A novel non-redundant contourlet transform for robust image watermarking against non-geometrical and geometrical attacks

In contrast to conventional methods operating in the wavelet domain, a new robust watermarking algorithm using non-redundant contourlet transform is presented in this paper. We explore the high degree of directionality and anisotropy of this transform to obtain a sparser image representation. Through experiments, we find that most of the energy relations between parent and children non-redundant contourlet coefficients maintain invariant before and after JPEG compression. Performance improvement is obtained by means of embedding a watermark exploiting the modulation of the energy relations. Test results based on 16 set of attacks using 6 images are obtained. The results show that our non-redundant contourlet method is highly robust to different kinds of attacks including non-geometrical and geometrical attacks. These include JPEG 2000 compression (as low as QF=10), 400 pixels circular shifting, and contrast stretching, (as low as 20%). Comparisons with two other wavelet methods further demonstrate the potential of the non-redundant contourlet in digital watermarking applications.