Robust and blind image watermarking via circular embedding and bidimensional empirical mode decomposition

In this paper, a robust and blind image watermarking algorithm via circular embedding and bidimensional empirical mode decomposition (BEMD) is developed. First, the watermark image is scrambled by Arnold transform to increase the security of the algorithm. Second, the Hilbert curve is adopted to reduce the scrambled 2D watermark image to one-dimensional watermark signal. Third, the host image is decomposed by BEMD to obtain the multi-scale representation in the forms of intrinsic mode functions (IMFs) and a residue. Then, the extreme points of the IMFs are extracted as the embedding locations. Finally, the one-dimensional watermark signal is repeatedly and cyclically embedded in the extreme locations of the first IMF according to the texture masking characteristics of the human visual system, which greatly improves the ability of our algorithm against various attacks. The final watermarked image is reconstructed by combining the modified first IMF and the residual. The watermark can be successfully extracted without resorting to the original host image. Furthermore, image correction can be applied before image watermarking extraction if there are geometric attacks in watermarked image. A large number of experimental results and thorough evaluations confirm that our method can obtain higher imperceptibility and robustness under different types of attacks, and achieve better performance than the current state-of-the-art watermarking algorithms, especially in large-scale cropping attack, JPEG compression, Gaussian noise, sharpening, Gamma correction, scaling, histogram equalization, and rotation attacks.