Nothing Special   »   [go: up one dir, main page]
Skip to main content

Advertisement

Springer Nature Link
Log in

Robust color image watermarking using invariant quaternion Legendre-Fourier moments

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

In this paper, a geometrically invariant color image watermarking method using Quaternion Legendre-Fourier moments (QLFMs) is presented. A highly accurate, fast and numerically stable method is proposed to compute the QLFMs in polar coordinates. The proposed watermarking method consists of three main steps. First, the Arnold scrambling algorithm is applied to a binary watermark image. Second, the QLFMs of the original host color image are computed. Third, the binary digital watermark is embedding by performing the quantization of selected QLFMs. Two different groups of attacks are considered. The first group includes geometric attacks such as rotation, scaling and translation while the second group includes the common signal processing attacks such as image compression and noise. Experiments are performed where the performance of proposed method is compared with the existing moment-based watermarking methods. The proposed method is superior over all existing quaternion moment-based watermarking in terms of visual imperceptibility capability and robustness to different attacks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

References

  1. Alghoniemy M, Tewfik AH (2004) Geometric invariance in image watermarking. IEEE Trans Image Process 13(2):145–153

    Article  Google Scholar 

  2. Al-Otum HA, Al-Taba AO (2009) Adaptive color image watermarking based on a modified improved pixel-wise masking technique. Comput Electr Eng 35(5):673–695

    Article  MATH  Google Scholar 

  3. Bianchi T (2013) Secure watermarking for multimedia content protection: a review of its benefits and open issues. IEEE Signal Process Mag 30(2):87–96

    Article  MathSciNet  Google Scholar 

  4. Chauhan DS, Singh AK, Kumar B, Saini JP (2017) Quantization based multiple medical information watermarking for secure e-health. Multimedia Tools and Applications:1–13. https://doi.org/10.1007/s11042-017-4886-4

  5. Chou CH, Liu KC (2010) A perceptually tuned watermarking scheme for color images. IEEE Trans Image Process 19(11):2966–2982

    Article  MathSciNet  MATH  Google Scholar 

  6. Chu SC, Huang HC, Shi Y, Wu SY, Shieh CS (2008) Genetic watermarking for Zerotree-based applications. Circuits, Syst, Signal Process 27(2):171–182

    Article  Google Scholar 

  7. Cox IJ, Millter ML, Bloom JA, Fridrich J, and Kalker T (2008) Digital watermarking and steganography. Morgan Kaufmann Publishers (Elsevier), Burlington,

  8. Ell TA, Sangwine SJ (2007) Hypercomplex Fourier transforms of color images. IEEE Trans Image Process 16:22–35

    Article  MathSciNet  MATH  Google Scholar 

  9. Hamilton WR (1866) Elements of quaternions. Longmans Green, London

    Google Scholar 

  10. Hosny KM (2011) Accurate orthogonal circular moment invariants of gray-level images. J Comput Sci 7(5):715–722

    Article  MathSciNet  Google Scholar 

  11. Hosny KM, Darwish MM (2016) A Kernel-Based method for Fast and accurate computation of PHT in polar coordinates, Journal of Real-Time Image Process., J Real-Time Image Proc, doi: https://doi.org/10.1007/s11554-016-0622-y, p. 1–13 (Online first)

  12. Hosny KM, Darwish MM (2017) Invariant image watermarking using accurate polar harmonic transforms. Comput Electr Eng 62:429–447

    Article  Google Scholar 

  13. Hussein JA (2012) Luminance-based embedding approach for color image watermarking. Int J Image Graph Signal Process 4(3):49–56

    Article  Google Scholar 

  14. Ismail IA, Shouman MA, Hosny KM, Abdel-Salam HM (2010) Invariant image watermarking using accurate Zernike moments. J Comput Sci 6(1):52–59

    Article  Google Scholar 

  15. Kumar C, Kumar Singh A, Kumar P (n.d.) A recent survey on image watermarking techniques and its application in e-governance, multimedia Tools Appl, Springer DOI: https://doi.org/10.1007/s11042-017-5222-8

