Because of its unique characteristics, digital watermarking technology effectively overcomes the shortcomings of traditional encryption technology. The performance is as follows: most digital watermarks are invisible and not easy to attract attention and malicious cracking. Without obtaining the original watermark, key and algorithm, it is difficult to detect or extract the watermark hidden in the printed carrier. Digital watermarking has strong anti attack ability. After the printed information is attacked, it can still extract the watermark information with less distortion [1]. On the basis of the first two points, digital watermarking technology can effectively prove the owner of digital works and play the role of copyright protection. Due to its own characteristics and practical value, digital watermarking technology has attracted more and more attention from industry and academia at home and abroad, and has become a research hotspot in the fields of information industry, data security and so on. The preprocessing of watermark information refers to the research on different scrambling methods of watermark information, such as adaptive scrambling preprocessing combining preprocessing process with carrier information to improve the invisibility and robustness of watermark. The research on watermark embedding algorithm mainly focuses on frequency domain algorithm, algorithm combining spatial domain and frequency domain, adaptive embedding algorithm combining embedding process with carrier information, multiple watermark embedding algorithm, etc. [2]. The purpose is to improve the invisibility and robustness of watermark information and achieve a better balance between them. The research on the watermark detection and extraction algorithm and the process of detecting or extracting the watermark from the printed carrier can further optimize the watermark preprocessing and embedding algorithm, and reduce the missed detection rate and false alarm rate. The main function of digital watermarking technology is to protect digital works from malicious attacks and cracking [3]. However, with the progress of watermarking technology, various attack algorithms and technologies are also improving, which also promotes the research on anti attack technology of watermarking system. The research on watermark attack and anti attack will be a major research direction of digital watermarking technology. Research on fragile watermarking technology for preventing tampering or recording tampering process intentional or unintentional attacks in the process of transmission will change the content of digital works. In order to avoid this change or record the process of this change, a special digital watermark fragile watermarking is needed. Fragile watermarking can be used to prevent works from being tampered or record the process of tampering because it is easy to be distorted after being attacked. Fragile watermark is also called fragile watermark [4]. The establishment and improvement of the evaluation standard of the watermark system, and the study of richer attack means, more detailed and reasonable evaluation steps and more appropriate evaluation parameters are conducive to the further optimization and improvement of the watermark embedding and detection system, as well as the practicability and popularization of the digital watermark technology [5]. Digital watermarking technology plays an extensive and important role in the field of copyright protection of digital works. At present, its application fields can be summarized as follows: copyright certificate. In the past, manufacturers usually printed the copyright statement of works on the front and back pages of books, the outer packaging paper of records, or inserted it into the beginning or end of films. However, the copyright notices made by these methods can be easily removed. Digital watermarking technology embeds the information of the copyright owner of digital works into the works, which is invisible to users and difficult to remove. This provides strong evidence of copyright ownership and is a powerful weapon for the owner of the work to prove that the copyright belongs to himself. Integrity authentication digital works are often tampered with intentionally or unintentionally in the process of dissemination, which makes the receiver receive the distorted work content. Therefore, whether the works are tampered with in the process of communication and how they are tampered with is a problem that people focus on [6]. Digital watermarking technology can solve this problem. As one of the digital watermarks, fragile watermarks can not only judge whether the works have been tampered in the process of transmission, but also determine the location of tampering and the ways and means used in tampering, and even partially or completely restore the distorted works to their original state. Broadcast monitoring: that is to detect and record the time and times of uploading and broadcasting digital works in various media (radio, television, website, etc.), so as to facilitate the owners of works to safeguard their legitimate rights and interests. If the record company wants to know the number of times the radio and