{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T15:26:26Z","timestamp":1769268386779,"version":"3.49.0"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2021,2,2]],"date-time":"2021-02-02T00:00:00Z","timestamp":1612224000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,2,2]],"date-time":"2021-02-02T00:00:00Z","timestamp":1612224000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Multimed Tools Appl"],"published-print":{"date-parts":[[2021,4]]},"DOI":"10.1007\/s11042-020-10432-4","type":"journal-article","created":{"date-parts":[[2021,2,2]],"date-time":"2021-02-02T19:42:59Z","timestamp":1612294979000},"page":"15273-15289","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Multilevel image thresholding with multimodal optimization"],"prefix":"10.1007","volume":"80","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4070-1058","authenticated-orcid":false,"given":"Taymaz","family":"Rahkar Farshi","sequence":"first","affiliation":[]},{"given":"Recep","family":"Demirci","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,2,2]]},"reference":[{"key":"10432_CR1","doi-asserted-by":"crossref","unstructured":"Alihodzic A, Tuba M (2014) Improved bat algorithm applied to multilevel image thresholding. The Scientific World Journal 2014","DOI":"10.1155\/2014\/176718"},{"issue":"2","key":"10432_CR2","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/j.patrec.2007.09.005","volume":"29","author":"S Arora","year":"2008","unstructured":"Arora S, Acharya J, Verma A, Panigrahi PK (2008) Multilevel thresholding for image segmentation through a fast statistical recursive algorithm. Pattern Recognit Lett 29(2):119\u2013125","journal-title":"Pattern Recognit Lett"},{"key":"10432_CR3","doi-asserted-by":"crossref","unstructured":"Barrera J, Coello CAC (2009) A particle swarm optimization method for multimodal optimization based on electrostatic interaction, in Mexican International Conference on Artificial Intelligence, pp. 622\u2013632: Springer.","DOI":"10.1007\/978-3-642-05258-3_55"},{"issue":"2\u20133","key":"10432_CR4","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/0098-3004(84)90020-7","volume":"10","author":"JC Bezdek","year":"1984","unstructured":"Bezdek JC, Ehrlich R, Full W (1984) FCM: The fuzzy c-means clustering algorithm. Comput Geo 10(2\u20133):191\u2013203","journal-title":"Comput Geo"},{"issue":"7","key":"10432_CR5","doi-asserted-by":"publisher","first-page":"3538","DOI":"10.1016\/j.eswa.2013.10.059","volume":"41","author":"AK Bhandari","year":"2014","unstructured":"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\u2019s entropy. Expert Syst Appl 41(7):3538\u20133560, 2014\/06\/01\/","journal-title":"Expert Syst Appl"},{"issue":"3","key":"10432_CR6","doi-asserted-by":"publisher","first-page":"1573","DOI":"10.1016\/j.eswa.2014.09.049","volume":"42","author":"AK Bhandari","year":"2015","unstructured":"Bhandari AK, Kumar A, Singh GK (2015) Modified artificial bee colony based computationally efficient multilevel thresholding for satellite image segmentation using Kapur\u2019s, Otsu and Tsallis functions. Expert Syst Appl 42(3):1573\u20131601, 2015\/02\/15\/","journal-title":"Expert Syst Appl"},{"key":"10432_CR7","unstructured":"Brajevic I, Tuba M (2014) Cuckoo search and firefly algorithm applied to multilevel image thresholding, in Cuckoo Search and Firefly Algorithm: Theory and Applications, X.-S. Yang, Ed. Cham: Springer International Publishing, pp. 115\u2013139."