  16. Kuo-Cheng L (2010) Wavelet-based watermarking for color images through visual masking. AEU-Int J Electron Commun 64(2):112–124

    Article  Google Scholar 

  17. Lin P-Y, Lee J-S, Chang C-C (2011) Protecting the content integrity of digital imagery with fidelity preservation. ACM Trans Multimed Comput Commun Appl, Article 15 7(3):20

    Article  Google Scholar 

  18. Niu PP, Wang XY, Yang YP, Lu MY (2011) A novel color image watermarking scheme in non-sampled contourlet domain. Expert Syst Appl 38(3):2081–2098

    Article  Google Scholar 

  19. Niu P, Wang P, Liu Y, Yang H, Wang X (2015) Invariant color image watermarking approach using quaternion radial harmonic Fourier moments, Multimed. Tools Appl

  20. Pan JS, Hsin YC, Huang HC, Huang KC (2004) Robust image watermarking based on multiple description vector quantisation. Electron Lett 40(22):1409–1410

    Article  Google Scholar 

  21. Peng H, Wang J, Wang WX (2010) Image watermarking method in multi-wavelet domain based on support vector machines. J Syst Softw 83(8):1470–1477

    Article  Google Scholar 

  22. Ren WH, Li X, Lu ZM (2017) Reversible data hiding scheme based on fractal image coding. J Inf Hiding Multimedia Signal Process 8(3):544–550

    Google Scholar 

  23. Sebastiano B, Sabu E, Adrian U, Marcel W (2012) Multimedia in forensics, security, and intelligence. IEEE Multimedia 19(1):17–19

    Article  Google Scholar 

  24. Shokrollahi Z, Yazdi M (2017) A Robust Blind Watermarking scheme based on stationary wavelet transform. J Inf Hiding Multimedia Signal Process, vol. 8, no. 3, pp. 676–687

  25. Singh AK Improved hybrid technique for robust and imperceptible multiple watermarking using medical images. Multimedia Tools Appl 76(6):8881–8900

  26. Singh C, Ranade SK (2013) Geometrically invariant and high capacity image watermarking scheme using accurate radial transform. Opt Laser Technol 54:176–184

    Article  Google Scholar 

  27. Singh AK, Kumar B, Dave M, Mohan A (2014) Robust and imperceptible dual watermarking for telemedicine applications. Wirel Pers Commun 80(4):1415–1433

    Article  Google Scholar 

  28. Singh A.K, Kumar B, Mohan A (2017) Medical image watermarking: techniques and applications”, book series on multimedia systems and applications. Springer, USA

  29. Singh AK, Kumarb B, Singh SK, Ghrera SP, Mohan A Multiple watermarking technique for securing online social network contents using back propagation neural network. Futur Gener Comput Syst:1–16. https://doi.org/10.1016/j.future.2016.11.023

  30. Srivastav R, Kumar B, Kumar Singh A, Mohan A (n.d.) Computationally efficient joint imperceptible image watermarking and JPEG compression: a green computing approach, Multimedia Tools and Applications, Springer US DOI: https://doi.org/10.1007/s11042-017-5214-8

  31. Suk T, Flusser J (2009) Affine moment invariants of color images, in: The 13th International Conference on Computer Analysis of Images and Patterns, Lecture Notes Computer Science, vol. 5702, Münste, Germany, pp. 334–341

  32. Tsougenis ED, Papakostas GA, Koulouriotis DE, Tourassis VD (2013) Towards adaptivity of image watermarking in polar harmonic transforms domain. Opt Laser Technol 54:84–97

    Article  Google Scholar 

  33. Tsougenis ED, Papakostas GA, Koulouriotis DE, Karakasis EG (2014) Adaptive color image watermarking by the use of quaternion image moments. Expert Syst Appl 41(14):6408–6418

    Article  Google Scholar 

  34. Tsui TK, Zhang XP, Androutsos D (2008) Color image watermarking using multidimensional Fourier transforms. IEEE Trans Inf Forensics Secur 3(1):16–28

