Repeated Embedding Algorithm for Image Watermarking Based on BEMD and Hilbert Curve

In order to solve the limitation of size matching between watermarking image and host image in digital image watermarking algorithm and improve the robustness of image watermarking algorithm against large-scale shearing,Gauss noise,salt and pepper noise attacks,a repeated embedding algorithm for image watermarking is proposed by combining bi-dimensional empirical mode decomposition(BEMD)algorithm and Hilbert curve.Firstly,the watermarking image is scrambled by Arnold transform to increase the security of the watermarking image.Secondly,the scrambled bi-dimensional watermarking image is dimensionally reduced to get one-dimensional watermarking signal using Hilbert curve.The data dimensionality reduction not only solves the limitation of size matching between watermarking image and host image in watermarking embedding,but also further scrambles the watermarking image and enhances the security of the watermarking image.Then,BEMD is applied to the host image to obtain the intrinsic mode function(IMFs)and a residual information at different scales,and the extremum of the image corresponding to the first IMF are detected as the embedding position of the watermarking.Finally,according to the texture masking characteristics of human visual system,the one-dimensional watermarking signal is repeatedly embedded in the extreme positions of the corresponding image of the first IMF in order from left to right and from top to bottom.The embedded image is reconstructed by combining other IMFs and the residual.The extraction of watermarking image is an inverse process of the embedding process.Watermark images are embedded into several groups of host images,and the peak signal-to-noise ratios(PSNR)of the embedded images are above 40 dB.The watermarked images are attacked by Gauss noise,salt and pepper noise,large-scale shearing,and the normalized correlation coefficients between the extracted watermarking images and the original watermarking images are above 0.96.Experimental results show that the embedded watermarking images have good invisibility,and are robust to Gauss noise,salt and pepper noise,especially to large-scale shearing.