As one of the research hotspots of computer vision, visual matching has the preponderance of estimating the 3D structure and appearance information of the scene. The advantages of convenience and low cost of this technology promote the development of artificial intelligence, pattern recognition and machine vision. However, with the development of industrial refinement, people put forward higher requirements for the accuracy and range of measurement information [1, 2]. For example, for accurate identification of workpiece position, precise data are needed to calculate centroid coordinates on this basis, which introduces the need for higher measurement accuracy. At the same time, most of these devices are foreign products, which are expensive, suitable for customisation and detection of specific scenes, and not universal, which severely restricts the development of China's manufacturing industry [3,4,5]. In addition, with the continuous development of visual matching techniques, the single-scale application scenarios represented by mobile phones will greatly increase. At the same time, among the many ways of visual model reconstruction, 3D reconstruction technology, which is based on stereo vision matching, utilises the bionics principle. The acquired images are processed by imitating human visual perception, which makes the effect relatively close to the recognition result of human eyes, and endows it with the capability to flexibly process data information in complex scenes. Therefore, this function cannot be replaced by other computer vision methods, and it is also the general trend of future development.
Extraction and matching of a feature point is an important step in determining whether the result of visual matching is accurate or not, and is also an important cornerstone to ensure the smooth development of the follow-up work. Among the existing 3D reconstruction methods, SIFT fast feature matching algorithm, SURF accelerated robust feature matching algorithm and ORB algorithm are commonly used [6, 7]. But the real-time performance of SIFT is poor, even after the underlying optimisation, through several times improvement, the time performance is not enough to meet the real-time requirements of current application scenarios. In the application scenario of scale-free variation, if SURF algorithm is used, the time cost will increase, while if ORB algorithm is used, the accuracy will decrease [8, 9]. Therefore, for the inherent constraint problem of images in the scale-free variation scene, we need to find a better way to solve the balance between visual matching effect and speed from the extraction, matching and misjudgement point elimination of feature point.
The environment of visual imaging process consists of scene illumination, light propagation, illumination of image plane and signal processing. Natural scenery is ever-changing with different shapes. It is necessary to know the background characteristics of various radiation sources and targets, whether the scenery can be imaged and with what means it is suitable to be converted into an image. First, most of the images used in image processing are collected according to the principle of reflected light imaging. In the design of actual imaging system, it is generally simplified to Lambert model, and the ideal diffuse reflector is the typical Lambert , where the scenery emits light in all directions. Take a point in the scene as an example to analyse the light propagation. Figure 1 is a sectional view of an imaging system, and point P emits spherical waves; when it reaches the lens system, due to the differences between points on the surface of spherical waves and the refractive index of the lens, the light rays converge to point P′ of the image plane. Due to the coaxial sphericity of the imaging system, the object point P corresponds to the only image point P′. When the spherical waves emitted by all points in the field of view can be received by the imaging system, a two-dimensional image of the scene is formed.
As shown in Figure 2, the light received by the human eye reaches the fundus, and passes through the human eye imaging and the eyepiece after reflection, thereby forming an image at plane S behind the eyepiece. Then, the light passes through the reducing glass, and the common objective glass receives light rays where the plane S becomes the common focal plane of the eyepiece and the two lenses behind it. Afterwards, the imaging beam forms two parallel beams after sharing the objective lens, and the distance between the two parallel beams is increased by the reflector group, which provides space for adding mirror of illumination light path and OCT mirror . Through the focusing lens and CCD camera, the images of the two parallel lights are collected, individually. The focusing system can adjust the range of the camera-receiving surface, so as to obtain the appropriate fundus retinal images. The common objective lens and the structure in front of the objective lens of the imaging system are mainly designed by using principle of Kepler telescope system, and the parallax principle of binocular vision is used in the two-way camera shooting after sharing the objective lens.
The physical world is imaged on the photo sensor through the camera model, and is stored on the storage device after analogue–digital conversion. In this process, it involves the transformation of four coordinate systems, including the world coordinate system (X
To transform a point P in space into a point P′ in the image, it is necessary to master the physical meaning and mathematical transformation relationship of the four coordinate systems. Without considering the distortion, that is, under the ideal perspective condition, the principle of transformation of object point into image point is shown in Figure 3. P is located in the real space, and its position relationship can be accurately expressed only by determining the reference frame in the 3D scene . The coordinate system with O
Point P in space is a point of the actual object, and the difference of coordinates is only relative to different reference systems, which shows that reference is very important when determining the position of spatial points. The world coordinate system is transformed into the camera coordinate system through transformation of rotation and translation, and the mathematical expression of coordinate transformation in different reference frames is shown in Eq. (1).
