# Blind Image Watermarking in Canonical and Cepstrum Domains Based on 4-Connected t-o’clock Scrambling

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## Abstract

**:**

## 1. Introduction

## 2. Background Information

#### 2.1. The Discrete Linear Canonical Transform (DLCT)

#### 2.2. The Cepstrum Transform (CT)

## 3. Proposed Watermarking Framework

#### 3.1. Watermark Preprocessing

#### 3.2. Embedding Location

#### 3.3. Watermark Embedding Framework

- The original host image H is separated into three channels R, G, and B.
- Select the channel G for embedding watermark information.
- A region $R=\{r\left(p,q\right)\mid {i}^{\prime}\le p\le P,{j}^{\prime}\le q\le Q\}$ using Equations (5) and (6) is extracted from channel G, where the watermark bit is embedded, with $P=X-{i}^{\prime}$, $Q=Y-{j}^{\prime}$, ${i}^{\prime}\in \{5,6,\dots ,X-{i}^{\prime}\}$, and ${j}^{\prime}\in \{5,6,\dots ,Y-{j}^{\prime}\}$.
- Apply DLCT to R to obtain $T=\{t\left({a}^{\prime},{b}^{\prime}\right)\mid 1\le {a}^{\prime}\le P$, $1\le {b}^{\prime}\le Q\}$ using Equation (2).
- Then, apply CT to T with Equation (3) to obtain C denoted as $C=\{c\left(u,v\right)\mid 1\le u\le P$, $1\le v\le Q\}$.
- The cepstrum region C is segmented into L non-overlapping blocks B with size $m\times m$, where $B=\{{B}_{1},{B}_{2},{B}_{3},\dots ,{B}_{L}\}$.
- Watermark image W is encrypted using four-connected t-o’clock scrambling to get W’ image.
- Watermark bit is embedded into each blocks B using max-heap tree and min-heap tree property to obtain B’, where ${B}^{\prime}=\{{B}_{1}^{\prime},{B}_{2}^{\prime},{B}_{3}^{\prime},\dots ,{B}_{L}^{\prime}\}$. A max-heap is a complex binary tree in which the value of each internal node is greater than or equal to the value of the children of that node. For the min-heap tree, the value of each internal node is less than its child node. If $w(i,j)=1$, then apply max heap tree procedure to the block. If $w(i,j)=0$, then apply min-heap tree property. This process is described in Figure 3.
- After embedding all watermark bits, concatenate all sub-blocks B’ to obtain watermarked CT region C’.
- Then, apply inverse CT to C’ to obtain watermarked region T’.
- Apply inverse DLCT to T’ to obtain watermarked region R’.
- Reinsert the watermarked region R’ to obtain G’ channel and finally concatenate all three channels to get the watermarked image H’.

#### 3.4. Watermark Extraction Framework

- Apply DLCT to the extracted region R* to get T* and then apply CT to that region T* to obtain region C*.
- Divide the C* region into non-overlapping block B* with size $m\times m$.
- Extract the watermark bit from each block. If a selected block satisfies the max-heap tree property, then the watermark bit will be 1. If the selected block satisfies the min-heap tree property, then the watermark bit will be 0.
- Finally, the inverse four-connected t-o’clock method is applied to reconstruct each component of watermark image W*.

## 4. Experimental Results

#### 4.1. Imperceptibility Test

#### 4.2. Robustness Test

- JPEG compression: JPEG compression is a standard lossy compression technique in which an image is compressed to reduce its memory space and bandwidth requirements for transmission over the Internet. In our simulation, JPEG compression with $QF=90$ was applied to the watermarked images.
- Cropping: The watermarked images were cropped 50% from the top.
- Rotation attack: The watermarked images were rotated by ${3}^{\circ}$ and the rotated images were re-rotated in a counter-clockwise for extraction of watermark images.
- Gaussian noise: Gaussian noise with variance 0.1 was applied to the watermarked images.
- Speckle noise: Speckle noise with variance 0.01 was applied to the watermarked images.
- Salt and pepper noise: Salt and pepper noise with variance 0.01 was applied to the watermarked images.
- Poison noise: Poison noise was applied to the watermarked images.
- Contrast adjustment: Contrast adjustment with minimum 0.2 and maximum 0.6 was applied to the watermarked images.
- Sharpening: Sharpening with tolerance 0.1 was applied to the watermarked images.
- Median filtering: $3\times 3$ median filter was applied to the watermarked images.
- Wiener filtering: $3\times 3$ wiener filter was applied to the watermarked images.

