Space analytic geometry virtual operation teaching system based on gesture recognition

Abstract

The invention discloses a space analytic geometry virtual operation teaching system based on gesture recognition, which comprises a hardware module and a software module, the hardware module constructs a closed-loop collaborative link through a binocular high-definition camera group, an anti-dazzle blackboard, a 5G + optical fiber transmission link and the like, and the software module integrates a light reflection detection unit, a collaborative confirmation unit, a data completion unit, a virtual optimization unit and the like. A reflective area is accurately positioned through a multi-index weighted summation algorithm, logical complementation of missing information subjects is realized by combining a double-level mechanism of machine automatic confirmation and teacher manual confirmation, and a fusion weight is adjusted through a dynamic optimization coefficient including a subject adaptation factor, a reflective influence factor and a historical matching factor. The system can adapt to different light environments and spatial analytic geometry teaching requirements, guarantees the continuity and accuracy of virtual interactive teaching, is high in practicability, and is suitable for wide popularization.

Description

Spatial Analytic Geometry Virtual Operation Teaching System Based on Gesture Recognition Technical Field

[0001] This invention belongs to the field of interactive teaching technology, specifically, it relates to a spatial analytical geometry virtual operation teaching system based on gesture recognition. Background Technology

[0002] Interactive instruction is an interactive teaching method based on scaffolded instruction principles and built upon teacher-student dialogue. Interactive learning in a network environment is a human-computer-human interaction based on computer multimedia technology and network communication technology. An interactive learning tutorial system is a teaching system based on computer technology that utilizes interactive instruction and interactive learning methods.

[0003] However, in the current teaching process, the areas on the blackboard that are reflective can cause exposure and gaps when the camera recognizes them, resulting in delays and collapses in the construction of the entire spatial analytical geometry virtual image, which affects the final actual teaching effect and efficiency.

[0004] Therefore, we want to use the camera to identify the target point by combining the overall image with the spatial analytical geometry after the blackboard reflects a reflective area. This data is then transmitted to a large database and an online teacher terminal for querying and coordination. This allows us to quickly determine the true data and pattern of the missing location, and then optimize and fill in the gaps in the entire recognition process in a timely manner by constructing optimization factors.

[0005] In view of this, the present invention is proposed. Summary of the Invention

[0006] To solve the above-mentioned technical problems, the basic concept of the technical solution adopted by the present invention is as follows:

[0007] A spatial analytical geometry virtual operation teaching system based on gesture recognition includes hardware and software modules. These modules collaboratively construct an integrated mechanism for reflection detection, point positioning, collaborative verification, precise completion, and dynamic optimization. Through proprietary algorithm formulas, it achieves accurate recognition of gestures and blackboard content in reflective blackboard scenarios, logical completion of missing information, and real-time optimization of the virtual image. The collaborative verification mechanism is a two-tiered verification system combining automatic machine verification and manual teacher verification.

[0008] In a preferred embodiment of the present invention, the hardware module includes an image acquisition module, a blackboard module, a data transmission module, a data processing center, a teacher terminal module, and a virtual construction and display module. Each module forms a closed-loop collaborative link through the data transmission module. The image acquisition module is a binocular high-definition camera group with a built-in light sensor and exposure adjustment unit, supporting adaptive adjustment of frame rate from 20 to 60 frames per second. The blackboard module has a built-in pressure sensing unit and coordinate positioning unit with a positioning accuracy of ≤ ±0.5mm, and integrates 5G and WiFi dual-mode communication interfaces at the edge.

[0009] Image acquisition module: It adopts a binocular high-definition camera group, which is fixed on the top and side of the classroom to form a multi-view acquisition network, and captures the gestures, writing content and ambient light information of the blackboard area in real time; the camera group has a built-in light sensor and exposure adjustment unit, which can initially detect areas with abnormal light intensity, and supports adaptive adjustment of frame rate from 20 to 60 frames per second to ensure the real-time acquisition accuracy of gesture trajectory and geometric shape.

