Benford's Law for Natural and Synthetic Images
Inhaltsverzeichnis
Reference
Esteve del Acebo, Mateu Sbert: Benford's Law for Natural and Synthetic Images. In: László Neumann, Mateu Sbert, Bruce Gooch, Werner Purgathofer (Eds.): Eurographics Workshop on Computational Aesthetics. 2005. 169-176
DOI
http://dx.doi.org/10.2312/COMPAESTH/COMPAESTH05/169-176
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.
Extended Abstract
Bibtex
@inproceedings{Acebo:2005:BLN:2381219.2381243,
author = {Acebo, E. and Sbert, M.},
title = {Benford's Law for Natural and Synthetic Images},
booktitle = {Proceedings of the First Eurographics Conference on Computational Aesthetics in Graphics, Visualization and Imaging},
series = {Computational Aesthetics'05},
year = {2005},
isbn = {3-905673-27-4},
location = {Girona, Spain},
pages = {169--176},
numpages = {8},
url = {http://dx.doi.org/10.2312/COMPAESTH/COMPAESTH05/169-176 http://de.evo-art.org/index.php?title=Benford's_Law_for_Natural_and_Synthetic_Images },
doi = {10.2312/COMPAESTH/COMPAESTH05/169-176},
acmid = {2381243},
publisher = {Eurographics Association},
address = {Aire-la-Ville, Switzerland, Switzerland},
}
Used References
Suyash P. Awate , Ross T. Whitaker, Higher-Order Image Statistics for Unsupervised, Information-Theoretic, Adaptive, Image Filtering, Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2, p.44-51, June 20-26, 2005 http://dx.doi.org/10.1109/CVPR.2005.176
J. L. Barlow , E. H. Bareiss, On roundoff error distributions in floating point and logarithmic arithmetic, Computing, v.34 n.4, p.325-347, 1985 http://dx.doi.org/10.1007/BF02251833
CHERNOFF H.: How to beat the massachusetts numbers game. Math. Intel. 3 (1981), 166-172.
Francesc Castro , László Neumann , Mateu Sbert, Extended ambient term, Journal of Graphics Tools, v.5 n.4, p.1-7, Nov. 2000 http://dx.doi.org/10.1080/10867651.2000.10487527
Philip Dutre , Kavita Bala , Philippe Bekaert, Advanced Global Illumination, A. K. Peters, Ltd., Natick, MA, 2002 http://dl.acm.org/citation.cfm?id=863241&CFID=588525319&CFTOKEN=29804931
ERIK REINHARD P. S., TROSCIANKO T.: Natural image statistics for computer graphics. Research Report UUCS-01-002, School of Computing, University of Utah, Salt Lake City, Salt Lake City, UT 84112 USA, 2001.
FELDSTEIN A., TURNER P.: Overflow, underflow and severe loss of significance in floating-point addition. IMA J. Numerical Analysis 6 (1986), 241-251.
HILL T.: A statistical derivation of the significant-digit law. Statistical Science 10, 4 (1996), 354-363.
Andrey Iones , Anton Krupkin , Mateu Sbert , Sergey Zhukov, Fast, Realistic Lighting for Video Games, IEEE Computer Graphics and Applications, v.23 n.3, p.54-64, May 2003 http://dx.doi.org/10.1109/MCG.2003.1198263
Jean-Michel Jolion, Images and Benford's Law, Journal of Mathematical Imaging and Vision, v.14 n.1, p.73-81, Feb. 2001 http://dx.doi.org/10.1023/A:1008363415314
KNUTH D.: The art of computer programming. Vol. 2. Addison-Wesley. New York, 1969.
NIGRINI M. J.: Note on the frequency of use of the diferent digits in natural numbers. The White Paper (1996).
NIGRINI M. J., MITTERMAIER L. I.: The use of benford's law as an aid in analytical procedures. Auditing: A Journal of Practice and Theory 16 (1997), 52-67.
NIGRINI N., WOOD W.: Assessing the integrity of demographic tabulated data, 1995.
The persistence of vision ray-tracer, http://www.povray.com.
RAIMI R.: The first digit problem. American Mathematical Monthly 83 (1976), 521-538.
P. Schatte, On mantissa distributions in computing and Benford's law, Journal of Information Processing and Cybernetics, v.24 n.9, p.443-455, Sept. 1988 http://dl.acm.org/citation.cfm?id=56195&CFID=588525319&CFTOKEN=29804931
SIMONCELLI E. P., OLSHAUSEN B. A.: Natural image statistics and neural representation. Annu. Rev. Neurosci. 24 (2001), 193-216.
VARIAN H.: Benford's law. Amer. Statician 23 (1972), 65-66.
Links
Full Text
[extern file]
Sonstige Links
http://dl.acm.org/citation.cfm?id=2381219.2381243&coll=DL&dl=GUIDE&CFID=588525319&CFTOKEN=29804931
