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We present a generalization of Benford's law for the first sig-nificant digit. This generalization is based on keeping two terms of the Fourier expansion of the probability density func-tion of the data in the modular logarithmic domain. We prove that images in the Discrete Cosine Transform domain closely follow this generalization. We use this property to propose an application in image forensics, namely, detecting that a given image carries a hidden message.
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... This property has been largely exploited in multimedia forensics to detect image tampering. In fact, natural image DCT coefficients can be typically modeled by a Laplacianlike distribution [21], which naturally follow Benford's law, and for this reason, the mentioned rule can be successfully used in image forensic applications [22]. ...
... This processing chain is used by the JPEG coding standards and proves to be tailored to the spectral characteristics of images. Some of the past works highlight that, in the frequency domain, the quantized DCT coefficient statistics of natural images must follow Benford's law [22]. ...
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The advent of Generative Adversarial Network (GAN) architectures has given anyone the ability of generating incredibly realistic synthetic imagery. The malicious diffusion of GAN-generated images may lead to serious social and political consequences (e.g., fake news spreading, opinion formation, etc.). It is therefore important to regulate the widespread distribution of synthetic imagery by developing solutions able to detect them. In this paper, we study the possibility of using Benford's law to discriminate GAN-generated images from natural photographs. Benford's law describes the distribution of the most significant digit for quantized Discrete Cosine Transform (DCT) coefficients. Extending and generalizing this property, we show that it is possible to extract a compact feature vector from an image. This feature vector can be fed to an extremely simple classifier for GAN-generated image detection purpose.
... Também conhecida como Lei do primeiro dígito, possui aplicaçaplicaç˜aplicação prática em diversasáreasdiversas´diversasáreas do conhecimento e ´ e utilizada para diferentes finalidades. Por exemplo, na computaçcomputaç˜computação especificamente, pode ser empregada na detecçdetecç˜detecção de anomalias na rede [Arshadi and Jahangir 2014] ou identificaçidentificaç˜identificação de mensagens escondidas em imagens [Pérez-González et al. 2007]. ...
Conference Paper
The exploration of human behavior patterns is a central question for the development of new applications and technological solutions. However, few studies investigate how user habits can improve the performance of Information-Centric Network architectures. This work presents an analysis of the behavioral profiles of music users and how different profiles influence the performance of cache replacement policies. The results of an experimental study using ndnSIM with real traces from several users show that user habits are determining factors in choosing an optimized cache replacement policy. This research also reveals that the popularity distribution of the songs follows an approximation of Benford's Law, and it is possible to differentiate profiles for different users according to the behavior of Benford curve for these accessed songs.
Article
Benford’s law states that the frequency of lower first significant digits(FSD) is higher than that of upper FSD in many naturally produced numbers. The law can be applied to many various fields, so it is important to know which common probability distributions obey Benford’s law. We revisit whether the Log-normal probability distribution obeys the law by using the method of Fourier analysis and numerical simulation. Moreover, we use simulation method to judge whether the Weibull distribution and the Inverse Gamma distribution are close to Benford’s law under some conditions. Our work give some reasons to support why Benford’s law is universal in real world.
Chapter
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Conference Paper
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Benford's law states that many data sets have a bias towards lower leading digits (about 30% are 1s). There are numerous applications, from designing efficient computers to detecting tax, voter and image fraud. It's important to know which common probability distributions are almost Benford. We show the Weibull distribution, for many values of its parameters, is close to Benford's law, quantifying the deviations. As the Weibull distribution arises in many problems, especially survival analysis, our results provide additional arguments for the prevalence of Benford behavior. The proof is by Poisson summation, a powerful technique to attack such problems.
Book
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Benford's law states that the leading digits of many data sets are not uniformly distributed from one through nine, but rather exhibit a profound bias. This bias is evident in everything from electricity bills and street addresses to stock prices, population numbers, mortality rates, and the lengths of rivers. Here, Steven Miller brings together many of the world's leading experts on Benford's law to demonstrate the many useful techniques that arise from the law, show how truly multidisciplinary it is, and encourage collaboration. Beginning with the general theory, the contributors explain the prevalence of the bias, highlighting explanations for when systems should and should not follow Benford's law and how quickly such behavior sets in. They go on to discuss important applications in disciplines ranging from accounting and economics to psychology and the natural sciences. The contributors describe how Benford's law has been successfully used to expose fraud in elections, medical tests, tax filings, and financial reports. Additionally, numerous problems, background materials, and technical details are available online to help instructors create courses around the book. Emphasizing common challenges and techniques across the disciplines, this accessible book shows how Benford's law can serve as a productive meeting ground for researchers and practitioners in diverse fields.
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