On The Generalized Additivity Of Kaniadakis Entropy

On The Generalized Additivity Of Kaniadakis Entropy

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Author(s)

Author(s): Amelia Carolina Sparavigna

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DOI: 10.18483/ijSci.627 415 1263 44-48 Volume 4 - Feb 2015

Abstract

Since entropy has several applications in the information theory, such as, for example, in bi-level or multi-level thresholding of images, it is interesting to investigate the generalized additivity of Kaniadakis entropy for more than two systems. Here we consider the additivity for three, four and five systems, because we aim applying Kaniadakis entropy to such multi-level analyses.

Keywords

Kaniadakis Entropy, Data segmentation, Image processing, Thresholding

References

  1. Kaniadakis, G. Theoretical foundations and mathematical formalism of the power-law tailed statistical distributions, Entropy, 2013, 15, 3983-4010. http://dx.doi.org/10.3390/e15103983
  2. Kaniadakis, G. Statistical mechanics in the context of special relativity, Phys. Rev. E, 2002, 66, 056125. http://dx.doi.org/10.1103/physreve.66.056125
  3. Tsallis, C. Introduction to nonextensive statistical mechanics, 2009, Springer. http://dx.doi.org/10.1007/978-0-387-85359-8_6
  4. Gull, S.F.; Skilling, J. Maximum entropy method in image processing. Communications, Radar and Signal Processing, IEE Proceedings F, 1984, 131, 646-659. http://dx.doi.org/10.1049/ip-f-1.1984.0099
  5. Portes de Albuquerque, M.; Esquef, I.A.; Gesualdi Mello, A.R.; Portes de Albuquerque, M. Image thresholding using Tsallis entropy. Pattern Recognition Letters, 2004, 25, 1059-1065. http://dx.doi.org/10.1016/j.patrec.2004.03.003
  6. Kapur, J.N.; Sahoo, P.K.; Wong, A.K.C. A new method for gray-level picture thresholding using the entropy of the histogram. Comput. Vision Graphics Image Process., 1985, 29, 273-285. http://dx.doi.org/10.1016/0734-189x(85)90125-2
  7. Jaynes, E.T. Where do we go from here?, in C. Ray Smith and W.T. Grandy, Jr. (eds.), Maximum-entropy and Bayesian methods in inverse problems, 21-58, 1985, D. Reidel Publishing Company. http://dx.doi.org/10.1007/978-94-017-2221-6_2
  8. Sparavigna, A.C. Shannon, Tsallis and Kaniadakis entropies in bi-level image thresholding, International Journal of Sciences, 2015, in print.
  9. Tsallis, C. Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics, 1988, 52, 479–487. http://dx.doi.org/10.1007/bf01016429
  10. Scarfone, A.M.; Wada, T. Thermodynamic equilibrium and its stability for microcanonical systems described by the Sharma-Taneja-Mittal entropy, 2005, Phys. Rev. E 72, 026123. http://dx.doi.org/10.1103/physreve.72.026123

Cite this Article:

International Journal of Sciences is Open Access Journal.
This article is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License.
Author(s) retain the copyrights of this article, though, publication rights are with Alkhaer Publications.

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