Fast and accurate ternary number orthogonal-Fourier-Mellin moment zero watermark construction method

Abstract

The invention discloses a ternary number fast and accurate orthogonal-Fourier Mellin moment zero watermark construction method, which relates to the technical field of watermark construction, and is characterized by comprising the following steps: S1, obtaining an original color image; s2, initial orthogonal Fourier Mellin moment feature extraction calculation is carried out, and initial matrix features are obtained; s3, a data optimization method; s31, carrying out orthogonal Fourier Mellin moment feature extraction and parameter optimization; s32, carrying out multi-stage optimization on the framework; s321, global optimization: optimizing a singular value and a Fourier coefficient by adopting particle swarm optimization. The technical problem to be solved by the invention is to provide a ternary number rapid and accurate orthogonal-Fourier-Mellin moment zero watermark construction method, and aims to solve the technical challenges, optimize the reconstruction quality in the image reconstruction process by combining an integrated optimization method with a zero watermark technology, ensure the integrity and safety of watermark information, and improve the image reconstruction efficiency. Therefore, more efficient and safer image reconstruction and copyright protection are realized.

Description

Technical Field

[0001] The invention relates to the technical field of watermark construction, and in particular to a ternary fast and accurate orthogonal-Fourier Mellin moment zero watermark construction method. Background Art

[0002] Existing image reconstruction technologies often use traditional optimization methods. Although these methods can achieve good reconstruction results in theory, they face the problems of large computational complexity and low efficiency in practical applications. Especially when processing large-scale or high-resolution images, the computational complexity of traditional algorithms increases dramatically, resulting in a slow reconstruction process and requiring a large amount of storage resources.

[0003] It is difficult to strike a balance between global and local optimization: Existing image reconstruction optimization methods often rely on a single optimization algorithm, which makes it difficult to effectively balance global search and local fine-tuning during the optimization process. Although many algorithms can find a relatively accurate global solution, they cannot further improve the reconstruction quality during local fine-tuning, resulting in failure to achieve the best reconstruction effect.

[0004] Watermark information is easily lost or attacked: In the process of image reconstruction, traditional watermarking technology, especially explicit watermarking, is easily affected by compression, transformation and reconstruction operations in the image processing process, resulting in the loss or tampering of watermark information. Even zero watermarking technology faces the problem of watermark information being destroyed or unextractable during the low-rank approximation or matrix partitioning of the image.

[0005] Difficulty in combining zero watermark with image reconstruction: Current zero watermark technology is usually used alone for image protection, but how to optimize both image quality and watermark information protection in image reconstruction is still a difficult problem. Especially in complex image reconstruction algorithms, the embedding and extraction process of watermark information may be affected by reconstruction errors and optimization algorithms, resulting in the inextractability or extraction errors of watermark information. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a ternary fast and accurate orthogonal-Fourier Mellin moment zero watermark construction method. The present invention aims to solve the above technical challenges by combining the integrated optimization method (Hybrid Optimization) with the zero watermark technology to optimize the reconstruction quality in the image reconstruction process while ensuring the integrity and security of the watermark information, thereby achieving more efficient and secure image reconstruction and copyright protection.

[0007] The present invention adopts the following technical solutions to achieve the invention objectives: A ternary fast and accurate orthogonal-Fourier-Mellin moment zero watermark construction method, characterized by comprising the following steps: S1: Get the original color image; S2: Initial orthogonal Fourier Mellin moment feature extraction calculation to obtain initial matrix features; S3: Data optimization methods; S31: Orthogonal Fourier Mellin moment feature extraction and parameter optimization; S32: Multi-stage optimization framework; S321: Global optimization, using particle swarm optimization for singular values ​​and Fourier coefficients; S322: local optimization, using simulated annealing to optimize matrix partitioning; S323: Fine Optimization, using genetic algorithms to optimize low-rank approximations and local solutions; S33: Optimize process integration; S4: Adaptive adjustment and dynamic optimization, design of efficient and reliable zero watermark algorithm; S41: zero watermark construction; S42: Zero watermark verification.