[0010] Blackboard module: It adopts an anti-glare composite panel and has a built-in pressure sensing unit and coordinate positioning unit (positioning accuracy ≤ ±0.5mm). It can mark the spatial coordinate points corresponding to the blackboard content, and at the same time help identify the coordinate range and area of ​​the reflective area on the blackboard surface; the edge of the blackboard integrates a 5G and WiFi dual-mode wireless communication interface to realize low-latency data interaction with other modules.

[0011] Data transmission module: Based on 5G and fiber optic dual-mode communication protocol, it builds an encrypted transmission link with a latency of ≤10ms and uses AES encryption algorithm to ensure data security. It is used to transmit image data from the image acquisition module and coordinate data from the blackboard module to the data processing center in real time, and at the same time receive feedback supplementary data and optimization instructions.

[0012] Data processing center: includes cloud database server and edge computing nodes. The cloud database storage space is used to analyze the geometry knowledge base (including various geometric models, formulas, and typical whiteboard examples), historical reflection completion data, and gesture command mapping library; the edge computing nodes are used to quickly process image data and perform algorithm calculations to reduce cloud transmission latency.

[0013] Teacher terminal module: It adopts a portable touch tablet with built-in customized teaching interaction software. It can receive reflection warning information, images of missing areas, candidate completion schemes and corresponding spatial coordinate data in real time. It supports teachers to manually annotate the completion content and correct the virtual model parameters. At the same time, it can call cloud database reference materials to assist in the judgment. The instructions are fed back to the data processing center in real time.

[0014] Virtual construction and display module: including graphics workstation and holographic projection device / interactive electronic screen. The graphics workstation constructs a spatial analytical geometric virtual model based on gesture recognition results, completion data and algorithm calculation results, and supports model rotation, disassembly and scaling; the holographic projection device can project the virtual model in front of the blackboard to achieve accurate superposition display of the virtual model and the blackboard content, allowing for two-way interaction between teachers and students.

[0015] In a preferred embodiment of the present invention, the software module includes a reflection detection and area positioning unit, a spatial geometric point extraction unit, a collaborative verification unit, a data completion and optimization factor construction unit, a virtual image reconstruction and real-time optimization unit, and a data feedback and knowledge base update unit. Each unit achieves full-process processing of the reflection scene through the linkage of algorithm formulas.

[0016] In a preferred embodiment of the present invention, the reflectivity detection and region positioning unit uses a multi-index weighted summation algorithm to determine the reflectivity region, the core formula of which is: in A value ≥0.6 is considered a reflective area. The values ​​are 0.4, 0.4, and 0.2 respectively. ∈[0,255], ∈[0,1], ∈[0,255]; where: The reflectivity determination factor is... A value ≥0.6 is considered a reflective area; These are the weights for brightness, pixel dispersion, and edge gradient, respectively. The grayscale value of the target pixel ( =0、 =255), This is the normalized value for brightness; Pixel dispersion (0-1, calculated from the ratio of the grayscale variance of the target area to the overall image); The gray-level gradient at the edge of the target region ( =0、 =255), the lower the gradient, the more severe the reflection blur, and the higher the proportion of this item. After locating the coordinate range and area of ​​the reflective area using the above formula, this unit, combined with the coordinate positioning unit of the blackboard module, associates the reflective area with the existing spatial geometric target points (vertices, intersections, vector starting points, etc.) on the blackboard, and marks the mathematical logical relationship corresponding to the missing points.

[0017] In a preferred embodiment of the present invention, the machine-automated verification of the collaborative verification unit uses a cosine similarity algorithm to match cloud cases, and the core formula is: in, A value ≥ 0.9 indicates a successful match; vector This is the feature vector of the current scene. Feature vectors of historical cases in the cloud; For two vectors, the first... Each dimension has its own components. The machine automatically retrieves cloud-based cases using the above formula, generating 3-5 sets of candidate completion solutions and confidence scores; the teacher manually verifies the information while simultaneously receiving a reflective warning, candidate solutions, and related knowledge points. When the confidence score is less than 60%, a strong reminder is triggered on the terminal, allowing the teacher to filter or manually complete the solution to ensure the rigor of the subject.

