Estimating JPEG2000 Compression for Image Forensics Using the Benford’s Law

With the tremendous growth and usage of digital images nowadays, the integrity and authenticity of digital content is becoming increasingly important, and a growing concern to many government and commercial sectors. Image Forensics, based on a passive statistical analysis of the image data only, is an alternative approach to the active embedding of data associated with Digital Watermarking. Benford’s Law was first introduced to analyse the probability distribution of the 1 digit (1-9) numbers of natural data, and has since been applied to Accounting Forensics for detecting fraudulent income tax returns [9]. More recently, Benford's Law has been further applied to image processing and image forensics. For example, Fu et al. [5] proposed a Generalised Benford’s Law technique for estimating the Quality Factor (QF) of JPEG compressed images. In our previous work, we proposed a framework incorporating the Generalised Benford’s Law to accurately detect unknown JPEG compression rates of watermarked images in semi-fragile watermarking schemes. JPEG2000 (a relatively new image compression standard) offers higher compression rates and better image quality as compared to JPEG compression. In this paper, we propose the novel use of Benford’s Law for estimating JPEG2000 compression for image forensics applications. By analysing the DWT coefficients and JPEG2000 compression on 1338 test images, the initial results indicate that the 1 digit probability of DWT coefficients follow the Benford's Law. The unknown JPEG2000 compression rates of the image can also be derived, and proved with the help of a divergence factor, which shows the deviation between the probabilities and Benford’s Law. Based on 1338 test images, the mean divergence for DWT coefficients is approximately 0.0016, which is lower than DCT coefficients at 0.0034. However, the mean divergence for JPEG2000 images compression rate at 0.1 is 0.0108, which is much higher than uncompressed DWT coefficients. This result clearly indicates a presence of compression in the image. Moreover, we compare the results of 1 digit probability and divergence among JPEG2000 compression rates at 0.1, 0.3, 0.5 and 0.9. The initial results show that the expected difference among them could be used for further analysis to estimate the unknown JPEG2000 compression rates.