When solving the 3D coordinates of an object, as long as the reference object is selected and the position is fixed, a camera corresponds to a certain external parameter. P′ is also at the same point of image coordinates and pixel coordinates, of which the transformation mathematical expression is shown in Eq. (3).
After the image points are collected by the camera, they are projected onto the imaging surface, and the computer stores them in the form of a two-dimensional array, where they are referred to as a pixel point; and each value of the two-dimensional array is called a pixel, which can be converted into matrix form as shown in Eq. (4).
At this point, the conversion relationship between the four different coordinate systems can be connected through the camera coordinate system and the image coordinate system, and the conversion between these two coordinate systems is obtained under the ideal pinhole camera imaging model.
The P point of the object is imaged at the P′ point through the lens, and the actual image is on the plane behind the lens. However, for convenience, we move the focal plane to the front of the lens’ optical centre, and the distance between the camera optical centre and the origin of the image coordinate system is the focal length value, f, of the lens. The conversion formula of the two coordinate systems can be obtained by the principle of geometric knowledge, as shown in Eq. (5).
Combining the above formulas, the conversion formula of point P in spatial coordinates projected to P′ in pixel coordinates is as follows:
The above situation is a pinhole camera imaging model, that is, a linear model, where the imaging coordinates are linearly related to the coordinates of spatial physical points. However, due to the lens process and the installation deviation between sensors and lenses, the lens system will be distorted, which often leads to the non-linear correspondence between points and a distortion in the imaging system [14, 15]. For this distortion problem, in this paper, a distortion coefficient is introduced to correct it, which is transformed into a linear model.
The lens system usually has two forms of distortion, as shown in Figure 4, which are radial variation along the circle diameter direction and tangential variation along the circle circumference direction. When the ideal imaging point is located at point A because of the distortion, the position of the ideal point is shifted, and the actual imaging point is point B. In Figure 4, dr is radial change and dt is tangential change.
The radial distortion of the image not only affects the visual effect of the image but also increases the difficulty of calculation in 3D coordinates after feature point matching . In reality, most lenses are circularly symmetric, and the distortion changes with the distance from the centre of the circle. Generally, Taylor series near the distortion centre is used to expand the first three terms . Thus, the formula of distortion of a point in the radial direction is shown in Eqs (8) and (9).
Eq. (10) shows the change of coordinate position before and after distortion, where (
Assuming that the position of the point in the object space is determined, the coordinate information of the point in the pixel coordinate system has also been determined. From Eq. (10), it can be found that this is a linear equation set consisting of two equations, but it contains three unknowns, and the equation set has no definite solution from the knowledge of mathematical equations. Only by finding another set of equations in the same form can the accurate information be determined, that is, only when two cameras image the same object can the 3D coordinate information of space object points be determined.
The coordinates of the pixel points of the same object point in two images can be found by technical means, and the 3D coordinates of the space point can be determined by mathematical calculation after obtaining two sets of equations. However, as the calculation procedure associated with this method is complicated, we usually calculate the positional deviation of image points, that is, parallax; then the depth information can be obtained by using the similar triangle principle, and finally the above equations are substituted to obtain the 3D coordinate information . It can be seen from Figure 5 that any point in space will be at the intersection of two straight lines, and that this point is unique. Assuming that the two cameras are of the same model, the optical centre distance is T and the focal length is f; so, the depth information Z can be calculated according to the similar triangle principle, and the calculation formula is shown in Eq. (11).
The depth information, namely the vertical distance Z, can be obtained from Eq. (12):
Feature matching is the most important link in the process of 3D reconstruction, which directly determines the accuracy of 3D coordinate points. The coordinates of two correctly matched pixel points can directly calculate
According to the principle of visual imaging mentioned above, the calculation model of images under atmospheric scattering can be obtained as the following:
Figure 6 is an inherently constrained imaging model. From a geometric point of view, in the RGB colour space model, the vectors
According to the idea of linear extrapolation, Eq. (13) is deformed, and the following formula can be derived:
All pixel values of each image have boundary constraints, assuming that the boundary value of each colour channel in the image
As shown in Figure 7, for any pixel in the image
The errors that affect the visual matching effect include the measurement of the distance between optical centres, corner detection position error and feature point detection and matching in camera construction. This paper mainly studies the influence of the distance between cameras and the measured depth information on
Analysis of visual matching error under different test distances
It can be concluded from the table that there is an optimal measuring distance between two cameras, and when the camera distance is about 65 mm, the measuring accuracy is the highest. At the same time, it can also be found that the depth and parallax are inversely proportional and non-linear. When the parallax is very small, the small change can causes a large change in the measurement distance, while when the parallax is very large, the change of small parallax will not cause the change of measurement distance.
