A blind and robust color images watermarking method based on block transform and secured by modified 3-dimensional Hénon map

  • Milad Yousefi ValandarEmail author
  • Milad Jafari Barani
  • Peyman Ayubi


This paper proposes a blind and robust color image watermarking method based on a new three-dimensional Hénon chaotic map and uses integer wavelet transform, discrete wavelet transform and contourlet transform in embedding and extracting processes. In the presented approach, color images are divided into \(4\times 4\) main nonoverlapping parts, and one of the transforms is applied to these parts. Then the low–low sub-band of transform is selected. The suggested map is used to find \(2\times 2\) blocks in the embedding process. The bits of watermark are embedded in the parts of images to increase the robustness of the proposed watermarking scheme. To improve the quality of the final watermark, the suggested technique uses a correction process in the extracting process. In this paper, the bifurcation diagram, Lyapunov exponent, cobweb plot and trajectory diagram are used to show the chaotic behavior of the proposed map. Based on DIEHARD, ENT and NIST test suites, the suggested map can be used as a pseudo-random number generator. The simulation results show that the proposed watermarking algorithm is robust against most image processing attacks like salt & pepper, cropping, low-pass filter, wiener filter, blurring, etc. The comparison results between the suggested watermarking scheme, and some similar methods show that the presented technique has good performance, imperceptibility, acceptable robustness and outperforms most related methods.


Watermarking Color image 3D Hénon chaotic map Integer wavelet transform Discrete wavelet transform Contourlet transform 



There is no source of funding for this paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


  1. Abdallah HA, Faragallah OS, Elsayed HS, Shaalan AA, El-samie FEA et al (2016) Robust image watermarking method using homomorphic block-based KLT. Optik Int J Light Electron Opt 127(4):2374–2381CrossRefGoogle Scholar
  2. Abdelhakim AM, Saad M, Sayed M, Saleh H (2018) Optimized SVD-based robust watermarking in the fractional Fourier domain. Multimed Tools Appl 77:27895–27917CrossRefGoogle Scholar
  3. Ali M, Ahn CW (2014) An optimized watermarking technique based on self-adaptive DE in DWT–SVD transform domain. Signal Process 94:545–556CrossRefGoogle Scholar
  4. Aslantas V (2008) A singular-value decomposition-based image watermarking using genetic algorithm. AEU Int J Electron Commun 62(5):386–394CrossRefGoogle Scholar
  5. Azar AT, Vaidyanathan S, Huynh-Thu Q, Ghanbari M (2015) Chaos modeling and control systems design. Springer, BerlinCrossRefGoogle Scholar
  6. Barani MJ, Ayubi P, Jalili F, Valandar MY, Azariyun E (2015) Image forgery detection in contourlet transform domain based on new chaotic cellular automata. Secur Commun Netw 8(18):4343–4361CrossRefGoogle Scholar
  7. Barani MJ, Valandar MY, Ayubi P (2019) A new digital image tamper detection algorithm based on integer wavelet transform and secured by encrypted authentication sequence with 3D quantum map. Optik 187:205–222CrossRefGoogle Scholar
  8. Basener WF (2006) Topology and its applications. Wiley, HobokenzbMATHCrossRefGoogle Scholar
  9. Benedicks M, Carleson L (1991) The dynamics of the Hénon map. Ann Math 133(1):73–169MathSciNetzbMATHCrossRefGoogle Scholar
  10. Chang Y-J, Wang R-Z, Lin J-C (2008) A sharing-based fragile watermarking method for authentication and self-recovery of image tampering. EURASIP J Adv Signal Process 2008:1–17 zbMATHCrossRefGoogle Scholar
  11. Chen S-T, Wu G-D, Huang H-N (2010) Wavelet-domain audio watermarking scheme using optimisation-based quantisation. IET Signal Process 4(6):720–727CrossRefGoogle Scholar
  12. Dadkhah S, Manaf AA, Hori Y, Hassanien AE, Sadeghi S (2014) An effective svd-based image tampering detection and self-recovery using active watermarking. Sig Process Image Commun 29(10):1197–1210CrossRefGoogle Scholar
