Skip to main content
SpringerLink
Log in

A Statistical Color Image Watermarking Scheme Using Local QPCET and Cauchy–Rayleigh Distribution

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

Based on local quaternion polar complex exponential transform (QPCET) and Cauchy–Rayleigh distribution, we propose a statistical color image watermarking scheme in this paper, which can achieve the trade-off among imperceptibility, robustness and data payload. Our color image watermarking scheme consists of two parts, namely embedding and detecting. In the embedding process, we divide the color host image into non-overlapping blocks and compute the local QPCET of color image blocks and then insert the watermark signal into the robust local QPCET magnitudes through multiplicative approach. In the detecting phase, robust local QPCET magnitudes are firstly modeled by employing the Cauchy–Rayleigh distribution, where the statistical properties of local QPCET magnitudes are captured accurately. Then, genetic algorithm-based maximum likelihood approach is introduced to estimate the statistical parameters of Cauchy–Rayleigh distribution model. And finally a color image watermark detector for multiplicative watermarking is developed using Cauchy–Rayleigh distribution and locally most powerful test. Also, we utilize the Cauchy–Rayleigh statistical model to derive the closed-form expressions for the watermark detector. Experimental results on some standard test images and comparison with well-known existing methods demonstrate the efficacy and superiority of the proposed scheme.

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

Similar content being viewed by others

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. B. Ahmaderaghi, F. Kurugollu, J.M.D. Rincon, Blind image watermark detection algorithm based on discrete Shearlet transform using statistical decision theory. IEEE Trans. Comput. Imaging 4(1), 46–59 (2018)

    Article  MathSciNet  Google Scholar 

  2. M. Amini, H. Sadreazami, M.O. Ahmad, M.N.S. Swamy, Multichannel color image watermark detection utilizing vector-based hidden Markov model, in IEEE International Symposium on Circuits and Systems (ISCAS), Baltimore, MD, USA (2017), pp. 1–4

  3. M. Amini, H. Sadreazami, M.O. Ahmad, M.N.S. Swamy, A channel-dependent statistical watermark detector for color images. IEEE Trans. Multimed. 21(1), 65–73 (2019)

    Article  Google Scholar 

  4. M. Amirmazlaghani, Additive watermark detection in the wavelet domain using 2D-GARCH model. Inf. Sci. 370, 1–17 (2016)

    Article  MathSciNet  Google Scholar 

  5. M. Amirmazlaghani, M. Rezghi, H. Amindavar, A novel robust scaling image watermarking scheme based on Gaussian mixture model. Expert Syst. Appl. 42(4), 1960–1971 (2015)

    Article  Google Scholar 

  6. M. Barni, F. Bartolini, A.D. Rosa, A. Piva, A new decoder for the optimum recovery of nonadditive watermarks. IEEE Trans. Image Process. 10(5), 755–766 (2001)

    Article  Google Scholar 

  7. A. Bera, P. Klęsk, D. Sychel, Constant-time calculation of Zernike moments for detection with rotational invariance. IEEE Trans. Pattern Anal. Mach. Intell. 41(3), 537–551 (2018)

    Article  Google Scholar 

  8. P. Bhinder, K. Singh, N. Jindal, Image-adaptive watermarking using maximum likelihood decoder for medical image. Multimed. Tools Appl. 3, 1–26 (2018)

    Google Scholar 

  9. H. Bi, Y. Liu, M. Wu, Y. Ge, NSCT domain additive watermark detection using RAO hypothesis test and Cauchy distribution. Math. Probl. Eng. 7, 1–18 (2016)

    MATH  Google Scholar 

  10. Y. Bian, S. Liang, Locally optimal detection of image watermarks in the wavelet domain using Bessel K form distribution. IEEE Trans. Image Process. 22(6), 2372–2384 (2013)

    Article  MathSciNet  Google Scholar 

  11. Y. Bian, S. Liang, Image watermark detection in the wavelet domain using Bessel k densities. IET Image Proc. 7(4), 281–289 (2013)

    Article  MathSciNet  Google Scholar 

  12. L. Dong, Q. Yan, Y. Lv, S. Deng, Full band watermarking in DCT domain with Weibull model. Multimed. Tools Appl. 76(2), 1–18 (2016)

    Google Scholar 

  13. S. Etemad, M. Amirmazlaghani, A new multiplicative watermark detector in the Contourlet domain using t location-scale distribution. Pattern Recogn. 77, 99–112 (2018)

    Article  Google Scholar 

  14. J.R. Hernandez, M. Amado, F. Perez-Gonzalez, DCT-domain watermarking techniques for still images: detector performance analysis and a new structure. IEEE Trans. Image Process. 9(1), 55–68 (2000)

    Article  Google Scholar 

  15. J.R. Hernández, F. Pérez-González, Statistical analysis of watermarking schemes for copyright protection of images. Proc. IEEE 87(7), 1142–1166 (1999)

    Article  Google Scholar 

  16. K.M. Hosny, M.M. Darwish, Resilient color image watermarking using accurate quaternion radial substituted Chebyshev moments. ACM Trans. Multimed. Comput. Commun. Appl. 15(2), 1–46 (2019)

    Article  Google Scholar 

  17. G. Hua, L. Zhao, H. Zhang, G. Bi, Random matching pursuit for image watermarking. IEEE Trans. Circuits Syst. Video Technol. 29(3), 625–639 (2019)

