Visual tracking research is one of the most important visual research directions in the field of computer vision. Its application fields include visual navigation, intelligent video surveillance, intelligent city, and military precision guidance [1–3]. In practical application scenarios, the tracking target state will be affected by many factors, such as deformation, illumination intensity, rotation, and so on, which makes single target tracking still a very challenging task. In recent years, the convolutional neural network has been successfully applied to various image processing problems (such as target detection, object classification and image segmentation), which significantly improves the performance of corresponding tasks [4–7].
The introduced self-attention mechanism is realised by the spatial attention module and channel attention module. The spatial attention module selectively aggregates the weighted sum of all eigenvalues to the corresponding position in the original input feature map, which enhances the correlation between similar features. After integrating all the feature maps, the channel attention module selectively emphasises the importance of each channel feature by weighting the channel space of the feature. In part of the training data of MDnet, the semantics of the targets are the same but the categories are different, so the discrimination ability of the model is reduced. To solve this problem, a composite loss function is constructed. The composite loss function is composed of the classification loss function and instance discrimination loss function. The classification loss function is used to count the loss value of target classification, and the instance discrimination loss function is used to improve the weight of the target in the current video sequence and suppress its weight in other sequences [8–12]. In the target tracking algorithm MDnet based on the CNN framework, several down sampling structures are used to obtain the depth features of the target, resulting in the loss of more detailed information in the downsampling process. The feature maps of different depths of targets extracted by CNN, especially the shallow feature map, contain more spatial position information of target objects, which is very important for target tracking tasks requiring accurate positioning. For deep features, the deep features of the target cover the semantic information about the robustness of the target, which makes the discrimination ability of the network model not easy to be affected in some tracking scenes including light intensity change, object deformation and rotation. Therefore, aiming at the problem that the tracking network cannot make full use of different levels of features, taking MDnet as the benchmark algorithm, a multi-domain convolution neural network based on multi-level feature aggregation is designed. By aggregating different levels of features, the tracker can make full use of the characteristics of different levels, and improve the feature representation ability of the tracking network. The designed feature aggregation network is still an end-to-end model without introducing the problem of specific parameter settings, which maintains the universality of the target tracker. A specific data augmentation strategy is used for network pre-training, which fully takes into account various conditions that may occur in the target tracking scene. The training samples are processed by pre-simulating the change in the target state, which makes the network model more discriminative after training . In addition, the anomaly detection module is embedded in the tracking algorithm, and a perfect anomaly response strategy is designed to improve the problem of template drift caused by the drastic change of target state or long-term tracking.
The proposed algorithm has carried out detailed quantitative and qualitative experiments on the widely used OTB and vot2015 data sets. The experiments show that the proposed algorithm shows good tracking performance and is superior to many top-notch algorithms, which fully verifies the effectiveness of the proposed algorithm.
The convolutional neural network was proposed in 1989 when it was built by Yann Lecun of New York University. It is the optimal version after multiple version iterations, and its computational performance has been greatly improved. Since ancient times, the main way for human beings to obtain information is the eyes and ears. They analyse what they see and hear, to make a corresponding response. For computing devices, to solve what they see in front of them, they need to capture and save the images with cameras. Next, they use the powerful computing function of computers to analyse pictures to get relevant information. With the development of technology, the current research field does not refer to the shallow convolutional neural network, and the complexity of the number of layers can be large or small. Its application has also made a great breakthrough in speech recognition, image processing, and natural language processing [14–16].
A complete convolutional neural network structure includes three layers: input layer, hidden layer, and output layer . Due to the input features and marks, they are corresponding one by one in the convolution neural network. In this way, compared with the above neural network learning mode, the convolution neural network belongs to supervised learning, and the input features are standardised. The vector group of early training samples is composed of data annotation and input eigenvalues. Through the early normalisation processing, in this learning mode, the size of weight data is repeatedly corrected, making the whole convolutional neural network converge. In the input layer, the standardised operation of input features has an obvious positive relationship between improving the performance of the whole network and learning rate. This layer includes three types: convolution layer, pooling layer, and full connection layer.
