# Zero Watermarking Algorithm for Vector Geographic Data Based on the Number of Neighboring Features

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Neighboring Features

#### 2.2. The Determination of the Watermark Bit

#### 2.3. The Determination of the Watermark Index

#### 2.4. Watermark Generation and Extraction

## 3. Experiments

#### 3.1. Datasets

#### 3.2. Experiment Design and Implementation

#### 3.2.1. Geometrical Attacks

#### 3.2.2. Vertex Attacks

#### 3.2.3. Object attacks

#### 3.2.4. Projection Transformation Attacks

#### 3.3. Evaluation

## 4. Results and Analyses

#### 4.1. The Results of Geometrical Attacks

#### 4.2. The Results of Vertex Attacks

#### 4.3. The Results of Object Attacks

#### 4.4. The Results of Projection Transformation Attacks

## 5. Discussions

#### 5.1. Local Characteristics

#### 5.2. Applied to Polyline Data

#### 5.3. The Watermark Uniqueness

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Three types of neighbors: (

**a**) Overlapping neighbors; (

**b**) Edge neighbors; (

**c**) Node neighbors.

**Figure 5.**The data after geometrical attacks: (

**a**) Rotation angle = 60°; (

**b**) Rotation angle = 180°; (

**c**) Sx = 0.8, Sy = 0.8; (

**d**) Sx = 0.8, Sy = 1; (

**e**) Translation distance = 100 m; (

**f**) Translation distance = 200 m.

**Figure 6.**The data after vertex attacks: (

**a**) Interpolation tolerance = 600 m; (

**b**) Simplification tolerance = 600 m.

**Figure 7.**The data after object attacks: (

**a**) Addition ratio = 5%; (

**b**) Addition ratio = 15%; (

**c**) Addition ratio = 30%; (

**d**) Deletion ratio = 5%; (

**e**) Deletion ratio = 15%; (

**f**) Deletion ratio = 30%.

**Figure 8.**The data after projection transformation attacks: (

**a**) To Beijing 1954; (

**b**) To Xian 1980; (

**c**) To CGCS 2000; (

**d**) To cylindrical equal area; (

**e**) To Lambert conformal conic; (

**f**) To azimuthal equidistant.

**Figure 19.**The test data for the watermark uniqueness: (

**a**) Data 1; (

**b**) Data 2; (

**c**) Data 3; (

**d**) Data 4; (

**e**) Data 5; (

**f**) Data 6.

Type | Subtype |
---|---|

Geometrical attacks | Rotation |

Scaling | |

Translation | |

Vertex attacks | Interpolation |

Simplification | |

Object attacks | Object addition |

Object deletion | |

Projection transformation attacks | Projected coordinate systems to geographic coordinate systems |

Projected coordinate systems to projected coordinate systems |

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**MDPI and ACS Style**

Zhou, Q.; Zhu, C.; Ren, N.; Chen, W.; Gong, W.
Zero Watermarking Algorithm for Vector Geographic Data Based on the Number of Neighboring Features. *Symmetry* **2021**, *13*, 208.
https://doi.org/10.3390/sym13020208

**AMA Style**

Zhou Q, Zhu C, Ren N, Chen W, Gong W.
Zero Watermarking Algorithm for Vector Geographic Data Based on the Number of Neighboring Features. *Symmetry*. 2021; 13(2):208.
https://doi.org/10.3390/sym13020208

**Chicago/Turabian Style**

Zhou, Qifei, Changqing Zhu, Na Ren, Weitong Chen, and Weiteng Gong.
2021. "Zero Watermarking Algorithm for Vector Geographic Data Based on the Number of Neighboring Features" *Symmetry* 13, no. 2: 208.
https://doi.org/10.3390/sym13020208