[0008] As a further limitation of the technical solution, the specific steps of S2 are: Optimized orthogonal Fourier-Mellin moment calculation: Orthogonal Fourier-Mellin moment polar coordinate system, is the angular component, image Repeatability The definition of is as follows: (1); in: is a non-negative integer; represents an imaginary unit; Radial Basis Function yes of The polynomial expression is: (2); in: are the coefficients of the polynomial, are the coefficients of the polynomial; exist is weighted orthogonal in the range: (3) in: express k Radial basis function of order; is the Kronecker symbol; is the normalization factor; According to radial basis function Angular harmonic factor The properties of the orthogonal Fourier-Mellin moments Orthogonal inside the unit circle: (4); in: represents radial basis function and Orthogonality conditions between ; represents the angular basis function and Orthogonality conditions between ; According to the orthogonal function system theory, the original image Reconstructed approximately using a finite number of orthogonal Fourier Mellin moments, it is known that the highest order and maximum repetition The orthogonal Fourier-Mellin moments of Refactor as follows: (4); Ternaries are usually represented as ,in is the real part, is the imaginary part; The conjugate of a ternary is defined as: (5); In color image processing, each color channel is processed by a corresponding function To represent, define a ternary image function to represent the color image: (6) in: Represent the red, green and blue channels of the image respectively.

[0009] As a further limitation of the technical solution, the specific steps of S31 are: Original input color image After processing by orthogonal Fourier-Mellin moments, a set of moment features, namely images, is generated. , recorded as: (7); in: Indicates n Stage, m Angular coefficient; These moment coefficients are affected by multiple parameters, and the parameters are optimized so that the image error reconstructed by the orthogonal Fourier-Mellin moment is minimized. Let the parameter vector be: (8); The optimization objective is defined as the reconstruction error between the reconstructed image and the original image: (9); in: Represents the parameter vector The reconstructed image after processing with orthogonal Fourier-Mellin moments.

[0010] As a further limitation of the present technical solution, the specific steps of S321 are: Particle swarm optimization is used to perform a global search of the parameter space, where each particle represents a candidate solution for a parameter. , and its speed update formula is: (10); in: is the inertia weight; is the acceleration constant; is a random number between [0,1]; It is a particle The best historical position of g; g is the global best position; The particle's position is updated as: (11).

[0011] As a further limitation of the present technical solution, the specific steps of S322 are: introducing a simulated annealing algorithm to locally refine the parameters, assuming that the current state is , generating a new state , the objective function changes to , the probability of accepting the new state is: (12); in: is the current temperature.

[0012] As a further limitation of the present technical solution, the specific steps of S323 are: Genetic algorithms are suitable for dealing with complex combinatorial optimization problems; Genetic algorithms use crossover operations to combine parameters from different individuals to generate new solutions; mutation operations can introduce randomness to avoid falling into local optimal solutions; Crossover operation: (13); in: and is the selected parent, is the mixing coefficient; Mutation operation: (14) in: is the random perturbation vector; Through the continuous iteration of the genetic algorithm selection, crossover and mutation process, a global optimal or approximately global optimal parameter combination is finally obtained. .

[0013] As a further limitation of the technical solution, the specific steps of S33 are: After the above three stages of integrated optimization, an optimal parameter combination is finally obtained. , the orthogonal Fourier Mellin moment matrix feature extraction process at this time is: (15).

[0014] As a further limitation of the technical solution, the specific steps of S41 are: Zero watermark construction: Assume is the original ternary Fourier-Mellin moment image, For the original binary Logo image, the zero watermark construction process is as follows: S411: Calculate the ternary Fourier-Mellin moment image The orthogonal Fourier-Mellin moments of Moment values; S412: What you will get The moment values ​​are replicated and expanded multiple times to obtain moment values, and then calculate the amplitude of the moment to construct the length The amplitude sequence of ; represents the first The magnitude of the moment value; S413: The amplitude sequence Binarization, get the binary amplitude sequence : (16); in: After binarization, elements, the value is 0 or 1; is the binarization threshold, here we take The mean of S414: Binarize the amplitude sequence becomes OK Binary feature image of the column: (17); S415: Use XOR operation to convert the Logo image Embedded into binary feature image Get the zero watermark image : (18).

[0015] As a further limitation of the technical solution, the specific steps of S42 are: Zero watermark verification: Zero watermark verification is mainly a logo image detection process. Detect the Logo image in To verify copyright, the specific process is as follows: S421: Calculate the original image to be verified The QFMM gives Moment values; S422: The above The moment values ​​are replicated and expanded multiple times to obtain moment values, and then calculate the amplitude of the moment to construct the length The amplitude sequence of ; S423: The amplitude sequence Binarization, get the binary amplitude sequence : (19); in: is the binarization threshold, here we take The mean of S424: Binarize the amplitude sequence becomes OK Binary feature image of the column; (20); S425: Zero watermark image With binary feature image Perform XOR operation to obtain the Logo image that needs to be detected : (twenty one).

