Variable Multi-dimensional Co-occurrence for Steganalysis

Abstract

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.