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Thermodynamics-Based Evaluation of Various Improved Shannon Entropies for Configurational Information of Gray-Level Images

by 1, 1,2,* and 2
1
Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong, China
2
Faculty of Geosciences & Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China
*
Author to whom correspondence should be addressed.
Received: 14 November 2017 / Revised: 17 December 2017 / Accepted: 23 December 2017 / Published: 2 January 2018
(This article belongs to the Section Information Theory, Probability and Statistics)
The quality of an image affects its utility and image quality assessment has been a hot research topic for many years. One widely used measure for image quality assessment is Shannon entropy, which has a well-established information-theoretic basis. The value of this entropy can be interpreted as the amount of information. However, Shannon entropy is badly adapted to information measurement in images, because it captures only the compositional information of an image and ignores the configurational aspect. To fix this problem, improved Shannon entropies have been actively proposed in the last few decades, but a thorough evaluation of their performance is still lacking. This study presents such an evaluation, involving twenty-three improved Shannon entropies based on various tools such as gray-level co-occurrence matrices and local binary patterns. For the evaluation, we proposed: (a) a strategy to generate testing (gray-level) images by simulating the mixing of ideal gases in thermodynamics; (b) three criteria consisting of validity, reliability, and ability to capture configurational disorder; and (c) three measures to assess the fulfillment of each criterion. The evaluation results show only the improved entropies based on local binary patterns are invalid for use in quantifying the configurational information of images, and the best variant of Shannon entropy in terms of reliability and ability is the one based on the average distance between same/different-value pixels. These conclusions are theoretically important in setting a direction for the future research on improving entropy and are practically useful in selecting an effective entropy for various image processing applications. View Full-Text
Keywords: Shannon entropy; information entropy; information content; configurational information Shannon entropy; information entropy; information content; configurational information
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MDPI and ACS Style

Gao, P.; Li, Z.; Zhang, H. Thermodynamics-Based Evaluation of Various Improved Shannon Entropies for Configurational Information of Gray-Level Images. Entropy 2018, 20, 19. https://0-doi-org.brum.beds.ac.uk/10.3390/e20010019

AMA Style

Gao P, Li Z, Zhang H. Thermodynamics-Based Evaluation of Various Improved Shannon Entropies for Configurational Information of Gray-Level Images. Entropy. 2018; 20(1):19. https://0-doi-org.brum.beds.ac.uk/10.3390/e20010019

Chicago/Turabian Style

Gao, Peichao, Zhilin Li, and Hong Zhang. 2018. "Thermodynamics-Based Evaluation of Various Improved Shannon Entropies for Configurational Information of Gray-Level Images" Entropy 20, no. 1: 19. https://0-doi-org.brum.beds.ac.uk/10.3390/e20010019

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