Abstract
Since the conventional multilevel thresholding approaches exhaustively search the optimal thresholds to optimize objective functions, they are computational expensive. In this paper, the modified particle swarm optimization (MPSO) algorithm is proposed to overcome this drawback. The MPSO employs two new strategies to improve the performance of original particle swarm optimization (PSO), which are named adaptive inertia (AI) and adaptive population (AP), respectively. With the help of AI strategy, inertia weight is variable with the searching state, which helps MPSO to increase search efficiency and convergence speed. Moreover, with the help of AP strategy, the population size of MPSO is also variable with the searching state, which mainly helps the algorithm to jump out of local optima. Here, the searching state is estimated as exploration or exploitation simply according to whether the gBest has been updated in \(k\) consecutive generations or not, where the gBest stands for the position with the best fitness found so far among all the particles in the swarm. The MPSO has been evaluated on 12 unimodal and multimodal Benchmark functions, and the effects of AI and AP strategies are studied. The results show that MPSO improves the performance of the PSO paradigm. The MPSO is also used to find the optimal thresholds by maximizing the Otsu’s objective function, and its performance has been validated on 16 standard test images. The experimental results of 30 independent runs illustrate the better solution quality of MPSO when compared with the global particle swarm optimization and standard genetic algorithm.
Similar content being viewed by others
References
Abak AT, Baris U, Sankur B (1997) The performance evaluation of thresholding algorithms for optimal character recognition. In: IEEE proceedings international conference document analysis and recognition, Germany, pp 697–700
Alatas B, Akin E (2008) Rough particle swarm optimization and its applications in data mining. Soft Comput 12:1205–1218
Al-Obeidat F, Belacel N, Carretero JA, Mahanti P (2011) An evolutionary framework using particle swarm optimization for classification method PROAFTN. Appl Soft Comput 11:4971–4980
Alteanu D, Ristic D, Graser A (2005) Content based threshold adaptation for image processing in industrial application. In: International conference on control and automation, Budapest, Hungary, pp 1022–1027
Atkins MS, Mackiewich BT (1998) Fully automatic segmentation of the brain in MRI. IEEE Trans Med Imaging 17(1):98–107
Brink AD (1995) Minimum spatial entropy threshold selection. IEE Proc Vis Image Signal Process 142:128–132
Cheng HD, Chen J, Li J (1998) Threshold selection based on fuzzy c-partition entropy approach. Pattern Recognit 31:857–870
Chien SY, Huang YW, Hsieh BY, Ma SY, Chen LG (2004) Fast video segmentation algorithm with shadow cancellation, global motion compensation, and adaptive threshold techniques. IEEE Trans Multimed 6(5):732–748
Eberhart RC, Shi Y (2001) Particle swarm optimization: Developments, applications and resources. In: Proceedings of the 2001 Congress on evolutionary computation. Seoul, Korea, pp 81–86
Hertz L, Schafer RW (1988) Multilevel thresholding using edge matching. Comput Vis Graph Image Process 44(3):279–295
Ho S-Y, Lin H-S, Liauh W-H, Ho S-J (2008) OPSO: Orthogonal particle swarm optimization and its application to task assignment problems. IEEE Trans Syst Man Cybern Part A Syst Hum 38(2):288–298
Horng M-H (2011) Multilevel thresholding selection based on the artificial bee colony algorithm for image segmentation. Expert Syst Appl. doi:10.1016/j.eswa.2011.04.180
Houck CR, Joines JA, Kay MG (1995) A genetic algorithm for function optimization: a Matlab implementation. Technical Report: NCSU-IE-TR-95-09. North Carolina State University, Raleigh, NC
Kapur JN, Sahoo PK, Wong AKC (1985) A new method for gray-level picture thresholding using the entropy of the histogram. Comput Vis Graph Image Process 29(3):273–285
Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: IEEE proceedings of international conference neural network, Perth, Australia, vol 4, pp 1942–1948
Kennedy J, Eberhart RC, Shi YH (2001) Swarm intelligence. Morgan Kaufmann, San Mateo
Kittler J, Illingworth J (1986) Minimum error thresholding. Pattern Recognit 19:41–47
Li X, Zhao Z, Cheng HD (1995) Fuzzy entropy threshold approach to breast cancer detection. Inf Sci 4:49–56
Li S, Wu X, Tan M (2008) Gene selection using hybrid particle swarm optimization and genetic algorithm. Soft Comput 12:1039–1048
Mohemmed AW, Sahoo NC, Geok TK (2008) Solving shortest path problem using particle swarm optimization. Appl Soft Comput 8:1643–1653
Otsu N (1979) A threshold selection method from gray level histograms. IEEE Trans Syst Man Cybern SMC-9:62–66
Pal NR, Pal SK (1993) A review on image segmentation techniques. Pattern Recognit 26(9):1277–1294
Pikaz A, Averbuch A (1996) Digital image thresholding based on topological stable state. Pattern Recognit 29(5):829–843
Saha PK, Udupa JK (2001) Optimum image thresholding via class uncertainty and region homogeneity. IEEE Trans Pattern Anal Mach Intell 23:689–706
Sahoo PK, Soltani S, Wong AKC (1988) A survey of thresholding techniques. IEEE Trans Comput Vis Graph Image Process 41(2):233–260
Sathya PD, Kayalvizhi R (2011a) Optimal multilevel thresholding using bacterial foraging algorithm. Expert Syst Appl. doi:10.1016/j.eswa.2011.06.004
Sathya PD, Kayalvizhi R (2011b) Modified bacterial foraging algorithm based multilevel thresholding for image segmentation. Eng Appl Artif Intell 24:595–615
Sezgin M, Sankur B (2004) Survey over image thresholding techniques and quantitative performance evaluation. J Electron Imaging 13(1):146–165
Shi Y, Eberhart RC (1998) A modified particle swarm optimizer. In: Proceedings of the IEEE world Congress on computational intelligence, pp 69–73
Shi Y, Eberhart RC (1999) Empirical study of particle swarm optimization. In: Proceedings of the IEEE Congress on evolutionary computation, pp 1945–1950
Su C, Amer A (2006) A real-time adaptive thresholding for video change detection. In: Proceedings of the IEEE international conference on image processing, Atlanta, Georgia, USA, pp 157–160
Valdez F, Melin P, Castillo O (2010) Fuzzy logic for parameter tuning in evolutionary computation and bio-inspired methods. MICAI 2:465–474
Valdez F, Melin P, Castillo O (2011) An improved evolutionary method with fuzzy logic for combining particle swarm optimization and genetic algorithms. Appl Soft Comput 11(2):2625–2632
Ye Q, Danielsson P (1988) On minimum error thresholding and its implementations. Pattern Recognit Lett 7:201–206
Zhan Z-H, Zhang J, Li Y, Chung HS-H (2009) Adaptive particle swarm optimization. IEEE Trans Syst Man Cybern Part B Cybern 39(6):1362–1381
Acknowledgments
This paper was supported by the National Natural Science Foundation of China under Grant Nos. 61003199, 61303032, 61373111, the Fundamental Research Funds for the Central Universities under Grant Nos. JB140216, K5051202019, the Natural Science Foundation of Shaanxi Province of China under Grant No. 2014JQ5183, and the Special Foundation for Natural Science of the Education Department of Shaanxi Province of China under Grant No. 2013JK1129.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by V. Loia.
Rights and permissions
About this article
Cite this article
Liu, Y., Mu, C., Kou, W. et al. Modified particle swarm optimization-based multilevel thresholding for image segmentation. Soft Comput 19, 1311–1327 (2015). https://doi.org/10.1007/s00500-014-1345-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-014-1345-2