Benford's Law for Natural and Synthetic Images

Abstract

Benford's Law (also known as the First Digit Law) is well known in statistics of natural phenomena. It states that, when dealing with quantities obtained from Nature, the frequency of appearance of each digit in the first significant place is logarithmic. This law has been observed over a broad range of statistical phenomena. In this paper, we will explore its application to image analysis. We will show how light intensities in natural images, under certain constraints, obey this law closely. We will also show how light intensities in synthetic images follow this law whenever they are generated using physically realistic methods, and fail otherwise. Finally, we will study how transformations on the images affect the adjustment to the Law and how the fitting to the law is related to the fitting of the distribution of the raw intensities of the image to a power law.