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Entropy 2016, 18(8), 299; doi:10.3390/e18080299

Determining the Entropic Index q of Tsallis Entropy in Images through Redundancy

1
PhD Program on Science, Technology and Society, CINVESTAV-IPN, AP 14-740, Mexico City 07000, Mexico
2
Center for Research on Artificial Intelligence, University of Veracruz, Sebastian Camacho 5, Xalapa Veracruz 91000, Mexico
3
Physics Department, CINVESTAV-IPN, AP 14-740, Mexico City 07000, Mexico
*
Author to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Received: 7 June 2016 / Revised: 3 August 2016 / Accepted: 8 August 2016 / Published: 15 August 2016
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Abstract

The Boltzmann–Gibbs and Tsallis entropies are essential concepts in statistical physics, which have found multiple applications in many engineering and science areas. In particular, we focus our interest on their applications to image processing through information theory. We present in this article a novel numeric method to calculate the Tsallis entropic index q characteristic to a given image, considering the image as a non-extensive system. The entropic index q is calculated through q-redundancy maximization, which is a methodology that comes from information theory. We find better results in the image processing in the grayscale by using the Tsallis entropy and thresholding q instead of the Shannon entropy. View Full-Text
Keywords: Shannon entropy; Tsallis entropy; entropic index q; information theory; redundancy; maximum entropy principle; image thresholding Shannon entropy; Tsallis entropy; entropic index q; information theory; redundancy; maximum entropy principle; image thresholding
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Ramírez-Reyes, A.; Hernández-Montoya, A.R.; Herrera-Corral, G.; Domínguez-Jiménez, I. Determining the Entropic Index q of Tsallis Entropy in Images through Redundancy. Entropy 2016, 18, 299.

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