#### 4.3. The Computational Time Comparison Analysis

#### 4.4. Security Analysis of Proposed Scrambling Method

#### 4.4.1. Correlation Coefficient (CC)

#### 4.4.2. Information Entropy (IE)

#### 4.4.3. Relative Entropy (RE)

#### 4.4.4. Differential Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Example of four-connected t-o’clock scrambling method: (

**a**) block diagram of the scrambled block; and (

**b**) detailed steps when $t=12$.

**Figure 6.**Analysis of the proposed method under no attack, compression (quality factor: 90%), cropping (50%), and rotation ${3}^{\circ}$.

**Figure 7.**Analysis of the proposed method under salt and pepper noise (0.01), Gaussian noise (0.01), speckle noise (0.01), and poison noise attack.

**Figure 8.**Analysis of the proposed method under Contrast adjustment, Sharpening (0.1), median filtering, and wiener filtering.

Images | PSNR | SSIM |
---|---|---|

Lena | 53.04 | 0.9980 |

Pepper | 52.71 | 0.9985 |

Mandrill | 51.02 | 0.9969 |

Fruits | 53.39 | 0.9988 |

Watermarking Methods | Cover Image | PSNR | SSIM |
---|---|---|---|

[17] | Lena | 41.5391 | 0.9975 |

Mandrill | 40.8315 | 0.9918 | |

Pepper | 39.8431 | 0.9821 | |

Fruits | 41.4162 | 0.9972 | |

[24] | Lena | 38.5471 | 0.9804 |

Mandrill | 41.2176 | 0.9870 | |

Pepper | 41.3236 | 0.9908 | |

Fruits | 40.59041 | 0.9911 | |

Proposed Method | Lena | 53.04 | 0.9980 |

Mandrill | 51.02 | 0.9969 | |

Pepper | 52.71 | 0.9985 | |

Fruits | 53.39 | 0.9988 |

Attack Type | [17] | [24] | Proposed Method |
---|---|---|---|

Gaussian $\left(0.1\right)$ | 0.9625 | 0.8823 | 0.9925 |

Speckle noise $\left(0.01\right)$ | 0.9663 | 0.9647 | 0.9915 |

Cropping $\left(50\%\right)$ | 0.6482 | 0.8619 | 0.9719 |

Sharpening $\left(tol=0.1\right)$ | 0.9935 | 0.9882 | 0.9567 |

Rotation (${3}^{\circ}$) | 0.9361 | 0.9225 | 0.9760 |

Wiener filtering | 0.9578 | 0.9765 | 0.9934 |

Salt and pepper noise $\left(0.01\right)$ | 0.9478 | 0.9733 | 0.9945 |

Median filtering | 0.9419 | 0.8997 | 0.9902 |

JPEG Compression | 0.9998 | 0.9791 | 0.9986 |

Method | Embedding Time | Extraction Time | Total Time |
---|---|---|---|

[17] | 0.274117 | 0.238315 | 0.512432 |

[24] | 0.810820 | 0.269506 | 1.080326 |

Proposed Method | 0.5016456 | 0.2394905 | 0.7411361 |

CC | [17] | [24] | Proposed Method |
---|---|---|---|

Horizontal | 0.0074 | 0.0082 | 0.00040 |

Vertical | 0.0065 | 0.0070 | 0.0024 |

Diagonal | 0.0098 | 0.0058 | 0.0039 |

Scrambling Methods | Watermarked Image | ||
---|---|---|---|

Red | Green | Blue | |

[17] | 2.2902 | 2.3444 | 2.4673 |

[24] | 2.6372 | 2.4108 | 2.1091 |

Proposed Method | 3.3553 | 3.4476 | 3.3274 |

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**MDPI and ACS Style**

Chowdhury, F.S.; Dhar, P.K.; Deb, K.; Koshiba, T. Blind Image Watermarking in Canonical and Cepstrum Domains Based on 4-Connected t-o’clock Scrambling. *Symmetry* **2020**, *12*, 266.
https://doi.org/10.3390/sym12020266

**AMA Style**

Chowdhury FS, Dhar PK, Deb K, Koshiba T. Blind Image Watermarking in Canonical and Cepstrum Domains Based on 4-Connected t-o’clock Scrambling. *Symmetry*. 2020; 12(2):266.
https://doi.org/10.3390/sym12020266

**Chicago/Turabian Style**

Chowdhury, Farhana Shirin, Pranab Kumar Dhar, Kaushik Deb, and Takeshi Koshiba. 2020. "Blind Image Watermarking in Canonical and Cepstrum Domains Based on 4-Connected t-o’clock Scrambling" *Symmetry* 12, no. 2: 266.
https://doi.org/10.3390/sym12020266