Abstract
Multilevel thresholding for image segmentation is one of the crucial techniques in image processing. Even though numerous methods have been proposed in literature, it is still a challenge for the existing methods to produce steady satisfactory thresholds at manageable computational cost in segmenting images with various unknown properties. In this paper, a non-revisiting quantum-behaved particle swarm optimization (NrQPSO) algorithm is proposed to find the optimal multilevel thresholds for gray-level images. The proposed NrQPSO uses the non-revisiting scheme to avoid the re-evaluation of the evaluated solution candidates. To reduce the unnecessary computation cost, the NrQPSO provides an automatic stopping mechanism which is capable of gauging the progress of exploration and stops the algorithm rationally in a natural manner. For further improving the computation efficiency, the NrQPSO employs a meticulous solution search method to overcome the drawback of the existing QPSO algorithms using the original search methods. Performance of the NrQPSO is tested on the Berkeley segmentation data set. The experimental results have demonstrated that the NrQPSO can outperform the other state-of-the-art population-based thresholding methods in terms of efficiency, effectiveness and robustness; thus, the NrQPSO can be applied in real-time massive image processing.
Similar content being viewed by others
References
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(7):3538–3560
Pal NR, Pal SK (1993) A review on image segmentation techniques. Pattern Recogn 26(9):1277–1294
Sezgin M, Sankur B (2004) Survey over image thresholding techniques and quantitative performance evaluation. J Electron Imaging 13(1):146–166
Marciniak A, Kowal M, Filipczuk P, Korbicz J (2014) Swarm intelligence algorithms for multi-level image thresholding. In: Korbicz J, Kowal M (eds) Intelligent systems in technical and medical diagnostics. Advances in Intelligent Systems and Computing, vol 230. Springer, Berlin, Heidelberg, pp 301–311
Kittler J, Illingworth J (1986) Minimum error thresholding. Pattern Recogn 19(1):41–47
Bazi Y, Bruzzone L, Melgani F (2007) Image thresholding based on the EM algorithm and the generalized Gaussian distribution. Pattern Recogn 40(2):619–634
Abo-Eleneen Z (2011) Thresholding based on Fisher linear discriminant. J Pattern Recogn Res 2:326–334
Otsu N (1979) A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern 9(1):62–66
Ye Q-Z, Danielsson P-E (1988) On minimum error thresholding and its implementations. Pattern Recogn Lett 7(4):201–206
Kapur JN, Sahoo PK, Wong AK (1985) A new method for gray-level picture thresholding using the entropy of the histogram. Comput Vis Gr Image Process 29(3):273–285
Cheng H, Chen J-R, Li J (1998) Threshold selection based on fuzzy c-partition entropy approach. Pattern Recogn 31(7):857–870
Oliva D, Cuevas E, Pajares G, Zaldivar D, Osuna V (2014) A multilevel thresholding algorithm using electromagnetism optimization. Neurocomputing 139:357–381
Yildiz AR (2013) Comparison of evolutionary-based optimization algorithms for structural design optimization. Eng Appl Artif Intell 26(1):327–333
Horng M-H (2011) Multilevel thresholding selection based on the artificial bee colony algorithm for image segmentation. Expert Syst Appl 38(11):13785–13791
Gao H, Xu W, Sun J, Tang Y (2010) Multilevel thresholding for image segmentation through an improved quantum-behaved particle swarm algorithm. IEEE Trans Instrum Meas 59(4):934–946
Yıldız BS (2017) A comparative investigation of eight recent population-based optimisation algorithms for mechanical and structural design problems. Int J Veh Des 73(1–3):208–218
Kiani M, Yildiz AR (2016) A comparative study of non-traditional methods for vehicle crashworthiness and NVH optimization. Arch Comput Methods Eng 23(4):723–734
Yin P-Y (1999) A fast scheme for optimal thresholding using genetic algorithms. Sig Process 72(2):85–95
