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Quaternion cartesian fractional hahn moments for color image analysis

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Abstract

Moment descriptors have been widely used for the analysis and representation of images. In this paper, we propose a new set of discrete orthogonal moments of fractional order, called Quaternion Cartesian Fractional Hahn Moments. The proposed QCFrHMs are based on new Fractional Hahn Polynomials and generalize the classical Quaternion Hahn Moments. First, FrHPs are proposed and defined using eigenvalue decomposition and the spectral representation of the classical Hahn polynomial matrix. Then, the proposed FrHPs are used as a kernel function to define the new Fractional Hahn Moments. Finally, based on quaternion algebra, the FrHMs for grayscale images are generalized to the QCFrHMs for color images. The proposed QCFrHMs depend on four parameters: two polynomial parameters and two fractional orders, which allow us to use them to propose a robust, blind and efficient watermarking scheme for the copyright protection of color images where the requirements of a watermarking scheme are successfully ensured thanks to the performance of the proposed QCFrHMs. Experimental results are provided to illustrate the effectiveness of the proposed color image descriptors.

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Abbreviations

QCFrHMs :

Quaternion Cartesian Fractional Hahn Moments.

QCHMs :

Quaternion Cartesian Hahn Moments.

FrHMs :

Fractional Hahn Moments.

FrHPs :

Fractional Hahn Polynomials.

PSNR :

Peak Signal to Noise Ratio.

BER :

Bit Error Rate

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Acknowledgements

The authors would like to thank the anonymous referees for their helpful comments and suggestions.

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Authors and Affiliations

  1. CED-ST, STIC, Laboratory of Electronic Signals and Systems of Information LESSI, Faculty of Science Dhar El Mahrez, University Sidi Mohamed Ben Abdellah, Fez, Morocco

    M. Yamni, H. Karmouni & H. Qjidaa

  2. Engineering, Systems and Applications Laboratory, National School of Applied Sciences, Sidi Mohamed Ben Abdellah University, BP 72, My Abdallah Avenue Km. 5 Imouzzer Road, Fez, Morocco

    M. Sayyouri

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  1. M. Yamni
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Yamni, M., Karmouni, H., Sayyouri, M. et al. Quaternion cartesian fractional hahn moments for color image analysis. Multimed Tools Appl 81, 737–758 (2022). https://doi.org/10.1007/s11042-021-11432-8

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