Multimedia Tools and Applications

, Volume 75, Issue 15, pp 9371–9394 | Cite as

Lagrangian twin support vector regression and genetic algorithm based robust grayscale image watermarking

  • Ashok Kumar Yadav
  • Rajesh Mehta
  • Raj Kumar
  • Virendra P. Vishwakarma


A novel imperceptible, secure and robust grayscale image watermarking scheme using Lagrangian twin support vector regression (LTSVR) and genetic algorithm (GA) in discrete Cosine transform (DCT) domain is presented in this manuscript. Fuzzy entropy is used to select the relevant blocks for embedding the watermark. Selected number of blocks based on fuzzy entropy not only reduces the dimensionality of the watermarking problem but also discards redundant and irrelevant blocks. Significant DCT coefficients having high energy compaction property of each selected block are used to form the image dataset to train LTSVR to find the non-linear regression function between the input and target vector. The adaptive watermark strength, different for each selected block, is decided by the GA process based on well defined fitness function. Due to good learning capability of image characteristics and high generalization property of LTSVR, watermark is successfully extracted from the watermarked images against a series of image processing operations. From the experimental and comparison results performed on standard and real world images, it is inferred that the proposed method is suitable for copyright protection applications where high degree of robustness is desirable.


DCT Genetic algorithm Lagrangian Twin SVR Digital Image Watermarking 


  1. 1.
    Agarwal C, Mishra A, Sharma A (2013) Gray- scale image watermarking using GA-BPN hybrid network. J Vis Commun Image Represent 24(8):1135–1146CrossRefGoogle Scholar
  2. 2.
    Ali M, Ahn CW, Pant M (2014) A robust image watermarking technique using SVD and differential evolution in DCT domain. Optik 125(1):428–434CrossRefGoogle Scholar
  3. 3.
    Aslantas V (2008) A singular value decomposition based image watermarking using genetic algorithm. Int J Electron Commun 62(5):386–394CrossRefGoogle Scholar
  4. 4.
    Avci E, Avci D (2009) An expert system based on fuzzy entropy for automatic threshold selection in image processing. Expert Syst Appl 36:3077–3085CrossRefGoogle Scholar
  5. 5.
    Balasundaram S, Tanveer M (2013) On Lagrangian twin support vector regression. Naural Comput Appl 22:S257–S267CrossRefGoogle Scholar
  6. 6.
    Chu WC (2003) DCT based image watermarking using subsampling. IEEE Trans Multimedia 5(1):34–38CrossRefGoogle Scholar
  7. 7.
    Cox IJ, Kilian J, Leighton FT, Shamoon T (1997) Secure spread spectrum watermarking for multimedia. IEEE Trans Image Process 12(6):1673–1687CrossRefGoogle Scholar
  8. 8.
    Eyadat M, Vasikarla S (2005) Performance evaluation of an incorporated DCT block-based watermarking algorithm with human visual system model. Pattern Recogn Lett 26(11):1405–1411CrossRefGoogle Scholar
  9. 9.
    Huang H-C, Chu C-M, Pan J-S (2009) The optimized copyright protection scheme with genetic watermarking. Soft Comput 13:333–343CrossRefGoogle Scholar
  10. 10.
    Klir GJ, Yuan B (1995) Fuzzy sets and Fuzzy logic: theory and applications. Prentice Hall, New Jersey, MsmMATHGoogle Scholar
  11. 11.
    Kumar R, Das RR, Mishra VN, Dwivedi R (2011) Fuzzy entropy based neuro-wavelet identifier-cum-quantifier for discrimination of gases/odors. IEEE Sensors J 11(7):1548–1555CrossRefGoogle Scholar
  12. 12.
    Lee HM, Chen CM, Chen JM, Jou YL (2001) An efficient fuzzy classifier with feature selection based on fuzzy entropy. IEEE Trans Syst Man Cybern 31(3):426–432CrossRefGoogle Scholar
  13. 13.