Maitra M, Chatterjee A (2008) A hybrid cooperative–comprehensive learning based PSO algorithm for image segmentation using multilevel thresholding. Expert Syst Appl 34(2):1341–1350
Kennedy J, Eberhart R (1995) Particle swarm intelligence. In: Proceedings of the international conference on neural network, pp 1942–1948
Cuevas E, Sención F, Zaldivar D, Pérez-Cisneros M, Sossa H (2012) A multi-threshold segmentation approach based on artificial bee colony optimization. Appl Intell 37(3):321–336
Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical report-tr06, Erciyes university, engineering faculty, computer engineering department
Sathya P, Kayalvizhi R (2011) Amended bacterial foraging algorithm for multilevel thresholding of magnetic resonance brain images. Measurement 44(10):1828–1848
Passino KM (2002) Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst 22(3):52–67
Yang X-S, Deb S Cuckoo search via Lévy flights. In: Proceedings of 2009 world congress on nature & biologically inspired computing, 2009. IEEE, pp 210–214
Khairuzzaman AKM, Chaudhury S (2017) Multilevel thresholding using grey wolf optimizer for image segmentation. Expert Syst Appl 86:64–76
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61
Jain M, Singh V, Rani A (2019) A novel nature-inspired algorithm for optimization: squirrel search algorithm. Swarm and evolutionary computation 44:148–175
Jiang Y, Tsai P, Yeh W-C, Cao L (2017) A honey-bee-mating based algorithm for multilevel image segmentation using Bayesian theorem. Appl Soft Comput 52:1181–1190
Abbass HA (2001) MBO: Marriage in honey bees optimization-A haplometrosis polygynous swarming approach. In: Proceedings of the 2001 congress on evolutionary computation, pp 207–214
Połap D (2017) Polar bear optimization algorithm: meta-heuristic with fast population movement and dynamic birth and death mechanism. Symmetry 9(10):203
Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp Swarm Algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191
Satapathy SC, Raja NSM, Rajinikanth V, Ashour AS, Dey N (2018) Multi-level image thresholding using Otsu and chaotic bat algorithm. Neural Comput Appl 29(12):1285–1307
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67
Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27(4):1053–1073
Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249
Sarvamangala D, Kulkarni RV (2019) A comparative study of bio-inspired algorithms for medical image registration. In: Mandal J, Dutta P, Mukhopadhyay S (eds) Advances in intelligent computing. Studies in computational intelligence, vol 687. Springer, Singapore, pp 27–44
Woźniak M, Połap D (2018) Bio-inspired methods modeled for respiratory disease detection from medical images. Swarm Evolut Comput 41:69–96
Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82
Yang Z-L, Wu A, Min H-Q (2015) An improved quantum-behaved particle swarm optimization algorithm with elitist breeding for unconstrained optimization. Comput Intell Neurosci 2015:1–12
Hu W, Wang H, Qiu Z, Nie C, Yan L (2018) A quantum particle swarm optimization driven urban traffic light scheduling model. Neural Comput Appl 29(3):901–911
Wu A, Yang Z-L (2018) An elitist transposon quantum-based particle swarm optimization algorithm for economic dispatch problems. Complexity 2018:1–15
Yang X-S (ed) (2012) Artificial intelligence, evolutionary computing and metaheuristics: in the footsteps of Alan Turing. In: Studies in computational intelligence, vol 427. Springer, Berlin, Heidelberg
Huang Y, Wang S (2008) Multilevel thresholding methods for image segmentation with Otsu based on QPSO. In: Processings of 2008 image and signal congress, Sanya, Hainan, China, IEEE, pp 701–705
Akay B (2013) A study on particle swarm optimization and artificial bee colony algorithms for multilevel thresholding. Appl Soft Comput 13(6):3066–3091
Bhandari AK, Kumar A, Singh GK (2015) Modified artificial bee colony based computationally efficient multilevel thresholding for satellite image segmentation using Kapur’s, Otsu and Tsallis functions. Expert Syst Appl 42(3):1573–1601
