Skip to main content
SpringerLink
Log in

Estimation of Data Hiding Capacities in Spatio-Chromatic Fourier Transform (SCFT) Representations of Color Images

  • Research Article - Computer Engineering and Computer Science
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

Despite the abundance of color images, a vast majority of digital image watermarking algorithms are specifically designed for gray-scale images in terms of perceptual modeling, watermark embedding and data hiding capacity. This paper tries to bridge this gap and provides information theoretic estimates of data hiding capacities for standard color images using an improved version of the CIEL*a*b* color space. These capacity estimates are derived based on appropriate color models of the spatio-chromatic Fourier transform (SCFT) of the host image, distortion constraints imposed on the watermarking game players (watermark embedder and attacker), and side information available to both players. This paper considers full-frame and block-based SCFT statistical representations for color images and derive data hiding bounds for these image sources assuming invariance to affine and geometric attacks. Finally, the estimated data hiding capacities are used to assess the performance of a color-based SCFT image watermarking algorithm. The performance results highlight the importance of combining the estimated hiding capacities and perceptual model in designing a high capacity, robust and perceptual color image watermarking system.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Moulin, P.; O’Sullivan, J.: Information-theoretic analysis of information hiding. IEEE Trans. Inf. Theory 49(3), 563–593 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Voloshynovskiy, S.; Pereira, S.; Iquise, V.; Pun, T.: Attack modelling: towards a second generation watermarking benchmark. Signal Process. 81(6), 1177–1214 (2001)

    Article  MATH  Google Scholar 

  3. Costa, M.H.: Writing on dirty paper. IEEE Trans. Inf. Theory 29(3), 439–441 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gelfand, S.I.; Pinsker, M.S.: Coding for channel with random parameters. Probl. Control Inf. Theory 9(1), 19–31 (1983)

    MathSciNet  Google Scholar 

  5. Lin, C.-Y.; Wu, M.; Bloom, J.A.; Cox, I.J.; Miller, M.L.; Lui, Y.M.: Rotation, scale, and translation resilient watermarking for images. IEEE Trans. Image Process. 10(5), 767–782 (2001)

    Article  MATH  Google Scholar 

  6. Kutter, M.; Jordan, F.D.; Bossen, F.: Digital signature of color images using amplitude modulation. Electron. Imaging 3022, 518–526 (1997)

    Google Scholar 

  7. Fleet, D.J.; Heeger, D.J.: Embedding invisible information in color images. In: Proceedings of the IEEE International Conference on Image Processing (ICIP’ 97), vol. 1, pp. 532–535 (1997)

  8. Fairchild, M.D.: Color Appearance Models. Wiley, New York (2013)

    Book  Google Scholar 

  9. Sharma, G.; Wu, W.; Dalal, E.N.: The CIEDE2000 color-difference formula: implementation notes, supplementary test data, and mathematical observations. Color Res. Appl. 30(1), 21–30 (2005)

    Article  Google Scholar 

  10. Cox, I.J.; Miller, M.L.: The first 50 years of electronic watermarking. EURASIP J. Appl. Signal Process. 2002(1), 126–132 (2002)

    MATH  Google Scholar 

  11. Moulin, P.; Mihcak, M.K.: A framework for evaluating the data-hiding capacity of image sources. IEEE Trans. Image Process. 11(9), 1029–1042 (2002)

    Article  Google Scholar 

  12. Chou, C.-H.; Liu, K.-C.: Color image watermarking based on a color visual model. In: Proceedings of the Second IEEE Workshop on Multimedia Signal Processing, pp. 367–370 (2002)

  13. Chou, C.-H.; Wu, T.-L.: Embedding color watermarks in color images. EURASIP J. Appl. Signal Process. 2003, 32–40 (2003)

    Google Scholar 

  14. Bas, P.; Le Bihan, N.; Chassery, J.-M.: Color image watermarking using quaternion Fourier transform. In: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP’ 03), vol. 3, pp. 521–524 (2003)

  15. Tsui, T.K.; Zhang, X.-P.; Androutsos, D.: Color image watermarking using multidimensional Fourier transforms. IEEE Trans. Inf. Forensics Secur. 3(1), 16–28 (2008)

    Article  Google Scholar 

  16. Chou, C.-H.; Liu, K.-C.: A perceptually tuned watermarking scheme for color images. IEEE Trans. Image Process. 19(11), 2966–2982 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Ghouti, L.; Landolsi, M.A.: Robust color image watermarking using the spatio-chromatic Fourier transform and semi-random LDPC codes. In: International Conference on Computer and Communication Engineering (ICCCE’ 12), pp. 349–353 (2012)

  18. Lang, F.-N.; Zhou, J.-L.; Cang, S.; Yu, H.; Shang, Z.: A self-adaptive image normalization and quaternion PCA based color image watermarking algorithm. Expert Syst. Appl. 39(15), 12046–12060 (2012)

