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Improving a firefly meta-heuristic for multilevel image segmentation using Tsallis entropy

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Abstract

In this paper we show that the non-extensive Tsallis entropy, when used as kernel in the bio-inspired firefly algorithm for multi-thresholding in image segmentation, is more efficient than using the traditional cross-entropy presented in the literature. The firefly algorithm is a swarm-based meta-heuristic, inspired by fireflies-seeking behavior following their luminescence. We show that the use of more convex kernels, as those based on non-extensive entropy, is more effective at \(5\,\%\) of significance level than the cross-entropy counterpart when applied in synthetic spaces for searching thresholds in global minimum.

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Notes

  1. We define the composed distribution, also called direct product of \(P=(p_{1},\ldots ,p_{n})\) and \(Q=(q_{1},\ldots ,q_{m})\), as \(P*Q=\{p_{i}q_{j}\}_{i,j}\), with \(1\le i\le n\) and \(1\le j\le m\)

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Acknowledgement

The authors would like to thank the CNPq and CAPES, the Brazilian agencies for Scientific Financing, as well as to FEI (Ignatian Educational Foundation), a Brazilian Jesuit Faculty of Science Computing and Engineering, for the support of this work.

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Authors and Affiliations

  1. Electrical Engineering and Computer Science Department of Ignatian Educational Foundation (FEI), São Paulo, Brazil

    Paulo S. Rodrigues, Guilherme A. Wachs-Lopes & Horst R. Erdmann

  2. Center of Mathematics, Computation and Cognition (CMCC) of Federal University of ABC (UFABC), São Paulo, Brazil

    Monael P. Ribeiro

  3. Computer Science Department of National Laboratory for Scientific Computing, Petropólis, Brazil

    Gilson A. Giraldi

Authors
  1. Paulo S. Rodrigues
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  2. Guilherme A. Wachs-Lopes
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  3. Horst R. Erdmann
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  4. Monael P. Ribeiro
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  5. Gilson A. Giraldi
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Correspondence to Paulo S. Rodrigues.

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Rodrigues, P.S., Wachs-Lopes, G.A., Erdmann, H.R. et al. Improving a firefly meta-heuristic for multilevel image segmentation using Tsallis entropy. Pattern Anal Applic 20, 1–20 (2017). https://doi.org/10.1007/s10044-015-0450-x

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