},{"key":"10432_CR8","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1016\/j.asoc.2015.04.002","volume":"33","author":"W-D Chang","year":"2015","unstructured":"Chang W-D (2015) A modified particle swarm optimization with multiple subpopulations for multimodal function optimization problems. Applied Soft Computing 33:170\u2013182","journal-title":"Applied Soft Computing"},{"key":"10432_CR9","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/j.bspc.2018.01.010","volume":"42","author":"M Diwakar","year":"2018","unstructured":"Diwakar M, Kumar M (2018) A review on CT image noise and its denoising. Biomed Signal Process Control 42:73\u201388","journal-title":"Biomed Signal Process Control"},{"issue":"5","key":"10432_CR10","doi-asserted-by":"publisher","first-page":"708","DOI":"10.1049\/iet-ipr.2017.0639","volume":"12","author":"M Diwakar","year":"2018","unstructured":"Diwakar M, Kumar M (2018) CT image denoising using NLM and correlation-based wavelet packet thresholding. IET Image Processing 12(5):708\u2013715","journal-title":"IET Image Processing"},{"key":"10432_CR11","doi-asserted-by":"publisher","first-page":"101754","DOI":"10.1016\/j.bspc.2019.101754","volume":"57","author":"M Diwakar","year":"2020","unstructured":"Diwakar M, Singh P (2020) CT image denoising using multivariate model and its method noise thresholding in non-subsampled shearlet domain. Biomed Signal Process Control 57:101754","journal-title":"Biomed Signal Process Control"},{"key":"10432_CR12","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1109\/MHS.1995.494215","volume":"1","author":"RC Eberhart","year":"1995","unstructured":"Eberhart RC, Kennedy J (1995) A new optimizer using particle swarm theory. in Proceedings of the sixth international symposium on micro machine and human science 1:39\u201343 New York, NY","journal-title":"in Proceedings of the sixth international symposium on micro machine and human science"},{"key":"10432_CR13","doi-asserted-by":"crossref","unstructured":"Elaziz MA, Ewees AA, Oliva D (2020) Hyper-heuristic method for multilevel thresholding image segmentation. Expert Systems with Applications 146:113201, 2020\/05\/15\/","DOI":"10.1016\/j.eswa.2020.113201"},{"key":"10432_CR14","doi-asserted-by":"crossref","unstructured":"Epitropakis MG, Li X, Burke EK (2013) A dynamic archive niching differential evolution algorithm for multimodal optimization. in 2013 IEEE Congress on Evolutionary Computation:79\u201386 IEEE","DOI":"10.1109\/CEC.2013.6557556"},{"key":"10432_CR15","doi-asserted-by":"publisher","first-page":"113233","DOI":"10.1016\/j.eswa.2020.113233","volume":"149","author":"TR Farshi","year":"2020","unstructured":"Farshi TR, Drake JH, \u00d6zcan E (2020) A multimodal particle swarm optimization-based approach for image segmentation. Expert Syst Appl 149:113233","journal-title":"Expert Syst Appl"},{"issue":"9","key":"10432_CR16","doi-asserted-by":"crossref","first-page":"3302","DOI":"10.1016\/j.amc.2009.10.018","volume":"215","author":"M-H Horng","year":"2010","unstructured":"Horng M-H (2010) A multilevel image thresholding using the honey bee mating optimization. Appl Math Comput 215(9):3302\u20133310","journal-title":"Appl Math Comput"},{"key":"10432_CR17","doi-asserted-by":"crossref","unstructured":"Horng M-H, Jiang T-W (2010) Multilevel image thresholding selection based on the firefly algorithm. in Ubiquitous intelligence & computing and 7th international conference on autonomic & trusted computing (uic\/atc), 2010 7th international conference on:58\u201363 IEEE","DOI":"10.1109\/UIC-ATC.2010.47"},{"key":"10432_CR18","first-page":"2194","volume":"3","author":"A Jacobson","year":"2001","unstructured":"Jacobson A (2001) Auto-threshold peak detection in physiological signals. in Engineering in Medicine and Biology Society, 2001. Proceedings of the 23rd Annual International Conference of the IEEE 3:2194\u20132195 IEEE","journal-title":"in Engineering in Medicine and Biology Society, 2001. Proceedings of the 23rd Annual International Conference of the IEEE"},{"key":"10432_CR19","unstructured":"Kalyani R, Sathya PD, Sakthivel VP (2020) Trading strategies for image segmentation using multilevel thresholding aided with minimum cross entropy. Engineering Science and Technology, an International Journal, 2020\/08\/11\/ ."