Open Access Open Access  Restricted Access Subscription or Fee Access

QFT-QSVD Domain Colour Image Watermarking Scheme

B.D. Venkatramana Reddy, Dr. T. Jayachandra Prasad

Abstract


Watermarks can be embedded in the pixel domain or a transform domain. Discrete Fourier Transform (DFT), Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD) have been used as mathematical tools for embedding data into an image. In this paper, we present a new robust hybrid watermarking scheme for colour images based on Quaternion Fourier Transform (QFT) and Quaternion Singular Value Decomposition (QSVD). After applying the QFT to the cover image, we map the QFT coefficients into four quadrants, and apply the QSVD to each quadrant. The singular values in each quadrant are then modified by the singular values of the QFT-transformed visual watermark. The quality of the watermarked image and extracted watermark is measured using peak signal to noise ratio (PSNR) and normalized correlation (NC) respectively. Robustness of proposed algorithm is tested for various attacks. We assume that the size of the visual watermark is one quarter of the size of the image.

Keywords


Quaternion Fourier Transform, Quaternion Singular Value Decomposition, Singular Values, Watermark Embedding.

Full Text:

PDF

References


W. R. Hamilton, Elements of Quaternion. London, U.K.: Longmans Green, 1866.

Sangwine, S. J. and Ell, T. A., “Hypercomplex Fourier Transforms of Color Images”, IEEE International Conference on Image Processing (ICIP 2001), Thessaloniki, Greece, October 7-10,2001,I,137-140.

Todd A. Ell and Stephen J. Sangwine “Hypercomplex Fourier Transforms of Color Images,” in IEEE Transactions on Image Processing,Vol.16,No.1, pp. 22-35, 2007.

Pei, S.C., Chang, J.H., and Ding, J.J.,“ Quaternion matrix singular value decomposition and its applications for color image processing” ICIP03, 805-808.

Zhang, F., “Quaternions and matrices of quaternions,” Linear algebra and its applications, vol.251, pp.21-57, 1997.

Le Bihan, N. and Sangwine, S.J., "Quaternion Principal Component Analysis of Colour images," IEEE International Conference on Image Processing (ICIP), 2003, I, 808-812.

S.Sangwine and N. Le Bihan, Quaternion Toolbox for Matlab, Software Library [Online]. Available: http://qtfm.sourceforge.net/.

B.D. Venkatramana Reddy and Dr. T. Jayachandra Prasad, “Block based Colour Image Watermarking Scheme using QSVD”, CiiT International Journal of Digital Image Processing, March 2011.

M.L.Miller, I.J.Cox, J.M.G.Linnartz and T.Kalker, “A review of watermarking principles and practices”, IEEE International Conference on image processing, 1997.

C.Shoemaker, Rudko, “Hidden Bits: A survey of Techniques for Digital Watermarking” Independent study EER-290 Prof Rudko, Spring 2002.

R.Liu and T.Tan, “An SVD-Based Watermarking Scheme for protecting rightful ownership”, IEEE, Trans. on multimedia, Vol.4, no.1 March 2002.

Y.H.Wang, T.N.Tan and Y.Zhu, “Face Verification Based on Singular value Decomposition and Radial Basis Function Neural Network”, National Laboratory of Pattern Recognition (NLPR).Institute of Automation, Chinese Academy of Sciences.

J.M.Shieh, D.C.Lou, and M.C.Chang, “A semi-blind watermarking scheme based on singular value decomposition”, computer standards &interface 28(2006) 428-440.

A.Sverdlov, S.Dexter, A.M.Eskicioglu, “Robust DCT-SVD domain image watermarking for copyright protection: embedding data in all frequencies” 13th European Signal Processing Conference (EUSIPCO 2005), Antalya, Turkey, September 4-8, 2005.

R.A. Ghazy et.al., An efficient block-by-block SVD Based Image Watermarking Scheme, Ubiquitous Computing and Communication Journal.


Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.