Variable Multi-dimensional Co-occurrence for Steganalysis

In this paper, a novel multidimensional co-occurrence histogram scheme has been presented, in which the numbers of quantization levels for the elements in the co-occurrence are variable according to the distance among the elements, referred to as the co-occurrence with variable number of quantization levels, abbreviated as the VNQL co-occurrence or variable co-occurrence. Specifically, the longer the distance the smaller the number of quantization levels used. The dimensionality of the variable co-occurrence is therefore flexible and much smaller than that used in the traditional multidimensional co-occurrence of the same orders. Furthermore, the symmetry existed in the multidimensional co-occurrence is skillfully utilized in the proposed variable co-occurrence. Consequently, the feature dimensionality has been lowered dramatically. Thus, the fourth order variable co-occurrence applied to the residuals used in the spatial rich model results in \(1,704\) features, which work with a G-SVM classifier, can achieve an average detection rate similar to that of achieved by the TOP10 (dimension approximately 3,300) in the spatial rich model with a G-SVM classifier against the HUGO at 0.4 bpp on the same setup. The time consumed by the proposed \(1,704\) features is much shorter that used by the latter. Furthermore, the performance achieved by the proposed \(1,704\) together with a G-SVM classifier is on par with that achieved by the TOP39 with \(12,753\) features and an ensemble classifier on the same setup against two steganographic schemes, the HUGO and the edge adaptive. With another proposed set of \(1,977\) features, generated from the residuals used in the spatial rich model and from a few newly formulated residuals, and the G-SVM classifier, the performance achieved is better than that achieved by using the TOP39 feature-set with ensemble classifier on the same setup against the HUGO.