# Images and Benford's Law

@article{Jolion2004ImagesAB, title={Images and Benford's Law}, author={Jean-Michel Jolion}, journal={Journal of Mathematical Imaging and Vision}, year={2004}, volume={14}, pages={73-81} }

Benford's law had been proposed in the past as a way to modelize the probability distribution of the first digit in a set of natural numbers. We show in this paper that the magnitude of the gradient of an image obeys this law. We show, experimentally, that this also applies for the laplacian pyramid code. This yields to the field of entropy based coding which takes advantage of the a priori information about the probability of any symbol in the signal.

## 73 Citations

BENFORD ’ S LAW IN IMAGE PROCESSING

- Computer Science, Mathematics
- 2007

It is proved that images in the Discrete Cosine Transform domain closely follow a generalization of Benford's law for the first significant digit, and this property is used to propose an application in image steganalysis, namely, detecting that a given image carries a hidden message.

Benford's Lawin Image Processing

- Computer Science, Mathematics2007 IEEE International Conference on Image Processing
- 2007

It is proved that images in the discrete cosine transform domain closely follow a generalization of Benford's law for the first significant digit, and this property is used to propose an application in image steganalysis, namely, detecting that a given image carries a hidden message.

A generalization of Benford's law and its application to images

- Mathematics, Computer Science2007 European Control Conference (ECC)
- 2007

It is proved that images in the Discrete Cosine Transform domain closely follow a generalization of Benford's law for the first significant digit, and this property is used to propose an application in image forensics, namely, detecting that a given image carries a hidden message.

Benford's Law for Natural and Synthetic Images

- MathematicsCAe
- 2005

It is shown how light intensities in natural images, under certain constraints, obey Benford's Law closely and how light intensity in synthetic images follow this law whenever they are generated using physically realistic methods, and fail otherwise.

A generalized Benford's law for JPEG coefficients and its applications in image forensics

- Computer Science, MathematicsElectronic Imaging
- 2007

In this paper, a novel statistical model based on Benford's law for the probability distributions of the first digits of the block-DCT and quantized JPEG coefficients is presented. A parametric…

The Newcomb-Benford law: Scale invariance and a simple Markov process based on it

- Mathematics
- 2021

The Newcomb–Benford law, also known as the ﬁrst-digit law, gives the probability distribution associated with the ﬁrst digit of a dataset, so that, for example, the ﬁrst signiﬁcant digit has a…

Understanding benford's law and its vulnerability in image forensics

- Computer Science, Mathematics2009 IEEE International Conference on Multimedia and Expo
- 2009

This paper considers a generalized form of Benford's law and relates it to a random variable of a certain probability density function such as the generalized Gaussian or Laplacian function and examines its application to image forensic applications.

O T ] 3 0 A pr 2 01 9 First digit law from Laplace transform

- Mathematics
- 2019

The occurrence of digits 1 through 9 as the leftmost nonzero digit of numbers from real-world sources is distributed unevenly according to an empirical law, known as Benford’s law or the first digit…

ON SOME PROPERTIES OF BENFORD`S LAW

- Mathematics
- 2010

In presented paper there were studied some properties of Benford's law. The existence of this law in not necessary large sets of numbers is a very interesting example that can show how the complex…

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