Reducing overlapped pixels: a multi-objective color thresholding approach

  • Salvador HinojosaEmail author
  • Diego Oliva
  • Erik Cuevas
  • Gonzalo Pajares
  • Daniel Zaldivar
  • Marco Pérez-Cisneros
Methodologies and Application


This paper proposes a general multi-objective thresholding segmentation methodology for color images and a quality metric designed to prevent and quantify the overlapping effect of segmented images. Multi-level thresholding (MTH) has been used to segment color images in recent years; this process considers each channel as a single grayscale image and applies the MTH independently. Although this method provides competitive results, the inherent relationship among color channels is disregarded. Such approaches generate spurious classes on overlapping regions, where new colors are generated, especially on the borders of the objects. The proposed multi-objective color thresholding (MOCTH) approach performs image segmentation while preserving the relationship between image channels. MOCTH is aimed to reduce the overlapping effect on segmented color images without performing additional post-processing. To measure the overlapping classes on a thresholded color image, the overlapping index is proposed to quantify the pixels affected. The presented approach is analyzed on two color spaces (RGB and CIE L*a*b*) using three multi-objective algorithms; they are NSGA-III, SPEA-2, and MOPSO. Results provide evidence pointing out to a better segmentation from MOCTH over the traditional single-objective approaches while reducing overlapped areas on the image.


Multi-level thresholding Evolutionary algorithms Multi-objective optimization Overlapping Index 



The first author acknowledges The National Council of Science and Technology of Mexico (CONACyT) for the doctoral Grant Number 298285 for supporting this research.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.