  13. Elaydi SN (1999) Discrete chaos. Chapman and Hall/CRC, Boca RatonzbMATHGoogle Scholar
  14. Farri E, Ayubi P (2018) A blind and robust video watermarking based on IWT and new 3D generalized chaotic sine map. Nonlinear Dyn 93:1875–1897 CrossRefGoogle Scholar
  15. Giri KJ, Bashir R (2018) A block based watermarking approach for color images using discrete wavelet transformation. Int J Inf Technol 10(2):139–146Google Scholar
  16. Golea NEH, Seghir R, Benzid R (2010) A bind rgb color image watermarking based on singular value decomposition. In: IEEE/ACS international conference on computer systems and applications (AICCSA). IEEE, pp 1–5Google Scholar
  17. Gu Q, Gao T (2013) A novel reversible robust watermarking algorithm based on chaotic system. Digit Signal Process 23(1):213–217MathSciNetCrossRefGoogle Scholar
  18. Haddada LR, Dorizzi B, Amara NEB (2017) A combined watermarking approach for securing biometric data. Signal Process Image Commun 55:23–31CrossRefGoogle Scholar
  19. Haghighi BB, Taherinia AH, Harati A (2018) TRLH: fragile and blind dual watermarking for image tamper detection and self-recovery based on lifting wavelet transform and halftoning technique. J Vis Commun Image Represent 50:49–64CrossRefGoogle Scholar
  20. Hasselblatt B, Katok A (2003) A first course in dynamics: with a panorama of recent developments. Cambridge University Press, CambridgezbMATHCrossRefGoogle Scholar
  21. Hemamalini B, Nagarajan V (2018) Wavelet transform and pixel strength-based robust watermarking using dragonflyoptimization. Multimed Tools Appl 1–20 Google Scholar
  22. Henk B, Takens F (2010) Dynamical systems and chaos, vol 172. Springer, BerlinzbMATHGoogle Scholar
  23. Hénon M (1976) A two-dimensional mapping with a strange attractor, the theory of chaotic attractors. Springer, New York, pp 94–102Google Scholar
  24. Hua C-H, Tu NA, Hur T, Bang J, Kim D, Amin MB, Kang BH, Seung H, Lee S et al (2018) Selective bit embedding scheme for robust blind color image watermarking. Inf Sci 426:1–18CrossRefGoogle Scholar
  25. Huynh-Thu Q, Ghanbari M (2008) Scope of validity of psnr in image/video quality assessment. Electron Lett 44(13):800–801CrossRefGoogle Scholar
  26. Irani BY, Ayubi P, Jabalkandi FA, Valandar MY, Barani MJ (2019) Digital image scrambling based on a new one-dimensional coupled Sine map. Nonlinear Dyn 97:2693–2721CrossRefGoogle Scholar
  27. Jia S-L (2014) A novel blind color images watermarking based on SVD. Optik Int J Light Electron Opt 125(12):2868–2874CrossRefGoogle Scholar
  28. Kalra GS, Talwar R, Sadawarti H (2015) Adaptive digital image watermarking for color images in frequency domain. Multimed Tools Appl 74(17):6849–6869CrossRefGoogle Scholar
  29. Keshavarzian R, Aghagolzadeh A (2016) ROI based robust and secure image watermarking using DWT and Arnold map. AEU Int J Electron Commun 70(3):278–288CrossRefGoogle Scholar
  30. Kumar GD, Teja DP, Reddy SS, Sasikaladevi N (2017) An efficient watermarking technique for biometric images. Procedia Comput Sci 115:423–430CrossRefGoogle Scholar
  31. Lai C-C, Tsai C-C (2010) Digital image watermarking using discrete wavelet transform and singular value decomposition. IEEE Trans Instrum Meas 59(11):3060–3063CrossRefGoogle Scholar
  32. Laouamer L, AlShaikh M, Nana L, Pascu AC (2015) Robust watermarking scheme and tamper detection based on threshold versus intensity. J Innov Digit Ecosyst 2(1):1–12Google Scholar
  33. Leung HY, Cheng LM (2011) Robust watermarking scheme using wave atoms. EURASIP J Adv Signal Process 2011(1):184817CrossRefGoogle Scholar
  34. Li C, Wang Y, Ma B, Zhang Z (2013) Multi-block dependency based fragile watermarking scheme for fingerprint images protection. Multimed Tools Appl 64(3):757–776CrossRefGoogle Scholar