television stations play their works, it will charge the corresponding fee; Film companies want to prohibit TV stations or websites from illegally broadcasting their own films; Enterprise customers want radio and television stations to broadcast their own advertisements in accordance with the provisions of the contract, and ensure the number of broadcasts, the time point and length of each broadcast. Piracy tracking: manufacturers of digital works can embed different watermark information for different buyers when selling their products. In this way, on the premise that the identity of the buyer of each genuine work can be determined, if there is piracy of the work on the market, the person responsible for the source of illegal piracy can be easily traced according to the watermark information detected in the pirated work. At present, this is one of the ideas of anti-theft version of many charging software. Copy control: in the dissemination of digital works, copyright notices and embedded digital watermarks can only deter pirates and prove the copyright owner. In order to completely prohibit the illegal reproduction of digital works, it needs the mutual cooperation and simultaneous action of digital works playback and reproduction equipment in software and hardware. For example, a watermark that cannot be copied can be embedded in digital works. When the playback device detects the watermark, it is only allowed to play and copying is prohibited [7]. Of course, this requires adding a digital watermark detection circuit to the relevant hardware equipment. Covert communication: digital watermarking technology provides a new means for the secret transmission of information. Compared with the traditional encryption communication technology, digital watermarking technology uses the redundancy characteristics of human vision and hearing to hide the information to be transmitted in different positions of time domain, space domain or frequency domain of various plaintext information. It is not easy to attract the attention of attackers and is not easy to be broken. It can well complete the task of covert communication. Hidden annotation is to embed the relevant information of digital works into the content of works. This hidden annotation is easy to lose and will not occupy additional space. It is a good information annotation method. Bill anti-counterfeiting: the continuous development of high-quality image acquisition and printing equipment makes it easier to forge bills than before. Digital watermarking technology can embed invisible anti-counterfeiting watermark in bill image. The relevant detection equipment can judge whether the scanned bill image contains anti-counterfeiting watermark, so as to judge the authenticity of the bill. To solve this research problem, Lei Q and others proposed a robust watermarking algorithm based on neighborhood average from the perspective of time domain. The algorithm has good imperceptibility and resistance to conventional signal processing operations, desynchronization jitter attack and random clipping [8]. Jiang S and others proposed a maximum likelihood watermark detection method based on the statistical characteristics of audio DCT coefficients. The watermark is embedded into DCT domain by spread spectrum, and the corresponding Gaussian mixture model is obtained. Then, the watermark information is judged and extracted by the maximum likelihood detection method [9]. The watermark detection algorithm proposed by Li D and others is higher than the traditional detection method. However, in the detection process, this method also needs to find the initial watermark embedding position through the key, which has low practical application value [10]. Based on the current research, this paper proposes a combination of all-phase Biorthogonal Transform and watermark embedding to complete the experiment. Firstly, the all-phase biorthogonal transform is described. Referring to the construction process of APBT, combined with APDF and DST, a new all-phase biorthogonal transform, all-phase discrete sinusoidal biorthogonal transform (APDSBT), is proposed. Making full use of MPEG-2 compression format, watermark is embedded directly in DCT domain. The low-frequency coefficients in the DCT block of the brightness space of I frame are selected as the watermark embedding space. The brightness component of each image block is transformed by two-dimensional DCT in the unit of 8×8 image blocks. By introducing the idea of energy receiver into the detection of digital watermark, the following correlation detector can be obtained. Implemented with MATIAB and VC + +. In the experiment, the foreman video test sequence is used as the watermark carrier, and the copyright logo image designed by ourselves is used as the watermark image to test the video watermarking system. Experiments show that the video watermarking system is robust and highly transparent. In order to make the application range of HEVC video watermarking more extensive and practical, based on the video watermarking algorithm in this paper, some feature points in the video are selected for watermark embedding, which can further reduce the impact of watermark on video quality.

