Machine Learning in Image Steganalysis

Chapter 6

More Spatial Domain Features

We have looked at two fundamental concepts for the analysis of pixmap images, namely histograms and joint histograms, and individual bit planes. In this chapter we study two more, namely the difference matrices and image quality metrics (IQM). The image quality metrics were introduced by one of the pioneers in the use of machine learning for steganalysis, namely Avciba et al. (2003). The difference matrices are derived from joint histograms and have been used for several different feature vectors, including the recent subtractive pixel adjacency model (SPAM) features, which seem to be the current state of the art.

6.1 The Difference Matrix

The co-occurrence matrix, or 2-D histogram, from Chapter 4 contains a lot of information, with 2¹⁶ entries for 8-bit grey-scale images, and this makes it hard to analyse. Looking back at the scatter plots that we used to visualise the co-occurrence matrix, we note that most of the entries are zero and thus void of information. The interesting data are close to the diagonal, and the effect we are studying is the degree of spreading around the main diagonal; that is, the differences between neighbour pixels, rather than the joint distribution. This has led to the study of the difference matrix.

Definition 6.1.1 (Difference matrix)

The difference matrix of an M × N matrix I is defined as

The difference ...