The convolution layer is well known. In the direction of image processing, a convolution neural network has certain advantages over a depth neural network, and its use of local perception is stronger than the latter. In the convolution layer, we extract the input data to get its eigenvalues, and when these speech data are preprocessed, the extracted eigenvalues will be cut into rectangular blocks one by one. For the back-propagation algorithm, by calculating each convolution unit, the input data features pass through a convolution layer. Through the accumulation of convolution layers, more information on data features can be extracted more completely. When passing through more convolution layers, some complex features will be extracted from the basic data. Therefore, the calculation formula of convolution can be expressed by the following formula 1.
For example, in a simple convolution process, the initial output data
After these three layers of processing, it needs to be processed through softmax regression. In this process, it is to define the probability value that the initial sample does not match the same category, and obtain the probability that the input belongs to a certain category among different categories on the final output. Here, some processing of convolution is different from the category of signal operation. In this model, convolution processing is a linear weighted calculation. See the formula above (1).
The convolution layer contains many convolution kernels. The eigenvalues of different levels are learned by these convolution kernels, to obtain many output values. Of course, these convolution kernels are not directly connected with the whole characteristic graph. There is a layer of rules between them, which combine them. In the convolution core, its work is different from that of the full connection layer network. The convolution core in the convolution layer is connected to the areas where the features are input. Through such connection, the connection size of the whole network has been reduced to a certain extent. On the contrary, it can get enough structured features. Moreover, because the convolution core has a parameter sharing mechanism, the parameters of the training network have been reduced a lot.
Single depth slice is 4× The block of 4 is sampled with the maximum value, and the result is 2×2. In this way, the single depth slice can be divided into 2×2, as shown in the figure above, take the maximum value of each small square. We can use formula (2) to express the output size of the pooling layer.
In the above formula (2), we can see that there is a division operation, which shows that the characteristics of the input pool layer should be divided by the size of the pooling layer.
The processing of the pooling layer has achieved remarkable results in two aspects. One is to compress the data level of the whole neural network. At the same time, it will reduce the training parameters of the neural network and improve the constraint of the neural network. Based on these two, it will achieve a good effect, that is, it can maintain the invariance of the network, to improve the Luban of the whole network itself, In this way, the application in speech recognition can achieve an effect, that is, the speech recognition system will have certain fault tolerance in the translation caused by different wording techniques and some external environment noise.
After the cyclic calculation of the above two layers, for the data input into the network, after the cyclic calculation of the first two layers, for the input characteristic data, the relevant important data has been reorganised, and its key information can be better reflected. For the operation of the first two layers, they can be regarded as automatic calculation behaviour. After these two processes, the processing results are classified through the full connection layer. There is a rasterisation process, which reorganises the output results, and then obtains a feature vector, which also upgrades part of the feature information processed by the convolution layer and pooling layer to deeper dimensional space, and also classifies all the information. The tool of this classification is the full connection layer. For example, it can convolute a two-dimensional feature value through the above convolution, In this way, it is transformed into one-dimensional feature data so that the information can be reorganised globally. Softmax full connection is generally adopted, which is also the last checkpoint of a convolutional neural network. Its key role is to normalise the output results. The activation value obtained in this way is the speech feature calculated by a convolutional neural network.
After the first two layers of the convolutional neural network are calculated, if the output result has a flag, after the last softmax, the output result is a vector value with N dimensions. Each value in the vector has a corresponding probability, that is, it represents the occurrence probability of the first flag. Each flag corresponds to the probability one by one, and the sum of the probabilities of the N flags is 1. The expression (3) of softmax for the last level is as follows.
From the above formula, the function of this operation is to improve the nonlinear expression ability of the whole convolution model. The whole formula is actually a normalisation process. The meaning of the denominator part is the sum of N signs. The upper part is the result of the first sign. Obviously, the result of all signs will not be >1. When the corresponding probability of the result of a sign approaches 1, the result of this sign must be greater than that of other signs. In this way, the results of other signs must be infinitely close to each other. This is the normalisation process mentioned above.
