Virtual reality technology is a technical mode based on simulation system. On the basis of simulating the real world, it injects the design elements of the three-dimensional world into it to form a virtual world. With the support of virtual reality technology, such a virtual world concretizes abstract objects, so as to improve people's experience in observation or use. As a technical implementation method of diversified information integration, virtual reality technology interacts three-dimensional dynamic information with entity behavior, so as to guide users to immerse themselves in the environment simulated by their technical simulation.

Based on the real-time dynamic information generated from the two dimensions of virtual and reality, seek people's visual effects from perception and weaken the differences between the real world and the virtual world, then the sensory effects on the virtual world will arise spontaneously, and then form an artistic form of poor integration of virtual and reality. Before studying how to apply virtual reality technology to art design, we must analyze the immersion effect. The immersion effect mentioned here is a special definition of immersion mode. From the perspective of psychology and physiology, the reason why virtual reality technology can be fascinating and bring people's thoughts and consciousness into the virtual world created by artists completely depends on the immersion effect that users can achieve in the virtual world. If we rationally perceive the artistic atmosphere of the virtual world from the time and space dimensions of the objective world, its immersion effect is also difficult to achieve. The real attraction of users' thinking consciousness in the virtual world is the attraction of art design itself to users and the artistic atmosphere created by virtual reality technology [1]. Even if the problem of how to guide users' creation to approach the real world does not exist at all. Then we should think about the artistic expression of virtual reality technology from the perspective of users, and users perceive the artistic expression of virtual reality technology in the two dimensions of psychology and physiology. Therefore, from the perspective of the use of virtual reality technology, the more immersed in the virtual world, the higher the degree of experience, and the more obvious the effect of artistic expression. The three characteristics of virtual reality technology are imagination, interaction and immersion. The three are relatively independent and harmonious, forming different immersion dimensions. In art design, only by giving play to the imagination space and improving the interaction effect can we increase the immersion effect of art works. This immersion effect is also the most fascinating expression of art works in virtual reality technology. In virtual reality technology, the emergence of VR video technology improves the immersion experience of users [2]. The fundamental factor is that physiological immersion brings users into a specific virtual scene in visual effect, and produces psychological resonance with the virtual scene, resulting in corresponding psychological immersion. Most studies have analyzed immersive communication. This immersive mode based on user experience is an unprecedented expression of art design. If it is applied to different fields, it will also improve the internal expression and value of art design. Under the influence of immersive communication, virtual reality technology extends to different immersion dimensions, and then stimulates the immersion effect of art works from the two dimensions of physiology and psychology.

Liu J pointed out that this basic skill may take several months to develop, but most review systems can not solve the problem of students' lack of interest and motivation. This issue is particularly important for children who are exposed to music education through school courses or parents rather than their own wishes. Virtual reality technology can create perceptual and cognitive connections between musical instruments (keyboards), instructions (notes) and music (sounds). The connection between visual effects and physical keys can enable users to quickly play specific tunes, so it is possible to improve the learning experience and increase motivation. After consulting the literature, the author found that many excellent computer music education systems have been developed [3]. Chakrabarty N and others developed the system together with two music teachers. The application uses a standard MIDI interface to connect the piano to the computer to obtain performance data. MIDI was selected because it conveys a lot of information related to performance, including the speed and strength of playing notes, including the use of pedals [4]. Muhammed and others developed piano forte, which focuses on the interpretation of music rather than the teaching of basic skills. Muhammed pointed out that music is neither a note printed on paper nor a motor skill to execute computer instructions. Music is an art form, and computers cannot teach or analyze emotional content. The system introduces more advanced analysis functions, such as pronunciation accuracy and chord synchronization. This function clearly describes how each note is played. For example, staccato indicates that a note is separated from adjacent notes, while legato indicates a smooth transition between notes without pause. Synchronization refers to whether the notes in a chord are played at the same time and whether the notes of the same length are played evenly. These characteristics form the basis of advanced music performance ability. In terms of technology used, piano forte uses hardware settings similar to piano tutor [5].

Based on the current research. This paper presents a method of VR image recognition based on mapping equation. Firstly, through the feature extraction of the image, the main color of the target image is obtained, and the extracted results are smoothed. Through the two steps of color space conversion and tone reverse mapping, the morphological transformation of the image is realized to obtain the transition image. The K-means clustering matching operation is performed on the transition image, and the optimal energy equation of color migration is obtained by hierarchical migration and global migration. The reverse mapping color migration algorithm is put into the virtual reality technology. A virtual piano is developed with HTC Vive suite and Leap Motion sensor fixed on the helmet as the hardware platform, and Unity3D and related Stream VR plug-ins and Leap Motion plug-ins as the software platform. The virtual piano forms a virtual keyboard with a Cube component. By compiling the script response function of the Cube component being approached and pressed or released, the performance events of the virtual piano keyboard are recorded, and the sound of the virtual piano is further realized with the help of MIDI.

