License plate number identification method based on time fractional order homogeneous Chn-Hilliard equation reverse problem

Abstract

The invention discloses a license plate number recognition method based on a time fractional order homogeneous Cahn-Hilliard equation reverse problem, and belongs to the field of image processing, pattern recognition and inverse problem calculation, and the method comprises the steps: carrying out the preprocessing of a license plate image, and obtaining a terminal observation image; an image degradation model is constructed based on a time fractional order homogeneous Chn-Hilliard equation; solving an inverse problem of the equation through frequency domain filtering by using a simulated boundary correction method, and recovering an initial clear license plate image; and finally, character segmentation and recognition are carried out. According to the method, through physical-driven degradation modeling and efficient frequency domain inversion solution, character edges can be recovered in a high-precision manner, the method has high robustness to noise and fuzziness, and does not depend on a large amount of labeled data, and the accuracy and efficiency of license plate recognition in a complex scene are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the fields of image processing, pattern recognition and computational inverse problem technology, and particularly relates to a license plate number recognition method based on the inverse problem of the time fractional homogeneous Cahn-Hilliard equation. Background Technology

[0002] Automatic license plate recognition technology, as a core component of intelligent transportation systems, typically includes steps such as license plate localization, character segmentation, and character recognition. In the field of image restoration, existing mainstream methods for addressing license plate image degradation caused by shooting angle, lighting variations, motion blur, and noise interference mainly fall into the following categories: First, methods based on classical or constrained NavInfo filtering models, which achieve simultaneous processing of blur and noise by optimizing noise weights, offering high computational efficiency; second, deconvolution methods based on physical models, such as the Richardson-Lucy algorithm, which approximates the sharp image iteratively and has strong detail restoration capabilities for specific blur types (such as motion blur); and third, deep learning-based methods, which utilize a large number of "sharp-blurred" image pairs for end-to-end training, enabling adaptive learning of complex degradation patterns. Furthermore, fractional calculus theory, due to its advantages in describing "abnormal diffusion" processes, has been introduced into the field of image processing, for example, using time-fractional diffusion equations to model the gradual degradation process of images.

[0003] However, the aforementioned existing technologies still have significant limitations in practical applications. First, at the physical model level, there is a mismatch between traditional filtering or integer-order differential equation models and actual degradation mechanisms such as ink smudging and pigment diffusion in license plate characters. This makes it difficult to accurately characterize their non-local, memory-dependent, and slowly varying features, leading to artifacts or stair-step effects at the edges of the restored characters. Second, regarding solution efficiency and stability, iterative deconvolution methods are sensitive to noise, easily amplifying errors and producing ringing effects under noise interference, resulting in high computational costs. While frequency domain filtering methods are fast, their filter design often lacks rigorous degradation model guidance, leading to insufficient generalization ability. Finally, regarding data dependency, deep learning-based methods require large-scale, paired labeled data for training. However, in real-world scenarios, it is difficult to obtain clear-blurred license plate image pairs covering all degradation types, limiting their practical application scope. Therefore, there is an urgent need for a license plate image restoration and recognition method that is physically meaningful, computationally efficient, highly resistant to interference, and does not rely on a large amount of labeled data. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a license plate recognition method based on the inverse problem of the time fractional homogeneous Cahn-Hilliard equation, thereby resolving the issues present in the prior art.

[0005] To achieve the above objectives, in a first aspect, the present invention provides a license plate recognition method based on the inverse problem of the time fractional homogeneous Cahn-Hilliard equation, comprising: S1. Preprocess the input license plate image to obtain the terminal observation image; S2. Construct a degradation model for license plate images based on the time fractional homogeneous Cahn-Hilliard equation; S3. Based on the terminal observation image and the degradation model, the clear license plate image at the initial moment is recovered by solving the inverse problem through frequency domain filtering using the modified quasi-boundary method. S4. Perform character segmentation and recognition on the clear license plate image, and output the license plate number information.

[0006] Preferably, the process of obtaining the terminal observation image includes: Convert the input color license plate image to a grayscale image; The grayscale image is subjected to global threshold segmentation to obtain a binarized image; Morphological erosion is performed on the binarized image to remove noise, resulting in the terminal observation image.

[0007] Preferably, the time fractional homogeneous Cahn-Hilliard equation is a two-dimensional equation with Caputo fractional derivatives, and its governing equation is used to describe the degradation process from a sharp image to a blurred image.