The neural network optimisation algorithm is used in some schemes to accelerate the convergence speed of the network model or optimise the loss function. To obtain the optimal parameters and minimise the value of the loss function, optimization methods are commonly used in neural networks
There are three algorithms: random gradient descent method, momentum gradient descent method and Adam algorithm.
The random gradient descent method is a simple and effective method. It randomly extracts one group from all samples, updates it according to the gradient after training, and then extracts one group and updates it once. When the sample size is large, you may not need to train all samples to get a network model within an acceptable range. Because only one group of samples is updated each time. The parameters required for the updating of the network model will be greatly reduced and the training speed of the network will be accelerated, but this will also cause the problem of uncertain optimisation direction, which will eventually result in local optimisation rather than global optimisation, thus reducing the accuracy of the network model.
The momentum gradient descent method draws on the ideas of physics. Imagine rolling the ball into a frictionless bowl. The accumulated momentum does not stop at the bottom of the bowl but pushes it forward, which produces momentum. The descent process of the above random gradient descent method is not directly to the best, but back and forth, which will waste a lot of network training time. In addition, the random gradient descent algorithm needs to set a learning rate before training. Setting an excessive learning rate will lead to excessive updating of parameters and large errors of gradient swing. Setting a small learning rate will increase the number of iterations of training, which will increase the training time of the model and waste resources and time. The momentum gradient descent method can set a larger learning rate and reduce the training times in the training process so that the convergence speed of the network model is faster and more stable, and there will be no back-and-forth descent problem. The algorithm mainly sets an impulse in the process of random gradient descent to accelerate the gradient descent. The momentum gradient descent algorithm can be expressed by the following formula:
Adaptive motion estimation is a combination of rmsprop and random gradient descent methods. The algorithm uses the square gradient of rmsprop to scale the learning rate of the network model, and uses the average value of the gradient movement rather than the gradient itself to calculate. In this way, it can set different learning rates for different parameters. It is an adaptive learning rate method. Adam algorithm is named for its use of an adaptive matrix. It adjusts the learning rate in the network model by estimating the first-order matrix and the second-order matrix. The fluctuation problem of the previous algorithm is improved, which significantly improves the convergence speed and stability of the network model. Adam algorithm can be expressed by the following formula:
Image quality generally refers to the evaluation of people’s visual perception of images. Image quality assessment (IQA) includes a subjective assessment based on human perception (i.e. visual realism of images) and an objective assessment. Although human subjective evaluation meets our practical needs, this evaluation method consumes a lot of manpower and time, and is subject to too many human factors to obtain stable evaluation results. Therefore, the calculation method based on objective evaluation is the mainstream common method. This paper mainly introduces two common objective evaluation methods: peak signal-to-noise ratio (PSNR) and structural similarity (SSIM).
PSNR is the most commonly used objective evaluation method of image quality. It is usually compared with the original image after image compression and image restoration. It evaluates the image quality by comparing the difference in pixel values between the original image and the processed image. Its formula is as follows:
Generally speaking, it is easier for human vision to extract the structure of images. Therefore, according to the comparison of image brightness, contrast and structure, a structural similarity index (SSM) is proposed to measure the structural similarity between images. For an image
In the formula is the covariance between image
When calculating the formula, a
As a method of deep learning, convolutional neural networks have performed well in many fields, such as speech analysis and image recognition. In the convolutional neural network, over-complete filters can be used to extract various potential features. For example, if you want to extract a certain feature, you need to use enough filters to extract the possible situations of all the features, so that you can extract The features that actually need to be extracted are also covered.
Convolutional neural networks provide a hierarchical model that can learn features directly from image raw pixels. In the first stage, a preprocessed black and white image of size 32×32 is input into a convolutional layer consisting of six filters of size 5×5, and then the resulting six filters of size 28×28 are input. The feature map is input to a nonlinear transformation layer. For each pixel of all feature maps, the nonlinear transformation layer is obtained by the following transformation:
The resulting six feature maps are then input into a maximum downsampling layer, which takes the maximum value within each 2×2 spatial neighbourhood. Compared with the sigmoid and tanh functions, the RELU function can effectively solve the gradient dispersion problem. The maximum downsampling layer makes the convolutional neural network robust to small translations of the image. When applied to target tracking, they make the network more robust to tracking errors due to inaccurate target locations.