},{"issue":"3","key":"10432_CR20","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1016\/0734-189X(85)90125-2","volume":"29","author":"JN Kapur","year":"1985","unstructured":"Kapur JN, Sahoo PK, Wong AK (1985) A new method for gray-level picture thresholding using the entropy of the histogram. Computer vision, graphics, and image processing 29(3):273\u2013285","journal-title":"Computer vision, graphics, and image processing"},{"key":"10432_CR21","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1016\/j.eswa.2017.04.029","volume":"86","author":"AKM Khairuzzaman","year":"2017","unstructured":"Khairuzzaman AKM, Chaudhury S (2017) Multilevel thresholding using grey wolf optimizer for image segmentation. Expert Syst Appl 86:64\u201376, 2017\/11\/15\/","journal-title":"Expert Syst Appl"},{"issue":"1","key":"10432_CR22","first-page":"113","volume":"31","author":"M Kumar","year":"2019","unstructured":"Kumar M, Diwakar M (2019) A new exponentially directional weighted function based CT image denoising using total variation. J King Saud Univ Comput Info Sci 31(1):113\u2013124","journal-title":"J King Saud Univ Comput Info Sci"},{"issue":"3","key":"10432_CR23","doi-asserted-by":"publisher","first-page":"1722","DOI":"10.1109\/20.767361","volume":"35","author":"C-G Lee","year":"1999","unstructured":"Lee C-G, Cho D-H, Jung H-K (1999) Niching genetic algorithm with restricted competition selection for multimodal function optimization. IEEE Tran Magn 35(3):1722\u20131725","journal-title":"IEEE Tran Magn"},{"issue":"14","key":"10432_CR24","first-page":"281","volume":"1","author":"J MacQueen","year":"1967","unstructured":"MacQueen J (1967) Some methods for classification and analysis of multivariate observations. in Proceedings of the fifth Berkeley symposium on mathematical statistics and probability 1(14):281\u2013297 Oakland, CA, USA","journal-title":"in Proceedings of the fifth Berkeley symposium on mathematical statistics and probability"},{"key":"10432_CR25","doi-asserted-by":"crossref","unstructured":"Oliva D, Cuevas E, Pajares G, Zaldivar D, Perez-Cisneros M (2013) Multilevel thresholding segmentation based on harmony search optimization. J Appl Math 2013","DOI":"10.1155\/2013\/575414"},{"issue":"1","key":"10432_CR26","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1109\/TSMC.1979.4310076","volume":"9","author":"N Otsu","year":"1979","unstructured":"Otsu N (1979) A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybernetics 9(1):62\u201366","journal-title":"IEEE Trans Syst Man Cybernetics"},{"issue":"5","key":"10432_CR27","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1109\/TEVC.2011.2161873","volume":"16","author":"B-Y Qu","year":"2012","unstructured":"Qu B-Y, Suganthan PN, Liang J-J (2012) Differential evolution with neighborhood mutation for multimodal optimization. IEEE Trans Evol Comput 16(5):601\u2013614","journal-title":"IEEE Trans Evol Comput"},{"key":"10432_CR28","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/j.ins.2012.02.011","volume":"197","author":"B-Y Qu","year":"2012","unstructured":"Qu B-Y, Liang JJ, Suganthan PN (2012) Niching particle swarm optimization with local search for multi-modal optimization. Info Sci 197:131\u2013143","journal-title":"Info Sci"},{"issue":"1","key":"10432_CR29","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1007\/s42044-018-0022-5","volume":"2","author":"T Rahkar