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Improving the non-extensive medical image segmentation based on Tsallis entropy

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Abstract

Thresholding techniques for image segmentation is one of the most popular approaches in Computational Vision systems. Recently, M. Albuquerque has proposed a thresholding method (Albuquerque et al. in Pattern Recognit Lett 25:1059–1065, 2004) based on the Tsallis entropy, which is a generalization of the traditional Shannon entropy through the introduction of an entropic parameter q. However, the solution may be very dependent on the q value and the development of an automatic approach to compute a suitable value for q remains also an open problem. In this paper, we propose a generalization of the Tsallis theory in order to improve the non-extensive segmentation method. Specifically, we work out over a suitable property of Tsallis theory, named the pseudo-additive property, which states the formalism to compute the whole entropy from two probability distributions given an unique q value. Our idea is to use the original M. Albuquerque’s algorithm to compute an initial threshold and then update the q value using the ratio of the areas observed in the image histogram for the background and foreground. The proposed technique is less sensitive to the q value and overcomes the M. Albuquerque and k-means algorithms, as we will demonstrate for both ultrasound breast cancer images and synthetic data.

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Notes

  1. We define the composed distribution, also called direct product of \(P = [p_1, \ldots, p_n]\) and \(Q = [q_1,\ldots, q_n], \) as \(P \ast Q =\{p_iq_j\}_{i,j},\) with \(1 \leq i \leq n\) and \(1 \leq j \leq m\)

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Authors and Affiliations

  1. IAAA Group, University Center of FEI, São Paulo, Brazil

    Paulo S. Rodrigues

  2. Department of Computer Science, National Laboratory for Scientific Computing, Rio de Janeiro, Brazil

    Gilson A. Giraldi

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  1. Paulo S. Rodrigues
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  2. Gilson A. Giraldi
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Correspondence to Paulo S. Rodrigues.

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Rodrigues, P.S., Giraldi, G.A. Improving the non-extensive medical image segmentation based on Tsallis entropy. Pattern Anal Applic 14, 369–379 (2011). https://doi.org/10.1007/s10044-011-0225-y

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