# Research on the Multi-Screen Connection Interaction Method Based on Regular Octagon K-Value Template Matching

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. Direct Interaction with Large Data Visualization Screens

#### 2.2. Indirect Interaction with Large Data Visualization Screens

## 3. General Framework of Interaction

## 4. Fast Image Template Matching

#### 4.1. Rotationally Invariant Positive Octagonal K-Value Template

#### 4.2. Improved NCC Based on a Differential Summation of Ordered Arrays

_{y(x)}= y(x + 1) − y(x) in the dependent variable y = y(x) is called the difference in the function y(x) in steps of 1 at the point x.

_{1}(x) and f

_{2}(x), x = 1,2,3…K. Then the product of these two arrays is equal to the product of the cumulative summation of the difference in one of the arrays f

_{1}(n) with the other f

_{2}(n), which gives the following equation [27]:

_{1}(x), there are a large number of 0 s and 1 s in the differential array F

_{1}(x), and the result can be ignored in the case of 0 s and 1 s in the multiplication operation. Then the required computation time can be greatly reduced, and the computing speed can be improved.

## 5. Application Cases and Experiments

#### 5.1. Improved NCC Based on a Differential Summation of Ordered Arrays

#### 5.1.1. Positive Octagonal K-Value Template Matching Efficiency Testing Experiment

#### 5.1.2. Mobile Phone and Visualization Large Screen Simulation Matching Experiment

#### 5.2. Application Cases

#### 5.2.1. Assist in Observing Visualization Project Cases

#### 5.2.2. Case Evaluation

#### 5.2.3. Case Comparison Evaluation

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**General interaction framework. The general framework for users to establish connection and interaction with the data visualization screen through mobile phone photography mainly contains three parts: interaction device (mobile phone), interaction server, and interaction target (data visualization screen).

**Figure 3.**Demonstration diagram of integral image area calculation. The image on the left is an original image that identifies four regions: A, B, C, D. The pixel point at a corresponds to value in the integral image of sum(A), the pixel point at b corresponds to the value in the integral image of sum(A + B), the pixel point at c corresponds to the value in the integral image of sum(A + C), the pixel point at d corresponds to the value in the integral image of sum(A + B + C + D). Then the sum of the grauscale values of all the pixel points in region is: sum(A + B + C + D)“−” Usum(A + C)“−” Usum(A + B)“−” Usum(A).

Testing Index | Positive Octagonal K-Value Template Matching | K-Value Template Matching | NCC Matching |
---|---|---|---|

Matching Time (ms) | 485 | 1067 | 9073 |

Matching Accuracy | 0.984 | 0.973 | 0.982 |

Testing Index | Positive Octagonal K-Value Template Matching | K-Value Template Matching | NCC Matching |
---|---|---|---|

Matching Time (s) | 5.83 | 11.52 | 93.64 |

Matching Accuracy | 0.868 | 0.523 | 0.165 |

A | B | |
---|---|---|

1 | 4 | 8 |

2 | 5 | 7 |

3 | 5 | 8 |

4 | 6 | 7 |

5 | 5 | 8 |

6 | 4 | 7 |

7 | 5 | 10 |

8 | 6 | 9 |

9 | 5 | 8 |

10 | 5 | 8 |

Average Value | 5 | 7.9 |

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**MDPI and ACS Style**

Chen, L.; Zhang, S.; Liu, C.
Research on the Multi-Screen Connection Interaction Method Based on Regular Octagon K-Value Template Matching. *Symmetry* **2022**, *14*, 1528.
https://doi.org/10.3390/sym14081528

**AMA Style**

Chen L, Zhang S, Liu C.
Research on the Multi-Screen Connection Interaction Method Based on Regular Octagon K-Value Template Matching. *Symmetry*. 2022; 14(8):1528.
https://doi.org/10.3390/sym14081528

**Chicago/Turabian Style**

Chen, Liang, Shichen Zhang, and Changhong Liu.
2022. "Research on the Multi-Screen Connection Interaction Method Based on Regular Octagon K-Value Template Matching" *Symmetry* 14, no. 8: 1528.
https://doi.org/10.3390/sym14081528