Farshi","year":"2019","unstructured":"Rahkar Farshi T (2019) A multilevel image thresholding using the animal migration optimization algorithm. Iran Journal of Computer Science 2(1):9\u201322, 2019\/03\/01","journal-title":"Iran Journal of Computer Science"},{"issue":"4","key":"10432_CR30","first-page":"713","volume":"11","author":"T Rahkar Farshi","year":"2019","unstructured":"Rahkar Farshi T, Orujpour M (2019) Multi-level image thresholding based on social spider algorithm for global optimization. Int. J. Inf. Technol 11(4):713\u2013718, 2019\/12\/01","journal-title":"Int. J. Inf. Technol"},{"issue":"4","key":"10432_CR31","doi-asserted-by":"publisher","first-page":"296","DOI":"10.3390\/e20040296","volume":"20","author":"T Rahkar Farshi","year":"2018","unstructured":"Rahkar Farshi T, Demirci R, Feizi-Derakhshi M-R (2018) Image clustering with optimization algorithms and color space. Entropy 20(4):296","journal-title":"Entropy"},{"key":"10432_CR32","doi-asserted-by":"crossref","unstructured":"Rahkar-Farshi T, Behjat-Jamal S (2016) A multimodal firefly optimization algorithm based on coulomb\u2019s law. International Journal of Advanced Computer Science and Applications 7(5)","DOI":"10.14569\/IJACSA.2016.070521"},{"key":"10432_CR33","first-page":"37","volume":"2014","author":"N Raja","year":"2014","unstructured":"Raja N, Rajinikanth V, Latha K (2014) Otsu based optimal multilevel image thresholding using firefly algorithm. Modelling and Simulation in Engineering 2014:37","journal-title":"Modelling and Simulation in Engineering"},{"issue":"5","key":"10432_CR34","doi-asserted-by":"publisher","first-page":"764","DOI":"10.1109\/PROC.1979.11326","volume":"67","author":"A Rosenfeld","year":"1979","unstructured":"Rosenfeld A, Davis LS (1979) Image segmentation and image models. Proceedings of the IEEE 67(5):764\u2013772","journal-title":"Proceedings of the IEEE"},{"issue":"4","key":"10432_CR35","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1016\/j.engappai.2010.12.001","volume":"24","author":"PD Sathya","year":"2011","unstructured":"Sathya PD, Kayalvizhi R (2011) Modified bacterial foraging algorithm based multilevel thresholding for image segmentation. Engineering Applications of Artificial Intelligence 24(4):595\u2013615, 2011\/06\/01\/","journal-title":"Engineering Applications of Artificial Intelligence"},{"issue":"12","key":"10432_CR36","doi-asserted-by":"publisher","first-page":"15549","DOI":"10.1016\/j.eswa.2011.06.004","volume":"38","author":"P Sathya","year":"2011","unstructured":"Sathya P, Kayalvizhi R (2011) Optimal multilevel thresholding using bacterial foraging algorithm. Expert Syst Appl 38(12):15549\u201315564","journal-title":"Expert Syst Appl"},{"issue":"6","key":"10432_CR37","doi-asserted-by":"publisher","first-page":"653","DOI":"10.1016\/0167-8655(95)80011-H","volume":"16","author":"D-M Tsai","year":"1995","unstructured":"Tsai D-M (1995) A fast thresholding selection procedure for multimodal and unimodal histograms. Pattern Recognition Letters 16(6):653\u2013666","journal-title":"Pattern Recognition Letters"},{"key":"10432_CR38","doi-asserted-by":"publisher","first-page":"103836","DOI":"10.1016\/j.engappai.2020.103836","volume":"94","author":"A Wunnava","year":"2020","unstructured":"Wunnava A, Naik MK, Panda R, Jena B, Abraham A (2020) A novel interdependence based multilevel thresholding technique using adaptive equilibrium optimizer. Engineering Applications of Artificial Intelligence 94:103836, 2020\/09\/01\/","journal-title":"Engineering Applications of Artificial Intelligence"},{"key":"10432_CR39","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.swevo.2013.08.001","volume":"14","author":"S Yazdani","year":"2014","unstructured":"Yazdani