[0008] Preferably, the time fractional homogeneous Cahn-Hilliard equation is: ; in, The fractional derivative in the Caputo sense. The order of the fractional derivative. Let be the grayscale field of the license plate image at time t. For the Laplace operator, For a bilaplace operator, The spatial region of the license plate image. For the regional boundary, The initial clear license plate image is denoted as T, and the total evolution time is denoted as T.

[0009] Preferably, the process of obtaining a clear license plate image at the initial moment includes: Perform a two-dimensional Fourier transform on the terminal-observed image to obtain its frequency domain representation; Based on the characteristics of the time fractional homogeneous Cahn-Hilliard equation, a modified quasi-boundary deblurring filter is designed. Multiplying the frequency domain representation with the corrected pseudo-boundary deblurring filter yields the frequency domain representation of the restored image; A two-dimensional inverse Fourier transform and post-processing are performed on the frequency domain representation of the restored image to obtain a clear license plate image at the initial moment.

[0010] Preferably, the modified pseudo-boundary deblurring filter is: ; ; Where ξ and η are frequency domain coordinates, and β, γ, α, s are adjustment parameters of the RQB method used to optimize filter performance.

[0011] Preferably, the post-processing includes normalization and non-negative projection.

[0012] Preferably, the process of outputting license plate information includes: The clear license plate image is binarized. Character segmentation of a binary image is performed based on column projection to obtain individual character regions; Extract the features of the character region and perform character recognition; Integrate the recognition results and output complete license plate number information.

[0013] Preferably, the features include shape features and texture features.

[0014] In a second aspect, the present invention also discloses a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0015] Compared with the prior art, the present invention has the following advantages and technical effects: This invention employs a technical solution of "constructing a degradation model for license plate images based on the time fractional homogeneous Cahn-Hilliard equation," which accurately depicts the actual "abnormal diffusion" degradation physical processes such as ink smudging and pigment diffusion in license plate characters, making the modeling of the degradation process closer to the real physical mechanism. Inversion and restoration based on this accurate model can effectively avoid problems such as character edge artifacts, staircase effects, or contour breaks caused by model mismatch, thereby restoring the original image with natural edge transitions and clear details.

[0016] This invention transforms the complex inverse problem of partial differential equations into a frequency domain filtering operation by employing a technique that "based on the terminal-observed image and the degradation model, and using the revised quasi-boundary method (RQB) to solve the inverse problem through frequency domain filtering." This avoids the enormous computational overhead of traditional iterative methods (such as Richardson-Lucy deconvolution), significantly improving computational efficiency. Furthermore, the dedicated frequency domain filter designed in this invention has parameters directly related to the physical parameters of the degradation model (such as evolution time), effectively counteracting the diffusion effect described by the model while suppressing noise amplification. This ensures both efficient solution and the stability and robustness of the algorithm against noise and ambiguity interference.

[0017] Since the core of this invention is a complete inverse problem-solving framework built upon a mathematical model with a clearly defined physical mechanism (the time-fractional homogeneous Cahn-Hilliard equation) and a mathematical solution method (the modified quasi-boundary method), its restoration capability stems from the mathematical description and solution of physical laws, rather than from statistical learning of large datasets. Therefore, this invention does not require training on large-scale, difficult-to-obtain "clear-blurred" paired license plate image data, and can be applied to license plate image restoration tasks with different vehicle models, lighting conditions, and degrees of degradation, demonstrating excellent generalization performance.

[0018] This invention provides a complete technical solution from image degradation modeling and clear image inversion to final character recognition. It not only solves the core problem of image restoration but also integrates standardized preprocessing, character segmentation, and recognition processes, forming an end-to-end solution. The steps are logically clear and tightly connected, making the entire technical solution highly systematic and easy to integrate and deploy in practical systems. Attached Figure Description

[0019] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of a license plate recognition method based on the inverse problem of the time fractional homogeneous Cahn-Hilliard equation according to an embodiment of the present invention. Detailed Implementation

[0020] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0021] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0022] Example 1 like Figure 1 As shown, this embodiment provides a license plate recognition method based on the inverse problem of the time fractional homogeneous Cahn-Hilliard equation, including: S1. Preprocess the input license plate image to obtain the terminal observation image; Furthermore, the process of obtaining the terminal observation image includes: Convert the input color license plate image to a grayscale image; The grayscale image is subjected to global threshold segmentation to obtain a binarized image; Morphological erosion is performed on the binarized image to remove noise, resulting in the terminal observation image.