[0016] Compared with the prior art, the advantages and positive effects of the present invention are: 1. Improve the efficiency and quality of image reconstruction: The present invention uses an integrated optimization method (HybridOptimization) combined with particle swarm optimization (PSO), simulated annealing (SA) and genetic algorithm (GA) to fine-tune the key parameters of the reconstruction process in multiple optimization stages, thereby effectively improving the accuracy and efficiency of image reconstruction and solving the problems of high computational complexity and low efficiency in traditional optimization algorithms.

[0017] 2. Achieve an effective balance between global optimization and local optimization: Through a multi-stage optimization framework, PSO is used for global optimization to ensure the optimal selection of important global features (such as Fourier coefficients and singular values) in the reconstruction process; SA is used for local optimization to optimize the matrix block and region selection of the image; GA further fine-tunes the low-rank approximation and optimizes local details. In this way, an effective balance can be found between global search and local optimization, thereby improving the quality of image reconstruction.

[0018] 3. Ensure the security and integrity of zero watermark information: This invention embeds zero watermark information in the image reconstruction process through an integrated optimization method, ensuring that the watermark information is not affected while optimizing the image quality, and can ensure its security and extractability in the process after image reconstruction. By precisely controlling the embedding method of watermark information, the common loss or tampering problems in traditional watermark technology are avoided.

[0019] 4. Optimize the combination of zero watermark and image reconstruction: Another goal of the present invention is to achieve a deep integration of zero watermark information and image reconstruction process, so that when the image is subjected to low-rank approximation and other optimization processing, the watermark information can be retained and the image quality can be optimized at the same time. By combining the integrated optimization method, the watermark information can be protected at different optimization stages to ensure that the quality of the reconstructed image is not affected by the watermark information, while ensuring the integrity and extractability of the watermark information. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a schematic diagram of the overall process of the present invention.

[0021] Figure 2 It is a schematic diagram of the local three-dimensional structure of the present invention Figure 1 . DETAILED DESCRIPTION

[0022] A specific implementation of the present invention is described in detail below in conjunction with the accompanying drawings, but it should be understood that the protection scope of the present invention is not limited by the specific implementation.

[0023] The present invention comprises the following steps: S1: Get the original color image.

[0024] S2: Initial Orthogonal Fourier Melling Moments (OFMM) feature extraction calculation to obtain initial matrix features.

[0025] The specific steps of S2 are: Optimized orthogonal Fourier-Mellin moment calculation: Orthogonal Fourier-Mellin moment polar coordinate system, It is the angular component, which represents the angle from the 0 degree position of the polar coordinate system (usually the positive direction of the x-axis) to a certain point. The value range is ,image Repeatability The definition of is as follows: (1); in: is a non-negative integer; represents an imaginary unit; Radial Basis Function yes (It is the radial component, which represents the distance from the origin to a certain point. Its value range is usually [0, 1], because in image processing, the image is usually normalized to the unit circle) The polynomial expression is: (2); in: are the coefficients of the polynomial, are the coefficients of the polynomial; The polynomial of order is Weighting factor of the point, coefficient Determines the shape and size of the radial basis function; exist is weighted orthogonal in the range: (3) in: express The radial basis function of order , which is a polynomial function about the radial component; is the Kronecker symbol; is the normalization factor; According to radial basis function Angular harmonic factor The properties of the orthogonal Fourier-Mellin moments Orthogonal inside the unit circle: (4); in: represents radial basis function and The orthogonality condition between ,when hour, ;when hour, , this condition indicates that radial basis functions of different orders are in the interval The inside is orthogonal.

[0026] represents the angular basis function and The orthogonality condition between ,when hour; ;when hour; This condition indicates that the angular basis functions of different angular frequencies are in the interval is orthogonal only when and When the right side of the equal sign is , otherwise it is 0, which shows that the basis functions of the orthogonal Fourier Mellin moments form a complete orthogonal basis function system within the unit circle.

