Abstract
The Newcomb–Benford law states that in a set of natural numbers, the leading digit has a probability distribution that decays logarithmically. One of its major applications is the JPEG compression of images, a field of great interest for domains such as image forensics. In this article, we study JPEG compression from the point of view of Benford’s law. The article focuses on ways to detect fraudulent images and JPEG quality factors. Moreover, using the image’s luminance channel and JPEG coefficients, we describe a technique for determining the quality factor with which a JPEG image is compressed. The algorithm’s results are described in considerably more depth in the article’s final sections. Furthermore, the proposed idea is applicable to any procedure that involves the analysis of digital images and in which it is strongly suggested that the image authenticity be verified prior to beginning the analyzing process.
Highlights
The empirical gem of statistical folklore [1], a phenomenon well-known by some, yet little known by most, is the Newcomb–Benford law
When the Newcomb–Benford law (NBL) is used to detect various types of data tampering, the following assumption is made and tested: the real data will follow the distribution given by this law, while the altered data will not
A popular claim states that to follow the NBL, a distribution must extend over several orders of magnitude [24,25,26]
Summary
The empirical gem of statistical folklore [1], a phenomenon well-known by some, yet little known by most, is the Newcomb–Benford law. Since in 1881, pocket calculators had not yet been invented, the Newcomb–Benford law (NBL) was first discovered by S. Newcomb while he was looking through the pages of a logarithmic book. A further mathematical and experimental analysis was made by F. Benford, who named it The Law of Anomalous Numbers. He stated that the ten digits do not occur with equal frequency, but according to the following logarithmic relation [3]: a+1
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