] Step 4: Extract the image segmentation results based on the evolution results.
[0116] For specific limitations on each step, please refer to the section above regarding the basis. The limitations of the Laplacian operator's region active contour model for image segmentation are not elaborated here.
[0117] 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:
[0118] Step 1, build based on - The regional active contour model of the Laplacian operator includes:
[0119] Introducing Adaptive The function, whose value is dynamically adjusted according to the local image gradient, achieves a combination of isotropic and anisotropic diffusion, thereby realizing adaptive control of diffusion behavior.
[0120] Build based on - The adaptive regularization term of the Laplace operator is defined as the geometric length regularization term of the level set function;
[0121] An energy functional is constructed that integrates global features, local features, and sparse self-representation high-level features, and is used as the optimization objective for image segmentation.
[0122] Step 2: Solve for the optimal solutions of each variable in the energy functional using variational methods;
[0123] Step 3: Minimize the energy functional using the gradient descent method to obtain the final evolution result;
[0124] Step 4: Extract the image segmentation results based on the evolution results.
[0125] For specific limitations on each step, please refer to the section above regarding the basis. The limitations of the Laplacian operator's region active contour model for image segmentation are not elaborated here.
[0126] As a specific example, the invention will be further verified and illustrated in one embodiment.
[0127] like Figure 1 As shown, based on - The image segmentation method using the Laplacian operator's region active contour model specifically includes:
[0128] (1) Select a complex natural image to be segmented. , as input data.
[0129] (2) Set the initial level set function Weight parameters Gaussian kernel parameters Time step Stopping Criteria .
[0130] (3) Perform edge detection on the input complex natural image to obtain the gradient map. and using Gaussian kernel Smooth it to obtain the smoothed gradient. Based on the constructed adaptive function Perform the calculation.
[0131] (4) Introducing an adaptive - The energy functional corresponding to the Laplacian operator is used as the length regularization term of the level set function, introducing local fitting terms, global sparse self-representation terms, and distance regularization terms, specifically expressed as:
[0132]
[0133]
[0134] .
[0135] (5) The evolution equation of the level set is obtained by using the gradient descent flow method:
[0136] ,
[0137] in, .
[0138] (6) Keep other variables fixed, update each parameter separately, and update the average gray value inside and outside the contour. Slowly changing bias field Gray-scale variance and the mean of sparse self-representation coefficients .
[0139] (7) In each iteration step, update the numerical solution for the next time step based on the current solution. Repeat (5) and (6) until the convergence condition is met. If convergence is satisfied, the iteration stops.
[0140] Compared with existing models such as LBF, LIF, LSACM, and FeaACM, the results show that the model of this invention exhibits more stable segmentation performance on test images and can capture target boundaries more completely and accurately. This result verifies the adaptive function introduced in the model. The Laplacian operator can dynamically adapt to local image features and suppress background noise interference, thereby guiding the evolution curve to converge to the global optimum position of the true boundary, improving segmentation accuracy and robustness.
[0141] The convergence behavior of the proposed energy functional in numerical iteration was evaluated through energy convergence experiments. The numerical values of the energy functional were recorded during the iteration process, and its evolution curves were plotted. The results show that, compared with other models, the method of this invention can converge to a lower energy value faster and more stably.
[0142] Figure 2 The images show a comparison of the segmentation results of the method of this invention with existing models on two sets of complex natural images. It can be seen that when processing complex natural images, the method of this invention can effectively preserve edge details, while exhibiting strong robustness to noise interference, more accurately capturing target boundaries, and achieving higher segmentation accuracy.
[0143] 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. A method based on - An image segmentation method using the Laplacian operator's region active contour model, characterized by... The method includes the following steps: Step 1, build based on - The regional active contour model of the Laplacian operator includes: Introducing Adaptive The function, whose value is dynamically adjusted according to the local image gradient, achieves a combination of isotropic and anisotropic diffusion, thereby realizing adaptive control of diffusion behavior. Build based on - The adaptive regularization term of the Laplace operator is defined as the geometric length regularization term of the level set function; An energy functional is constructed that integrates global features, local features, and sparse self-representation high-level features, and is used as the optimization objective for image segmentation. Step 2: Solve for the optimal solutions of each variable in the energy functional using variational methods; Step 3: Minimize the energy functional using the gradient descent method to obtain the final evolution result; Step 4: Extract the image segmentation results based on the evolution results.