    Lian SU, Hong MA, Shifu T (2006) Adaptive image digital watermarking with DCT and FCM. Wuhan Univ J Nat Sci 11(6):1657–1660CrossRefMATHGoogle Scholar
  14. 14.
    Maity SP, Maity S, Sil J, Delpha C (2013) Collusion resilient spread spectrum watermarking in M-band wavelet using GA-fuzzy hybridization. J Syst Softw 86(1):47–59CrossRefGoogle Scholar
  15. 15.
    Mangasarian OL (1994) Nonlinear programming. SIAM, PhiladelphiaCrossRefMATHGoogle Scholar
  16. 16.
    Mangasarian OL, Musciant DR (2001) Lagrangian support vector machines. J Mach learn Res 1:161–177MathSciNetMATHGoogle Scholar
  17. 17.
    Mangasarian OL, Musicant DR (2001) Lagrangian support vector machines. J Mach Learn 1:161–177MathSciNetMATHGoogle Scholar
  18. 18.
    Mehta R, Rajpal N, Vishwakarma VP (2015) Robust image watermarking scheme in lifting wavelet domain using GA-LSVR hybridization. Int J Mach Learn Cybern. doi: 10.1007/s-13042-015-0329-6, Springer VerlagGoogle Scholar
  19. 19.
    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. doi: 10.1007/s-13042-015-0331-z, Springer VerlagGoogle Scholar
  20. 20.
    Mehta R, Rajpal N, Vishwakarma VP (2015) Gray scale image watermarking using fuzzy entropy and Lagrangian support vector regression in DCT domain. Int J Appl Pattern Recog 2(3):255–279CrossRefGoogle Scholar
  21. 21.
    Meng F, Pei Z, Wang J (2008) A novel blind image watermarking scheme based on support vector machine in DCT domain. In: IEEE international Conference on Computational Intelligence and Security, pp 16–20Google Scholar
  22. 22.
    Murphy PM, Aha DW (1992) UCI repository of machine learning databases. University of California: Irvine,
  23. 23.
    Nikolaidis N, Pitas I (1998) Robust image watermarking in the spatial domain. Signal Process 66(3):385–403CrossRefMATHGoogle Scholar
  24. 24.
    Peng H, Wang J, Wang W (2010) Image watermarking method in multiwavelet domain based on support vector machines. J System Softw 83(9):1470–1477MathSciNetCrossRefGoogle Scholar
  25. 25.
    Petitcolas FAP (2000) Watermarking schemes evaluation. IEEE Signal Process Mag 2000:58–64CrossRefGoogle Scholar
  26. 26.
    Piao CR, Beack S, Woo D-M, Han S-S (2006) A blind watermarking algorithm based on HVS and RBF neural network for digital image. Lect Notes Comput Sci 4221:493–496CrossRefGoogle Scholar
  27. 27.
    Shen R, Fu Y, Lu H (2005) A novel image watermarking scheme based on support vector regression. J Syst Softw 78(1):1–8CrossRefGoogle Scholar
  28. 28.
    Tao H, Zain JM, Ahmed N, Hingwu Q (2010) An implementation of digital image watermarking based on particle swarm optimization. Commun Comput Inf Sci 87:314–320CrossRefGoogle Scholar
  29. 29.
    Wu L, Deng W, Zhang J, He D (2009) Arnold transformation algorithm and anti Arnold transformation algorithm. In: Proc. of 1st International Conference on Information Science and Engineering (ICISE), pp 1164–1167Google Scholar
  30. 30.
    Xianghong T, Shuqin X, Qiliang Li (2003) Watermarking for the digital images based on model of human perception. In: IEEE International Conference on Neural Networks & Signal Processing, pp. 1509–1512.Google Scholar
  31. 31.
    Yadav A, Mehta R, Kumar R (2015) Gray scale image watermarking using fuzzy entropy and lagrangian twin SVR in DCT domain. In: IEEE International Conference on Contemporary Computing, pp. 19–24. doi: 10.1109/IC3.2015.7346646

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Computer Science and Engineering, University Institute of Engineering and TechnologyMaharishi Dayanand UniversityRohtakIndia
  2. 2.Amity School of Engineering and TechnologyNew DelhiIndia
  3. 3.University School of Information and Communication Technology, Guru Gobind Singh Indraprastha UniversityNew DelhiIndia

Personalised recommendations