  35. Li J, Lin Q, Yu C, Ren X, Li P (2018a) A QDCT- and SVD-based color image watermarking scheme using an optimized encrypted binary computer-generated hologram. Soft Comput 22(1):47–65CrossRefGoogle Scholar
  36. Li J, Yu C, Gupta B, Ren X (2018b) Color image watermarking scheme based on quaternion Hadamard transform and Schur decomposition. Multimed Tools Appl 77(4):4545–4561CrossRefGoogle Scholar
  37. Liu N, Li H, Dai H, Guo D, Chen D (2015) Robust blind image watermarking based on chaotic mixtures. Nonlinear Dyn 80(3):1329–1355CrossRefGoogle Scholar
  38. Loan NA, Hurrah NN, Parah SA, Lee JW, Sheikh JA, Bhat GM (2018) Secure and robust digital image watermarking using coefficient differencing and chaotic encryption. IEEE Access 6:19876–19897CrossRefGoogle Scholar
  39. Loukhaoukha K, Nabti M, Zebbiche K (2014) A robust svd-based image watermarking using a multi-objective particle swarm optimization. Opto-Electron Rev 22(1):45–54CrossRefGoogle Scholar
  40. Lu Z-M, Xu D-G, Sun S-H (2005) Multipurpose image watermarking algorithm based on multistage vector quantization. IEEE Trans Image Process 14(6):822–831CrossRefGoogle Scholar
  41. Luo L, Chen Z, Chen M, Zeng X, Xiong Z (2010) Reversible image watermarking using interpolation technique. IEEE Trans Inf Forensics Secur 5(1):187–193CrossRefGoogle Scholar
  42. Lv X, Liao X, Yang B (2018) A novel pseudo-random number generator from coupled map lattice with time-varying delay. Nonlinear Dyn 94(1):325–341CrossRefGoogle Scholar
  43. Marsaglia G (1998) Diehard test suite. Last visited 8 (01)
  44. Michel H (1969) Numerical study of quadratic area-preserving mappings. Q Appl Math 27(3):291–312MathSciNetzbMATHCrossRefGoogle Scholar
  45. Moeinaddini E (2019) Selecting optimal blocks for image watermarking using entropy and distinct discrete firefly algorithm. Soft Comput 23(19):9685–9699CrossRefGoogle Scholar
  46. Mohananthini N, Yamuna G (2016) Comparison of multiple watermarking techniques using genetic algorithms. J Electr Syst Inf Technol 3(1):68–80Google Scholar
  47. Moosazadeh M, Ekbatanifard G (2017) An improved robust image watermarking method using DCT and YCoCg-R color space. Optik Int J Light Electron Opt 140:975–988CrossRefGoogle Scholar
  48. Najafia E, Loukhaoukha K (2019) Hybrid secure and robust image watermarking scheme based on SVD and sharp frequency localized contourlet transform. J Inf Secur Appl 44:144–156Google Scholar
  49. Najih A, Al-Haddad S, Ramli AR, Hashim S, Nematollahi MA (2017) Digital image watermarking based on angle quantization in discrete contourlet transform. J King Saud Univ Comput Inf Sci 29(3):288–294Google Scholar
  50. Otto PH, Jürgens H, Saupe D (2006) Chaos and fractals: new frontiers of science. Springer, BerlinzbMATHGoogle Scholar
  51. Pan-Pan N, Xiang-Yang W, Yu-Nan L, Hong-Ying Y (2017) A robust color image watermarking using local invariant significant bitplane histogram. Multimed Tools Appl 76(3):3403–3433CrossRefGoogle Scholar
  52. Parekh M, Bidani S, Santhi V (2018) Spatial domain blind watermarking for digital images. In: Progress in computing, analytics and networking. Springer, pp 519–527Google Scholar
  53. Ponomarenko N, Jin L, Ieremeiev O, Lukin V, Egiazarian K, Astola J, Vozel B, Chehdi K, Carli M, Battisti F et al (2015) Image database TID2013: peculiarities, results and perspectives. Sig Process Image Commun 30:57–77CrossRefGoogle Scholar
  54. Richter H (2002) The generalized Henon maps: examples for higher-dimensional chaos. Int J Bifurc Chaos 12(06):1371–1384zbMATHCrossRefGoogle Scholar
  55. Roy S, Pal AK (2017) A blind DCT based color watermarking algorithm for embedding multiple watermarks. AEU Int J Electron Commun 72:149–161CrossRefGoogle Scholar
  56. Roy S, Pal AK (2018) An svd based location specific robust color image watermarking scheme using RDWT and Arnold scrambling. Wirel Pers Commun 98(2):2223–2250CrossRefGoogle Scholar
