Geometrical attacks resilient statistical watermark decoder using polar harmonic Fourier moments

This paper presents a new robust multiplicative watermark detector. Due to the strong robustness against various attacks, polar harmonic Fourier moment (PHFM) magnitudes are used as the employed watermark carrier. The distribution of PHFM magnitudes is highly non-Gaussian and can be properly modeled by a heavy-tailed probability density function (PDF). In this paper, we proved that Weibull distribution can suitably fit the distribution of PHFM magnitudes, and based on this, we presented a statistics-based watermark decoder by using the Weibull as a prior for the PHFM magnitudes. In watermark embedding, a multiplicative manner was used to embed watermark information in PHFM magnitudes of the highest entropy blocks to achieve better robustness and imperceptibility. In watermark detection, we developed a Weibull distribution-based statistical watermark decoder, which uses the maximum likelihood (ML) decision rule. Compared with Bessel K form (BKF), Cauchy, and generalized Gaussian (GG)-based decoders, the Weibull-based decoder demonstrates stronger robustness. In addition, the proposed watermark decoder is more robust against geometrical and common image processing attacks than existing statistical watermark decoders.