Robust Reversible Watermarking by Fractional Order Zernike Moments and Pseudo-Zernike Moments

Robust reversible watermarking (RRW) can be used to guarantee the security of special images. Existing schemes basically cannot resist geometric attacks. In this paper, the extraction of auxiliary information is optimized so that the information can be smaller and more stable. Meanwhile, Zernike moment and pseudo-Zernike moment (ZM/PZM) are modified by fractional order, namely fractional-order Zernike moments (FoZM) and fractional-order pseudo-Zernike moments (FoPZM), to improve the robustness. Specifically, firstly, the error source is calculated by the difference between the watermarked image and the cover image, and it is used as the auxiliary information to be embedded into the cover image. Secondly, FoZM/FoPZM revises the amplitude of ZM/PZM, then the watermark is embedded into the low-order FoZM/FoPZM moment. Finally, the watermarked image is denoised before the watermark extraction, so that to enhance the ability to resist the noise attack. Experimental results show that the scheme has good stability and strong robustness.