    Article  Google Scholar 

  35. Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612

    Article  Google Scholar 

  36. Wang XY, Yang YP, Yang HY (2010) Invariant image watermarking using multi-scale Harris detector and wavelet moments. Comput Electr Eng 36(1):31–44

    Article  MATH  Google Scholar 

  37. Wang XY, Niu PP, Yang HY, Wang CP, Wang AL (2014) A new robust color image watermarking using local quaternion exponent moments. Inf Sci 277:731–754

    Article  Google Scholar 

  38. Wang C-p, Wang X-y, Zhi-qiu X (2016) Geometrically invariant image watermarking based on fast radial harmonic Fourier moments. Signal Process Image Commun 45:10–23

    Article  Google Scholar 

  39. Wang XY, Yang HY, Niu PP, Wang CP (2016) Quaternion exponent moments based robust color image watermarking. J Comput Res Dev 53:651–665

    Google Scholar 

  40. Wang XY, Liu YN, Han MM, Yang HY (2016) Local quaternion PHT based robust color image watermarking algorithm. J Vis Commun Image Represent 38:678–694

    Article  Google Scholar 

  41. Xiao B, Wang G, Li W (2014) Radial shifted Legendre moments for image analysis and invariant image recognition. Image Vis Comput 32(12):994–1006

    Article  Google Scholar 

  42. Xin Y, Liao S, Pawlak M (2007) Circularly orthogonal moments for geometrically robust image watermarking. Pattern Recogn 40:3740–3752

    Article  MATH  Google Scholar 

  43. Xin Y, Pawlak M, Liao S (2007) Accurate computation of Zernike moments in polar coordinates. IEEE Trans Image Process 16(2):581–587

    Article  MathSciNet  Google Scholar 

  44. Yang H, Zhang Y, Wang P, Wang X, Wang C (2014) A geometric correction based robust color image watermarking scheme using quaternion exponent moments. Optik 125:4456–4469

    Article  Google Scholar 

  45. Yang HY, Wang XY, Wang P, Niu PP (2015) Geometrically resilient digital watermarking scheme based on radial harmonic Fourier moments magnitude. AEU - Int J Electron Commun 69:389–399

    Article  Google Scholar 

  46. Yang HY, Wang XY, Niu PP, Wang AL (2015) Robust color image watermarking using geometric invariant quaternion polar harmonic transform. ACM Trans Multimed Comput Commun Appl 11(3):1–26

    Google Scholar 

  47. Yu M, Wang J, Jiang G, Peng Z, Shao F, Luo T (2015) New fragile watermarking method for stereo image authentication with localization and recovery. AEU Int J Electron Commun 69(1):361–370

    Article  Google Scholar 

  48. Zear A, Singh AK, Kumar P (2016) A proposed secure multiple watermarking technique based on DWT, DCT and SVD for application in medicine. Multimedia Tools Appl. doi:https://doi.org/10.1007/s11042-016-3862-8

  49. Zhang H, Shu H, Coatrieux G (2011) Affine Legendre moment invariants for image watermarking robust to geometric distortions. IEEE Trans Image Process 20(8):2189–2199

    Article  MathSciNet  MATH  Google Scholar 

  50. Zhu HQ, Liu M, Li Y (2010) The RST invariant digital image watermarking using radon transforms and complex moments. Digital Signal Processing 20(6):1612–1628

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Technology, Faculty of Computers and Informatics, Zagazig University, Zagazig, 44519, Egypt

    Khalid M. Hosny

  2. Department of Mathematics, Faculty of Science, Assiut University, Assiut, 71516, Egypt

    Mohamed M. Darwish

Authors
  1. Khalid M. Hosny
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohamed M. Darwish
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Khalid M. Hosny.