In order to realize the color migration between two uncorrelated images, it is necessary to establish a color channel in lab space. Therefore, it is necessary to establish a relationship between the color features of color images and shape images. Then first extract the main color descriptor of the two images, set the main color of the color image as _{y}

Where N represents the number of main color pixels in the color image, _{a}_{a}_{a}

Where _{s}^{r}_{1}, which contains n pixels. Then the average brightness value in the segmented region can be calculated by equation (3)

In equation (3), A (x, y) represents the brightness of the pixel with the position of (x, y) on the image, so the feature results about brightness can be extracted. Similarly, the feature values about transparency, chromaticity and so on can be extracted from the image.

Perform boundary smoothing on the source image to solve the error caused by segmentation, and use bilateral filter to smooth color and spatial information at the same time:

In the formula, parameter a represents the balanced color coefficient of the image, and

Generally, the format of the image is RGB format, which is the spatial standard of one color in the image, in which R represents red, G represents green and B represents blue. Other different colors can be obtained by changing these three colors and superimposing points. However, in the process of color migration, it is necessary to convert the format of target image and source image from RGB color space format to color space. Because the color transfer algorithm between images involves reverse mapping, it is easy to cross map in RGB color space. The correlation between the three channels of the image in

Then, the image under LMS can be converted into

In

In order to ensure the accuracy of color migration, it is necessary to reverse map the tone pixels in the image, and its processing flow is shown in Figure 1.

It can be seen from the figure that the color needs to be edited and defined before reverse mapping. The initial color feature of pixel I in the defined color image is represented by ac, and its color feature is represented as

Where _{c}_{c}_{c}

Taking the color brightness between images as an example, the average value of logarithmic brightness is used as the scale factor of its characteristic value, and the input brightness value is linearly scaled, then the expression can be expressed as:

In equation (8), _{0} is the input brightness value. Then the inverse mapping formula of color migration about brightness between images can be expressed as:

Where _{out}

According to the result of tone reverse mapping, the K-means clustering method is used to cluster the pixels of the same type, and the pixels of the same area between the two images are matched as the color migration range. Firstly, K pixels are selected as the clustering center in the color image, then the distance between each pixel in the color image and the clustering center is calculated, and the calculation results are compared to assign it to the nearest clustering center until each pixel in the image is assigned. Then, the region is allocated according to the clustering results, the closest region is matched first according to the reverse mapping method, and then the region of the remaining shape image and the region of the color image are matched in turn, so as to achieve the best matching result.

This paper uses HTC Vive virtual reality suite as the hardware platform of virtual piano. A complete set of HTC Vive virtual reality equipment is composed of a helmet, two handles and two locators.

Vive uses the indoor positioning technology of lighting house. The two rows of LED lights in the locator send out scanning beams six times per second and scan the positioning space of 15×15 feet in turn in the horizontal and vertical directions. The HTC Vive helmet and handle have more than 70 photosensitive sensors. When the beam is scanned, the helmet starts counting. After the sensor receives the scanning beam, the accurate position relative to the locator is calculated by using the relationship between the sensor position and the receiving laser time. With the help of positioning technology, users can walk around the virtual piano within the detection range, and even play the piano on the other side of the keyboard to further increase the sense of three-dimensional and immersion.

Under normal conditions, HTC Vive needs to operate the menu through the handle. However, holding the handle is not convenient for playing the virtual piano. After wearing the helmet, you can't observe the surrounding environment and pick up the handle. Therefore, the virtual piano developed in this paper does not use the handle, but controls the virtual piano through gesture recognition, such as timbre setting and rhythm adjustment. The Leap Motion sensor is directly installed on the Vive helmet.

HTC Vive helmet and Leap Motion sensor are connected to the computer through HDMI and USB interfaces respectively. The configuration properties of the computer and built-in independent graphics card used in this paper are shown in Table 1.

Computer configuration of virtual piano

GPU | NVIDIA GeForce GTX 1060 |

CPU | Intel (R) Xeon (R) E5-2630 |

RAM | 16.0GB |

Video output | HDMA1.4 |

USB port | USB3. 0 port |

Operating system | Windows 7 operating system |

Unity3D is a professional game engine developed by unity technologies, which allows game developers to easily complete various game creativity and 3D interactive development. Unity3D has rendering resources such as physical simulation, normal mapping, screen space environment masking and dynamic shadow. Compared with other game development tools, it has two main advantages: it provides extremely high visual workflow and multi-dimensional cross platform support. With the help of visual workflow, scene layout editing, resource binding and interactive object scripting language coding can be carried out conveniently. In terms of deployment targets, Unity3D spans multiple platforms and can run on 21 platforms, including current Windows, Mac, Wi i, iPhone, WebGL, Windows phone8 and Android. Unity3D is usually used for ordinary 3D game development. To develop virtual reality projects, you need to obtain the VR plug-in steamvt SDK. The steamvt SDK can be downloaded for free on the official website of Unity3D or HTC Vive [9–10].