  57. Rukhin A, Soto J, Nechvatal J, Smid M, Barker E (2001) A statistical test suite for random and pseudorandom number generators for cryptographic applications. Technical Report, Booz-Allen and Hamilton Inc Mclean VaGoogle Scholar
  58. Sachnev V, Kim HJ, Nam J, Suresh S, Shi YQ (2009) Reversible watermarking algorithm using sorting and prediction. IEEE Trans Circuits Syst Video Technol 19(7):989–999CrossRefGoogle Scholar
  59. Sahari ML, Boukemara I (2018) A pseudo-random numbers generator based on a novel 3D chaotic map with an application to color image encryption. Nonlinear Dyn 94(1):723–744CrossRefGoogle Scholar
  60. Shih FY, Wu Y-T (2005) Robust watermarking and compression for medical images based on genetic algorithms. Inf Sci 175(3):200–216MathSciNetCrossRefGoogle Scholar
  61. Slotine JE, Li W (1991) Applied nonlinear control. Prentice-Hall, Englewood ClifszbMATHGoogle Scholar
  62. Su Q (2016) Novel blind colour image watermarking technique using Hessenberg decomposition. IET Image Proc 10(11):817–829CrossRefGoogle Scholar
  63. Su Q, Chen B (2018) Robust color image watermarking technique in the spatial domain. Soft Comput 22(1):91–106 MathSciNetCrossRefGoogle Scholar
  64. Su Q, Niu Y, Liu X, Zhu Y (2012) Embedding color watermarks in color images based on Schur decomposition. Opt Commun 285(7):1792–1802CrossRefGoogle Scholar
  65. Su Q, Niu Y, Zou H, Zhao Y, Yao T (2014) A blind double color image watermarking algorithm based on QR decomposition. Multimed Tools Appl 72(1):987–1009CrossRefGoogle Scholar
  66. Su Q, Wang G, Lv G, Zhang X, Deng G, Chen B (2017) A novel blind color image watermarking based on Contourlet transform and Hessenberg decomposition. Multimed Tool Appl 76(6):8781–8801CrossRefGoogle Scholar
  67. Su Q, Wang G, Zhang X, Lv G, Chen B (2018) A new algorithm of blind color image watermarking based on lu decomposition. Multidimens Syst Signal Process 29(3):1055–1074MathSciNetCrossRefGoogle Scholar
  68. Vaidya P, PVSSR CM (2017) A robust semi-blind watermarking for color images based on multiple decompositions. Multimed Tools Appl 76(24):25623–25656CrossRefGoogle Scholar
  69. Valandar MY, Ayubi P, Barani MJ (2017) A new transform domain steganography based on modified logistic chaotic map for color images. J Inf Secur Appl 34:142–151Google Scholar
  70. Valandar MY, Barani MJ, Ayubi P (2019a) A fast color image encryption technique based on three dimensional chaotic map. Optik 193:162921CrossRefGoogle Scholar
  71. Valandar MY, Barani MJ, Ayubi P, Aghazadeh M (2019b) An integer wavelet transform image steganography method based on 3D sine chaotic map. Multimed Tools Appl 78(8):9971–9989CrossRefGoogle Scholar
  72. Walker J (1998) ENT test suiteGoogle Scholar
  73. Wang Z, Bovik AC, Sheikh HR, Simoncelli EP et al (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612CrossRefGoogle Scholar
  74. Wang C, Wang X, Zhang C, Xia Z (2017) Geometric correction based color image watermarking using fuzzy least squares support vector machine and bessel K form distribution. Signal Process 134:197–208CrossRefGoogle Scholar
  75. Weber AG (1997) The USC-SIPI image database version 5. USC-SIPI Report 315:1–24Google Scholar
  76. Zhang Y, Lu Z, Zhao D (2012) An oblivious fragile watermarking scheme for images utilizing edge transitions in btc bitmaps. Sci China Inf Sci 55(11):2570–2581MathSciNetzbMATHGoogle Scholar
  77. Zhou NR, Hou WMX, Wen RH, Zou WP (2018) Imperceptible digital watermarking scheme in multiple transform domains. Multimed Tools Appl 77(23):30251–30267CrossRefGoogle Scholar
  78. Zhu P, Zhao MS (2010) A chaotic system based watermarking algorithm for image copyright protection. In: 2010 3rd international conference on computer science and information technology 6Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Young Researchers and Elite Club, Urmia BranchIslamic Azad UniversityUrmiaIran
  2. 2.Department of Computer Engineering, Urmia BranchIslamic Azad UniversityUrmiaIran

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