Under the constraint of inherent conditions, the error of corner detection position mainly lies in the error of pixel position during detection. Since the corner has a certain size, and the number of pixels in the digital image is large and the actual length is small, it may not be the central position when the position is determined, and the actual length corresponds to an offset. Therefore, the error of the calculated internal and external parameters can be effectively analysed.
Corner test is implemented by matching algorithm. First, the 9 × 9 window is used to select the pixel value of the left image, and the pixel value of the right image is calculated by the same calculation method, so as to further compare the sizes of two pixel values. First, when the difference between the two values is less than a certain threshold, it is considered that the initial matching point has been found, the pixel coordinates of the centre point are recorded and all pixel points are matched in turn. Then, we calculate the sum of all pixel values of the matching points of the two images, and take the sum and difference of the pixels of the two images as a cost function. Finally, according to the value of the cost function, we determine whether the next re-matching calculation is needed and if the matching points need to be polished, re-select the starting position of the window according to the form of genetic mutation learning and then determine the centre point to start the next cycle until the matching cost function meets the requirements to finish the calculation and output the best matching result.
The selection of the initial window starts with the origin of the left image, and the matching of the right image also starts with the origin, except that each movement of the left image corresponds to six window movements of the right image. That is, every time the left image moves, the right image moves 2, 6 and 12 pixels in the right and down directions, respectively. Afterwards, the sum of pixel values in the window is calculated, and the threshold value is compared to determine the centre position of the matching start. Similarly, after the right image is moved for six times, the left image is moved for the next round, and the moving mode is to move 2 pixels to the right and down each time.
From Figure 8, we can see that the detection results based on ordinary visual matching have a high degree of confusion and many error points are detected. In contrast, the detection results after considering inherent constraints are very accurate, the accuracy rate is increased from 60.1% to 85.7% and almost all the detected points are corner points. Further statistics are computed based on the test results indicated in Table 2, where the experimental results are analysed and explained in detail using specific data.
Corner extraction results
|General visual matching||52||26||8||60.1|
|Considering inherent constraints||54||3||6||85.7|
Visual matching under inherent constraints filters out most pixels that are not corners through pre-screening, thus reducing the probability of errors and effectively controlling the number of detected wrong corners. The original model can also detect 54 correct corners, and the performance of the two algorithms is similar in detecting correct corners. However, in terms of the detected wrong corners, by considering the inherent constraints, only three wrong corners were detected, while the original model detected 26 wrong corners, which was about nine times that of the improved algorithm.
Making research on the precise error control of visual matching in geometric calculation can realise high-precision measurement. In order to solve the shortcomings of the visual matching model, such as large error of camera internal and external parameters, low-matching accuracy of feature points and long running time, etc. in this paper, the inherent constraints of images are introduced, and a non-linear visual matching model considering the constraints is established. Test results show that under the inherent constraints, there is an optimal measuring distance between two cameras, and the relationship between depth and parallax is inversely proportional, but non-linear. In visual matching under inherent constraints, most pixels that are not corners are screened out, thus reducing the probability of error, and its matching accuracy rate is increased from 60.1% to 85.7%.
