Skip to main content
SpringerLink
Log in

Color Image Zero-Watermarking Using Accurate Quaternion Generalized Orthogonal Fourier–Mellin Moments

  • Published:
Journal of Mathematical Imaging and Vision Aims and scope Submit manuscript

Abstract

In recent years, digital image zero-watermarking algorithm has made great progress. But there are still some problems. First, most algorithms only focus on robustness and ignore discrimination. Second, most methods have good robustness against conventional signal attacks but poor robustness against geometric attacks. Thirdly, most of the existing zero-watermarking algorithms only focus on gray-scale images, and there are relatively few researches on color images. In order to cope with these issues, this paper introduces a novel color image zero-watermarking scheme using accurate quaternion generalized orthogonal Fourier–Mellin moments (AQGOFMMs). In the first stage of the proposed method, accurate computation of generalized orthogonal Fourier–Mellin moments (GOFMMs) based on the polar pixel tiling scheme. In the next stage, the high-precision GOFMMs are extended to the accurate quaternion GOFMMs (AQGOFMMs). Finally, the immutable set of features is extracted to construct a zero-watermark. It is worth mentioning that, different from the traditional way of constructing watermark with the amplitude of moments, this algorithm uses the full 4-D features of AQGOFMMs to construct watermark. The experiment proved that proposed zero-watermarking scheme gives a good balance between discriminability and robustness. Furthermore, the proposed algorithm achieves better performance than the other existing zero-watermarking.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

References

  1. Wen, Q., Sun, T.F., Wang, S.X.: Based zero-watermark digital watermarking technology. In: Proceedings of the 3rd National Conference in Information Hiding. Xidian University Press, Xi’an, 2001, pp. 102–109

  2. Wen, Q., Sun, T.F., Wang, S.X.: Concept and application of zero-watermark. Acta Electron. Sin. 31, 214–216 (2003)

    Google Scholar 

  3. Sang, J., Liao, X., Alam, M.S.: Neural-network-based zero-watermark scheme for digital images. Opt. Eng. 45, 965–974 (2006)

    Google Scholar 

  4. Chen, T.H., Horng, G.B., Lee, W.B.: A publicly verifiable copyright-proving scheme resistant to malicious attacks. IEEE Trans. Ind. Electron. 52(1), 327–334 (2005)

    Article  Google Scholar 

  5. Chang, C.C., Lin, P.Y.: Adaptive watermark mechanism for rightful ownership protection. J. Syst. Softw. 81(7), 1118–1129 (2008)

    Article  MathSciNet  Google Scholar 

  6. Tsai, H.H., Tseng, H.C., Lai, Y.S.: Robust lossless image watermarking based on α-trimmed mean algorithm and support vector machine. J. Syst. Softw. 83(6), 1015–1028 (2010)

    Article  Google Scholar 

  7. Tsai, H.H., Lai, Y.S., Lo, S.C.: A zero-watermark scheme with geometrical invariants using SVM and PSO against geometrical attacks for image protection. J. Syst. Softw. 86(2), 335–348 (2013)

    Article  Google Scholar 

  8. Gao, G.Y., Jiang, G.P.: A lossless copyright authentication scheme based on Bessel–Fourier moment and extreme learning machine in curvature-feature domain. J. Syst. Softw. 86(1), 222–232 (2013)

    Article  Google Scholar 

  9. Gao, G.Y., Jiang, G.P.: Bessel-Fourier moment-based robust image zero-watermarking. Multimed. Tools Appl. 74(3), 841–858 (2015)

    Article  Google Scholar 

  10. Sun, L., Xu, J.C., Zhang, X.X., Dong, W., Tian, Y.: A novel generalized Arnold transform-based zero-watermarking scheme. Appl. Math. Inf. Sci. 4, 2023–2035 (2015)

    Google Scholar 

  11. Wang, C.P., Wang, X.Y., Xia, Z.Q., Zhang, C., Chen, X.J.: Geometrically resilient color image zero-watermarking algorithm based on quaternion exponent moments. J. Vis. Commun. Image Represent. 41, 247–259 (2016)

    Article  Google Scholar 

  12. Wang, C.P., Wang, X.Y., Chen, X.J., Zhang, C.: Robust zero-watermarking algorithm based on polar complex exponential transform and logistic mapping. Multimed. Tools Appl. 76(24), 26355–26376 (2017)

    Article  Google Scholar 

  13. Ali, M., Ahn, C.W., Pant, M.: An efficient lossless robust watermarking scheme by integrating redistributed invariant wavelet and fractional Fourier transforms. Multimed. Tools Appl. 77(10), 11751–11773 (2018)

    Article  Google Scholar 

  14. Fan, T.Y., Chao, H.C., Chieu, B.C.: Lossless medical image watermarking method based on significant difference of cellular automata transform coefficient. Sig. Process. Image Commun. 70, 174–183 (2019)

    Article  Google Scholar 

  15. Xia, Z.Q., Wang, X.Y., Zhou, W., Li, R., Wang, C., Zhang, C.: Color medical image lossless watermarking using chaotic system and accurate quaternion polar harmonic transforms. Sig. Process. 157, 108–118 (2019)

