Relating the Detection Rate, Capacity and the Cost of Steganography by Steganographer Modeling

Statistical detectablity of a steganalyser declares its ability to distinguish between cover and stego images. Optimum steganographer must be designed to confuse the corresponding steganalysers in detecting stego images. Thus, designing a steganographic algorithm based on reducing statistical detectability is of great importance. Unfortunately establishing a perfect relation between pixel cost and statistical detectability is still an open problem. In this paper, we have modelled steganalyser by special graphical models, called topic models, to estimate the error rate of a steganalyser in terms of the steganographic pixel cost. Morover, we have redefined the steganographic capacity and pixel cost based on such models. It is also shown that the new critera are compatible with classical ones, like PSNR. Then, an algorithm is designed as per such criteria. It is shown empirically that the presented algorithm is comparable to the best analytically designed algorithms presented so far. It is worth mentioning that the paper is focused on establishing a mathematical basis for the relation between the steganalyzer error and pixel cost and not improving the current algorithms. Nonetheless, as compared to the rivals, a small improvement, about 0.5% in steganalysis error, has also been achieved.