    Article  Google Scholar 

  19. Shao, Z.; Duan, Y.; Coatrieux, G.; Wu, J.; Meng, J.; Shu, H.: Combining double random phase encoding for color image watermarking in quaternion gyrator domain. Opt. Commun. 343(X), 56–65 (2015)

    Article  Google Scholar 

  20. Shao, Z.; Wu, J.; Coatrieux, J.-L.; Coatrieux, G.; Shu, H.: Quaternion gyrator transform and its application to color image encryption. In: Proceedings of the 20th IEEE International Conference on Image Processing (ICIP’ 13), pp. 4579–4582 (2013)

  21. Lusson, F.; Bailey, K.; Leeney, M.; Curran, K.: A novel approach to digital watermarking, exploiting colour spaces. Signal Process. 93(5), 1268–1294 (2013)

    Article  Google Scholar 

  22. Wang, X.-Y.; Wang, C.-P.; Wang, H.-Y.; Niu, P.-P.: A robust blind color image watermarking in quaternion Fourier transform domain. J. Syst. Softw. 86(2), 255–277 (2013)

    Article  Google Scholar 

  23. Ouyang, J.; Shu, H.; Wen, X.; Wu, J.; Liao, F.; Coatrieux, G.: A blind robust color image watermarking method using quaternion Fourier transform. In: Proceedings of the 2013 6th International Congress on Image and Signal Processing, CISP 2013, pp. 485–489 (2013)

  24. Tsougenis, E.D.; Papakostas, G.A.; Koulouriotis, D.E.; Karakasis, E.G.; Karras, D.A.: Color image watermarking via quaternion radial Tchebichef moments. In: Proceedings of the IEEE International Conference on Imaging Systems and Techniques (IST’ 13), pp. 101–105 (2013)

  25. Chen, B.; Coatrieux, G.; Sun, X.; Coatrieux, J.-L.; Shu, H.: Full 4-D quaternion discrete Fourier transform based watermarking for color images. Digit. Signal Process. 28(X), 106–119 (2014)

    Article  Google Scholar 

  26. Wang, X.-Y.; Niu, P.-P.; Wang, C.-P.; Wang, A.-L.: A new robust color image watermarking using local quaternion exponent moments. Inf. Sci. 277(X), 731–754 (2014)

    Article  Google Scholar 

  27. Tsougenis, E.D.; Papakostas, G.A.; Koulouriotis, D.E.; Karakasis, E.G.: Adaptive color image watermarking by the use of quaternion image moments. Expert Syst. Appl. 41(14), 6408–6418 (2014)

    Article  Google Scholar 

  28. Yang, H.-Y.; Wang, X.-Y.; Niu, P.-P.; Wang, A.-L.: Robust color image watermarking using geometric invariant quaternion polar harmonic transform. ACM Trans. Multimed. Comput. Commun. Appl. 11(3), 1–26 (2015)

    Google Scholar 

  29. Amini, M.; Sadreazami, H.; Ahmad, M.O.; Swamy, M.: A channel-dependent statistical watermark detector for color images. IEEE Trans. Multimed. (2018). https://doi.org/10.1109/TMM.2018.2851447

  30. Liu, X.-L.; Lin, C.-C.; Yuan, S.-M.: Blind dual watermarking for color images authentication and copyright protection. IEEE Trans. Circuits Syst. Video Technol. 28(5), 1047–1055 (2018)

    Article  Google Scholar 

  31. Hou, D.; Zhang, W.; Chen, K.; Lin, S.-J.; Yu, N.: Reversible data hiding in color image with grayscale invariance. IEEE Trans. Circuits Syst. Video Technol. (2018). https://doi.org/10.1109/TCSVT.2018.2803303

  32. Jiang, R.; Zhou, H.; Zhang, W.; Yu, N.: Reversible data hiding in encrypted three-dimensional mesh models. IEEE Trans. Multimed. 20(1), 55–67 (2018)

    Article  Google Scholar 

  33. Wu, H.-Z.; Shi, Y.-Q.; Wang, H.-X.; Zhou, L.-N.: Separable reversible data hiding for encrypted palette images with color partitioning and flipping verification. IEEE Trans. Circuits Syst. Video Technol. 27(8), 1620–1631 (2017)

    Article  Google Scholar 

  34. Douglas, M.; Bailey, K.; Leeney, M.; Curran, K.: An overview of steganography techniques applied to the protection of biometric data. Multimed. Tools Appl. 77(13), 17333–17373 (2018)

    Article  Google Scholar 

  35. Gutub, A.; Al-Juaid, N.: Multi-bits stego-system for hiding text in multimedia images based on user security priority. J. Comput. Hardw. Eng. 1(2), 1–9 (2018)