[0023] Specifically, license plate image preprocessing, as the first core step in the entire license plate recognition process, requires first converting the color license plate image to grayscale according to international standards, then using the Otsu's algorithm (maximum inter-class variance method) to achieve global adaptive threshold binarization, and finally using morphological erosion to eliminate isolated noise points and character edge spikes, thereby outputting a terminal observation image that meets the requirements of subsequent algorithm processing. License plate image preprocessing specifically includes: ① Grayscale Conversion: Convert a 400×140 resolution color blue sign image to grayscale according to international standards. The formula is: ; in, , , The pixel positions of the color image are respectively The red, green, and blue component values ​​at the location, The converted grayscale value; ②Otsu binarization: Calculate the inter-class variance of the grayscale image, determine the optimal threshold, and convert the grayscale image into a binary image, with character regions set to 1 and background regions set to 0; ③ Morphological erosion: A 3×3 all-1 structuring element is used to perform erosion operation on the binary image to remove isolated noise points and character edge burrs, resulting in the terminal observation image M.

[0024] S2. Construct a degradation model for license plate images based on the time fractional homogeneous Cahn-Hilliard equation; Furthermore, the time fractional homogeneous Cahn-Hilliard equation is a two-dimensional equation with Caputo fractional derivatives, and its governing equation is used to describe the degradation process from a sharp image to a blurred image.

[0025] Specifically, the forward problem of the time-fractional homogeneous Cahn-Hilliard equation aims to simulate the evolution of a clear license plate image into a blurred and degraded image. First, it constructs governing equations describing the diffusion and aggregation characteristics of the image's grayscale field. Then, combining spatial and temporal discretization strategies, it forms a fully discrete format. By inputting initial images covering different license plate types and character styles, it completes the numerical solution of the forward problem, storing the image solutions and chemical potential data at each time point. This reconstructs the physical process of ink smudging and edge blurring of the license plate characters, providing a reference for retrieving the initial clear image. This step specifically includes: ① Equation Selection: The time fractional homogeneous Cahn-Hilliard equation is adopted as the degradation model. The time fractional homogeneous Cahn-Hilliard equation is as follows: ; in, The fractional derivative in the Caputo sense. The order of the fractional derivative. Let be the grayscale field of the license plate image at time t. For the Laplace operator, For a bilaplace operator, The spatial region of the license plate image. For the regional boundary, The initial clear license plate image is denoted as T, and the total evolution time is denoted as T.

[0026] ② Parameter settings: Set the interface width parameter ε and the total evolution time T for different application scenarios. These parameters are used to guide the design of subsequent RQB filters.

[0027] S3. Based on the terminal observation image and the degradation model, the clear license plate image at the initial moment is recovered by solving the inverse problem through frequency domain filtering using the modified quasi-boundary method. Furthermore, the process of obtaining a clear license plate image at the initial moment includes: Perform a two-dimensional Fourier transform on the terminal-observed image to obtain its frequency domain representation; Based on the characteristics of the time fractional homogeneous Cahn-Hilliard equation, a modified quasi-boundary deblurring filter is designed. Multiplying the frequency domain representation with the corrected pseudo-boundary deblurring filter yields the frequency domain representation of the restored image; A two-dimensional inverse Fourier transform and post-processing are performed on the frequency domain representation of the restored image to obtain a clear license plate image at the initial moment.

[0028] Furthermore, the post-processing includes normalization and nonnegative projection.

[0029] Specifically, traditional methods for solving inverse problems of partial differential equations are often computationally complex. This invention employs the RQB method to directly construct filters in the frequency domain to approximate the inverse evolution process.

[0030] (1) Frequency domain transformation: Perform a two-dimensional Fourier transform (FFT) on the preprocessed terminal observation blurred image (degraded image at time t=T) to obtain its frequency domain representation. .

[0031] (2) RQB filter design: Based on the mathematical form of the time fractional homogeneous Cahn-Hilliard equation and the set parameters (such as... Design a frequency domain filter H (T). This filter aims to counteract the diffusion effect described by the equation. Its design draws inspiration from the RQB method, using an exponential function and a Gaussian term to balance deblurring and noise suppression. A typical RQB filter is as follows: ; in, ; ; ξ and η are frequency domain coordinates, and β, γ, α, and s are adjustment parameters of the RQB method used to optimize filter performance.

