Color image watermark decoder by modeling quaternion polar harmonic transform with BKF distribution

Abstract

It still remains a challenging problem to improve both of the imperceptibility and robustness for the digital image watermarking task. In this study, a color image watermarking scheme is proposed based on quaternion polar harmonic transform (QPHT) with maximum likelihood decoder, which better balances imperceptibility and robustness in a novel fashion. Thanks to the strong robustness of QPHT, the digital watermark is embedded into the QPHT magnitudes using a multiplicative approach. At the receiver, the watermark decoder can be formulated as a problem of weak signal detection, as the QPHT magnitudes are highly non-Gaussian. In view of this, selection of proper models is of great importance to construct a suitable watermark decoder. Further, we validate that the probability density function of Bessel K form suitably models the heavy tail behavior of QPHT magnitudes, and thus the maximum likelihood decoder is developed by modeling QPHT magnitudes with Bessel K form distribution. Experimental results on standard benchmarks demonstrate that the proposed approach provides better imperceptibility and robustness against various kinds of attacks compared to previous state-of-the-art methods.