# Robust Image Hashing Using Histogram Reconstruction for Improving Content Preservation Resistance and Discrimination

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Transform Domain Feature

#### 2.2. Spatial Feature

#### 2.3. Statistical Features

#### 2.4. Matrix Decomposition

## 3. The Proposed Scheme

#### 3.1. Pre-Processing

**I**is the image, * means convolution operation, and

**G**${}_{\sigma}$ is defined as

#### 3.2. Reconstructing Histogram

#### 3.3. Pixel Selecting

#### 3.4. Hash Generation

#### 3.5. Similarity Metric

## 4. Simulation Results

#### 4.1. Perceptual Robustness

#### 4.2. Discrimination

#### 4.3. Tamper Detection Test

#### 4.4. Influence of Neighborhood Size on Hash Performances

#### 4.5. Performance Comparison

#### 4.6. Key Sensitivity

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Image and its corresponding histogram. (

**a**) Kangaroo, (

**b**) Kangaroo with Arnold Scrambling, (

**c**) Histogram of kangaroo, and (

**d**) Histogram of kangaroo with Arnold Scrambling.

**Figure 3.**Evaluation of robustness performance under various operations using five standard benchmark color images.

**Figure 5.**Original and tampered images for tamper detection. The left column contains 6 original images (

**a**,

**c**,

**e**,

**g**,

**i**,

**k**), and the right column contains 6 corresponding tampered images (

**b**,

**d**,

**f**,

**h**,

**j**,

**l**).

Non-Malicious Attacks | Description | Parameter Value | Number |
---|---|---|---|

Average filtering | Filter size | 3, 5, 7 | 3 |

Median filtering | Filter size | 3, 5, 7, 9 | 4 |

3 × 3 Gaussian low-pass filtering | Standard deviation | 0.3, 0.4, …, 1.0 | 8 |

JPEG compression | Quality factor | 30, 40, …, 100 | 8 |

Salt and pepper noise | Density | 0.001, 0.002, …, 0.007 | 7 |

Scaling | Ratio | 0.5, 1.5, 2.0, …, 5.0 | 9 |

X-Shearing | Angle | 1, 2, …, 8 | 8 |

Rotation | Rotation angle | ±5, ±10, ±15, …, ±45, ±90 | 20 |

Non-Malicious Attack | Minimum | Maximum | Mean | Standard Deviation |
---|---|---|---|---|

Average filtering | 0 | 63 | 16.71 | 13.14 |

Median filtering | 0 | 62 | 18.12 | 12.82 |

Gaussian filtering | 0 | 47 | 9.12 | 8.75 |

JPEG compression | 0 | 33 | 6.66 | 5.76 |

Salt and pepper noise | 0 | 62 | 10.35 | 10.16 |

Scaling | 0 | 49 | 4.72 | 6.36 |

X-Shearing | 1 | 40 | 11.5 | 8.12 |

Rotation | 0 | 57 | 17.16 | 13.07 |

Threshold | Collision Probability |
---|---|

40 | $5.03\times {10}^{-4}$ |

42 | $6.03\times {10}^{-4}$ |

45 | $7.04\times {10}^{-4}$ |

48 | $1.01\times {10}^{-3}$ |

51 | $1.26\times {10}^{-3}$ |

54 | $1.61\times {10}^{-3}$ |

57 | $2.31\times {10}^{-3}$ |

60 | $3.07\times {10}^{-3}$ |

63 | $3.62\times {10}^{-3}$ |

Images | Hamming Distance |
---|---|

(a)–(b) | 107 |

(c)–(d) | 72 |

(e)–(f) | 153 |

(g)–(h) | 93 |

(i)–(j) | 199 |

(k)–(l) | 133 |

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**MDPI and ACS Style**

Jia, Y.; Cui, C.; El-Latif, A.A.A.
Robust Image Hashing Using Histogram Reconstruction for Improving Content Preservation Resistance and Discrimination. *Symmetry* **2023**, *15*, 1088.
https://doi.org/10.3390/sym15051088

**AMA Style**

Jia Y, Cui C, El-Latif AAA.
Robust Image Hashing Using Histogram Reconstruction for Improving Content Preservation Resistance and Discrimination. *Symmetry*. 2023; 15(5):1088.
https://doi.org/10.3390/sym15051088

**Chicago/Turabian Style**

Jia, Yao, Chen Cui, and Ahmed A. Abd El-Latif.
2023. "Robust Image Hashing Using Histogram Reconstruction for Improving Content Preservation Resistance and Discrimination" *Symmetry* 15, no. 5: 1088.
https://doi.org/10.3390/sym15051088