  1. Agrawal S, Panda R, Bhuyan S, Panigrahi BK (2013) Tsallis entropy based optimal multilevel thresholding using cuckoo search algorithm. Swarm Evol Comput 11:16–30. CrossRefGoogle Scholar
  2. Akay B (2013) A study on particle swarm optimization and artificial bee colony algorithms for multilevel thresholding. Appl Soft Comput 13:3066–3091. CrossRefGoogle Scholar
  3. Banerjee S, Saha D, Jana ND (2015) Color image segmentation using Cauchy-mutated PSO. In: Mandal D, Kar R, Das S, Panigrahi B (eds) Intelligent computing and applications. Advances in intelligent systems and computing, vol 343. Springer, New Delhi, pp 239–250Google Scholar
  4. Bhandari AK, Singh VK, Kumar A, Singh GK (2014) Cuckoo search algorithm and wind driven optimization based study of satellite image segmentation for multilevel thresholding using Kapur’s entropy. Expert Syst Appl 41:3538–3560. CrossRefGoogle Scholar
  5. Bhandari AK, Kumar A, Singh GK (2015a) Modified artificial bee colony based computationally efficient multilevel thresholding for satellite image segmentation using Kapur’s, Otsu and Tsallis functions. Expert Syst Appl 42:1573–1601. CrossRefGoogle Scholar
  6. Bhandari AK, Kumar A, Singh GK (2015b) Tsallis entropy based multilevel thresholding for colored satellite image segmentation using evolutionary algorithms. Expert Syst Appl 42:8707–8730CrossRefGoogle Scholar
  7. Coello CAC (2009) Evolutionary multi-objective optimization: some current research trends and topics that remain to be explored. Front Comput Sci China 3:18–30. CrossRefGoogle Scholar
  8. Coello CAC, Pulido GTGTGT, Lechuga MSMS et al (2004) Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 8:256–279. CrossRefGoogle Scholar
  9. Deb K (1999) Multi-objective genetic algorithms: problem difficulties and construction of test problems. Evol Comput 7:205–230. CrossRefGoogle Scholar
  10. Deb K, Jain H (2013) An evolutionary many-objective optimization algorithm using reference-point based non-dominated sorting approach, part I: solving problems with box constraints. IEEE Trans Evol Comput 18:1. CrossRefGoogle Scholar
  11. Deb K, Pratab S, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NGSA-II. IEEE Trans Evol Comput 6:182–197. CrossRefGoogle Scholar
  12. Deng W, Zhao H, Yang X et al (2017a) Study on an improved adaptive PSO algorithm for solving multi-objective gate assignment. Appl Soft Comput 59:288–302. CrossRefGoogle Scholar
  13. Deng W, Zhao H, Zou L et al (2017b) A novel collaborative optimization algorithm in solving complex optimization problems. Soft Comput 21:4387–4398. CrossRefGoogle Scholar
  14. Deng W, Xu J, Zhao H (2019a) An improved ant colony optimization algorithm based on hybrid strategies for scheduling problem. IEEE Access 7:20281–20292. CrossRefGoogle Scholar
  15. Deng W, Yao R, Zhao H et al (2019b) A novel intelligent diagnosis method using optimal LS-SVM with improved PSO algorithm. Soft Comput 23:2445–2462. CrossRefGoogle Scholar
  16. Dhal KG, Das A, Ray S et al (2019) Nature-inspired optimization algorithms and their application in multi-thresholding image segmentation. Arch Comput Methods Eng. CrossRefGoogle Scholar
  17. El Aziz MA, Ewees AA, Hassanien AE (2017) Whale optimization algorithm and moth-flame optimization for multilevel thresholding image segmentation. Expert Syst Appl 83:242–256CrossRefGoogle Scholar
  18. Elaziz MA, Oliva D, Ewees AA, Xiong S (2019) Multi-level thresholding-based grey scale image segmentation using multi-objective multi-verse optimizer. Expert Syst Appl 125:112–129. CrossRefGoogle Scholar
  19. Fausto F, Reyna-Orta A, Cuevas E et al (2019) From ants to whales: metaheuristics for all tastes. Artif Intell Rev. CrossRefGoogle Scholar
  20. Glover F, Kochenberger GA (2003) Handbook of metaheuristics. Kluwer Academic Publishers, DordrechtzbMATHCrossRefGoogle Scholar
  21. Hammouche K, Diaf M, Siarry P (2010) A comparative study of various meta-heuristic techniques applied to the multilevel thresholding problem. Eng Appl Artif Intell 23:676–688. CrossRefGoogle Scholar
  22. Hinojosa S, Avalos O, Galvez J, et al (2018a) Remote sensing imagery segmentation based on multi-objective optimization algorithms. In: 2018 IEEE Latin American conference on computational intelligence (LA-CCI). IEEE, pp 1–6Google Scholar
  23. Hinojosa S, Avalos O, Oliva D et al (2018b) Unassisted thresholding based on multi-objective evolutionary algorithms. Knowl Based Syst 159:221–232. CrossRefGoogle Scholar
  24. Kapur JNN, Sahoo PKK, Wong AKCKC (1985) A new method for gray-level picture thresholding using the entropy of the histogram. Comput Vis Graph Image Process 29:273–285. CrossRefGoogle Scholar