2. The method based on claim 1 - An image segmentation method using the Laplacian operator's region active contour model, characterized by... Adaptive in step 1 The function is defined as follows: In the formula, Indicates adaptive function, The standard deviation is Gaussian kernel function, For edge maps, Represents the gradient. This represents the gradient of the convolution between the edge map and the Gaussian kernel. This represents the modulo operation. " indicates a definition.
3. The method based on claim 2 - An image segmentation method using the Laplacian operator's region active contour model, characterized by... Adaptive in step 1 The function value is dynamically adjusted based on the local image gradient, specifically: When the image gradient approaches zero, i.e. When, satisfy ,at this time The Laplacian operator degenerates into the Laplacian operator, whose diffusion behavior is isotropic, effectively smoothing homogeneous regions in an image and suppressing noise; as the image gradient approaches infinity, i.e. When, satisfy ,at this time The Laplacian operator degenerates into a total variational regularization term, whose diffusion behavior is characterized by anisotropic edge-preserving diffusion, thereby effectively suppressing noise while preserving the edge details of the image.
4. The method based on claim 3 - An image segmentation method using the Laplacian operator's region active contour model, characterized by... In step 1 - The energy functional corresponding to the Laplace operator, that is, the regularization term of the constructed level set function, is defined as: : In the formula, " " indicates a definition, For definition Bounded regions in Indicates the integral symbol, Representative on Integral infinitesimal domain, This is the Dirac function for regularization, where z has no actual meaning and is only used to refer to the variable. A constant that is greater than zero. It is a level set function.
5. The method based on claim 4 - An image segmentation method using the Laplacian operator's region active contour model, characterized by... The energy functional in step 1 is defined as follows: In the formula, Represents the energy functional. It is a bias field for a local region, used to adjust the offset of the local fit. This represents the average intensity value inside and outside the evolution profile. This represents the gray-level variance inside and outside the evolutionary contour. It is the mean of the sparse self-representation coefficients inside and outside the contour. For weight parameters, Parameters for balancing local and global information. , For the region any point in, for Points within the neighborhood, For threshold parameters, This represents the grayscale value at position y. For symbolic distance regularization parameters, This is the length regularization parameter; Representatives respectively on Integral infinitesimal domain, , , Refer to respectively according to the specific location or ; This is the regularization heaviside function, where z has no actual meaning and is only used to refer to the variable. It is the defined adaptive function. The sparse self-representation coefficients are defined as follows: In the formula, yes Norm, It is the Frobenius norm. This represents taking the minimum value. For weighted parameters, Represents the entire sample set. This indicates that the diagonal elements are extracted. here, and These are the mean values of the sparse self-representation coefficients inside and outside the contour, expressed as: In the formula, Indicates double integral; and These are the bias fields that change slowly inside and outside the contour, expressed as: In the formula, The symbol is for convolution, and I represents the input image; and The average intensity values inside and outside the evolution profile are represented by the following expressions: and The gray-level variances inside and outside the evolutionary contour are represented by the following expressions: 。 6. The method based on claim 5 - An image segmentation method using the Laplacian operator's region active contour model, characterized by... In step 3, the energy functional is minimized using the gradient descent method, and the corresponding variational level set evolution formula is obtained: In the formula, Called -Laplace operator, For divergence operators, It is a logarithmic function. The definition of is: 。 7. The method based on claim 6 - An image segmentation method using the Laplacian operator's region active contour model, characterized by... Step 3 employs an explicit time discretization method to numerically solve the gradient descent equation, progressively updating the level set function until convergence. Specifically: in, Terminate iteration. As a stopping criterion, For time step, They represent the first Sublevel set functions.
8. An image segmentation system based on the method of any one of claims 1 to 7, characterized in that, The system includes: The first module is used to build based on - A regional active profile model of the Laplace operator; The second module is used to solve for the optimal solutions of each variable in the energy functional using variational methods; The third module is used to minimize the energy functional using the gradient descent method to obtain the final evolution result; The fourth module is used to extract image segmentation results based on the evolution results.
9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method according to any one of claims 1 to 7.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 7.