Color image watermarking using vector SNCM-HMT

An image watermarking scheme is typically evaluated using three main conflicting characteristics: imperceptibility, robustness, and capacity. Developing a good image watermarking method is challenging because it requires a trade-off between these three basic characteristics. In this paper, we proposed a statistical color image watermarking based on robust discrete nonseparable Shearlet transform (DNST)-fast quaternion generic polar complex exponential transform (FQGPCET) magnitude and vector skew-normal-Cauchy mixtures (SNCM)-hidden Markov tree (HMT). The proposed watermarking system consists of two main parts: watermark inserting and watermark extraction. In watermark inserting, we first perform DNST on R, G, and B components of color host image, respectively. We then compute block FQGPCET of DNST domain color components, and embed watermark signal in DNST-FQGPCET magnitudes using multiplicative approach. In watermark extraction, we first analyze the robustness and statistical characteristics of local DNST-FQGPCET magnitudes of color image. We then observe that, vector SNCM-HMT model can capture accurately the marginal distribution and multiple strong dependencies of local DNST-FQGPCET magnitudes. Meanwhile, vector SNCM-HMT parameters can be computed effectively using variational expectation–maximization (VEM) parameter estimation. Motivated by our modeling results, we finally develop a new statistical color image watermark decoder based on vector SNCM-HMT and maximum likelihood (ML) decision rule. Experimental results on extensive test images demonstrate that the proposed statistical color image watermarking provides a performance better than that of most of the state-of-the-art statistical methods and some deep learning approaches recently proposed in the literature.