[0018] In a preferred embodiment of the present invention, the data completion and optimization factor construction unit constructs a dynamic optimization factor including a subject-matching factor α, a reflectivity influence factor β, and a historical matching factor γ, and uses a weighted formula... Calculate the optimization coefficient K and dynamically adjust the weights for data fusion to complete the data.

[0019] As a preferred embodiment of the present invention, the subject adaptation factor The calculation formula is The reflectivity factor β is segmented based on the proportion of reflective area, and the historical matching factor is also included. α∈[0.3,0.9], β∈[0.4,0.8], γ∈[0.7,0.9]; m is the number of geometric logic relation types. For the first Class relation weights (key relations such as perpendicular, intersecting) =0.8-0.9, auxiliary lines =0.3-0.5), To complete the content and the fit degree (0-1) with the j-th type of relationship.

[0020] In a preferred embodiment of the present invention, the virtual image reconstruction and real-time optimization unit adopts an inter-frame interpolation algorithm to control the virtual image delay within 50ms; the data feedback and knowledge base update unit forms a closed-loop self-evolution mechanism of acquisition-processing-feedback-optimization to update the historical supplementary data and optimization factor parameters in the cloud database.

[0021] As a preferred embodiment of the present invention, the system has a reflective area positioning accuracy of ≥95%, a single-scene completion time of ≤2s, and a subject logic accuracy of ≥99% for completed content, as determined by the performance evaluation formula. Quantify the operational effect, among which ∈[0,1], The comprehensive performance coefficient (0-1, the closer to 1 the better the performance). For reflective positioning accuracy ( = Actual reflective area area (correctly located reflective area). The time (s) for completing single-scene completion. To complete the efficiency normalization value; To supplement the content, the subject-specific logical accuracy rate (0-1); The virtual screen delay (ms) To optimize the normalized value for delay.

[0022] Compared with the prior art, the present invention has the following advantages:

[0023] This invention uses a dedicated reflection detection algorithm to accurately locate reflective areas. Combined with a "machine + teacher" collaborative verification and dynamic optimization coefficient algorithm, it replaces the traditional pixel completion and parameter adjustment methods, controlling the virtual screen delay to within 50ms and achieving a reflection area positioning accuracy of ≥95%. This completely solves the problem of screen collapse caused by reflection and ensures the continuity of teaching.

[0024] This invention uses a subject-specific adaptation factor α to align with the logic of spatial geometry and mathematics, avoiding logical errors in the completed content. Automatic machine verification achieves rapid matching through a similarity algorithm, while manual verification by teachers ensures accuracy in handling ambiguous cases, thus improving the accuracy of the subject-specific logic in the completed content and balancing processing efficiency with teaching precision. The reflectivity impact factor β can dynamically adjust its weight based on the reflective area, adapting to different lighting environments and reflective scenarios of varying intensities. The algorithm is compatible with various teaching contents such as point-line-plane relationships, surface equations, and vector operations in spatial analytic geometry, demonstrating strong versatility and requiring no additional hardware adjustments.

[0025] This invention updates the cloud-based knowledge base and optimizes factor parameters through data feedback. The system's accuracy in handling similar reflective scenarios increases with the number of uses, gradually reducing the frequency of manual intervention by teachers, forming a self-evolving capability, and exhibiting good technical scalability.

[0026] The specific embodiments of the present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0027] In the attached diagram:

[0028] Figure 1 is a diagram of the spatial analytical geometry virtual operation teaching system based on gesture recognition.

[0029] Figure 2 is a schematic diagram of the hierarchical operation of the collaborative verification unit of the present invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments will be clearly and completely described below with reference to the accompanying drawings. The following embodiments are used to illustrate the present invention.

[0031] Example 1:

[0032] A spatial analytical geometry virtual operation teaching system based on gesture recognition includes hardware and software modules. These modules collaboratively construct an integrated mechanism for reflection detection, point positioning, collaborative verification, precise completion, and dynamic optimization. Through proprietary algorithm formulas, it achieves accurate recognition of gestures and blackboard content in reflective blackboard scenarios, logical completion of missing information, and real-time optimization of the virtual image. The collaborative verification mechanism is a two-tiered verification system combining automatic machine verification and manual teacher verification.

