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  4. A watermarking scheme for color images that achieves optimality using the Transit Search Algorithm

A watermarking scheme for color images that achieves optimality using the Transit Search Algorithm

MMC.
2024;
Volume 11, Number 3
: pp. 848–855
https://doi.org/10.23939/mmc2024.03.848
Received: January 06, 2024
Revised: August 19, 2024
Accepted: August 21, 2024

Tamimi M., Bencherqui A., Tahiri M. A., Karmouni H., El Mloufy A., Qjidaa H., Sayyouri M.  A watermarking scheme for color images that achieves optimality using the Transit Search Algorithm.  Mathematical Modeling and Computing. Vol. 11, No. 3, pp. 848–855 (2024)

Authors:
  1. M. Tamimi
  2. A. Bencherqui
  3. M. A.Tahiri
  4. H. Karmouni
  5. A. El Mloufy
  6. H. Qjidaa
  7. M. Sayyouri
1
Engineering, Systems and Applications Laboratory, National School of Applied Sciences, Sidi Mohamed Ben Abdellah University, Fez
2
Engineering, Systems and Applications Laboratory, National School of Applied Sciences, Sidi Mohamed Ben Abdellah University, Fez
3
Engineering, Systems and Applications Laboratory, National School of Applied Sciences, Sidi Mohamed Ben Abdellah University, Fez
4
National School of Applied Sciences, Cadi Ayyad University, Marrakech
5
Engineering, Systems and Applications Laboratory, National School of Applied Sciences, Sidi Mohamed Ben Abdellah University, Fez
6
CED-ST, STIC, Laboratory of Electronic Signals and Systems of Information LESSI, Dhar El Mahrez, Faculty of Science, Sidi Mohamed Ben Abdellah-Fez University, Fez
7
Engineering, Systems and Applications Laboratory, National School of Applied Sciences, Sidi Mohamed Ben Abdellah University, Fez

This paper describes an innovative watermarking method that combines discrete wavelet transform (DWT), Hessenberg decomposition (HD), and singular value decomposition (SVD).  To do this, the main image and the watermark are divided into three channels (red, green and blue – RGB).  Then, each part of the main image individually undergoes the steps of DWT, HD and SVD, while the watermark components are processed by SVD. Insertion of the watermark is carried out by adjusting the singular values of the watermark and the main image, using a watermark scaling factor ($\alpha$).  The optimal choice of $\alpha$ poses a challenge, so the transit search algorithm is employed to find a trade-off between visibility and robustness.  To evaluate this method, comparisons are made with other studies using various optimization algorithms such as particle swarm optimization, artificial bee colony and fly optimization algorithm.  The results of the experiments confirm the effectiveness of this technique.

watermark
transit search
color images
DWT
HD
SVD
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