    Google Scholar 

  36. Al-Otaibi, N.A.; Gutub, A.A.: 2-Leyer security system for hiding sensitive text data on personal computers. Lect. Notes Inf. Theory 2(2), 151–157 (2014)

    Google Scholar 

  37. Abu-Marie, W.; Gutub, A.; Abu-Mansour, H.: Image based steganography using truth table based and determinate array on RGB indicator. Int. J. Signal Image Process. 1(3), 1–9 (2010)

    Google Scholar 

  38. Gutub, A.; Ankeer, M.; Abu-Ghalioun, M.; Shaheen, A.; Alvi, A.: Pixel indicator high capacity technique for RGB image based steganography. J. Emerg. Technol. Web Intell. (JETWI) 2(1), 5664 (2010)

    Google Scholar 

  39. Parvez, M.T.; Gutub, A.A.-A.: Vibrant color image steganography using channel differences and secret data distribution. Kuwait J Sci Eng 38(1B), 127–142 (2011)

    Google Scholar 

  40. Gutub, A.; Al-Juaid, N.; Khan, E.: Counting-based secret sharing technique for multimedia applications. Multimed. Tools Appl. (2017). https://doi.org/10.1007/s11042-017-5293-6

  41. Poljicak, A.; Botella, G.; Garcia, C.; Kedmenec, L.; Prieto-Matias, M.: Portable real-time DCT-based steganography using OpenCL. J. Real Time Image Process. 14(1), 87–99 (2018)

    Article  Google Scholar 

  42. Ghouti, L.; Bouridane, A.; Ibrahim, M.K.; Boussakta, S.: Digital image watermarking using balanced multiwavelets. IEEE Trans. Signal Process. 54(4), 1519–1536 (2006)

    Article  MATH  Google Scholar 

  43. McCabe, A.; Caelli, T.; West, G.; Reeves, A.: Theory of spatiochromatic image encoding and feature extraction. J. Opt. Soc. Am. Part A 17(10), 1744–1754 (2000)

    Article  Google Scholar 

  44. Hunter, R.S.; Harold, R.W.: The Measurement of Appearance, 2nd edn. Wiley, New York (1987)

    Google Scholar 

  45. Bastug, A.; Sankur, B.: Improving the payload of watermarking channels via LDPC coding. IEEE Signal Process. Lett. 11(2), 90–92 (2004)

    Article  Google Scholar 

  46. Novey, M.; Adali, T.; Roy, A.: A complex generalized Gaussian distribution characterization, generation, and estimation. IEEE Trans. Signal Process. 58(3), 1427–1433 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  47. Venkatraman, D.; Reddy, V.; Khong, A.W.H.: On the use of the quaternion generalized Gaussian distribution for footstep detection. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP’ 13), pp. 6521–6525 (2013)

  48. LoPresto, S.; Ramchandran, K.; Orchard, M.T.: Image coding based on mixture modeling of wavelet coefficients and a fast estimation–quantization framework. In: Data Compression Conference (DCC’ 97), pp. 221–230 (1997)

  49. Bocher, P.K.; McCloy, K.R.: The fundamentals of average local variance. Part I. detecting regular patterns. IEEE Trans. Image Process. 15(2), 300–310 (2006)

    Article  Google Scholar 

  50. Cox, I.J.; Miller, M.L.; McKellips, A.L.: Watermarking as communications with side information. Proc. IEEE 87(7), 1127–1141 (1999)

    Article  Google Scholar 

  51. Cox, I.J.; Kilian, J.; Leighton, F.T.; Shamoon, T.: Secure spread spectrum watermarking for multimedia. IEEE Trans. Image Process. 6(12), 1673–1687 (1997)

    Article  Google Scholar 

  52. Landolsi, M.A.: A comparative performance and complexity study of short-length LDPC and turbo product codes. In: Proceedings of the IEEE International Conference on Information and Communications (ICTTA’ 06), vol. 2, pp. 2359–2364 (2006)

  53. Gonzalez, R.C.; Woods, R.E.: Digital Image Processing, 4th edn. Pearson Education, London (2017)

    Google Scholar 

Download references

Acknowledgements

The author would like to acknowledge the support provided by the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum and Minerals (KFUPM) for funding this work through Project No. IN171034.

Author information

Authors and Affiliations

  1. Department of Information and Computer Science, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Lahouari Ghouti

Authors
  1. Lahouari Ghouti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lahouari Ghouti.

Additional information

This research is supported by King Fahd University of Petroleum and Minerals under DSR Grant No. IN171034.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghouti, L. Estimation of Data Hiding Capacities in Spatio-Chromatic Fourier Transform (SCFT) Representations of Color Images. Arab J Sci Eng 44, 3699–3718 (2019). https://doi.org/10.1007/s13369-018-3630-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-018-3630-3

Keywords

Search

Navigation