# A Reversible Watermarking Scheme for Vector Maps Based on Multilevel Histogram Modification

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. Reversible Watermarking Based on Histogram Shifting

#### 2.2. Zhao’s Multilevel Histogram Modification-Based Reversible Watermarking Scheme

#### 2.3. Analysis of Vector Map Histogram Features

## 3. Proposed Reversible Watermarking Scheme

#### 3.1. Histogram Construction and Processing

**Definition**

**1.**

#### 3.2. Watermark Embedding

_{p}

#### 3.3. Watermark Extraction and Data Recovery

_{L}represents the watermark extracted at level L.

## 4. Experimental Results and Analysis

#### 4.1. Invisibility

#### 4.2. Analysis of Reversibility

^{−17}, which indicates that after the watermark extraction, the map data were recovered to their original state, and thus the algorithm was fully reversible and met the demand of vector maps for high precision.

#### 4.3. Watermark Capacity

#### 4.4. Time Complexity

#### 4.5. Application in Integrity Authentication

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Zhao’s histogram modification scheme: (

**a**) original histogram; (

**b**) shifted histogram; (

**c**) 2nd-level modification; (

**d**) 1st-level modification; (

**e**) 0th-level modification; (

**f**) modified histogram.

**Figure 4.**Test vector maps: (

**a**) contour data, (

**b**) river data, (

**c**) road data, and (

**d**) habitation data.

**Figure 5.**Relationship between the invisibility and the valuation of the parameters: (

**a**) the relationship between t and RMSE, and (

**b**) the relationship between L and RMSE.

**Figure 6.**Relationship between the embedding capacity and the valuation of different parameters: (

**a**) the relationship between t and E, and (

**b**) the relationship between L and E.

**Figure 7.**The comparison of the capacity between the proposed method and Zhao’s method: (

**a**) contour data, (

**b**) river data, (

**c**) road data, and (

**d**) habitation data.

**Figure 8.**Comparisons on the watermark capacity and embedding distortion: (

**a**) contour data, (

**b**) river data, (

**c**) road data, and (

**d**) habitation data.

**Figure 9.**Relationships between algorithm implementation time and embedding level for different experimental data: (

**a**) watermark embedding process, and (

**b**) watermark extraction process.

**Figure 10.**Results of integrity authentication: (

**a**) the tampered contour data, and (

**b**) the tamper localization results.

Map Data | Scale | Entities Number | Vertices Number | Error Tolerance/m |
---|---|---|---|---|

Contour data | 1:1,000,000 | 329 | 6845 | 100 |

River data | 1:500,000 | 3669 | 52,275 | 50 |

Road data | 1:250,000 | 1058 | 44,260 | 25 |

Habitation data | 1:50,000 | 3765 | 27,372 | 5 |

**Table 2.**RMSE (×10

^{−17}) of the recovered data under different values of (t, L) and the original data.

Map Data | (4, 5) | (5, 4) | (6, 1) | (7, 3) | (8, 2) |
---|---|---|---|---|---|

Contour data | 9.6701 | 8.2261 | 3.7842 | 1.1265 | 8.7861 |

River data | 3.8617 | 3.0829 | 1.3943 | 3.9659 | 3.2255 |

Road data | 4.2025 | 3.4189 | 1.4989 | 4.3202 | 3.5186 |

Habitation data | 5.5138 | 4.2963 | 1.9761 | 5.5893 | 4.4623 |

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**MDPI and ACS Style**

Hou, X.; Min, L.; Yang, H.
A Reversible Watermarking Scheme for Vector Maps Based on Multilevel Histogram Modification. *Symmetry* **2018**, *10*, 397.
https://doi.org/10.3390/sym10090397

**AMA Style**

Hou X, Min L, Yang H.
A Reversible Watermarking Scheme for Vector Maps Based on Multilevel Histogram Modification. *Symmetry*. 2018; 10(9):397.
https://doi.org/10.3390/sym10090397

**Chicago/Turabian Style**

Hou, Xiang, Lianquan Min, and Hui Yang.
2018. "A Reversible Watermarking Scheme for Vector Maps Based on Multilevel Histogram Modification" *Symmetry* 10, no. 9: 397.
https://doi.org/10.3390/sym10090397