Image Watermarking Based on Various Discrete Fractional Fourier Transforms

In this paper, we use discrete fractional Fourier transform (DFRFT) and its other four generalized transforms to embed watermarks and analyze their robustness. The resulting watermarking schemes belong to the transformdomain watermarking schemes. Experiment results show that, among the five transforms, random DFRFT (RDFRFT) is most robust to cropping attack as well as salt-and-pepper noise attack. In general, the two real transforms, real DFRFT and real DFRHT, are good choices for watermark applications because they are not only resistant to cropping and salt-and-pepper noise attacks, but also have the merit of less computations as compared with other three complex DFRFT transforms.