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Statistical image watermark decoder by modeling local NSST-PHFMs magnitudes with Morgenstern-type bivariate-generalized exponential distribution

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Abstract

For any image watermarking system, there are three indispensable and mutually constrained requirements, namely robustness, invisibility, and payload. Recently, to achieve the trade-off among three requirements, statistical watermarking schemes have gained a lot of attention. Despite their powerfulness and effectiveness, most existing statistical image watermarking approaches bear a number of drawbacks, in particular: (i) They all employ directly transform coefficients, which are always fragile to some attacks, for watermark embedding and statistical modeling; (ii) The adopted statistical model cannot capture accurately the marginal distributions of the transform coefficients. Moreover, the significant coefficients dependencies are ignored. To deal with these issues, this paper introduces a new statistical image watermarking method in non-subsampled shearlet transform (NSST)-polar harmonic Fourier moments (PHFMs) magnitude domain, wherein a PDF based on the bivariate-generalized exponential distribution (MTBGED) is employed, in view of the fact that this PDF provides a better statistical match to the empirical PDF of the robust NSST-PHFMs magnitudes of the image. In watermark embedding, we first perform the NSST on the carrier image. We then select the maximum energy subband and divide it into blocks and compute the PHFMs for each block. Finally, we embed watermark in NSST-PHFMs magnitudes using multiplicative approach. In the decoding process, we first analyze the robustness and statistical characteristics of local NSST-PHFMs magnitudes. We then observe that, with a small number of parameters, the new MTBGED model can capture accurately the statistical distributions of the robust NSST-PHFMs magnitudes of the image. Meanwhile, statistical model parameters can be estimated effectively by using the method of logarithmic cumulants (MoLC). Motivated by our modeling results, we finally develop a new statistical image watermark decoder using the MTBGED distribution and maximum likelihood (ML) decision rule. Experimental results on extensive test images demonstrate that the proposed blind watermark decoder provides a performance better than that of most of the state-of-the-art statistical methods and deep learning approaches recently proposed in the literature.

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References

  1. Singh AK (2020) Data hiding: current trends, innovation and potential challenges. ACM Trans Multimed Comput Commun Appl 16(3s):101

    Article  Google Scholar 

  2. Quan Y, Teng H, Chen Y (2021) Watermarking deep neural networks in image processing. IEEE Trans Neural Netw Learn Syst 32(5):1852–1865

    Article  Google Scholar 

  3. Amini M, Ahmad MO, Swamy MNS (2018) A robust multibit multiplicative watermark decoder using vector-based hidden Markov model in wavelet domain. IEEE Trans Circuits Syst Video Technol 28(2):402–413

    Article  Google Scholar 

  4. Zebbiche K, Khelifi F, Loukhaoukha K (2018) Robust additive watermarking in the DTCWT domain based on perceptual masking. Multimed Tools Appl 77(16):1–24

    Article  Google Scholar 

  5. Niu PP, Shen X, Wen TT, Yang HY, Wang XY (2020) Blind image watermark decoder in UDTCWT domain using Weibull mixtures-based vector HMT. IEEE Access 8:46624–46641

    Article  Google Scholar 

  6. Niu PP, Wang XY, Yang HY (2020) A blind watermark algorithm in SWT domain using bivariate generalized Gaussian distributions. Multimed Tools Application 79(19–20):13351–13377

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. Amini M, Sadreazami H, Ahmad MO (2019) A channel-dependent statistical watermark detector for color images. IEEE Trans Multimed 21(1):65–73

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  12. Wang XY, Wen TT, Shen X, Niu PP, Yang HY (2020) A new watermark decoder in DNST domain using singular values and Gaussian-Cauchy mixture-based Vector HMT. Inf Sci 535:81–106

    Article  MathSciNet  Google Scholar 

  13. Ahmaderaghi B, Kurugollu F, Rincon JMD, Bouridane A (2018) Blind image watermark detection algorithm based on discrete shearlet transform using statistical decision theory. IEEE Trans Comput Imag 4(1):46–59

    Article  MathSciNet  Google Scholar 

  14. Liu J, Rao Y (2019) Optimization-based image watermarking algorithm using a maximum-likelihood decoding scheme in the complex wavelet domain. KSII Trans Internet Inf Syst 13(1):452–472

    Google Scholar 

  15. Barazandeh M, Amirmazlaghani M (2016) A new statistical detector for additive image watermarking based on dual-tree complex wavelet transform. In: The second international conference of signal processing and intelligent systems (ICSPIS), Tehran, Iran. pp 1–5

  16. Bhinder P, Singh K, Jindal N (2018) Image-adaptive watermarking using maximum likelihood decoder for medical images. Multimed Tools Appl 77(8):10303–10328

    Article  Google Scholar 

  17. Sadreazami H, Ahmad MO, Swamy MNS (2016) Multiplicative watermark decoder in contourlet domain using the normal inverse Gaussian distribution. IEEE Trans Multimed 18(2):196–207

