Variance Analysis of Pixel-Value Differencing Steganography

As the adaptive steganography selects edge and texture area for loading, the theoretical analysis is limited by modeling difficulty. This paper introduces a novel method to study pixel-value difference (PVD) embedding scheme. First, the difference histogram values of cover image are used as parameters, and a variance formula for PVD stego noise is obtained. The accuracy of this formula has been verified through analysis with standard pictures. Second, the stego noise is divided into six kinds of pixel regions, and the regional noise variances are utilized to compare the security between PVD and least significant bit matching (LSBM) steganography. A mathematical conclusion is presented that, with the embedding capacity less than 2.75 bits per pixel, PVD is always not safer than LSBM under the same embedding rate, regardless of region selection. Finally, 10000 image samples are used to observe the validity of mathematical conclusion. For most images and regions, the data are also shown to be consistent with the prior judgment. Meanwhile, the cases of exception are analyzed seriously, and are found to be caused by randomness of pixel selection and abandoned blocks in PVD scheme. In summary, the unity of theory and practice completely indicates the effectiveness of our new method.