[0027] According to the orthogonal function system theory, the original image Reconstructed approximately using a finite number of orthogonal Fourier Mellin moments, it is known that the highest order and maximum repetition The orthogonal Fourier-Mellin moments of Refactor as follows: (4); Trinomials are a simpler mathematical structure than complex numbers and quaternions, usually expressed as ,in is the real part, is the imaginary part; unlike quaternions, ternions have only two imaginary units and , which makes calculations much easier. The multiplication of ternaries also follows specific rules, where the multiplication of imaginary units is non-commutative.

[0028] The conjugate of a ternary is defined as: (5); In color image processing, each color channel (such as red, green, blue) is processed by a corresponding function To represent, define a ternary image function to represent the color image: (6) in: Represent the red, green and blue channels of the image respectively.

[0029] In order to calculate the ternary Fourier-Mellin moments (TFOFM) of a color image, the ternary representation of each color channel will be used for the Fourier-Mellin transform. Compared with quaternions, the advantage of ternaries in this calculation is their lower dimensionality and simpler multiplication rules, making the calculation process more efficient. By combining the Fourier-Mellin transform results of each channel, the Fourier-Mellin moments of the image in ternary form can be obtained.

[0030] The traditional method of calculating factorial is usually implemented by direct multiplication, that is, from 1 to However, for very large numbers, the traditional calculation method will consume a lot of computing time and storage space, especially when the factorial numbers are as large as When it becomes very big.

[0031] The advantage of using ternaries instead of quaternions is that the simplification of the ternary structure can reduce the amount of calculation and storage space required. Since ternaries have only two imaginary units, the multiplication rules involved in their calculations are relatively simple, and the storage space and computing resources required are significantly lower than those of quaternions. This allows ternaries to provide higher efficiency and less resource consumption when processing large-scale calculations.

[0032] When dealing with large-scale calculations, especially when it comes to ternary numbers, factorial and exponential operations may still face complexity issues. To solve this problem, an optimization algorithm is proposed that combines the advantages of ternary numbers to effectively reduce calculation time, optimize storage usage, and maintain high precision when dealing with large numbers. Through the Fourier-Mellin moment (TFOFM) in the form of ternary numbers, we can not only simplify the calculation process, but also improve the stability and efficiency of the calculation.

[0033] Compared to quaternions, ternions offer several key advantages: Ternions only contain two imaginary parts. Compared with quaternions (containing three imaginary parts), their multiplication rules are simpler, reducing the complexity of calculations.

[0034] Since ternary numbers have a simpler structure, less storage space is required during calculations, which can significantly reduce the consumption of storage resources, especially when processing large amounts of data.

[0035] The simplified structure of ternary numbers can effectively control the loss of precision when calculating large numbers and avoid precision errors caused by insufficient computing resources.

[0036] In summary, the Fourier-Mellin moment calculation method combined with ternary numbers provides higher computational efficiency and lower resource consumption, and is particularly suitable for large-scale image processing and other fields that require efficient mathematical operations.

[0037] S3: Data optimization method.

[0038] Implementation ideas of hybrid optimization in image reconstruction. By combining the advantages of multiple optimization algorithms, the hybrid optimization method can give full play to their respective strengths in different optimization stages to achieve a balance between global optimization and local fine optimization. Specifically, by combining the application of particle swarm optimization (PSO), simulated annealing (SA) and genetic algorithm (GA) in image reconstruction, there are several specific implementation stages.

[0039] S31: Orthogonal Fourier Mellin moment feature extraction and parameter optimization;

[0040] The specific steps of S31 are: Original input color image After processing by orthogonal Fourier-Mellin moments, a set of moment features, namely images, is generated. , recorded as: (7); in: Indicates n Stage, m Angular coefficient; These moment coefficients are affected by multiple parameters, such as the scale factor of the Fourier basis function, the singular value truncation threshold, etc. In order to improve the stability and robustness of the orthogonal Fourier Mellin moment matrix, these parameters need to be optimized so that the image error reconstructed by the orthogonal Fourier Mellin moment is minimized. Let the parameter vector be: (8); The optimization objective is defined as the reconstruction error between the reconstructed image and the original image: (9); in: Represents the parameter vector The reconstructed image after processing with orthogonal Fourier-Mellin moments.