Analysis of visual matching error under different test distances
Corner extraction results
|General visual matching||52||26||8||60.1|
|Considering inherent constraints||54||3||6||85.7|Law of interest rate changes in financial markets based on the differential equation model of liquidity Research and implementation of smart city public information mining analysis system based on mobile edge model of game theory Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Design of college education evaluation based on accompanying data acquisition and mathematical analysis Enterprise financial strategy and performance management analysis based on principal component analysis Study on the Dynamic Change of Regional Water Level and Climate Based on Forecast Equation Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Municipal Civil Engineering Construction Based on Finite Element Differential Equations Financial Risk Prevention Model of Financial Institutions Based on Linear Partial Differential Equation Influence of heterogeneity of local officials on the economy of resource-based cities developed with high quality Analysis of influencing factors of SPOC course teaching effect using structural equation modelling An intelligent campus simulation system based on game Research on an intelligent game simulation system based on road network Training Model of Basketball Offensive Route Based on Nonlinear Differential Equation Research on the construction of rural interface style based on aesthetic rules Optimization Algorithm of New Media Hot Event Push Based on Nonlinear Differential Equation Mathematical Differential Equation in Calculating the Strength of Building Beam Structure Impact Resistance Stability of Building Structural Engineering Based on Fractional Differential Equations The Technical Research on the Assessment of Network Security Situation Based on D-S Evidence Theory Computer big data modeling system based on finite element mathematical equation simulation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation The Composition System of Pop Music Movement Based on Finite Element Differential Equations The Structure and Influencing Factors of Innovation and Entrepreneurship Ability of Higher Vocational Students Based on Structural Equation Model Model System Study of Accordion Score Based on Fractional Differential Equations Data mining of Chain convenience stores location Parameter Id of Metal Hi-pressure State Equation P-Matrix Reasoning and Information Intelligent Mining Research on Detection Model of Abnormal Data in Engineering Cost List Research on deformation monitoring of tunnel engineering based on 3D laser scanning Solidification treatment effect of wellsite waste mud based on physical adsorption of a composite curing agent Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms Application of calculus function and value chain analysis method in the quantification of financial flexibility management indicators Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Mathematical methodology in the seismic resilience evaluation of the water supply system Prediction of surface quality in end milling based on modified convolutional recurrent neural network Analysis of IPO pricing efficiency under the registration system Case application data research of traditional ink art elements in packaging design Research on an early warning model of effectiveness evaluation in ideological and political teaching based on big data Application of intelligent teaching resource organisation model and construction of performance evaluation model Secure transmission of simultaneous wireless information and power transfer system for Internet of things Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Numerical simulation of vortex vibration in main girder of cable-stayed bridge based on bidirectional fluid–structure coupling Research on location algorithm of new energy vehicle charging station based on multi-objective decision Optimisation of construction mode of residential houses based on the genetic algorithm under BIM technology A study on the reform of college English education inspired by the cultural differences between China and the United States Research on innovative strategies of college students’ English teaching under the blessing of big data Research on multi-dimensional optimisation design of user interface under Rhino/GH platform First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe80Si10Nb6B2Cu2 Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption Attitude control for the rigid spacecraft with the improved extended state observer A long command subsequence algorithm for manufacturing industry recommendation systems with similarity connection technology Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Evaluation of spoken English self-study system considering speech knowledge recognition algorithm Application research on piano teaching in colleges and universities based on remote wireless network communication Construction of Financial Risk Evaluation Index System for Biomass Graphene Fibre Industrialisation Project System dynamics model of output of ball mill Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Design of Morlet wavelet neural network to solve the non-linear influenza disease system An online statistical analysis of the hotel management and operation performance model Research on the post-purchase behaviour tendency of the product quality to customers in fast-selling marketing Motion about equilibrium points in the Jupiter-Europa system with oblateness Ultra-short-term power forecast of photovoltaic power station based on VMD–LSTM model optimised by SSA Optimal preview repetitive control for impulse-free continuous-time descriptor systems Design of information management system based on wireless communication under the background of Internet of Things The impact of global warming on the small Scottish Fishing Company Development of main functional modules for MVB and its application in rail transit Analysis of agricultural economic development and optimisation measures under the strategy of rural revitalisation Study on the impact of forest fire prevention policy on the health of forest resources Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Research on the relationship between government subsidies, R&D investment and high-quality development of manufacturing industry Research on the protection and inheritance of intangible cultural heritage under the background of rural revitalisation Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model Computer vision recognition and tracking algorithm based on convolutional neural network A review of the treatment techniques of VOC Study on structural parameter design and life analysis of large four-point contact ball bearing channel Some classes of complete permutation polynomials in the form of ( x p m− x+ δ) s+ ax p m+ bxover F p2 m Digital marketing solutions based on consumer data and homomorphic encryption The consistency method of linguistic information and other four preference information in group decision-making Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Research on the driving principle and guiding strategy of the public's collaborative supervision of the sharing economy in my country Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development Nonlinear Differential Equation in Anti-aging Test of Polymer Nanomaterials Application research of bel canto performance based on artificial intelligence technology Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Application