In 1990, Perona and Malik proposed a nonlinear anisotropic diffusion equation, namely the P-M model, in order to maintain image edge information. Definitions are as follows:

All phase biorthogonal transformation can be divided into the following three types according to different orthogonal transformation bases: All phase discrete cosine biorthogonal transform (APDCBT), all phase Walsh biorthogonal transform (APWBT) and all phase inverse discrete cosine biorthogonal transform (APIDCBT). All phase biorthogonal transform has similar properties to DCT transform, in which the transformation matrix of all phase discrete cosine biorthogonal transform can be expressed as:

In image coding, APBT transformation is performed on the image block X with the size of N×N, which can be expressed as:
^{−1} ^{−1})^{T} can be used to reconstruct the image. Where (⋅)^{T} represents matrix transpose and ^{−1} is the inverse of matrix V.

Discrete sinusoidal transform is used in HEVC video compression standard for the first time because of its excellent performance in 4×4 coding block of intra luminance component [11]. Based on the analysis of the construction process of all phase biorthogonal transform, combined with all phase digital filter and discrete sinusoidal transform, this section proposes a new transform all phase discrete sinusoidal biorthogonal transform (APDSBT), which is used in JPEG coding framework, and proposes a JPEG like video compression coding algorithm based on APDSBT.

The idea of all phase is to intercept different phases of n-dimensional vectors containing time series {_{N} (_{0}, _{1}, …, _{N−1}].

All phase digital filter is an FIR digital filter based on all phase theory, and its performance is better than other traditional filters. With the development of all phase digital filtering theory, related technologies have been further developed in recent years, such as all phase biorthogonal transform based on all phase digital filtering and windowed all phase biorthogonal transform. Based on the construction process of APBT, combined with APDF and DST, this paper proposes a new all phase biorthogonal transform, all phase discrete sinusoidal biorthogonal transform (APDSBT). Similar to the construction process of APDCBT based on APDF and DCT [12]. Where, f is the n-dimensional expected generalized frequency response vector, and the generalized frequency can also be called column rate _{N} (0), _{N} (1), …, _{N} (^{T}. The DST transformation adopts type VII DST transformation used in HEVC standard:
^{−1} = ^{T}. The input-output response of all phase digital filter based on DST, where x (n) is the input signal and y (n) is the output signal. In order to further elaborate the design process of all phase digital filter based on DST and all phase discrete sinusoidal biorthogonal transform, it will be deduced from a mathematical point of view. Assume that _{i} (^{i} (

Where, “.” represents the point multiplication operation. _{i} (_{i} is “1” and the other elements are “0”.

This algorithm embeds the watermark information into the brightness space of MPEG-2 video stream frame, makes full use of MPEG-2 compression format, and embeds the watermark directly in DCT domain. The specific steps of watermark embedding are as follows:

An image P with a gray level of 28 can be decomposed into 8 binary images. According to the idea of LSB, the least significant bit of the image represents the detail part of the image. On the premise of not affecting the visual effect, when p is embedded into the video carrier as a watermark, it only needs to be embedded, and P7... Pt is decomposed from the most significant bit part, generally t = 4.

Because the human eye is sensitive to the brightness part, in order to improve the robustness of the watermark, the watermark is usually embedded in the most sensitive part of perception. Therefore, the low-frequency coefficients in the DCT block of the brightness space of I frame are selected as the watermark embedding space [13]. The brightness component of each image block is transformed by two-dimensional DCT in the unit of 8×8 image blocks. According to the idea of ISB, the weight of the low bit plane of the watermark image in the reconstructed watermark image is different, so different bit planes are embedded in DCT coefficients with different numbers [14]. Assuming _{i}, |0 ≤

According to the different weights of different bit planes when reconstructing image p, the number of DCT coefficients modified when embedding the bit plane into the video carrier is also different. This algorithm embeds each data bit of bit planes P7, P6, P5 and P4 into Fa, Fb, Fc and Fd of each image block respectively.

The bit plane decomposed by the copyright mark image P is scanned into a one-dimensional 0–1 watermark sequence, and the information bits of the four bit planes that need to be embedded in the watermark carrier are spread spectrum modulated [15]. Using the opposite pseudo-random mode
_{t}, and the - 1 and 1 random sequence generated by the seed. The lengths of

Modify the DCT medium and low frequency coefficients of the luminance component of the video I frame image block and embed the watermark. When modifying the DCT coefficients of image blocks, the restriction that must be met is that it can not cause perceptual distortion. In the general embedding mode, the watermark embedding strength of the modulated watermark signal obtained from experience is directly superimposed on the carrier, which is formally expressed as follows:
^{t} can be expressed as:
_{I,ij} is the luminance sensitivity of each DCI block coefficient calculated according to Watson visual model.