[0041] In the integrated optimization framework, we first need to clarify the optimization objectives and constraints. The main goal of image reconstruction is usually to minimize the reconstruction error, that is, to optimize the difference between the reconstructed image and the original image, which may involve the following specific objectives: Singular value optimization: In low-rank approximation, choose the appropriate number and size of singular values.

[0042] Fourier coefficient optimization: Optimizes the frequency components of the image to ensure that the details and texture of the image are accurately preserved.

[0043] Matrix Block Optimization: Image block optimization is used to improve computational efficiency and reduce storage requirements.

[0044] Low-rank approximation: Optimize the matrix rank to find the optimal rank that balances compression and accuracy.

[0045] Orthogonal Fourier Mellin moment feature extraction and parameter optimization.

[0046] S32: Multi-stage optimization framework.

[0047] The optimization problem is divided into different stages, and different optimization algorithms are used in each stage to optimize specific optimization goals. Specifically, the following steps can be followed.

[0048] S321: Global optimization, using Particle Swarm Optimization (PSO) to optimize singular values ​​and Fourier coefficients.

[0049] The specific steps of S321 are: Initialize the particle swarm, each particle represents a potential solution, and the particle dimension corresponds to the number of optimized singular values, Fourier coefficients, etc. The position of the particle represents the combination of different Fourier coefficients and singular values, and the velocity of the particle indicates how to adjust these parameters to approach the global optimal solution. By calculating the fitness of each particle (such as reconstruction error, image quality, etc.), the particle continuously updates its position and velocity until the convergence condition is reached.

[0050] Particle swarm optimization (PSO) is used to perform a global search of the parameter space, with each particle representing a candidate solution for the parameter. , and its speed update formula is: (10); in: is the inertia weight; is the acceleration constant; is a random number between [0,1]; It is a particle The best historical position of g; g is the global best position; The particle's position is updated as: (11).

[0051] The goal of the PSO stage is to search the parameter space as globally as possible so that the objective function Obtaining a lower value provides a better starting point for subsequent local optimization.

[0052] S322: Local optimization, using simulated annealing (SA) to optimize matrix blocks.

[0053] The specific steps of S322 are: after PSO obtains a preliminary optimal solution, the simulated annealing algorithm is introduced to locally refine the parameters, and the current state is set to , generating a new state , the objective function changes to , the probability of accepting the new state is: (12); in: is the current temperature; by gradually lowering the temperature, we can avoid falling into the local optimum and gradually converge to the optimal solution. SA here mainly adjusts the parameters of the local blocks or regions of the image, so that the orthogonal Fourier Mellin moment features of each region are more refined and the reconstruction error is further reduced. The SA algorithm is used to optimize the matrix block of the image (for example, which areas are selected for fine processing). For an image, the image may be divided into multiple small blocks, each of which can be processed independently. SA optimization can select the most important areas for high-precision reconstruction, reducing the amount of calculation and storage requirements.

[0054] The annealing process of SA simulates the physical annealing process, which accepts inferior solutions by probability to avoid the algorithm falling into the local optimal solution. In this way, SA can find a better matrix partitioning strategy.

[0055] At this stage, SA can help adjust the structure of image blocks, select appropriate image blocks for key optimization, and reduce redundant calculations.

[0056] S323: Fine optimization, using genetic algorithm (GA) to optimize low-rank approximation and local solutions.

[0057] The specific steps of S323 are: Advantages of GA: Genetic algorithms are suitable for dealing with complex combinatorial optimization problems; GA can search the solution space through population iteration, and locally refine the solution through operations such as crossover and mutation, thereby achieving the purpose of optimization.

[0058] Implementation: GA performs further optimization of the low-rank approximation at this stage, such as selecting the most appropriate singular value combination, or adjusting the matrix rank (determining how many singular values ​​to retain).

[0059] Corresponding to different matrix partitioning schemes, GA selects the optimal singular value combination or the optimal matrix partitioning strategy through global search and local fine operations.

[0060] Genetic algorithms use crossover operations to combine parameters from different individuals to generate new solutions; mutation operations can introduce a certain amount of randomness to avoid falling into local optimal solutions; Crossover operation: (13); in: and is the selected parent, is the mixing coefficient; Mutation operation: (14) in: is the random perturbation vector; Through the continuous iteration of the genetic algorithm selection, crossover and mutation process, a global optimal or approximately global optimal parameter combination is finally obtained. GA can select appropriate singular value combinations in the process of low-rank approximation and optimize singular value decompositions of different orders, thereby improving the quality of image reconstruction.

