Pattern Analysis and Applications

, Volume 20, Issue 1, pp 1–20 | Cite as

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

  • Paulo S. RodriguesEmail author
  • Guilherme A. Wachs-Lopes
  • Horst R. Erdmann
  • Monael P. Ribeiro
  • Gilson A. Giraldi
Theoretical Advances


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.


Firefly meta-heuristic Tsallis entropy Image segmentation Optimization 



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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Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Paulo S. Rodrigues
    • 1
    Email author
  • Guilherme A. Wachs-Lopes
    • 1
  • Horst R. Erdmann
    • 1
  • Monael P. Ribeiro
    • 2
  • Gilson A. Giraldi
    • 3
  1. 1.Electrical Engineering and Computer Science Department of Ignatian Educational Foundation (FEI)São PauloBrazil
  2. 2.Center of MathematicsComputation and Cognition (CMCC) of Federal University of ABC (UFABC)São PauloBrazil
  3. 3.Computer Science Department of National Laboratory for Scientific ComputingPetropólisBrazil

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