Appendices

Appendix 1

A counter-clockwise rotation with an angle α, the transformed image intensity function is defined as:

$$ {\mathrm{f}}^{\mathrm{rot}}\left(\mathrm{r},\uptheta \right)=\mathrm{f}\left(\mathrm{r},\uptheta +\upalpha \right) $$
(49)

Assume \( \widehat{\uptheta}=\uptheta +\upalpha \), then \( \uptheta =\widehat{\uptheta}-\upalpha \), \( \mathrm{d}\uptheta =\mathrm{d}\widehat{\uptheta} \). The QLFMs of the two images frot and f have the following relations:

$$ {\displaystyle \begin{array}{l}{\mathrm{M}}_{\mathrm{p}\mathrm{q}}^{\mathrm{R}}\left({\mathrm{f}}^{\mathrm{rot}}\right)=\frac{2\mathrm{p}+1}{\uppi}{\int}_0^{2\uppi}{\int}_0^1{\mathrm{f}}^{\mathrm{rot}}\left(\mathrm{r},\uptheta \right){\left[{\mathrm{L}}_{\mathrm{p}\mathrm{q}}\left(\mathrm{r},\uptheta \right)\right]}^{\ast}\mathrm{rdrd}\uptheta\ \\ {}\kern4em =\frac{2\mathrm{p}+1}{\uppi}{\int}_0^{2\uppi}{\int}_0^1\mathrm{f}\left(\mathrm{r},\uptheta +\upalpha \right){\overline{\mathrm{P}}}_{\mathrm{p}}\left(\mathrm{r}\right){\mathrm{e}}^{-\upmu \mathrm{q}\uptheta}\mathrm{rdrd}\uptheta \\ {}\kern4em =\frac{2\mathrm{p}+1}{\uppi}{\int}_0^{2\uppi}{\int}_0^1\mathrm{f}\left(\mathrm{r},\widehat{\uptheta}\right){\overline{\mathrm{P}}}_{\mathrm{p}}\left(\mathrm{r}\right){\mathrm{e}}^{-\upmu \mathrm{q}\left(\widehat{\uptheta}-\upalpha \right)}\ \mathrm{rdrd}\widehat{\uptheta}\\ {}\kern4em =\frac{2\mathrm{p}+1}{\uppi}{\int}_0^{2\uppi}{\int}_0^1\mathrm{f}\left(\mathrm{r},\widehat{\uptheta}\right){\overline{\mathrm{P}}}_{\mathrm{p}}\left(\mathrm{r}\right){\mathrm{e}}^{-\upmu \mathrm{q}\widehat{\uptheta}}{\mathrm{e}}^{\upmu \mathrm{q}\upalpha}\mathrm{rdrd}\widehat{\uptheta}\\ {}\kern4em ={\mathrm{M}}_{\mathrm{p}\mathrm{q}}^{\mathrm{R}}\left(\mathrm{f}\right){\mathrm{e}}^{\upmu \mathrm{q}\upalpha}\end{array}} $$
(50)

Where \( {\mathrm{M}}_{\mathrm{pq}}^{\mathrm{R}}\left({\mathrm{f}}^{\mathrm{rot}}\right) \) and \( {\mathrm{M}}_{\mathrm{pq}}^{\mathrm{R}}\left(\mathrm{f}\right) \) are the QLFM of frot and f respectively.

Appendix 2

Let fS be the scaled version of the image f. Let fS(r, θ) = \( \mathrm{f}\left(\ \frac{\mathrm{r}}{\mathrm{a}},\uptheta \right) \) be the color image expanded by the scale factor a, and \( \widehat{\mathrm{r}}=\frac{\mathrm{r}}{\mathrm{a}} \), then \( \mathrm{dr}=\mathrm{ad}\widehat{\mathrm{r}},\kern0.5em \)we could express the scaling QLFMs using the following equation:

$$ {\displaystyle \begin{array}{l}{\mathrm{M}}_{\mathrm{p}\mathrm{q}}^{\mathrm{R}}\left({\mathrm{f}}^{\mathrm{S}}\right)=\frac{2\mathrm{p}+1}{\uppi}\underset{0}{\overset{2\uppi}{\int }}\underset{0}{\overset{1}{\int }}{\mathrm{f}}^{\mathrm{s}}\left(\mathrm{r},\uptheta \right){\left[{\mathrm{L}}_{\mathrm{p}\mathrm{q}}\left(\mathrm{r},\uptheta \right)\right]}^{\ast}\mathrm{rdrd}\uptheta \\ {}\kern3.5em =\frac{2\mathrm{p}+1}{\uppi}\underset{0}{\overset{2\uppi}{\int }}\underset{0}{\overset{1}{\int }}{\mathrm{f}}^{\mathrm{S}}\left(\mathrm{r},\uptheta \right){\overline{\mathrm{P}}}_{\mathrm{p}}\left(\mathrm{r}\right){\mathrm{e}}^{-\upmu \mathrm{q}\uptheta}\mathrm{rdrd}\uptheta \\ {}\kern3.5em =\frac{2\mathrm{p}+1}{\uppi}\underset{0}{\overset{2\uppi}{\int }}\underset{0}{\overset{1}{\int }}\mathrm{f}\left(\frac{\mathrm{r}}{\mathrm{a}},\uptheta \right){\overline{\mathrm{P}}}_{\mathrm{p}}\left(\mathrm{r}\right){\mathrm{e}}^{-\upmu \mathrm{q}\uptheta}\mathrm{rdrd}\uptheta\ \\ {}\kern3.5em =\frac{2\mathrm{p}+1}{\uppi}\underset{0}{\overset{2\uppi}{\int }}\underset{0}{\overset{1}{\int }}\mathrm{f}\left(\widehat{\mathrm{r}},\uptheta \right){\overline{\mathrm{P}}}_{\mathrm{p}}\left(\mathrm{a}\widehat{\mathrm{r}}\right){\mathrm{e}}^{-\upmu \mathrm{q}\uptheta}{\mathrm{a}}^2\widehat{\mathrm{r}}\mathrm{d}\widehat{\mathrm{r}}\mathrm{d}\uptheta \\ {}\kern3.5em ={\mathrm{a}}^2\frac{2\mathrm{p}+1}{\uppi}\underset{0}{\overset{2\uppi}{\int }}\underset{0}{\overset{1}{\int }}\mathrm{f}\left(\widehat{\mathrm{r}},\uptheta \right){\overline{\mathrm{P}}}_{\mathrm{p}}\left(\mathrm{a}\widehat{\mathrm{r}}\right){\mathrm{e}}^{-\upmu \mathrm{q}\uptheta}\widehat{\mathrm{r}}\mathrm{d}\widehat{\mathrm{r}}\mathrm{d}\uptheta \end{array}} $$
(51)

Where \( {\overline{\mathrm{P}}}_{\mathrm{p}}\left(\mathrm{a}\widehat{\mathrm{r}}\right) \) is scaled version of \( {\overline{\mathrm{P}}}_{\mathrm{p}}\left(\widehat{\mathrm{r}}\right) \). The scaled substituted shifted Legendre polynomials \( {\overline{\mathrm{P}}}_{\mathrm{p}}\left(\mathrm{a}\widehat{\mathrm{r}}\right) \) could be expressed in terms of the substituted shifted Legendre polynomials \( {\overline{\mathrm{P}}}_{\mathrm{p}}\left(\widehat{\mathrm{r}}\right) \) as follows:

$$ {\overline{\mathrm{P}}}_{\mathrm{p}}\left(\mathrm{a}\widehat{\mathrm{r}}\right)=\sum \limits_{\mathrm{k}=0}^{\mathrm{p}}\left(\sum \limits_{\mathrm{i}=\mathrm{k}}^{\mathrm{p}}{\mathrm{a}}^{2\mathrm{i}}{\mathrm{C}}_{\mathrm{p}\mathrm{i}}{\mathrm{d}}_{\mathrm{i}\mathrm{k}}\right){\overline{\mathrm{P}}}_{\mathrm{k}}\left(\widehat{\mathrm{r}}\right) $$
(52)

