Skip to main content
SpringerLink
Log in

Multi-threshold segmentation of grayscale and color images based on Kapur entropy by bald eagle search optimization algorithm with horizontal crossover and vertical crossover

  • Optimization
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

For multi-threshold segmentation of grayscale and color images, the computational complexity increases exponentially with the increase of the number of threshold levels. In this paper, we propose a new method to segment grayscale and color images with Kapur entropy as the objective function. The method introduces four strategies such as horizontal crossover and vertical crossover into the bald eagle search optimization algorithm, forming an advanced bald eagle search optimization algorithm (ABES). In the benchmark function comparison experiments at IEEE CEC 2017, ABES was compared with classical and novel algorithms, and the results proved to have stronger convergence speed, convergence accuracy, and stability than other algorithms. To demonstrate the effectiveness of the method in multi-thresholding segmentation of grayscale and color images, it is applied to low-level and high-level image multi-thresholding experiments, and the experimental results show that ABES outperforms other algorithms in the evaluation of PSNR, MSSIM, and FSIM, and ABES is a high-quality image segmentation method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

References

  • Alsattar Hassan A, Zaidan AA, Zaidan BB (2020) Novel meta-heuristic bald eagle search optimisation algorithm. Artif Intell Rev 53(3):2237–2264

    Google Scholar 

  • Amlak A, El Sehiemy Ragab A, Attia E-F, Abdelrazek BAS (2022) Optimal parameter estimation of solid oxide fuel cells model using bald eagle search optimizer. Int J Energy Res 46(10):13657–13669

    Google Scholar 

  • Bansal P, Vaid M, Gupta S (2022) Obcd-hh: an object-based change detection approach using multi-feature non-seed-based region growing segmentation. Multimed Tools Appl 81(6):8059–8091

    Google Scholar 

  • Bao W, Yang B (2023) Protein acetylation sites with complex-valued polynomial model. Front Comput Sci

  • Barbarossa S, Sardellitti S (2020) Topological signal processing over simplicial complexes. IEEE Trans Signal Process 68:2992–3007

    MATH  Google Scholar 

  • Bo W, Zhou J, Ji X, Yin Y, Shen X (2020) An ameliorated teaching-learning-based optimization algorithm based study of image segmentation for multilevel thresholding using kapur’s entropy and otsu’s between class variance. Inf Sci 533:72–107

    MathSciNet  MATH  Google Scholar 

  • Chen X, Pan S, Chong Y (2022) Unsupervised domain adaptation for remote sensing image semantic segmentation using region and category adaptive domain discriminator. IEEE Trans Geosci Remote Sens 60:1–13

    Google Scholar 

  • Dong W, Xiao-Ping W (2022) The iterative convolution-thresholding method (ictm) for image segmentation. Pattern Recognit 130:108794

    Google Scholar 

  • Dong-yuan G, Xi-fan Y, Wen-jiang X, Yue-ping C (2022) Vehicle detection and tracking based on video image processing in intelligent transportation system. Neural Comput Appl 35:1–13

    Google Scholar 

  • Eberhart R and Kennedy J (1995) A new optimizer using particle swarm theory. In: MHS’95. Proceedings of the sixth international symposium on micro machine and human science, pp 39–43. Ieee

  • Eberhart Russell C, Shi Y (1998) Comparison between genetic algorithms and particle swarm optimization. In: International conference on evolutionary programming, pp 611–616. Springer

  • Fan Y, Liu P, Tang J, Luo Y, Yongzhao D (2018) Fuzzy entropy based on differential evolution for breast gland segmentation. Aust Phys Eng Sci Med 41(4):1101–1114

    Google Scholar 

  • Guanghui SHI, Chengqi GUAN, Dongliang QUAN, Dongtao WU, Lei TANG, Tong GAO (2020) An aerospace bracket designed by thermo-elastic topology optimization and manufactured by additive manufacturing. Chin J Aeronaut 33(4):1252–1259