The implementation of the second stage is similar to the first stage. First, the output of the first stage is subjected to convolution operation. The convolution layer consists of 12 filters with a size of 5×5. The feature map is input to the ReLU function, and each 2×2 field is subjected to maximum downsampling. The downsampled feature map is transformed into the form of a vector, and each node is regarded as one dimension in the high-level features. After a two-stage convolution operation, ReLU transform and maximum downsampling, this network can extract higher-level features.
The particle filter implements a recursive Bayesian filtering method through the sequential Monte Carlo importance sampling method. The main idea of a particle filter is to use a series of random particles to represent the posterior probability. Particle filter consists of two main parts: 1. Dynamic model: generate candidate samples based on previous particles. 2. Observation model: Calculate the similarity between the candidate sample and the target apparent model. Given all the observations
In the formula,
Finally, the optimal target state
To improve the computational efficiency, this algorithm chooses to track only the position and size of the target. let
In order to obtain the apparent change, the apparent model of the convolutional neural network will be continuously updated, and the likelihood function also needs to be continuously adapted over time. However, the main disadvantage of the apparent adaptation method is that it is sensitive to drift problems, such as possible gradual adaptation to non-objects. In order to alleviate the drift problem, this algorithm uses the real appearance information of the target marked in the first frame and the image observations obtained online.
Usually, the centre point error is used to evaluate the pros and cons of tracking performance. As an evaluation criterion to quantitatively analyse the quality of tracking results, the centre point error calculates the square error of the coordinates of the centre point of the tracker tracking result and the centre point of the real label value in the
The average centre point error is the average value of the centre point error in the whole time. The smaller the average centre point error value, the better the tracking result of the tracker in the entire video sequence. In the ideal case, the average centre point error value is 0. But to be precise, sometimes the average centre point error is not a good measure of the tracking performance of the tracker. If a better tracking algorithm tracks the target well most of the time, but only loses the target at certain moments, the tracking results obtained by the tracker at these moments are likely to be random. The point error will become very large, pulling up the average centre point error, and the result obtained from the average centre point error will consider the tracking algorithm not an excellent tracking algorithm to better evaluate the performance of the tracker.
Accuracy Statistics In the video sequence, the percentage of frames where the error between the centre point of the tracker’s tracking result and the centre point of the real label value is within a certain threshold range of all frames. The setting of the precision reading value is very important here. Generally, the reading value will be set to 20 pixels. A good tracking algorithm can get a relatively high accuracy value when the reading value is set relatively low. If one arrives at the position of the target and only loses the target at certain moments, the accuracy of the tracking algorithm in the video sequence will not be very high, and the tracking algorithm will still be considered a better tracking method if the accuracy method is used., so the accuracy can better evaluate the performance of the tracker than the average center point error. The centre point error mainly evaluates the stability of the tracker, and the method to evaluate the robustness of the tracker is mainly the overlap rate method.
Both the accuracy method and the success rate method are indispensable. For example, if a tracking method is difficult to deal with the problem of target scale change well, the value of the average centre point error of the tracking method will be relatively small but the value of the average overlap rate may be very low. Similarly, if a tracking method does not track the target very stably, but keeps shaking around the target object, the value of the average overlap rate of the tracking method may be relatively high, but the average centre point error will be very large. Therefore, when the accuracy and the success rate are considered together, the pros and cons of the tracking algorithm can be objectively and comprehensively investigated.
The target tracking algorithm based on the convolutional neural network has achieved a good tracking effect. The algorithm is completely pre-trained with convolutional neural networks in natural scenes that are not related to the tracking task, which shows that by learning and transferring the mid-level general features of the convolutional neural network, the tracking algorithm can effectively construct the target appearance model, which can be used in a certain amount of time. To a certain extent, the drift problem in the tracking process is alleviated.
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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 Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises 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 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 Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective 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