El Aziz MA, Ewees AA, Hassanien AE (2017) Whale optimization algorithm and moth-flame optimization for multilevel thresholding image segmentation. Expert Syst Appl 83:242–256
Sun J, Feng B, Xu W (2004) Particle swarm optimization with particles having quantum behavior. In: Proceedings of 2004 congress on evolutionary computation, Portland, OR, USA, IEEE, pp 325–331
Clerc M, Kennedy J (2002) The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6(1):58–73
Sun J, Fang W, Wu X, Palade V, Xu W (2012) Quantum-behaved particle swarm optimization: analysis of individual particle behavior and parameter selection. Evol Comput 20(3):349–393
Yuen SY, Chow CK (2009) A genetic algorithm that adaptively mutates and never revisits. IEEE Trans Evol Comput 13(2):454–472
Lou Y, Yuen SY (2016) Non-revisiting genetic algorithm with adaptive mutation using constant memory. Memetic Comput 8(3):189–210
Yuen SY, Chow CK (2008) A non-revisiting simulated annealing algorithm. In: Proceedings of 2008 IEEE congress on evolutionary computation, IEEE, pp 1886–1892
Chow CK, Yuen SY (2008) A non-revisiting particle swarm optimization. In: Proceedings of 2008 IEEE congress on evolutionary computation, IEEE, pp 1879–1885
Hernandez G, Wilder K, Nino F, Garcia J (2005) Towards a self-stopping evolutionary algorithm using coupling from the past. In: Proceedings of the 7th annual conference on Genetic and evolutionary computation, ACM, pp 615–620
Zielinski K, Laur R (2007) Stopping criteria for a constrained single-objective particle swarm optimization algorithm. Informatica 31(1):51–59
Wessing S, Preuss M, Trautmann H (2014) Stopping criteria for multimodal optimization. In: International conference on parallel problem solving from nature, Springer, pp 141–150
Martí L, García J, Berlanga A, Molina JM (2016) A stopping criterion for multi-objective optimization evolutionary algorithms. Inf Sci 367:700–718
Oldewage ET, Engelbrecht AP, Cleghorn CW (2018) The importance of component-wise stochasticity in particle swarm optimization. In: Proceedings of 2018 international conference on swarm intelligence, Springer, pp 264–276
Yu H, Tan Y, Zeng J, Sun C, Jin Y (2018) Surrogate-assisted hierarchical particle swarm optimization. Inf Sci 454:59–72
Mlakar U, Potočnik B, Brest J (2016) A hybrid differential evolution for optimal multilevel image thresholding. Expert Syst Appl 65:221–232
Mirjalili S (2015) How effective is the Grey Wolf optimizer in training multi-layer perceptrons. Appl Intell 43(1):150–161
Mirjalili S, Saremi S, Mirjalili SM, Coelho LdS (2016) Multi-objective grey wolf optimizer: a novel algorithm for multi-criterion optimization. Expert Syst Appl 47:106–119
Yıldız BS, Yıldız AR (2018) Comparison of grey wolf, whale, water cycle, ant lion and sine-cosine algorithms for the optimization of a vehicle engine connecting rod. Mater Test 60(3):311–315
Yıldız BS, Yıldız AR (2017) Moth-flame optimization algorithm to determine optimal machining parameters in manufacturing processes. Mater Test 59(5):425–429
Arora S, Acharya J, Verma A, Panigrahi PK (2008) Multilevel thresholding for image segmentation through a fast statistical recursive algorithm. Pattern Recogn Lett 29(2):119–125
Acknowledgements
This study was funded by the Education Department of Guangdong Province of China (Research Grant No. 2017GKTSCX047), the Education Department of Guangzhou City of China (Research Grant No. 201831785), the Technology Department of Guangdong Province of China (Research Grant No. 706049150203) and the Guangzhou Panyu Polytechnic (Research Grant No. 2011Y05PY).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there are no conflicts of interests regarding the publication of this article.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Yang, Z., Wu, A. A non-revisiting quantum-behaved particle swarm optimization based multilevel thresholding for image segmentation. Neural Comput & Applic 32, 12011–12031 (2020). https://doi.org/10.1007/s00521-019-04210-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-019-04210-z