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A q-Extension of Sigmoid Functions and the Application for Enhancement of Ultrasound Images

1
Computer Science Department, Centro Universitário FEI, São Bernardo do Campo 09850-901, SP, Brazil
2
National Laboratory for Scientific Computing, Petrópolis 25651-075, RJ, Brazil
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(4), 430; https://doi.org/10.3390/e21040430
Received: 14 March 2019 / Revised: 14 April 2019 / Accepted: 17 April 2019 / Published: 23 April 2019
(This article belongs to the Special Issue Entropy in Image Analysis)
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Abstract

This paper proposes the q-sigmoid functions, which are variations of the sigmoid expressions and an analysis of their application to the process of enhancing regions of interest in digital images. These new functions are based on the non-extensive Tsallis statistics, arising in the field of statistical mechanics through the use of q-exponential functions. The potential of q-sigmoids for image processing is demonstrated in tasks of region enhancement in ultrasound images which are highly affected by speckle noise. Before demonstrating the results in real images, we study the asymptotic behavior of these functions and the effect of the obtained expressions when processing synthetic images. In both experiments, the q-sigmoids overcame the original sigmoid functions, as well as two other well-known methods for the enhancement of regions of interest: slicing and histogram equalization. These results show that q-sigmoids can be used as a preprocessing step in pipelines including segmentation as demonstrated for the Otsu algorithm and deep learning approaches for further feature extractions and analyses. View Full-Text
Keywords: contrast enhancement; sigmoid; Tsallis statistics; q-exponential; q-sigmoid; q-Gaussian; ultra-sound images contrast enhancement; sigmoid; Tsallis statistics; q-exponential; q-sigmoid; q-Gaussian; ultra-sound images
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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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Sergio Rodrigues, P.; Wachs-Lopes, G.; Morello Santos, R.; Coltri, E.; Antonio Giraldi, G. A q-Extension of Sigmoid Functions and the Application for Enhancement of Ultrasound Images. Entropy 2019, 21, 430.

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