[0033] Furthermore, the hardware module includes an image acquisition module, a blackboard module, a data transmission module, a data processing center, a teacher terminal module, and a virtual construction and display module. Each module forms a closed-loop collaborative link through the data transmission module. The image acquisition module is a binocular high-definition camera group with a built-in light sensor and exposure adjustment unit, supporting adaptive adjustment of frame rate from 20 to 60 frames per second. The blackboard module has a built-in pressure sensing unit and coordinate positioning unit with a positioning accuracy of ≤ ±0.5mm, and integrates 5G and WiFi dual-mode communication interfaces at the edge.

[0034] Image acquisition module: It adopts a binocular high-definition camera group, which is fixed on the top and side of the classroom to form a multi-view acquisition network, and captures the gestures, writing content and ambient light information of the blackboard area in real time; the camera group has a built-in light sensor and exposure adjustment unit, which can initially detect areas with abnormal light intensity, and supports adaptive adjustment of frame rate from 20 to 60 frames per second to ensure the real-time acquisition accuracy of gesture trajectory and geometric shape.

[0035] Blackboard module: It adopts an anti-glare composite panel and has a built-in pressure sensing unit and coordinate positioning unit (positioning accuracy ≤ ±0.5mm). It can mark the spatial coordinate points corresponding to the blackboard content, and at the same time help identify the coordinate range and area of ​​the reflective area on the blackboard surface; the edge of the blackboard integrates a 5G and WiFi dual-mode wireless communication interface to realize low-latency data interaction with other modules.

[0036] Data transmission module: Based on the 5G+fiber dual-mode communication protocol, it constructs an encrypted transmission link with a latency of ≤10ms and uses the AES encryption algorithm to ensure data security. It is used to transmit the image data from the image acquisition module and the coordinate data from the blackboard module to the data processing center in real time, while receiving feedback supplementary data and optimization instructions.

[0037] Data processing center: includes cloud database server and edge computing nodes. The cloud database storage space is used to analyze the geometry knowledge base (including various geometric models, formulas, and typical whiteboard examples), historical reflection completion data, and gesture command mapping library; the edge computing nodes are used to quickly process image data and perform algorithm calculations to reduce cloud transmission latency.

[0038] Teacher terminal module: It adopts a portable touch tablet with built-in customized teaching interaction software. It can receive reflection warning information, images of missing areas, candidate completion schemes and corresponding spatial coordinate data in real time. It supports teachers to manually annotate the completion content and correct the virtual model parameters. At the same time, it can call cloud database reference materials to assist in the judgment. The instructions are fed back to the data processing center in real time.

[0039] Virtual construction and display module: including graphics workstation and holographic projection device / interactive electronic screen. The graphics workstation constructs a spatial analytical geometric virtual model based on gesture recognition results, completion data and algorithm calculation results, and supports model rotation, disassembly and scaling; the holographic projection device can project the virtual model in front of the blackboard to achieve accurate superposition display of the virtual model and the blackboard content, allowing for two-way interaction between teachers and students.

[0040] Furthermore, the software module includes a reflection detection and area positioning unit, a spatial geometric point extraction unit, a collaborative verification unit, a data completion and optimization factor construction unit, a virtual image reconstruction and real-time optimization unit, and a data feedback and knowledge base update unit. Each unit works together through algorithmic formulas to achieve full-process processing of the reflection scene.

[0041] Furthermore, the reflectivity detection and region positioning unit uses a multi-index weighted summation algorithm to determine reflectivity regions. The core formula is: in A value ≥0.6 is considered a reflective area. The values ​​are 0.4, 0.4, and 0.2 respectively. ∈[0,255], ∈[0,1], ∈[0,255]; where: The reflectivity determination factor is... A value ≥0.6 is considered a reflective area; These are the weights for brightness, pixel dispersion, and edge gradient, respectively. The grayscale value of the target pixel ( =0、 =255), This is the normalized value for brightness; Pixel dispersion (0-1, calculated from the ratio of the grayscale variance of the target area to the overall image); The gray-level gradient at the edge of the target region ( =0、 =255), the lower the gradient, the more severe the reflection blur, and the higher the proportion of this item. After locating the coordinate range and area of ​​the reflective area using the above formula, this unit, combined with the coordinate positioning unit of the blackboard module, associates the reflective area with the existing spatial geometric target points (vertices, intersections, vector starting points, etc.) on the blackboard, and marks the mathematical logical relationship corresponding to the missing points.

