An efficient distortion cost function design for image steganography in spatial domain using quaternion representation

It is well known that an effective steganographic distortion cost function is essential for spatial image steganography in the framework of minimal distortion embedding. To define the embedding cost by exploiting the texture complexity characterized by the high-pass filtered image residuals has been a popular approach. In this paper, by incorporating the quaternion representation of cover images, the image complexity is evaluated in terms of quaternion magnitude and phase, and a quaternion magnitude-based distortion (QMD) and a quaternion phase-based distortion (QPD) can be defined accordingly. With Hadamard product of QMD and QPD, a novel distortion cost function, namely QMP (Quaternion Magnitude-Phase), is obtained, aiming to efficiently allocate embedding modifications in complex regions of cover images with rich texture contents to improve the statistical undetectability (i.e., security). In addition, the generalized QMP (GQMP) in exponential form is further developed to boost the security performance. Experimental results demonstrate that both the proposed QMP and its generalized variant GQMP can outperform the state-of-the-art schemes, e.g., S-UNIWARD, HiLL, and MiPOD, in terms of empirical security performance against steganalysis.