Geometric attacks resistant double zero-watermarking using discrete Fourier transform and fractional-order Exponent-Fourier moments

Zero-watermarking algorithms provide the means of effective, lossless copyright protection, but the existing ones can only resist a limited variety of geometric attacks. To overcome this limitation, a novel zero-watermarking algorithm resistant to an extensive variety of geometric attacks is suggested, in which fractional-order Exponent-Fourier moments (FrEFMs) and discrete Fourier transform (DFT) are used as complementary geometric invariant features to construct zero-watermarks. Relying on the rotation, scaling, aspect ratio changing and cropping invariance of FrEFMs amplitude and the perfect translation invariance of DFT amplitude, our algorithm can effectively resist a wider variety of geometric and common image processing attacks, which has been experimentally illustrated in this work. Therefore, the proposed zero-watermarking algorithm is superior to other cutting-edge ones.