The program of this experiment is implemented with MATIAB and VC + +. In the experiment, the foreman video test sequence is used as the watermark carrier, and the copyright logo image designed by ourselves is used as the watermark image to test the video watermarking system. The key experimental parameters are shown in Table 1. The PSNR before and after embedding watermark is 43.69. Table 2, Figure 1 and Figure 2 show the accuracy of extracting each bit plane under different coding rates.

Experimental parameter setting

Parameter | Value |
---|---|

frame size | 353×289 |

frame rate | 26 fps |

frame in GOP | 13 |

I/P frame distance | 4 |

bit rate | 4Mbps |

Y:U:V | 6:4:0 |

video pattern | PAL |

Extraction accuracy of each watermark bit plane under different coding rates

Bit plane | Accuracy of extracting watermark /% | ||
---|---|---|---|

Non-compressed | 3Mbps | 2.6Mbps | |

P7 | 100 | 100 | 100 |

P6 | 100 | 97.99 | 97.01 |

P5 | 100 | 96.01 | 95.02 |

P4 | 100 | 95.99 | 94.98 |

In MPEG2 coding, the reference frames of P and B cannot be deleted and skipped. This algorithm selects the frame of video to embed watermark. It can be seen from Table 3 that this algorithm is robust to common video watermark attacks (MPEG compression, frame loss, frame clipping and frame rearrangement) on the premise of ensuring video quality.

Extraction accuracy of watermark under different attacks

Attack type | Specific attack methods | Watermark extraction results |
---|---|---|

Lost I frame | Delete frame 12 | Video quality is seriously degraded |

Lost B or P frames | Delete frame 4 and 7 | Correct extraction |

Frame clipping | Frame I part cut | Partial loss of watermark |

Frame rearrangement | Rearrange frames 4 ∼ 8 ∼ 9 ∼ 12 | Correct extraction |

This paper is a research on video adaptive watermark embedding and detection algorithm based on phase function equation. Aiming at the problems of video watermark embedding strength in balancing the robustness and invisibility of watermark system, a video watermark algorithm based on variable length bit plane decomposition is proposed. According to the different weights of each plane in reconstructing the watermark image after the bit plane decomposition of the 8-bit gray watermark image, the algorithm embeds different bit planes into different numbers of DCT medium and low frequency coefficients, and adaptively adjusts the watermark embedding intensity by using the brightness masking characteristics of HVS and Watson visual model, so as to realize the adaptive embedding of watermark. Experiments show that the video watermarking system is robust and highly transparent. In order to make the application range of HEVC video watermarking more extensive and practical, based on the video watermarking algorithm in this paper, some feature points in the video are selected for watermark embedding, which can further reduce the impact of watermark on video quality. Whether it is HEVC video coding or HEVC video watermarking, there is still room for further improvement. Send some w as further research work in the future.

#### Extraction accuracy of each watermark bit plane under different coding rates

Bit plane | Accuracy of extracting watermark /% | ||
---|---|---|---|

Non-compressed | 3Mbps | 2.6Mbps | |

P7 | 100 | 100 | 100 |

P6 | 100 | 97.99 | 97.01 |

P5 | 100 | 96.01 | 95.02 |

P4 | 100 | 95.99 | 94.98 |

#### Experimental parameter setting

Parameter | Value |
---|---|

frame size | 353×289 |

frame rate | 26 fps |

frame in GOP | 13 |

I/P frame distance | 4 |

bit rate | 4Mbps |

Y:U:V | 6:4:0 |

video pattern | PAL |

#### Extraction accuracy of watermark under different attacks

Attack type | Specific attack methods | Watermark extraction results |
---|---|---|

Lost I frame | Delete frame 12 | Video quality is seriously degraded |

Lost B or P frames | Delete frame 4 and 7 | Correct extraction |

Frame clipping | Frame I part cut | Partial loss of watermark |

Frame rearrangement | Rearrange frames 4 ∼ 8 ∼ 9 ∼ 12 | Correct extraction |

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Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability 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Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model