[0042] Furthermore, the machine-automated verification of the collaborative verification unit uses a cosine similarity algorithm to match cloud-based cases, with the core formula being: in, A value ≥ 0.9 indicates a successful match; vector This is the feature vector of the current scene. Feature vectors of historical cases in the cloud; For two vectors, the first... Each dimension has its own components. The machine automatically retrieves cloud-based cases using the above formula, generating 3-5 sets of candidate completion solutions and confidence scores; the teacher manually verifies the information while simultaneously receiving a reflective warning, candidate solutions, and related knowledge points. When the confidence score is less than 60%, a strong reminder is triggered on the terminal, allowing the teacher to filter or manually complete the solution to ensure the rigor of the subject.

[0043] Furthermore, the data completion and optimization factor construction unit constructs a dynamic optimization factor including a subject-matching factor α, a reflective influence factor β, and a historical matching factor γ, which is then weighted using a formula. Calculate the optimization coefficient K and dynamically adjust the weights for data fusion to complete the data.

[0044] Furthermore, the subject-specific adaptation factors The calculation formula is The reflectivity factor β is segmented based on the proportion of reflective area, and the historical matching factor is also included. α∈[0.3,0.9], β∈[0.4,0.8], γ∈[0.7,0.9]; m is the number of geometric logical relation types, wⱼ is the weight of the j-th relation (key relations such as vertical and intersecting wⱼ=0.8-0.9, auxiliary lines wⱼ=0.3-0.5), and Sⱼ is the fit between the completed content and the j-th relation (0-1).

[0045] Furthermore, the virtual image reconstruction and real-time optimization unit adopts an inter-frame interpolation algorithm to control the virtual image latency to within 50ms; the data feedback and knowledge base update unit forms a closed-loop self-evolution mechanism of acquisition-processing-feedback-optimization to update the historical supplementary data and optimization factor parameters in the cloud database.

[0046] Furthermore, the system achieves a reflective area positioning accuracy of ≥95%, a single-scene completion time of ≤2s, and a subject-matter logic accuracy of ≥99% for completed content, passing the performance evaluation formula. Quantify the operational effect, among which ∈[0,1], The comprehensive performance coefficient (0-1, the closer to 1 the better the performance). For reflective positioning accuracy ( = Actual reflective area area (correctly located reflective area). The time (s) for completing single-scene completion. To complete the efficiency normalization value; To supplement the content, the subject-specific logical accuracy rate (0-1); The virtual screen delay (ms) To optimize the normalized value for delay.

[0047] The implementation principle of the spatial analytical geometry virtual operation teaching system based on gesture recognition of the present invention is as follows:

[0048] 1. Initialization and Startup: After the system is powered on, all hardware modules start synchronously, complete camera calibration, coordinate positioning initialization and database connection, and the virtual construction module loads the basic spatial analytical geometry model library.

[0049] 2. Image Acquisition and Reflection Detection: The binocular camera group acquires the blackboard image in real time. The reflection detection and area positioning unit calculates the reflection judgment formula R to determine whether there is reflection and missing information. When there is no reflection, the system normally parses the gesture commands and blackboard content to drive the construction of the virtual model.

[0050] 3. Target point extraction and collaborative verification: When reflection is detected (R≥0.6), the geometric points and logical relationships of the non-reflective areas are extracted, and cloud cases are matched using the cosine similarity formula to generate candidate completion solutions; at the same time, manual verification by teachers is initiated to determine the final completion solution.

[0051] 4. Data Completion and Optimization: Based on the final solution, complete the missing data, calculate the K value through the optimization coefficient formula, and adjust the fusion weight of the completed data to avoid virtual screen collapse.