    Article  Google Scholar 

  16. Yang, H., Qi, S., Niu, P., Wang, X.: Color image zero-watermarking based on fast quaternion generic polar complex exponential transform. Sig. Process. Image Commun. 82, 115747 (2020)

    Article  Google Scholar 

  17. Zhu, H., Yang, Y., Zhu, X., Gui, Z., Shu, H.: General form for obtaining unit disc-based generalized orthogonal moments. IEEE Trans. Image Process. 23(12), 5455–5469 (2014)

    Article  MathSciNet  Google Scholar 

  18. Hoang, T.V., Tabbone, S.: Generic polar harmonic transforms for invariant image description. In: 2011 18th IEEE International Conference on Image Processing. IEEE, 2011. pp. 829–832

  19. Xin, Y., Pawlak, M., Liao, S.: Accurate computation of Zernike moments in polar coordinates. IEEE Trans. Image Process. 16(2), 581–587 (2007)

    Article  MathSciNet  Google Scholar 

  20. Camacho-Bello, C., Toxqui-Quitl, C., Padilla-Vivanco, A., Báez-Rojas, J.J.: High-precision and fast computation of Jacobi–Fourier moments for image description. JOSA A 31(1), 124–134 (2014)

    Article  Google Scholar 

  21. Karakasis, E.G., Papakostas, G.A., Koulouriotis, D.E., Tourassis, V.D.: A unified methodology for computing accurate quaternion color moments and moment invariants. IEEE Trans. Image Process. 23(2), 596–611 (2013)

    Article  MathSciNet  Google Scholar 

  22. The, C.H., Chin, R.T.: On image analysis by the methods of moments. IEEE Trans. Pattern Anal. Mach. Intell. 10(4), 496–513 (1988)

    Article  Google Scholar 

  23. Yang, H., Niu, Y., Jiao, L., Liu, Y., Wang, X.: Robust copy-move forgery detection based on multi-granularity superpixels matching. Multimed. Tools Appl. 77, 13615–13641 (2018)

    Article  Google Scholar 

  24. Xiao, B., Wang, G., Li, W.: Radial shifted Legendre moments for image analysis and invariant image recognition. Image Vis. Comput. 32, 994–1006 (2014)

    Article  Google Scholar 

  25. Qi, M., Li, B., Sun, H.: Image representation by harmonic transforms with parameters in SL (2, R). J. Vis. Commun. Image Represent. 35, 184–192 (2016)

    Article  Google Scholar 

  26. Batioua, R., Benouini, K., Zenkouar, H.E.: Fadili, Image analysis using new set of separable two-dimensional discrete orthogonal moments based on Racah polynomials. EURASIP J. Image Video Process. 20, 1–17 (2017)

    Google Scholar 

  27. Guo, F., Ye, S., Yang, T., Wang, X.: Robust circularly orthogonal moment based on Chebyshev rational function. Digit. Signal Proc. 62, 249–258 (2017)

    Article  Google Scholar 

  28. Chen, B., Coatrieux, G., Chen, G., Sun, X., Coatrieux, L.J., Shu, H.: Full 4-D quaternion discrete Fourier transformation based watermarking for color images. Digit. Signal Proc. 28, 106–119 (2014)

    Article  Google Scholar 

  29. Shao, Z., Shang, Y., Zeng, R., Shu, H., Coatrieux, G., Wu, J.: Robust watermarking scheme for color image based on quaternion-type moment invariants and visual cryptography. Sig. Process. Image Commun. 48, 12–21 (2016)

    Article  Google Scholar 

  30. Wu, X., Sun, W.: Robust copyright protection scheme for digital images using overlapping DCT and SVD. Appl. Soft Comput. 13(2), 1170–1182 (2013)

    Article  Google Scholar 

  31. Parah, S.A., Sheikh, J.A., Ahad, F., Loan, N.A., Bhat, G.M.: Information hiding in medical images: a robust medical image watermarking system for E-healthcare. Multimed. Tools Appl. 76(8), 10599–10633 (2017)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported partially by the National Natural Science Foundation of China (Nos. 61472171 & 61701212), Key Scientific Research Project of Liaoning Provincial Education Department (LZ2019001) and Natural Science Foundation of Liaoning Province (2019-ZD-0468).

Author information

Authors and Affiliations

  1. School of Computer and Information Technology, Liaoning Normal University, Dalian, 116029, People’s Republic of China

    Xiang-yang Wang, Li Wang, Jia-lin Tian, Pan-pan Niu & Hong-ying Yang

Authors
  1. Xiang-yang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jia-lin Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pan-pan Niu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hong-ying Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiang-yang Wang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical standard

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards.

Informed consent

Informed consent was obtained from all individual participants included in the study.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Xy., Wang, L., Tian, Jl. et al. Color Image Zero-Watermarking Using Accurate Quaternion Generalized Orthogonal Fourier–Mellin Moments. J Math Imaging Vis 63, 708–734 (2021). https://doi.org/10.1007/s10851-020-01002-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10851-020-01002-2

Keywords

Search

Navigation