of regression function model based on panel data in financial risk management of bank resource allocation Application of knowledge graph in smart grid fault diagnosis University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Research on the optimisation of logistics parcel intelligent sorting and conveying chain combined with variable clustering mathematical method Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on Resonance Properties of Semantic Wave Fractal Fractals Based on Quantitative Analysis of English Corpus Research on urban landscape big data information processing system based on ordinary differential equations Modeling of fractional differential equation in cloud computing image fusion algorithm Application of Discriminative Training Algorithm Based on Intelligent Computing in English Translation Evaluation Research on the application of GLE teaching mode in English-medium colleges The application of directional derivative in the design of animation characters and background elements Research on product process design and optimisation model based on IoT intelligent computing Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education LTE wireless network coverage optimisation based on corrected propagation model The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform Study on tourism development income index calculation of finite element ordinary differential mathematical equation The Security of Database Network Model Based on Fractional Differential Equations Electric Vehicle Mechanical Transmission System Based on Fractional Differential Equations The Practice System of Physics and Electronics Courses in Higher Vocational Colleges Based on Fractional Differential Equations The Economic Model of Rural Supply and Demand Under the Data Analysis Function Based on Ordered Probit 3D Modeling System of Indoor Environment Art Landscape Design under Statistical Equation Electronic Information Security Model of Nonlinear Differential Equations The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory Paris panxiensis, a new combination of Trilliaceae from Sichuan, China Impact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Application and risk assessment of the energy performance contracting model in energy conservation of public buildings Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas Criminal law imputation path for biometric information Research on composite dynamic disaster prevention and control system of mine earthquake and shock in thick and hard rock mines Research on innovative strategies of college students’ English teaching under the background of artificial intelligence Electromagnetic interference prediction technology of new energy motor drive system Research on the application of PLC technology in electrical automation engineering Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Application of matrix multiplication in signal sensor image perception Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Analysing the variation of metadiscourse verb patterns in English academic papers from within and between disciplines Impact of COVID-19 policy on stock prices of listed property companies Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Research on the experimental principle of deep integration of LETS software and criminal procedure under the background of artificial intelligence Study on Interactive Relations between Enterprise Social Media and Decision Style Based on a vector Autoregressive Model Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations Construction and application of automobile user portrait based on k-mean clustering model The Homework Model of Screening English Teaching Courses Based on Fractional Differential Equations VR-based computer maintenance practical training platform development design and application research Research on innovative human capital for China’s economic development based on STI model In-depth analysis of the artistic expression of paper-cut elements in the design of boat space Knowledge graph construction and Internet of Things optimisation for power grid data knowledge extraction Modeling the pathway of breast cancer in the Middle East Construction and intelligent analysis of power grid physical data knowledge graph based on Internet of Things for power system Research on industrial Internet of Things and power grid technology application based on knowledge graph and data asset relationship model Research on the effects of financial literacy on rural household credit constraint Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on educational resource recommendation system based on MRLG Rec The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations A study on the phenomenon of anaphoric correction in college students’ English conversation Computer Art Design Model Based on Nonlinear Fractional Differential Equations The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations The Approximate Solution of Nonlinear Vibration of Tennis Based on Nonlinear Vibration Differential Equation Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Economic Research on Multiple Linear Regression in Fruit Market inspection and Management Nonlinear Differential Equations in Preventing Financial Risks Lagrange’s Mathematical Equations in the Sports Training of College Students Simulation Research of Electrostatic Precipitator Power Supply Voltage Control System Based on Finite Element Differential Equation Research on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Limit cycles of a generalised Mathieu differential system Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Application of data mining in basketball statistics Design of fitness walker for the elderly based on ergonomic SAPAD model AtanK-A New SVM Kernel for Classification Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations Analysis and countermeasures of cultivating independent learning ability in colleges teaching English based on OBE theory A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection Projection of Early Warning Identification of Hazardous Sources of Gas Explosion Accidents in Coal Mines Based on NTM Deep Learning Network Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Enterprise Financial Risk Early Warning System Based on Structural Equation Model A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation 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 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 Research on evaluation system of cross-border E-commerce platform based on the combined model 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 Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in 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 Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas 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 of p-groups The 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 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 A study of local smoothness-informed convolutional neural network models for image inpainting 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 Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System 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 Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences 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 An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area 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 Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network