[0052] 5. Virtual screen reconstruction and interactive teaching: The reconstructed and optimized screen and virtual model are displayed through holographic projection or electronic screen. Teachers and students complete interactive teaching by controlling the model with gestures. The system monitors the running effect in real time through performance evaluation formula.

[0053] 6. Data Feedback and Knowledge Base Updates: After the teaching session, the system uploads the reflection processing data, K-value, and teaching feedback to the cloud database, updates and optimizes factor parameters, and completes the case library to improve subsequent processing capabilities.

[0054] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A spatial analytical geometry virtual operation teaching system based on gesture recognition, characterized in that: It includes hardware and software modules, which work together to build an integrated mechanism for reflection detection, point location, collaborative verification, accurate completion, and dynamic optimization. Through a dedicated algorithm formula, it achieves accurate recognition of hand gestures and blackboard content in blackboard reflection scenarios, logical completion of missing information in subject areas, and real-time optimization of virtual images. The collaborative verification mechanism is a two-level verification mechanism consisting of automatic machine verification and manual verification by teachers.

2. The spatial analytical geometry virtual operation teaching system based on gesture recognition according to claim 1, characterized in that, The hardware modules include an image acquisition module, a blackboard module, a data transmission module, a data processing center, a teacher terminal module, and a virtual construction and display module. Each module forms a closed-loop collaborative link through the data transmission module. The image acquisition module is a binocular high-definition camera group with a built-in light sensor and exposure adjustment unit. The blackboard module has a built-in pressure sensing unit and coordinate positioning unit.

3. The spatial analytical geometry virtual operation teaching system based on gesture recognition according to claim 1, characterized in that, The software module includes a reflection detection and area positioning unit, a spatial geometric point extraction unit, a collaborative verification unit, a data completion and optimization factor construction unit, a virtual image reconstruction and real-time optimization unit, and a data feedback and knowledge base update unit. Each unit works together through algorithmic formulas to achieve full-process processing of the reflection scene.

4. The spatial analytical geometry virtual operation teaching system based on gesture recognition according to claim 1, characterized in that, The reflectivity detection and region positioning unit uses a multi-index weighted summation algorithm to determine reflectivity regions. The core formula is: in A value ≥0.6 is considered a reflective area. The values ​​are 0.4, 0.4, and 0.2 respectively. ∈[0,255]， ∈[0,1]， ∈[0,255]。 5. The spatial analytical geometry virtual operation teaching system based on gesture recognition according to claim 1, characterized in that, The collaborative verification unit uses a cosine similarity algorithm to match cloud-based cases for automatic verification. The core formula is: in, A value ≥ 0.9 indicates a successful match; vector This is the feature vector of the current scene. This is a feature vector for historical cases in the cloud.

6. The spatial analytical geometry virtual operation teaching system based on gesture recognition according to claim 1, characterized in that, The data completion and optimization factor construction unit constructs dynamic optimization factors including subject adaptation factor α, reflectivity influence factor β, and historical matching factor γ, and uses a weighted formula. Calculate the optimization coefficient K and dynamically adjust the weights for data fusion to complete the data.

7. The spatial analytical geometry virtual operation teaching system based on gesture recognition according to claim 1, characterized in that, The subject-specific adaptation factors The calculation formula is The reflectivity factor β is segmented based on the proportion of reflective area, and the historical matching factor is also included. ,α∈[0.3,0.9]、β∈[0.4,0.8]、γ∈[0.7,0.9]。 8. The spatial analytical geometry virtual operation teaching system based on gesture recognition according to claim 1, characterized in that, The virtual image reconstruction and real-time optimization unit uses an inter-frame interpolation algorithm to control the virtual image latency to within 50ms; the data feedback and knowledge base update unit forms a closed-loop self-evolution mechanism of acquisition-processing-feedback-optimization, updating the historical supplementary data and optimization factor parameters in the cloud database.

9. The spatial analytical geometry virtual operation teaching system based on gesture recognition according to claim 1, characterized in that, The system achieves a reflective area positioning accuracy of ≥95%, a single-scene completion time of ≤2s, and a subject-matter logic accuracy of ≥99% for completed content, passing the performance evaluation formula. Quantify the operational effect, among which ∈[0,1]。

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