  Recent advances on adaptive steganography show that the performance of image
steganographic communication can be improved by incorporating the non-additive
models that capture the dependences among adjacent pixels. In this paper, a
Gaussian Markov Random Field model (GMRF) with four-element cross neighborhood
is proposed to characterize the interactions among local elements of cover
images, and the problem of secure image steganography is formulated as the one
of minimization of KL-divergence in terms of a series of low-dimensional clique
structures associated with GMRF by taking advantages of the conditional
independence of GMRF. The adoption of the proposed GMRF tessellates the cover
image into two disjoint subimages, and an alternating iterative optimization
scheme is developed to effectively embed the given payload while minimizing the
total KL-divergence between cover and stego, i.e., the statistical
detectability. Experimental results demonstrate that the proposed GMRF
outperforms the prior arts of model based schemes, e.g., MiPOD, and rivals the
state-of-the-art HiLL for practical steganography, where the selection channel
knowledges are unavailable to steganalyzers.