[0061] S33: Optimize process integration.

[0062] The specific steps of S33 are: After the above three stages of integrated optimization, an optimal parameter combination is finally obtained. , the orthogonal Fourier Mellin moment matrix feature extraction process at this time is: (15).

[0063] Using this optimal feature matrix, zero watermark information can be embedded. The specific process is as follows: right Perform copy expansion and amplitude binarization to construct a binary feature image; Use XOR operation to combine the logo information to be embedded with the binary feature image to generate a zero-watermark image; In the extraction stage, the zero watermark is restored through the same orthogonal Fourier-Mellin moment processing and optimization parameters to verify the watermark information.

[0064] This integrated optimization method ensures that the orthogonal Fourier Mellin moment feature extraction reaches the optimal state in both global parameter search and local detail adjustment, making the embedding and extraction process more robust and efficient, while having higher concealment and anti-attack capabilities.

[0065] S4: Adaptive adjustment and dynamic optimization, design of efficient and reliable zero watermark algorithm.

[0066] In addition, in order to improve the flexibility and efficiency of the optimization process, it is possible to consider introducing an adaptive adjustment strategy. For example, in different optimization stages, the parameters of each optimization algorithm (such as the number of particles in PSO, the temperature in SA, the population size in GA, etc.) are adjusted to achieve the best results under different conditions.

[0067] The hybrid optimization method combines the advantages of PSO, SA, and GA to handle different types of optimization problems in the image reconstruction process. PSO is used to globally search and optimize singular values ​​and Fourier coefficients, SA is used to locally optimize matrix blocks, and GA is used to fine-tune low-rank approximation and local details of the image. This multi-stage, multi-algorithm optimization framework can balance global and local optimization to ensure the quality and efficiency of image reconstruction.

[0068] Combined with the optimized TOFMM, an efficient and reliable zero watermark algorithm is designed. The algorithm mainly includes two processes: zero watermark construction and zero watermark verification. The addition of the improved TOFMM makes the entire zero watermark algorithm more efficient and reliable. The implementation process and specific steps of the algorithm will be introduced in detail below. Figure 2 The overall flow chart is shown.

[0069] S41: Zero watermark construction.

[0070] The specific steps of S41 are: Zero watermark construction: Assume is the original ternary Fourier-Mellin moment image, For the original binary Logo image, the zero watermark construction process is as follows: S411: Calculate the ternary Fourier-Mellin moment image The orthogonal Fourier-Mellin moments of Moment values; S412: What you will get The moment values ​​are replicated and expanded multiple times to obtain moment values, and then calculate the amplitude of the moment to construct the length The amplitude sequence of ; represents the first The amplitude (modulus) of the moment value reflects the spatial and frequency domain characteristics of the image. By calculating the amplitude sequence a ( i ), the continuously changing moment features can be converted into an amplitude sequence form suitable for watermark embedding, which is convenient for the subsequent amplitude binarization and zero watermark construction.

[0071] S413: The amplitude sequence Binarization, get the binary amplitude sequence : (16); in: After binarization, elements, with values ​​of 0 or 1, used to construct a binary feature image; is the binarization threshold, here we take The mean of S414: Binarize the amplitude sequence becomes OK Binary feature image of the column: (17); S415: Use XOR operation to convert the Logo image Embedded into binary feature image Get the zero watermark image : (18).

[0072] S42: Zero watermark verification.

[0073] The specific steps of S42 are: Zero watermark verification: Zero watermark verification is mainly a logo image detection process. Detect the Logo image in To verify copyright, the specific process is as follows: S421: Calculate the original image to be verified The QFMM gives Moment values; S422: The above The moment values ​​are replicated and expanded multiple times to obtain moment values, and then calculate the amplitude of the moment to construct the length The amplitude sequence of ; S423: The amplitude sequence Binarization, get the binary amplitude sequence : (19); in: is the binarization threshold, here we take The mean of S424: Binarize the amplitude sequence becomes OK Binary feature image of the column; (20); S425: Zero watermark image With binary feature image Perform XOR operation to obtain the Logo image that needs to be detected : (twenty one).