    Article  Google Scholar 

  18. Niu PP, Shen X, Song YF, Liu YN, Wang XY (2020) Locally optimum watermark decoder in NSST domain using RSS-based Cauchy distribution. Multimed Tools Appl 79:33071–33101

    Article  Google Scholar 

  19. Wang XY, Zhang SY, Wang L, Yang HY, Niu PP (2019) Locally optimum image watermark decoder by modeling NSCT domain difference coefficients with vector based Cauchy distribution. J Vis Commun Image Represent 62:309–329

    Article  Google Scholar 

  20. Wang XY, Tian J, Tian JL, Niu PP, Yang HY (2021) Statistical image watermarking using local RHFMs magnitudes and beta exponential distribution. J Vis Commun Image Represent 77:103123

    Article  Google Scholar 

  21. Amirmazlaghani M (2019) Heteroscedastic watermark detector in the contourlet domain. IET Comput Vision 13(3):249–260

    Article  MathSciNet  Google Scholar 

  22. Khawne A, Attachoo B, Hamamoto K (2014) Optimum watermark detection of ultrasonic echo medical images. IEEJ Trans Electr Electron Eng 10(2):149–156

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  24. Li L, Li X, Qiao T, Xu X, Zhang S (2018) A novel framework of robust video watermarking based on statistical model. In: The 4th international conference on cloud computing and security (ICCCS), Haikou, China. pp 160–172

  25. Wang XY, Wen TT, Wang L, Niu PP, Yang HY (2020) Contourlet domain locally optimum image watermark decoder using Cauchy mixtures based vector HMT model. Signal Process Image Commun 88:115972

    Article  Google Scholar 

  26. Fang H, Chen D, Huang Q, Zhang J, Ma Z (2021) Deep template-based watermarking. IEEE Trans Circuits Syst Video Technol 31(4):1436–1451

    Article  Google Scholar 

  27. Hatoum MW, Couchot JF, Couturier R (2021) Using deep learning for image watermarking attack. Signal Process Image Commun 90:116019

    Article  Google Scholar 

  28. Zhong X, Huang PC, Mastorakis S, Frank YS (2021) An automated and robust image watermarking scheme based on deep neural networks. IEEE Trans on Multimedia 23:1951–1961

    Article  Google Scholar 

  29. Easley G, Labate D, Lim Q (2018) Sparse directional image representations using the discrete shearlet transform. Appl Comput Harmon Anal 25(1):25–46

    Article  MathSciNet  MATH  Google Scholar 

  30. Wang XY, Liu YN, Xu H, Wang AL, Yang HY (2016) Blind optimum detector for robust image watermarking in nonsubsampled shearlet domain. Inf Sci 372:634–354

    Article  Google Scholar 

  31. Ren HP, Ping ZL, Bo WRG (2003) Multidistortion-invariant image recognition with radial harmonic Fourier moments. J Opt Soc Am 20(4):631–637

    Article  MathSciNet  Google Scholar 

  32. Wang CP, Wang XY, Xia ZQ, Ma B, Shi YQ (2019) Image description with polar harmonic Fourier moments. IEEE Trans Circuits Syst Video Technol 30(12):4440–4452

    Article  Google Scholar 

  33. Tahmasebi S, Jafari AA (2015) Concomitants of order statistics and record values from Morgenstern type bivariate-generalized exponential distribution. Bulletin Malaysian Math Sci Soc 38(4):1411–1423

    Article  MathSciNet  MATH  Google Scholar 

  34. Gupta RD, Kundu D (1999) Generalized exponential distributions. Australian New Zealand J Stat 41(2):173–188

    Article  MathSciNet  MATH  Google Scholar 

  35. Krylov VA, Moser G, Serpico SB, Zerubia J (2013) On the method of logarithmic cumulants for parametric probability density function estimation. IEEE Trans on Image Process 22(10):3791–3806

    Article  MathSciNet  MATH  Google Scholar 

  36. Zong T, Xiang Y, Natgunanathan I (2015) Robust histogram shape-based method for image watermarking. IEEE Trans Circuits Syst Video Technol 25(5):717–729

    Article  Google Scholar 

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Acknowledgements

This work was supported partially by the National Natural Science Foundation of China (Nos. 61472171 and 61701212), Scientific Research Project of Liaoning Provincial Education Department (No. LJKZ0985), and Natural Science Foundation of Liaoning Province (No. 2019-ZD-0468).

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Authors and Affiliations

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

    Xiangyang Wang, Yupan Lin, Yixuan Shen, Panpan Niu & Hongying Yang

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  1. Xiangyang Wang
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  2. Yupan Lin
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  3. Yixuan Shen
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  4. Panpan Niu
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  5. Hongying Yang
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Correspondence to Xiangyang Wang or Hongying Yang.

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Wang, X., Lin, Y., Shen, Y. et al. Statistical image watermark decoder by modeling local NSST-PHFMs magnitudes with Morgenstern-type bivariate-generalized exponential distribution. Pattern Anal Applic 26, 255–288 (2023). https://doi.org/10.1007/s10044-022-01105-z

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  • DOI: https://doi.org/10.1007/s10044-022-01105-z

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