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Robust hybrid watermarking approach for 3D multiresolution meshes based on spherical harmonics and wavelet transform

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Abstract

Since the 3D mesh security problems imposed themselves, attempts to design watermarking algorithms targeting this data type have continued to grow up to secure data shared by remote users. The originality of the present approach is to insert a whole grayscale image in hybrid domain by using wavelet transform and spherical harmonics. Our algorithm includes then two rounds of insertion. The first is operating multiresolution domain by applying wavelet transform. The watermark, which is an image already coded using a convolutional encoder, is embedded into wavelet coefficients (using Least Significant Bit method) after a transformation to spherical coordinate system and a modulation step. Finally watermarked mesh is reconstructed using inverse wavelet transform. This mesh undergoes a second round on watermarking using spherical harmonics. In this case the same steps are executed to embed data into SHs harmonic coefficients before reconstructing the final version of the watermarked mesh. The experimentation of our approach has shown a very high insertion rate due to the use of hybrid insertion domain, while maintaining the mesh quality. Watermarked mesh and extracted data are obtained in real time. Our approach is also robust against the most popular attacks. Our results show that the present approach improves the existing works.

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Data Availability

The data of this study are available upon request from the corresponding author.

Code Availability

The codes concerning this study are available from the corresponding author upon request.

Abbreviations

3D:

Three dimensional, Three dimension

MSQE:

Mean SQuare Error

PSNR:

Peak Signal to Noise Ratio

SHs:

Spherical Harmonics

WCV:

Wavelet Coefficients Vector

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Funding

The authors declare that no funding support is received from any organization for the present work.

Author information

Authors and Affiliations

  1. Research Groups on Intelligent Machines Laboratory, University of Sfax, ENIS, Sfax, Tunisia

    Ikbel Sayahi

  2. LATIS Laboratory of Advanced Technology and Intelligent Systems, Université de Sousse, Ecole Nationale d’Ingénieurs de Sousse, 4023, Sousse, Tunisie

    Malika Jallouli & Mohamed Ali Mahjoub

  3. Department of Mathematics, Higher Institute of Applied Mathematics and Computer Science, University of Kairouan, 3100, Kairouan, Tunisia

    Anouar Ben Mabrouk

  4. Laboratory of Algebra, Number Theory and Nonlinear Analysis, LR18ES15, Department of Mathematics, Faculty of Sciences, University of Monastir, 5019, Monastir, Tunisia

    Anouar Ben Mabrouk

  5. Computational and Analytical Mathematics and Application Research Unit, Department of Mathematics, Faculty of Sciences, University of Tabuk, 71491, Tabuk, Saudi Arabia

    Anouar Ben Mabrouk

  6. College of Computers and Information Technology, Taif University, Taif, Saudi Arabia

    Chokri Ben Amar

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  1. Ikbel Sayahi
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  2. Malika Jallouli
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  4. Mohamed Ali Mahjoub
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Correspondence to Ikbel Sayahi.

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Sayahi, I., Jallouli, M., Mabrouk, A.B. et al. Robust hybrid watermarking approach for 3D multiresolution meshes based on spherical harmonics and wavelet transform. Multimed Tools Appl 82, 39841–39866 (2023). https://doi.org/10.1007/s11042-023-14722-5

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