    Article  Google Scholar 

  18. http://decsai.ugr.es/cvg/dbimagenes/index.php

  19. N.K. Kalantari, S.M. Ahadi, M. Vafadust, A robust image watermarking in the Ridgelet domain using universally optimum decoder. IEEE Trans. Circuits Syst. Video Technol. 20(3), 396–406 (2010)

    Article  Google Scholar 

  20. A. Khawne, B. Attachoo, K. Hamamoto, Optimum watermark detection of ultrasonic echo medical images. IEEJ Trans. Electr. Electron. Eng. 10(2), 149–156 (2015)

    Article  Google Scholar 

  21. E.E. Kuruoglu, J. Zerubia, Modeling SAR images with a generalization of the Rayleigh distribution. IEEE Trans. Image Process. 13(4), 527–533 (2004)

    Article  Google Scholar 

  22. R. Kwitt, P. Meerwald, A Uhl, Color-image watermarking using multivariate power-exponential distribution, in The 16th IEEE International Conference on Image Processing, Cairo, Egypt (2009), pp. 4245–4248

  23. R. Kwitt, P. Meerwald, A. Uhl, Lightweight detection of additive watermarking in the DWT-domain. IEEE Trans. Image Process. 20(2), 474–484 (2011)

    Article  MathSciNet  Google Scholar 

  24. L. Li, X. Li, T. Qiao, X. Xu, S. Zhang, A novel framework of robust video watermarking based on statistical model, in The 4th International Conference on Cloud Computing and Security (ICCCS 2018), Haikou, China (2018), pp. 160–172

  25. J.H. Liu, An image watermarking algorithm based on energy scheme in the wavelet transform domain, in IEEE 3rd International Conference on Image, Vision and Computing (ICIVC), Chongqing, China (2018), pp. 668–672

  26. A. Mairgiotis, C. Koliopanos, L.P. Kondi, Rao based watermark detector through two-level hierarchical prior in transform domain, in Proceedings of the 21st Pan-Hellenic Conference on Informatics (PCI 2017), Larissa, Greece (2017), pp. 1–6

  27. M. Rabizadeh, M. Amirmazlaghani, M. Ahmadian-Attari, A new detector for Contourlet domain multiplicative image watermarking using Bessel K form distribution. J. Vis. Commun. Image Represent. 40, 324–334 (2016)

    Article  Google Scholar 

  28. S.M.M. Rahman, M.O. Ahmad, M.N.S. Swamy, A new statistical detector for DWT-based additive image watermarking using the Gauss–Hermite expansion. IEEE Trans. Image Process. 18(8), 1782–1796 (2009)

    Article  MathSciNet  Google Scholar 

  29. H. Sadreazami, M.O. Ahmad, M.N.S. Swamy, A study of multiplicative watermark detection in the contourlet domain using alpha-stable distributions. IEEE Trans. Image Process. 23(10), 4348–4360 (2014)

    Article  MathSciNet  Google Scholar 

  30. H. Sadreazami, M.O. Ahmad, M.N.S. Swamy, A robust multiplicative watermark detector for color images in sparse domain. IEEE Trans. Circuits Syst. II Express Briefs 62(12), 1159–1163 (2015)

    Article  Google Scholar 

  31. H. Sadreazami, M.O. Ahmad, M.N.S. Swamy, Multiplicative watermark decoder in contourlet domain using the normal inverse Gaussian distribution. IEEE Trans. Multimed. 18(2), 196–207 (2016)

    Article  Google Scholar 

  32. H. Sadreazami, M. Amini, A robust image watermarking scheme using local statistical distribution in the Contourlet domain. IEEE Trans. Circuits Syst. II Express Briefs 66(1), 151–155 (2019)

    Article  Google Scholar 

  33. K.C. Sharman, G.D. McClurkin, Genetic algorithms for maximum likelihood parameter estimation, in International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Glasgow, UK (1989), pp. 1520–6149

  34. X.Y. Wang, W.Y. Li, H.Y. Yang, P. Wang, Y.W. Li, Quaternion polar complex exponential transform for invariant color image description. Appl. Math. Comput. 256, 951–967 (2015)

    MathSciNet  MATH  Google Scholar 

  35. J. Wang, G. Liu, Y. Dai, J. Sun, Z. Wang, S. Lian, Locally optimum detection for Barni’s multiplicative watermarking in DWT domain. Signal Process. 88(1), 117–130 (2008)

    Article  Google Scholar 

  36. P.T. Yap, X. Jiang, A.C. Kot, Two-dimensional polar harmonic transforms for invariant image representation. IEEE Trans. Pattern Anal. Mach. Intell. 32(7), 1259–1270 (2010)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported partially by the National Natural Science Foundation of China (Nos. 61472171 and 61701212), China Postdoctoral Science Foundation (Nos. 2017M621135 and 2018T110220), Key Scientific Research Project of Liaoning Provincial Education Department (LZ2019001), 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, China

    Panpan Niu, Li Wang, Jialin Tian, Siyu Zhang & Xiangyang Wang

Authors
  1. Panpan Niu
    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. Jialin Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Siyu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xiangyang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiangyang Wang.

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

Niu, P., Wang, L., Tian, J. et al. A Statistical Color Image Watermarking Scheme Using Local QPCET and Cauchy–Rayleigh Distribution. Circuits Syst Signal Process 40, 4516–4545 (2021). https://doi.org/10.1007/s00034-021-01678-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-021-01678-w

Keywords

Search

Navigation