Robust 2D and 3D images zero - watermarking using dual Hahn moment invariants and Sine Cosine Algorithm

Achraf Daoui; Hicham Karmouni; Mhamed Sayyouri; Hassan Qjidaa

doi:10.1007/s11042-022-12298-0

Robust 2D and 3D images zero - watermarking using dual Hahn moment invariants and Sine Cosine Algorithm

Multimed Tools Appl. 2022;81(18):25581-25611. doi: 10.1007/s11042-022-12298-0. Epub 2022 Mar 23.

Authors

Achraf Daoui¹, Hicham Karmouni², Mhamed Sayyouri¹, Hassan Qjidaa²

Affiliations

¹ Laboratory of Engineering, Systems and Applications, National School of Applied Sciences, Sidi Mohamed Ben Abdellah-Fez University, Fez, Morocco.
² Laboratory of Electronic Signals and Systems of Information, Faculty of Science, Sidi Mohamed Ben Abdellah-Fez University, Fez, Morocco.

Abstract

In this paper, we initially provide significant improvements on the computational aspects of dual Hahn moment invariants (DHMIs) in both 2D and 3D domains. These improvements ensure the numerical stability of DHMIs for large-size images. Then, we propose an efficient method for optimizing the local parameters of dual Hahn polynomials (DHPs) when computing DHMIs using the Sine-Cosine Algorithm (SCA). DHMIs optimized via SCA are used to propose new and robust zero-watermarking scheme applied to both 2D and 3D images. On one hand, the simulation results confirm the efficiency of the proposed computation of 2D and 3D DHMIs regarding the numerical stability and invariability. Indeed, the proposed computation method of 2D DHMIs allows to reach a relative error (RE) of the order ≈10^-10 for images of size 1024 × 1024 with an execution time improvement ratio exceeds 70% ( ETIR ≥ 70%), which validates the efficiently of the proposed computation method. On the other hand, the simulation and comparison outcomes clearly demonstrate the robustness of the proposed zero-watermarking scheme against various geometric attacks (translation, rotation, scaling and combined transformations), as well as against other common 2D and 3D image processing attacks (compression, filtering, noise addition, etc.).

Keywords: 2D and 3D image zero-watermarking; Discrete orthogonal moments; Dual - Hahn moment invariants; Image reconstruction; Numerical stability; Sine cosine algorithm.