S, Nezamabadi-pour H, Kamyab S (2014) A gravitational search algorithm for multimodal optimization. Swarm and Evolutionary Computation 14:1\u201314","journal-title":"Swarm and Evolutionary Computation"},{"key":"10432_CR40","doi-asserted-by":"publisher","first-page":"2589","DOI":"10.1016\/j.egypro.2017.03.744","volume":"105","author":"C Yin","year":"2017","unstructured":"Yin C, Wu S, Zhou S, Wang W, Cheng Y, Huang X (2017) Peak searching for multimodal optimization through gradient-based stochastic extremum seeking technique. Energy Procedia 105:2589\u20132594","journal-title":"Energy Procedia"},{"key":"10432_CR41","unstructured":"Zhang Z, Lin Z, Xu J, Jin W, Lu S-P, Fan D-P (2020) Bilateral attention network for rgb-d salient object detection,\" arXiv preprint arXiv. 2004:14582"},{"key":"10432_CR42","doi-asserted-by":"crossref","unstructured":"Zhao J-X, Cao Y, Fan D-P, Cheng M-M, Li X-Y, Zhang L (2019) Contrast prior and fluid pyramid integration for RGBD salient object detection. ed","DOI":"10.1109\/CVPR.2019.00405"},{"key":"10432_CR43","doi-asserted-by":"crossref","unstructured":"Orujpour M,\u00a0 Feizi-Derakhshi MR, Rahkar-Farshi T, (2020) Multi-modal forest optimization algorithm. Neural Computing and Applications 32 (10):6159\u20136173","DOI":"10.1007\/s00521-019-04113-z"},{"key":"10432_CR44","doi-asserted-by":"crossref","unstructured":"A. Rahimzadeganasl and E. Sertel, (2017) Automatic building detection based on CIE LUV color space using very high resolution pleiades images, in 25th Signal Processing and Communications Applications Conference (SIU), Antalya, 2017, pp. 1\u20134\u00a0","DOI":"10.1109\/SIU.2017.7960711"},{"key":"10432_CR45","doi-asserted-by":"crossref","unstructured":"Rahkar Farshi T, (2020) Battle royale optimization algorithm. Neural Computing and Applications","DOI":"10.1007\/s00521-020-05004-4"},{"key":"10432_CR46","doi-asserted-by":"crossref","unstructured":"Rahkar Farshi T, Orujpour M, (2020) A multi-modal bacterial foraging optimization algorithm. J Ambient Intell Human Comput","DOI":"10.1007\/s12652-020-02755-9"},{"key":"10432_CR47","doi-asserted-by":"crossref","unstructured":"Yang XS, Gandomi AH, (2012) Bat algorithm: a novel approach for global engineering optimization. Engineering Computations 29 (5):464\u2013483","DOI":"10.1108\/02644401211235834"},{"key":"10432_CR48","unstructured":"BehjatJamal S, Bilgin G (2019), \"Use of Spatial Information via Markov and Conditional Random Fields in Histopathological Images,\" in 42nd International Conference on Telecommunications and Signal Processing (TSP), Budapest, Hungary, 2019, pp. 71\u201375"}],"container-title":["Multimedia Tools and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11042-020-10432-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11042-020-10432-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11042-020-10432-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,29]],"date-time":"2023-10-29T20:06:36Z","timestamp":1698609996000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11042-020-10432-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,2]]},"references-count":48,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["10432"],"URL":"https:\/\/doi.org\/10.1007\/s11042-020-10432-4","relation":{},"ISSN":["1380-7501","1573-7721"],"issn-type":[{"value":"1380-7501","type":"print"},{"value":"1573-7721","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,2]]},"assertion":[{"value":"21 February 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 September 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 December 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 February 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}