Imperceptible watermark for a game-theoretic watermarking system

  • S. Prasanth Vaidya
  • P. V. S. S. R. Chandra Mouli
  • K. C. SantoshEmail author
Original Article


This paper advances the game-theoretic approaches to design a robust watermarking scheme for embedding watermark in an image in discrete wavelet transform (DWT) domain. A reliable architecture for imperceptible watermarking system that provides an optimal solution for decision makers is proposed. Using iterative Elimination of strictly dominant strategies (IESDS), an optimal solution is computed to attain the best trade-off between embedding and extraction of the watermark. Under different attacks and strategies, embedder could be able to obtain the best strategy. Experimental results attested the fact that the proposed approach is robust to various signal and image processing attacks.


Game theory Watermarking Discrete wavelet transform Iterative elimination of strictly dominant strategies 


  1. 1.
    Agarwal C, Mishra A, Sharma A (2015) A novel gray-scale image watermarking using hybrid fuzzy-bpn architecture. Egypt Inf J 16(1):83–102CrossRefGoogle Scholar
  2. 2.
    Ansari IA, Pant M, Ahn CW (2016) Svd based fragile watermarking scheme for tamper localization and self-recovery. Int J Mach Learn Cybernet 7(6):1225–1239CrossRefGoogle Scholar
  3. 3.
    Barron EN (2013) Game theory: an introduction, vol. 2. WileyGoogle Scholar
  4. 4.
    Billings SA (2013) Nonlinear system identification: NARMAX methods in the time, frequency, and spatio-temporal domains. WileyGoogle Scholar
  5. 5.
    Chen YC, Van Long N, Luo X (2007) Iterated strict dominance in general games. Games Econ Behav 61(2):299–315MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Cox I, Miller M, Bloom J, Fridrich J, Kalker T (2007) Digital watermarking and steganography. Morgan KaufmannGoogle Scholar
  7. 7.
    Cox IJ, Kilian J, Leighton T, Shamoon T (1996) Secure spread spectrum watermarking for images, audio and video. In: Image Processing, 1996. Proceedings., International Conference on. vol. 3, pp 243–246. IEEEGoogle Scholar
  8. 8.
    Goteti AK, Moulin P (2004) Two private, perceptual data-hiding games. In: Acoustics, Speech, and Signal Processing, 2004. Proceedings.(ICASSP’04). IEEE International Conference on. vol. 3, pp iii–373. IEEEGoogle Scholar
  9. 9.
    Hofbauer J, Weibull JW (1996) Evolutionary selection against dominated strategies. J Econ Theory 71(2):558–573MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Huang BB, Tang SX (2006) A contrast-sensitive visible watermarking scheme. IEEE Multimed 13(2):60–66CrossRefGoogle Scholar
  11. 11.
    Huynh-Thu Q, Ghanbari M (2008) Scope of validity of psnr in image/video quality assessment. Electron Lett 44(13):800–801CrossRefGoogle Scholar
  12. 12.
    Kundur D, Lin CY, Macq B, Yu HH (2004) Special issue on enabling security technologies for digital rights management. Proc IEEE 92(6):879–882CrossRefGoogle Scholar
  13. 13.
    Mehta R, Rajpal N, Vishwakarma VP (2015) A robust and efficient image watermarking scheme based on lagrangian svr and lifting wavelet transform. Int J Mach Learn Cybern 1–17Google Scholar
  14. 14.
    Mehta R, Rajpal N, Vishwakarma VP (2015) Robust image watermarking scheme in lifting wavelet domain using ga-lsvr hybridization. Int J Mach Learn Cybern 1–17Google Scholar
  15. 15.
    Mohamed TM, Elmahdy HN, Onsi HM (2011) Efficient watermark detection by using the longest common substring technique. Egypt Inf J 12(2):115–123CrossRefGoogle Scholar
  16. 16.
    Mohanty SP, Ramakrishnan KR, Kankanhalli MS (2000) A dct domain visible watermarking technique for images. In: 2000 IEEE International Conference on Multimedia and Expo, 2000. ICME 2000. vol 2, pp 1029–1032. IEEEGoogle Scholar
  17. 17.
    Moon HS, You T, Sohn MH, Kim HS, Jang DS (2007) Expert system for low frequency adaptive image watermarking: using psychological experiments on human image perception. Expert Syst Appl 32(2):674–686CrossRefGoogle Scholar
  18. 18.
    Moulin P (2001) The role of information theory in watermarking and its application to image watermarking. Sig Process 81(6):1121–1139CrossRefzbMATHGoogle Scholar
  19. 19.
    Moulin P, Ivanovic A, Ivanovic A (2001) Game-theoretic analysis of watermark detection. ICIP (3):975–978. CiteseerGoogle Scholar
  20. 20.
    Osborne MJ (2004) An introduction to game theory, vol 3. Oxford University Press, New YorkGoogle Scholar
  21. 21.
    Pal SK, Sarma SS (2012) Graph coloring approach for hiding of information. Proc Technol 4:272–277CrossRefGoogle Scholar
  22. 22.
    Tadelis S (2013) Game theory: an introduction. Princeton University PressGoogle Scholar
  23. 23.
    Tian L, Zheng N, Xue J, Li C, Wang X (2011) An integrated visual saliency-based watermarking approach for synchronous image authentication and copyright protection. Sig Process Image Commun 26(8):427–437CrossRefGoogle Scholar
  24. 24.
    Tsai MJ (2009) A visible watermarking algorithm based on the content and contrast aware (cocoa) technique. J Vis Commun Image Represent 20(5):323–338MathSciNetCrossRefGoogle Scholar
  25. 25.
    Tsai MJ, Liu J, Wang CS (2011) A game-theoretic framework for the security system of visible watermarking. Expert Syst Appl 38(5):5748–5754CrossRefGoogle Scholar
  26. 26.
    Vaidya SP, Mouli PC (2015) Adaptive digital watermarking for copyright protection of digital images in wavelet domain. Proc Comput Sci 58:233–240CrossRefGoogle Scholar
  27. 27.
    Vorobeychik Y, Wellman MP, Singh S (2007) Learning payoff functions in infinite games. Mach Learn 67(1–2):145–168CrossRefGoogle Scholar
  28. 28.
    Wang XY, Miao EN, Yang HY (2012) A new svm-based image watermarking using Gaussian–Hermite moments. Appl Soft Comput 12(2):887–903CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Computing Science and EngineeringVIT UniversityVelloreIndia
  2. 2.Department of Computer ScienceThe University of South DakotaVermillionUSA

Personalised recommendations