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Using Contourlet Transform and Discrete Cosine Transform and SVD for Digital Watermarking

In this paper, embedding a watermark in the image is performed in discrete Contourlet transform (CT) domain. It is known that the CT is able to capture the directional edges and contours superior to discrete wavelet transform. We introduce three methods. The first proposed method is based on embedding watermark bits into the singular value of the selected blocks within low-pass sub-band of the original gray image CT and uses adaptive quantization. The second method uses quantization step, are implemented. Our experimental results show that the second method with quantization step has better fidelity in terms of peak signal to noise ratio (PSNR) and is more robust against geometrical and non-geometrical attacks in terms of normalized cross correlation (NC) in comparison with the first method, though, the method with adaptive quantization is blind in the sense only quantization strategies but not the original image is required. The third proposed method is based on embedding watermark bits into the selected blocks within last sub-band of first level of the original gray image CT. This method is semi-blind and our experimental results show that robustness against geometrical and non-geometrical attacks in terms of normalized cross correlation (NC) is better than two previous methods and third method robust against too many attacks type.