# Computationally Efficient Robust Color Image Watermarking Using Fast Walsh Hadamard Transform

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Walsh Hadamard Transform and Related Works

_{2}N) real additions and subtractions. Equations of forward Walsh Hadamard Transform of a one dimensional matrix u(m) is

## 3. Proposed Algorithm

#### 3.1. Computational Efficient Calculation

#### 3.2. Embedding Algorithm

_{1}, i

_{2}, i

_{3}, i

_{4}, …, i

_{k}). Each of these blocks is transformed using Fast Walsh Hadamard Transform to get the transformed blocks (h

_{1}, h

_{2}, h

_{3}, h

_{4}, …, h

_{k}). The binary watermark (B) is converted into one dimensional string (b

_{1}, b

_{2}, b

_{3}…, b

_{n}) each of the values either 1 or −1. For spreading, r numbers of, polar orthogonal hadamard codes are used. As shown in Figure 1 mutually similar mid band coefficients along the 3rd, 4th, 5th and 6th rows are selected for embedding the watermark and rest of the coefficients are left unchanged. Mid frequency coefficients are selected as the changes on them do not cause much changes to the perceptual quality compared to the lower frequency coefficients. In addition, these mid band frequencies are less affected by compression. The selected frequency coefficients along x

^{th}row are made into a single vector r

_{x}such that length of r

_{x}is same as that of spreading codes used. Each bit of the watermark in each modifying row is spread using different spreading codes, then, spread watermarks are added to the selected coefficient vector.

_{x}is the x

^{th}row used for watermarking and ${\overline{W}}_{x}$ is the FWHT of the x

^{th}row of the watermarked image. Watermarked image can be obtained after finding the inverse FWHT of all the watermarked blocks and reconstructing into their original locations. After watermarking, the Y plane is replaced back and the image is converted back to RGB format.

#### 3.3. Decoding Algorithm

## 4. Performance Evaluation and Simulation Results

#### 4.1. Performance Measures

#### 4.2. Computational Complexity and Execution Time

#### 4.3. Perceptual Quality

#### 4.4. Robustness Analysis

#### 4.5. Effect of Spreading Code Length on Robustness

#### 4.6. Effect of Number of Watermark Bits on Robustness

#### 4.7. Effect of Number of Spreading Codes on Robustness

#### 4.8. Effect of Type of Spreading Codes on Robustness

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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Existing FWHT Algorithms and Similar DCT Algorithm | Time for Embedding and Decoding (Seconds) |
---|---|

Samee (2013) | 1.9 |

S. Maity et al. (2012) | 3 |

M.K. Kundu et al. (2011) | 7.5 |

Anthony et al. (2003) | 3 |

Proposed Algorithm | 0.665 |

Attacks/Distortions (Level) | DCT Technique (Samee) | FWHT Technique |
---|---|---|

Original | ||

Scaling (6 times) | ||

Gaussian Noise (μ = 0, σ² = 0.005) | ||

Gaussian Noise (μ = 0.01, σ² = 0.005) | ||

Gaussian Noise (μ = 0, σ² = 0.05) | ||

Salt & Pepper Noise (Density—0.01) | ||

Salt & Pepper Noise (Density—0.1) | ||

Sharpen (3 × 3) | ||

Blur (2 × 2) | ||

Median filtering (3 × 3) | ||

Gaussian filtering (5 × 5) | ||

Crop (50%) |

Attacks (Level) | Length—512 | Length—256 | Length—128 |
---|---|---|---|

Original | |||

Scaling (6) | |||

Gaussian noise (μ = 0, σ^{2} = 0.05) | |||

Gaussian noise (μ = 0, σ^{2} = 0.05) | |||

Gaussian noise (μ = 0.01, σ^{2} = 0.005) | |||

Salt and Pepper noise (Density = 0.001) | |||

Salt and Pepper noise (Density = 0.1) | |||

Sharpen (5 × 5) | |||

Blur (3 × 3) |

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**MDPI and ACS Style**

Kalarikkal Pullayikodi, S.; Tarhuni, N.; Ahmed, A.; Shiginah, F.B.
Computationally Efficient Robust Color Image Watermarking Using Fast Walsh Hadamard Transform. *J. Imaging* **2017**, *3*, 46.
https://doi.org/10.3390/jimaging3040046

**AMA Style**

Kalarikkal Pullayikodi S, Tarhuni N, Ahmed A, Shiginah FB.
Computationally Efficient Robust Color Image Watermarking Using Fast Walsh Hadamard Transform. *Journal of Imaging*. 2017; 3(4):46.
https://doi.org/10.3390/jimaging3040046

**Chicago/Turabian Style**

Kalarikkal Pullayikodi, Suja, Naser Tarhuni, Afaq Ahmed, and Fahad Bait Shiginah.
2017. "Computationally Efficient Robust Color Image Watermarking Using Fast Walsh Hadamard Transform" *Journal of Imaging* 3, no. 4: 46.
https://doi.org/10.3390/jimaging3040046