[0074] The present invention proposes a ternary fast and accurate orthogonal-Fourier-Mellin moment zero watermark construction method, the core innovation of which is reflected in the following aspects: First, in terms of the optimization of OFMM moment feature extraction, the calculation efficiency and stability of OFMM moment are greatly improved by introducing optimization methods such as prime factorization algorithm. The extracted matrix features not only meet the strict orthogonality requirements, but also remain unchanged under geometric transformations such as rotation and scaling, which provides a solid foundation for subsequent watermark embedding and extraction. The protection of this part mainly focuses on the calculation process, parameter setting and specific application method of OFMM moment in zero watermark embedding.

[0075] Secondly, the present invention designs a feature expansion and binarization processing scheme. For the matrix data extracted from OFMM, the replication expansion and amplitude binarization processing flow is adopted to convert the original matrix features into a binary carrier suitable for watermark embedding, and ensure that it still maintains high robustness under different image conditions. The innovation and protection focus of this part lies in the specific implementation of feature expansion, binarization strategy and threshold selection method.

[0076] In addition, in terms of concealed embedding and accurate extraction of zero watermark, the present invention uses XOR operation to conceal the logo to be embedded, thereby forming a zero watermark image. When extracting the watermark, the steps consistent with the initial OFMM processing flow are used to accurately restore the embedded information, and the integrity of the watermark information is ensured by compensating for geometric transformations (such as rotation and scaling). In this regard, the encoding, decoding strategies and compensation methods in the embedding and extraction process constitute the important protection content of the present invention.

[0077] Finally, the robustness design of the overall system is also a highlight of the present invention. By utilizing the rotation and scaling invariance of the OFMM matrix, the constructed watermark system can still maintain a high watermark detection rate after the image is compressed, noisy, filtered and other common processing, while achieving high concealment. The protection focus of this part is on the overall architecture based on the combination of the OFMM matrix and the zero watermark and its technical strategy to resist various signal processing attacks.

[0078] Through the comprehensive application of the above key technologies, the present invention not only realizes the efficient protection of image copyright, but also takes into account the computational efficiency, robustness and concealment, and provides a safe, reliable and commercially promising image watermarking solution for practical applications.

[0079] The above disclosure is only a specific embodiment of the present invention, but the present invention is not limited thereto, and any changes that can be conceived by those skilled in the art should fall within the protection scope of the present invention.

Claims

1. A ternary fast and accurate orthogonal-Fourier-Mellin moment zero watermark construction method, characterized in that: The following steps are involved: S1: Get the original color image; S2: Initial orthogonal Fourier Mellin moment feature extraction calculation to obtain initial matrix features; S3: Data optimization methods; S31: Orthogonal Fourier Mellin moment feature extraction and parameter optimization; S32: Multi-stage optimization framework; S321: Global optimization, using particle swarm optimization for singular values ​​and Fourier coefficients; S322: local optimization, using simulated annealing to optimize matrix partitioning; S323: Fine Optimization, using genetic algorithms to optimize low-rank approximations and local solutions; S33: Optimize process integration; S4: Adaptive adjustment and dynamic optimization, design of efficient and reliable zero watermark algorithm; S41: zero watermark construction; S42: Zero watermark verification.

2. The ternary fast and accurate orthogonal-Fourier-Mellin moment zero watermark construction method according to claim 1 is characterized by: The specific steps of S2 are: Optimized orthogonal Fourier-Mellin moment calculation: Orthogonal Fourier-Mellin moment polar coordinate system, is the angular component, image Repeatability is defined as follows: （1）； in: is a non-negative integer; represents an imaginary unit; Radial Basis Function yes of The polynomial expression is: （2）； in: are the coefficients of the polynomial, are the coefficients of the polynomial; exist is weighted orthogonal in the range: （3） in: express k Radial basis function of order; is the Kronecker symbol; is the normalization factor; According to radial basis function Angular harmonic factor The properties of the orthogonal Fourier-Mellin moments Orthogonal inside the unit circle: （4）； in: represents radial basis function and Orthogonality conditions between ; represents the angular basis function and Orthogonality conditions between ; According to the orthogonal function system theory, the original image Reconstructed approximately using a finite number of orthogonal Fourier Mellin moments, it is known that the highest order and maximum repetition The orthogonal Fourier-Mellin moments of Refactor as follows: （4）； Ternaries are usually represented as ,in is the real part, is the imaginary part; The conjugate of a ternary is defined as: （5）； In color image processing, each color channel is processed by a corresponding function To represent, define a ternary image function to represent the color image: （6） in: Represent the red, green and blue channels of the image respectively.

