A proper transform for satisfying Benford´s Law and its application to double JPEG image forensics

This paper presents a new transform domain to evaluate the goodness of fit of natural image data to the common Benford´s Law. The evaluation is made by three statistical fitness criteria including Pearson´s chi-square test statistic, normalized cross correlation and a distance measure based on symmetrized Kullback-Leibler divergence. It is shown that the serial combination of variance filtering and block 2-D discrete cosine transform reveals the best goodness of fit for the first significant digit. We also show that the proposed transform domain brings reasonable fit for the second, third and fourth significant digits. As an application, the proposed transform domain is utilized to detect image manipulation by distinguishing single compressed images from doubly compressed ones.