Watermarking Images in the Frequency Domain by Exploiting Self-Inverting Permutations


In this work we propose efficient codec algorithms for watermarking images that are intended for uploading on the web under intellectual property protection. Headed to this direction, we recently suggested a way in which an integer number w which being transformed into a self-inverting permutation, can be represented in a two dimensional (2D) object and thus, since images are 2D structures, we have proposed a watermarking algorithm that embeds marks on them using the 2D representation of w in the spatial domain. Based on the idea behind this technique, we now expand the usage of this concept by marking the image in the frequency domain. In particular, we propose a watermarking technique that also uses the 2D representation of self-inverting permutations and utilizes marking at specific areas thanks to partial modifications of the image’s Discrete Fourier Transform (DFT). Those modifications are made on the magnitude of specific frequency bands and they are the least possible additive information ensuring robustness and imperceptiveness. We have experimentally evaluated our algorithms using various images of different characteristics under JPEG compression. The experimental results show an improvement in comparison to the previously obtained results and they also depict the validity of our proposed codec algorithms.

Share and Cite:

M. Chroni, A. Fylakis and S. Nikolopoulos, "Watermarking Images in the Frequency Domain by Exploiting Self-Inverting Permutations," Journal of Information Security, Vol. 4 No. 2, 2013, pp. 80-91. doi: 10.4236/jis.2013.42010.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] S. Garfinkel, “Web Security, Privacy and Commerce,” 2nd Edition, O’Reilly, Sebastopol, 2001.
[2] L. Chun-Shien, H. Shih-Kun, S. Chwen-Jye and M. L. Hong-Yuan, “Cocktail Watermarking for Digital Image Protection,” IEEE Transactions on Multimedia, Vol. 2, No. 4, 2000, pp. 209-224. doi:10.1109/6046.890056
[3] J. C. Davis, “Intellectual Property in Cyberspace—What Technological/Legislative Tools are Necessary for Building a Sturdy Global Information Infrastructure?” Proceedings of the IEEE International Symposium on Technology and Society, Glasgow, 20-21 June 1997, pp. 66-74.
[4] J. J. K. O’Ruanaidh, W. J. Dowling and F. M. Boland, “Watermarking Digital Images for Copyright Protection,” Proceedings of the IEE Vision, Image and Signal Processing, Vol. 143, No. 4, 1996, pp. 250-256. doi:10.1049/ip-vis:19960711
[5] I. J. Cox, M. L. Miller, J. A. Bloom, J. Fridrich and T. Kalker, “Digital Watermarking and Steganography,” 2nd Edition, Morgan Kaufmann, Burlington, 2008.
[6] D. Grover, “The Protection of Computer Software—Its Technology and Applications,” Cambridge University Press, New York, 1997.
[7] C. Collberg and J. Nagra, “Surreptitious Software,” Addison-Wesley, Boston, 2010.
[8] I. Cox, J. Kilian, T. Leighton and T. Shamoon, “A Secure, Robust Watermark for Multimedia,” Proccedings of the 1st International Workshop on Information Hiding, Vol. 1174, 1996, pp. 317-333.
[9] R. C. Gonzalez, R. E. Woods and S. L. Eddins, “Digital Image Processing Using Matlab,” Prentice-Hall, Upper Saddle River, 2003.
[10] R. Sedgewick and P. Flajolet, “An Introduction to the Analysis of Algorithms,” Addison-Wesley, Boston, 1996.
[11] M. C. Golumbic, “Algorithmic Graph Theory and Perfect Graphs,” Academic Press Inc., New York, 1980.
[12] M. Chroni and S. D. Nikolopoulos, “Encoding Watermark Integers as Self-Inverting Permutations,” Proccedings of the 11th International Conference on Computer Systems and Technologies, ACM ICPS 471, 2010, pp. 125-130.
[13] M. Chroni and S. D. Nikolopoulos, “An Efficient Graph Codec System for Software Watermarking,” Proceedings of the 36th International Conference on Computers, Software, and Applications, Workshop STPSA’12, 2012, pp. 595-600.
[14] R. C. Gonzalez and R. E. Woods, “Digital Image Processing,” 3rd Edition, Prentice-Hall, Upper Saddle River, 2007.
[15] V. Solachidis and I. Pitas, “Circularly Symmetric Watermark Embedding in 2D DFT Domain,” IEEE Transactions on Image Processing, Vol. 10, No. 11, 2001, pp. 1741-1753. doi:10.1109/83.967401
[16] V. Licks and R. Hordan, “On Digital Image Watermarking Robust to Geometric Transformations,” Proceedings of the IEEE International Conference on Image Proceesing, Vol. 3, 2000, pp. 690-693.
[17] E. Ganic, S. D. Dexter and A. M. Eskicioglu, “Embedding Multiple Watermarks in the DFT Domain Using Low and High Frequency Bands,” Proceedings of Security, Steganography, and Watermarking of Multimedia Contents VII, Jan Jose, 17 January 2005, pp. 175-184. doi:10.1117/12.594697
[18] F. Petitcolas, “Image Database for Watermarking,” September 2012. http://www.petitcolas.net/ fabien/watermarking/
[19] Z. Wang, A. C. Bovic, H. R. Sheikh and E. P. Simoncelli, “Image Quaity Assessment: From Error Visibility to Structural Similarity,” IEEE Transactions on Image Processing, Vol. 13, No. 4, 2004, pp. 600-612. doi:10.1109/TIP.2003.819861
[20] M. Kaur, S. Jindal and S. Behal, “A Study of Digital Image Watermarking,” Journal of Research in Engineering and Applied Sciences, Vol. 2, No. 2, 2012, pp. 126-136.
[21] J. M. Zain, “Strict Authentication Watermarking with JPEG Compression (SAW-JPEG) for Medical Images for Medical Images,” European Journal of Scientific Research, Vol. 42, No. 2, 2010, pp. 250-256.
[22] A. Hore and D. Ziou, “Image Quality Metrics: PSNR vs. SSIM,” Proceedings of the 20th International Conference on Pattern Recognition, Istanbul, 2010, pp. 2366-2369.
[23] N. Ahmed, T. Natarajan and K. R. Rao, “Discrete Cosine Transform,” IEEE Transactions on Computers, Vol. 23, No. 1, 1974, pp. 90-93. doi:10.1109/T-C.1974.223784
[24] S. Russell and P. Norvig, “Artificial Intelligence: A Modern Approach,” 3rd Edition, Prentice-Hall, Upper Saddle River, 2010.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.