Where:

$$ {\mathrm{C}}_{\mathrm{p}\mathrm{i}}={\left(-1\right)}^{\mathrm{p}-\mathrm{k}}\frac{\left(\mathrm{p}+\mathrm{k}\right)!}{\left(\mathrm{p}-\mathrm{k}\right)!{\left(\mathrm{k}!\right)}^2} $$
(53)
$$ {\mathrm{d}}_{\mathrm{pi}}=\frac{\left(2\mathrm{k}+1\right){\left(\mathrm{k}!\right)}^2}{\left(\mathrm{p}+\mathrm{k}+1\right)!\left(\mathrm{p}-\mathrm{k}\right)!} $$
(54)

Substitution equation (52) into equation (51) yields:

$$ {\displaystyle \begin{array}{l}{\mathrm{M}}_{\mathrm{p}\mathrm{q}}^{\mathrm{R}}\left({\mathrm{f}}^{\mathrm{S}}\right)\\ {}=\frac{2\mathrm{p}+1}{\uppi}\sum \limits_{\mathrm{k}=0}^{\mathrm{p}}\left(\sum \limits_{\mathrm{i}=\mathrm{k}}^{\mathrm{p}}{\mathrm{a}}^{2\mathrm{i}+2}{\mathrm{C}}_{\mathrm{p}\mathrm{i}}{\mathrm{d}}_{\mathrm{i}\mathrm{k}}{\int}_0^{2\uppi}{\int}_0^1\mathrm{f}\left(\widehat{\mathrm{r}},\uptheta \right){\overline{\mathrm{P}}}_{\mathrm{k}}\left(\widehat{\mathrm{r}}\right){\mathrm{e}}^{-\upmu \mathrm{q}\uptheta}\widehat{\mathrm{r}}\mathrm{d}\widehat{\mathrm{r}}\mathrm{d}\uptheta \right)\\ {}=\sum \limits_{\mathrm{k}=0}^{\mathrm{p}}\frac{2\mathrm{p}+1}{2\mathrm{k}+1}\left(\sum \limits_{\mathrm{i}=\mathrm{k}}^{\mathrm{p}}{\mathrm{a}}^{2\mathrm{i}+2}{\mathrm{C}}_{\mathrm{p}\mathrm{i}}{\mathrm{d}}_{\mathrm{i}\mathrm{k}}{\mathrm{M}}_{\mathrm{p}\mathrm{q}}^{\mathrm{R}}\left(\mathrm{f}\right)\right)\end{array}} $$
(55)

Where \( {\mathrm{M}}_{\mathrm{pq}}^{\mathrm{R}}\left({\mathrm{f}}^{\mathrm{s}}\right) \) and \( {\mathrm{M}}_{\mathrm{pq}}^{\mathrm{R}}\left(\mathrm{f}\right) \) are the QLFM of fs and f respectively. Use p = 0 and q = 0 in equation (55), yields:

$$ {\mathrm{M}}_{00}^{\mathrm{R}}\left({\mathrm{f}}^{\mathrm{s}}\right)={\mathrm{a}}^2\ {\mathrm{M}}_{00}^{\mathrm{R}}\left(\mathrm{f}\right) $$
(56)

The scale invariants can be constructed as follows:

$$ {\upvarphi}_{\mathrm{p}\mathrm{q}}=\sum \limits_{\mathrm{k}=0}^{\mathrm{p}}\frac{2\mathrm{p}+1}{2\mathrm{k}+1}\left(\sum \limits_{\mathrm{i}=\mathrm{k}}^{\mathrm{p}}\kern0.5em {\left({\mathrm{M}}_{00}^{\mathrm{R}}\left(\mathrm{f}\right)\right)}^{-\left(\mathrm{i}+1\right)}{\mathrm{C}}_{\mathrm{p}\mathrm{i}}{\mathrm{d}}_{\mathrm{i}\mathrm{k}}\right){\mathrm{M}}_{\mathrm{p}\mathrm{q}}^{\mathrm{R}}\left(\mathrm{f}\right) $$
(57)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hosny, K.M., Darwish, M.M. Robust color image watermarking using invariant quaternion Legendre-Fourier moments. Multimed Tools Appl 77, 24727–24750 (2018). https://doi.org/10.1007/s11042-018-5670-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-018-5670-9

Keywords

Search

Navigation