3. The ternary fast and accurate orthogonal-Fourier-Mellin moment zero watermark construction method according to claim 2 is characterized by: The specific steps of S31 are: Original input color image After processing by orthogonal Fourier-Mellin moments, a set of moment features, namely images, is generated. , recorded as: （7）； in: Indicates n Stage, m Angular coefficient; These moment coefficients are affected by multiple parameters, and the parameters are optimized so that the image error reconstructed by the orthogonal Fourier-Mellin moment is minimized. Let the parameter vector be: （8）； The optimization objective is defined as the reconstruction error between the reconstructed image and the original image: （9）； in: Represents the parameter vector The reconstructed image after processing with orthogonal Fourier-Mellin moments.

4. The ternary fast and accurate orthogonal-Fourier-Mellin moment zero watermark construction method according to claim 2 is characterized by: The specific steps of S321 are: Particle swarm optimization is used to perform a global search of the parameter space, where each particle represents a candidate solution for a parameter. , and its speed update formula is: （10）； in: is the inertia weight; is the acceleration constant; is a random number between [0,1]; It is a particle The best historical position of g; g is the global best position; The particle's position is updated as: （11）。 5. The ternary fast and accurate orthogonal-Fourier-Mellin moment zero watermark construction method according to claim 4 is characterized by: The specific steps of S322 are: The simulated annealing algorithm is introduced to locally refine the parameters. Suppose the current state is , generating a new state , the objective function changes to , the probability of accepting the new state is: （12）； in: is the current temperature.

6. The ternary fast and accurate orthogonal-Fourier-Mellin moment zero watermark construction method according to claim 4 is characterized by: The specific steps of S323 are: Genetic algorithms are suitable for dealing with complex combinatorial optimization problems; Genetic algorithms use crossover operations to combine parameters from different individuals to generate new solutions; mutation operations can introduce randomness to avoid falling into local optimal solutions; Crossover operation: （13）； in: and is the selected parent, is the mixing coefficient; Mutation operation: （14） in: is the random perturbation vector; Through the continuous iteration of the genetic algorithm selection, crossover and mutation process, a global optimal or approximately global optimal parameter combination is finally obtained. .

7. The ternary fast and accurate orthogonal-Fourier-Mellin moment zero watermark construction method according to claim 6 is characterized by: The specific steps of S33 are: After the above three stages of integrated optimization, an optimal parameter combination is finally obtained. , the orthogonal Fourier Mellin moment matrix feature extraction process at this time is: （15）。 8. The ternary fast and accurate orthogonal-Fourier-Mellin moment zero watermark construction method according to claim 7 is characterized by: The specific steps of S41 are: Zero watermark construction: Assume is the original ternary Fourier-Mellin moment image, For the original binary Logo image, the zero watermark construction process is as follows: S411: Calculate the ternary Fourier-Mellin moment image The orthogonal Fourier-Mellin moments of Moment values; S412: What you will get The moment values ​​are replicated and expanded multiple times to obtain moment values, and then calculate the amplitude of the moment to construct the length The amplitude sequence of ; represents the first The magnitude of the moment value; S413: The amplitude sequence Binarization, get the binary amplitude sequence : （16）； in: After binarization, elements, the value is 0 or 1; is the binarization threshold, here we take The mean of S414: Binarize the amplitude sequence becomes OK Binary feature image of the column: （17）； S415: Use XOR operation to convert the Logo image Embedded into binary feature image Get the zero watermark image : （18）。 9. The ternary fast and accurate orthogonal-Fourier-Mellin moment zero watermark construction method according to claim 8, characterized in that: The specific steps of S42 are: Zero watermark verification: Zero watermark verification is mainly a logo image detection process. Detect the Logo image in To verify copyright, the specific process is as follows: S421: Calculate the original image to be verified The QFMM gives Moment values; S422: The above The moment values ​​are replicated and expanded multiple times to obtain moment values, and then calculate the amplitude of the moment to construct the length The amplitude sequence of ; S423: The amplitude sequence Binarization, get the binary amplitude sequence : （19）； in: is the binarization threshold, here we take The mean of S424: Binarize the amplitude sequence becomes OK Binary feature image of the column; （20）； S425: Zero watermark image With binary feature image Perform XOR operation to obtain the Logo image that needs to be detected : （21）。

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