[0032] (3) Frequency domain filtering: representing the frequency domain of the observed image Multiplying with the RQB filter H yields the frequency domain representation of the recovered sharp image. ; (4) Inverse Transform and Post-processing: For Perform a two-dimensional inverse Fourier transform and take the real part to obtain the initial sharp license plate image estimate in the spatial domain. Finally, regarding Post-processing, such as normalization and non-negative projection, is performed to ensure that the grayscale values ​​are within a reasonable range, resulting in the final restored initial clear license plate image g. .

[0033] S4. Perform character segmentation and recognition on the clear license plate image, and output the license plate number information.

[0034] Furthermore, the process of outputting license plate information includes: The clear license plate image is binarized. Character segmentation of a binary image is performed based on column projection to obtain individual character regions; Extract the features of the character region and perform character recognition; Integrate the recognition results and output complete license plate number information.

[0035] Furthermore, the features include shape features and texture features.

[0036] Specifically, character segmentation and recognition follows the initial clear license plate image restoration step. Using a high-resolution license plate image as input, adaptive threshold binarization is first used to further separate characters from redundant background information. Then, column projection is used to calculate the pixels in each column and determine the character intervals, achieving accurate segmentation of individual character regions. Subsequently, multi-dimensional features such as character shape and texture are extracted, and a pre-trained machine learning classifier is used to complete accurate character recognition. Finally, the scattered character recognition results are integrated into a complete and readable license plate number. This step specifically includes: ① Character segmentation: Adaptive binarization is performed on the clear image g, and the sum of pixels in each column is calculated using the column projection method to determine the character interval and segment out 7 character regions; ②Character recognition: Extract features such as the Hu matrix and edge direction histogram of each character region and match them with a standard character template library; ③ Output Results: Integrate the recognition results and output the final license plate number.

[0037] Example 2 This embodiment also discloses a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0038] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A license plate recognition method based on the inverse problem of the time fractional homogeneous Cahn-Hilliard equation, characterized in that, Includes the following steps: S1. Preprocess the input license plate image to obtain the terminal observation image; S2. Construct a degradation model for license plate images based on the time fractional homogeneous Cahn-Hilliard equation; S3. Based on the terminal observation image and the degradation model, the clear license plate image at the initial moment is recovered by solving the inverse problem through frequency domain filtering using the modified quasi-boundary method. S4. Perform character segmentation and recognition on the clear license plate image, and output the license plate number information.

2. The license plate recognition method according to claim 1, characterized in that, The process of obtaining the terminal observation image includes: Convert the input color license plate image to a grayscale image; The grayscale image is subjected to global threshold segmentation to obtain a binarized image; The binarized image is subjected to morphological erosion to remove noise, thereby obtaining the terminal observation image.

3. The license plate recognition method according to claim 1, characterized in that, The time fractional homogeneous Cahn-Hilliard equation is a two-dimensional equation with Caputo fractional derivatives, and its governing equation is used to describe the degradation process from sharp image to blurred image.

4. The license plate recognition method according to claim 3, characterized in that, The time fractional homogeneous Cahn-Hilliard equation is as follows: ； in, The fractional derivative in the Caputo sense. The order of the fractional derivative. Let be the grayscale field of the license plate image at time t. For the Laplace operator, For a biLaplace operator, The spatial region of the license plate image. For the regional boundary, The initial clear license plate image is denoted as T, and the total evolution time is denoted as T.

5. The license plate recognition method according to claim 1, characterized in that, The process of obtaining a clear license plate image at the initial moment includes: Perform a two-dimensional Fourier transform on the terminal-observed image to obtain its frequency domain representation; Based on the characteristics of the time fractional homogeneous Cahn-Hilliard equation, a modified quasi-boundary deblurring filter is designed. Multiplying the frequency domain representation with the corrected pseudo-boundary deblurring filter yields the frequency domain representation of the restored image; A two-dimensional inverse Fourier transform and post-processing are performed on the frequency domain representation of the restored image to obtain a clear license plate image at the initial moment.

6. The license plate recognition method according to claim 5, characterized in that, The modified pseudo-boundary deblurring filter is: ； ； Where ξ and η are frequency domain coordinates, and β, γ, α, s are adjustment parameters of the RQB method used to optimize filter performance.

7. The license plate recognition method according to claim 5, characterized in that, The post-processing includes normalization and non-negative projection.

8. The license plate recognition method according to claim 1, characterized in that, The process of outputting license plate information includes: The clear license plate image is binarized. Character segmentation of a binary image is performed based on column projection to obtain individual character regions; Extract the features of the character region and perform character recognition; Integrate the recognition results and output complete license plate number information.

9. The license plate recognition method according to claim 8, characterized in that, The features include shape features and texture features.

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

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