Journal of Mathematical Imaging and Vision

, Volume 30, Issue 1, pp 13–21 | Cite as

Phase Watermarking Algorithm using Hybrid Multi-Polarity Hadamard Transform

  • Bogdan J. Falkowski


In this paper, a robust phase watermarking algorithm for still images is presented where the watermark information is conveyed in the phase spectrum in the transform domain. Phase watermarking algorithm that uses multi-polarity Walsh-Hadamard and Complex Hadamard transform is developed. The robustness of presented algorithm is investigated by its uniqueness, JPEG encoding, image resizing, dithering noise distortions, sharpening, cropping and successive watermarking.


Unified complex Hadamard transform Multi-polarity complex Hadamard transform Multi-polarity Walsh-Hadamard transform Phase watermarking Spectral techniques 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Agaian, S.S.: Hadamard Matrices and Their Applications. Lecture Notes in Mathematics, vol. 1168. Springer, Berlin (1980) Google Scholar
  2. 2.
    CityU-IPL Image Database at
  3. 3.
    Cox, I.J., Killian, J., Leighton, F.T., Shamoon, T.: Secure spread spectrum watermarking for multimedia. IEEE Trans. Image Process. 6(12), 1673–1687 (1997) CrossRefGoogle Scholar
  4. 4.
    Falkowski, B.J.: Properties and ways of calculation of multi-polarity generalized Walsh transforms. IEEE Trans. Circuits Syst. II: Analog Digit. Signal Process. 41(6), 380–391 (1994) MATHCrossRefGoogle Scholar
  5. 5.
    Falkowski, B.J.: Family of generalized multi-polarity complex Hadamard transforms. IEE Proc. Vis. Image Signal Process. 145(6), 371–378 (1998) CrossRefGoogle Scholar
  6. 6.
    Falkowski, B.J., Rahardja, S.: Complex Hadamard transforms: properties, relations and architecture. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E87-A(8), 2077–2083 (2004) Google Scholar
  7. 7.
    Jahne, B.: Digital Image Processing, 5th edn. Springer, Berlin (2002) Google Scholar
  8. 8.
    Ó Ruanaidh, J.J.K., Dowling, W.J., Boland, F.M.: Watermarking digital images for copyright protection. IEE Proc. Vis. Image Signal Process. 143(4), 250–256 (1996) CrossRefGoogle Scholar
  9. 9.
    Ó Ruanaidh, J.J.K., Dowling, W.J., Boland, F.M.: Phase watermarking of digital images. In: Proc. IEEE Int. Conf. on Image Processing, pp. 239–242 (1996) Google Scholar
  10. 10.
    Plataniotis, K.N., Venetsanopoulos, A.N.: Color Image Processing and Applications. Springer, Berlin (2000) Google Scholar
  11. 11.
    Proakis, J.G.: Digital Communications, 4th edn. McGraw-Hill, New York (2001) Google Scholar
  12. 12.
    Rahardja, S., Falkowski, B.J.: Comparative study of discrete orthogonal transforms in adaptive signal processing. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E82-A(8), 1386–1390 (1999) Google Scholar
  13. 13.
    Rahardja, S., Falkowski, B.J.: Family of unified complex Hadamard transforms. IEEE Trans. Circuits Syst. II: Analog Digit. Signal Process. 46(8), 1094–1100 (1999) MATHCrossRefGoogle Scholar
  14. 14.
    Rahardja, S., Falkowski, B.J.: Complex composite spectra of unified complex Hadamard transform for logic functions. IEEE Trans. Circuits Syst. II: Analog Digit. Signal Process. 47(11), 1291–1297 (2000) MATHCrossRefGoogle Scholar
  15. 15.
    Rahardja, S., Ser, W., Lin, Z.: UCHT-based complex sequences for asynchronous CDMA system. IEEE Trans. Commun. 51(4), 618–626 (2003) CrossRefGoogle Scholar
  16. 16.
    Robin, M., Poulin, M.: Digital Television Fundamentals: Design and Installation of Video and Audio Systems. McGraw-Hill, New York (1998) Google Scholar
  17. 17.
    Rojaini, K.B.: Programming in C with Numerical Methods for Engineers. Prentice Hall, Englewood Cliffs (1996) Google Scholar
  18. 18.
    Swanson, M.D., Kobayashi, M., Tewfik, A.H.: Multimedia data-embedding and watermarking techniques. Proc. IEEE 86(6), 1064–1087 (1998) CrossRefGoogle Scholar
  19. 19.
    Tian, J.: Wavelet-based reversible watermarking for authentication. In: Proc. SPIE Security and Watermarking of Multimedia Contents IV, San Jose, USA, pp. 679–690 (2002) Google Scholar
  20. 20.
    Wallace, G.K.: The JPEG still picture compression standard. Commun. ACM 34(4), 30–44 (1991) CrossRefGoogle Scholar
  21. 21.
    Xie, S., Rahardja, S.: Performance evaluation for quaternary DS-SSMA communications with complex signature sequences over Rayleigh-fading channels. IEEE Trans. Wirel. Commun. 4(1), 266–277 (2005) CrossRefGoogle Scholar
  22. 22.
    Yaroslavsky, L.P.: Digital Picture Processing. Springer, Berlin (1985) MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.School of Electrical & Electronic EngineeringNanyang Technological UniversitySingaporeSingapore

Personalised recommendations