  25. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39:459–471. MathSciNetzbMATHCrossRefGoogle Scholar
  26. Kennedy J, Eberhart RC (1997) A discrete binary version of the particle swarm algorithm. In: 1997 IEEE international conference on systems, man, and cybernetics. computational cybernetics and simulation. IEEE, pp 4104–4108Google Scholar
  27. Kurban T, Civicioglu P, Kurban R, Besdok E (2014) Comparison of evolutionary and swarm based computational techniques for multilevel color image thresholding. Appl Soft Comput 23:128–143. CrossRefGoogle Scholar
  28. Martin D, Fowlkes C, Tal D, Malik J (2001) A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings of 8th international conference on computer vision, vol 2, pp 416–423Google Scholar
  29. Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl Based Syst 96:120–133. CrossRefGoogle Scholar
  30. Olugbara OO, Adetiba E, Oyewole SA (2015) Pixel intensity clustering algorithm for multilevel image segmentation. Math Probl Eng. CrossRefGoogle Scholar
  31. Osuna-Enciso V, Cuevas E, Sossa H (2013) A comparison of nature inspired algorithms for multi-threshold image segmentation. Expert Syst Appl 40:1213–1219. CrossRefGoogle Scholar
  32. Otsu N (1979) A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern 9:62–66. CrossRefGoogle Scholar
  33. Rajinikanth V, Couceiro MS (2015) RGB histogram based color image segmentation using firefly algorithm. Procedia Comput Sci 46:1449–1457. CrossRefGoogle Scholar
  34. Rovcanin M, De Poorter E, Van Den Akker D et al (2014) Experimental validation of a reinforcement learning based approach for a service-wise optimisation of heterogeneous wireless sensor networks. Wirel Netw. CrossRefGoogle Scholar
  35. Sağ T, Çunkaş M (2015) Color image segmentation based on multiobjective artificial bee colony optimization. Appl Soft Comput 34:389–401. CrossRefGoogle Scholar
  36. Sarkar S, Das S, Chaudhuri SS (2015) A multilevel color image thresholding scheme based on minimum cross entropy and differential evolution. Elsevier, AMsterdamCrossRefGoogle Scholar
  37. Sarkar S, Das S, Chaudhuri SS (2016) Hyper-spectral image segmentation using Rényi entropy based multi-level thresholding aided with differential evolution. Expert Syst Appl 50:120–129. CrossRefGoogle Scholar
  38. Sathya PD, Kayalvizhi R (2011) Optimal multilevel thresholding using bacterial foraging algorithm. Expert Syst Appl 38:15549–15564. CrossRefGoogle Scholar
  39. Suman B (2005) Study of self-stopping PDMOSA and performance measure in multiobjective optimization. Comput Chem Eng 29:1131–1147. CrossRefGoogle Scholar
  40. Suresh S, Lal S (2017) Multilevel thresholding based on Chaotic Darwinian Particle Swarm Optimization for segmentation of satellite images. Appl Soft Comput 55:503–522. CrossRefGoogle Scholar
  41. Tang K, Xiao X, Wu J et al (2017) An improved multilevel thresholding approach based modified bacterial foraging optimization. Appl Intell 46:214–226. CrossRefGoogle Scholar
  42. Wang Z, Bovik ACAC, Sheikh HRHR, Simoncelli EPEP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612. CrossRefGoogle Scholar
  43. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82. CrossRefGoogle Scholar
  44. Zaitoun NM, Aqel MJ (2015) Survey on image segmentation techniques. Procedia Comput Sci 65:797–806. CrossRefGoogle Scholar
  45. Zhang YJ (1996) A survey on evaluation methods for image segmentation. Pattern Recognit 29:1335–1346. CrossRefGoogle Scholar
  46. Zhang L, Zhang L, Mou X, Zhang D (2011) FSIM: A feature similarity index for image quality assessment. IEEE Trans Image Process 20(8):2378–2386. MathSciNetzbMATHCrossRefGoogle Scholar
  47. Zhou A, Qu B-Y, Li H et al (2011) Multiobjective evolutionary algorithms: a survey of the state of the art. Swarm Evol Comput 1:32–49. CrossRefGoogle Scholar
  48. Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. Ph.D. Thesis 132. doi: citeulike-article-id:4597043Google Scholar
  49. Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3:257–271. CrossRefGoogle Scholar
  50. Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength pareto evolutionary algorithm. Eidgenössische Tech Hochschule Zürich (ETH), Inst Für Tech Inform Und Kommun (TIK)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dpto. Ingeniería del Software e Inteligencia Artificial, Facultad InformáticaUniversidad Complutense de MadridMadridSpain
  2. 2.Departamento de Electrónica, CUCEIUniversidad de GuadalajaraGuadalajaraMexico

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