From ordinary 3D game development to virtual game development, the key is to convert ordinary cameras to VR cameras. This can be achieved by setting up prefabricated parts. The preform is composed of parent and child objects. For example, the parent object [CameraRig] is a standard application combination of StreamVR, including VR camera, two handles and locator. When creating a scene, you need to drag the preform into the editor to change it into a VR scene. Sub objects include left hand, right hand and head display. There is a handle model under the left hand. In the actual project, the handle can be customized as the model 1 required by the user. Prefabricated parts play an important role in project development. Prefabricated parts are required for piano keyboard modeling and hand modeling in the next section.

An ordinary piano consists of 88 black-and-white keys separated by half tones. From left to right, there are bass area, midrange area and treble area respectively. For simplicity, the virtual piano developed in this paper sets 7 tones of do, re, mi, fa, suo, la and si in the bass area, midrange area and treble area respectively, with a total of 21 white keys and 15 black halftone keys. The piano interface in Unity3D uses canvas, which carries the area of all UI elements. This component is bound to the piano key object in the hierarchy panel. There are three canvas rendering modes: screen space overlay, world space and screenspace camera. Screen space - the canvas in the overlay mode will fill the entire screen space, and all UI elements under the canvas will be placed on the top layer of the screen, which will not be obscured by any object, and its contents can be seen without a camera; The world space mode is the world space mode. In this mode, the canvas will be located in the game scene like a 3D object, and its position and size can be set.

This paper adopts the screen space camera mode. The screen space camera mode is similar to the screen space overlay mode. The canvas also fills the whole screen space. If the screen size changes, the canvas will automatically change its size to match the screen. The difference is that in this mode, the canvas is placed in front of the camera. In this rendering mode, the canvas looks like it is drawn on a plane at a fixed distance from the camera. All UI elements are rendered by the camera. Canvas can also specify the camera for rendering, so the camera settings will affect the UI picture. Using this mode to display the piano model on the UI, the effect setting will be better than the other two.

Dynamically zoom according to the distance between the camera and the canvas and the size of the visual cone of the camera. When an object is closer to the camera than the canvas, the piano will be displayed in front of the canvas. Objects farther from the camera than the canvas will be blocked. Adjust the plane distance between the canvas and the camera to 100, set the reference resolution, select the scale with screen size / match width or height scaling method in UI scale mode to correspond to different size resolutions, and finally achieve the piano effect [11].

This section uses sliding window segmentation technology to extract a single gesture action. The data segmentation technology based on sliding window is to segment a fixed length window from a continuous motion signal. The window slides along the time axis and averages all the data in the window. Assuming that the average value represents the average speed of fingers in the window, if the average speed is very small and lower than a certain threshold, it is considered that there is no gesture movement in the time period of the window; If the average speed reaches the maximum, it indicates that there is gesture movement in the window time period, and the window time period just covers a single gesture movement. The instantaneous closing speed of the finger tip and the average closing speed in the whole window can be calculated by the following formula.

In formulas (10) and (11), _{i}

Figure 2 shows a schematic diagram of segmentation and extraction of finger click action. As can be seen from the figure, through the sliding window segmentation technology, the window can be accurately positioned at each click action time, so as to segment and extract a single click action.

Image equation image recognition is divided into two stages: training modeling and real-time recognition. Firstly, the data of each preset gesture is collected repeatedly, and the data is filtered and smoothed. Then the gesture action is extracted by frame and encoded by vector quantization, and each gesture action is modeled by using the temporal probability hidden Markov model, that is, the three main parameters of the hidden Markov model are obtained: initial probability, transition probability and observation probability. These parameters can take the vector coding observation sequence discussed in the previous section as input [13].

In the gesture recognition stage, after filtering and smoothing the current input gesture, the gesture action is extracted by frame, and then the velocity direction vector is encoded into the observation sequence as the input of each established gesture hidden Markov model. The occurrence probability of the best state sequence of the current gesture action under each model is obtained by using the verterbi algorithm, and the model with the largest output probability is the corresponding gesture action.

400 groups of data were collected for these four gestures, of which 300 groups were used for training modeling and 100 groups for recognition. The gesture recognition results based on HMM are shown in Figure 3, and the visible recognition rate can reach more than 88% [14–15].

Through reverse mapping, a better color migration algorithm can be obtained, and the obvious color features in color graphics and shape images can be presented in the final output composite image. Taking HTC Vive kit and Leap Motion sensor fixed on helmet as the hardware platform, and taking Unity3D and related StreamVR plug-ins and Leap Motion plug-ins as the software platform, a virtual piano is developed. Hidden Markov model is used to model, train and recognize gesture movements. This paper realizes four kinds of gesture recognition related to virtual piano attribute setting, and the recognition rate is more than 88%. The immersion of 3D virtual piano developed in this paper is much higher than that of 2D virtual piano displayed on ordinary computer screen; Moreover, it can be played naturally with both hands, and the sense of comfort and fluency is much stronger than the 2D virtual piano played with the help of mouse and keyboard.

#### Computer configuration of virtual piano

GPU | NVIDIA GeForce GTX 1060 |

CPU | Intel (R) Xeon (R) E5-2630 |

RAM | 16.0GB |

Video output | HDMA1.4 |

USB port | USB3. 0 port |

Operating system | Windows 7 operating system |

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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 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 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 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