    Google Scholar 

  • Han H, Han C, Huang L, Lan T, Xue X (2020) Irradiance restoration based shadow compensation approach for high resolution multispectral satellite remote sensing images. Sensors 20(21):6053

    Google Scholar 

  • Hashim Fatma A, Kashif H, Houssein Essam H, Mabrouk Mai S, Walid A-A (2021) Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems. Appl Intell 51(3):1531–1551

    MATH  Google Scholar 

  • He B (2021) Video teaching of piano playing and singing based on computer artificial intelligence system and virtual image processing. J Ambient Intell Hum Comput 1–12

  • Helong Yu, Jiuman S, Chengcheng C, Asghar HA, Jiawen L, Huiling C, Atef Z, Majdi M (2022) Image segmentation of leaf spot diseases on maize using multi-stage cauchy-enabled grey wolf algorithm. Eng Appl Artif Intell 109:104653

    Google Scholar 

  • Himanshu M, Chandra PA, Mukesh S, Sumit K, Raju P, Garv M (2021) A comprehensive survey of image segmentation clustering methods, performance parameters, and benchmark datasets. Multimed Tools Appl 81:1–26

    Google Scholar 

  • Hosny Khalid M, Khalid Asmaa M, Hamza Hanaa M, Seyedali M (2022) Multilevel thresholding satellite image segmentation using chaotic coronavirus optimization algorithm with hybrid fitness function. Neural Comput Appl 35:1–32

    Google Scholar 

  • Hou J, Li B (2021) Swimming target detection and tracking technology in video image processing. Microprocess Microsyst 80:103535

    Google Scholar 

  • Houssein Essam H, El-Din HB, Elngar Ahmed A, Salama AD, Hassan S (2021) An improved tunicate swarm algorithm for global optimization and image segmentation. IEEE Access 9:56066–56092

    Google Scholar 

  • Ismail SG, Soliman Mona M, Ella HA (2021) A novel melanoma prediction model for imbalanced data using optimized squeezenet by bald eagle search optimization. Comput Biol Med 136:104712

    Google Scholar 

  • Ji YD, Lai L, Zhong SC, Zhang L (2018) Bifurcation and chaos of a new discrete fractional-order logistic map. Commun Nonlinear Sci Numer Simul 57:352–358

    MathSciNet  MATH  Google Scholar 

  • Jia H, Lang C, Oliva D, Song W, Peng X (2019) Hybrid grasshopper optimization algorithm and differential evolution for multilevel satellite image segmentation. Remote Sens 11(9):1134

    Google Scholar 

  • Jiang M, Rao Y, Zhang J, Shen Y (2020) Automatic behavior recognition of group-housed goats using deep learning. Comput Electron Agric 177:105706

    Google Scholar 

  • Jianxun L, Jinfei S, Fei H, Min D, Zhisheng Z (2022) Arctangent entropy: a new fast threshold segmentation entropy for light colored character image on semiconductor chip surface. Pattern Anal Appl 25:1–16

    Google Scholar 

  • Kaipu W, Xinyu L, Liang G, Peigen L, Gupta Surendra M (2021) A genetic simulated annealing algorithm for parallel partial disassembly line balancing problem. Appl Soft Comput 107:107404

    Google Scholar 

  • Kitani M, Murakami H (2022) One-sample location test based on the sign and wilcoxon signed-rank tests. J Stat Comput Simul 92(3):610–622

    MathSciNet  MATH  Google Scholar 

  • Korodi A, Anitei D, Boitor A, Silea I (2020) Image-processing-based low-cost fault detection solution for end-of-line ecus in automotive manufacturing. Sensors 20(12):3520

    Google Scholar 

  • Kumar BA, Anil K, Kumar SG (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

    Google Scholar 

  • Kuo C-FJ, Li Y-C, Weng W-H, Leon KBP, Chu Y-H (2020) Applied image processing techniques in video laryngoscope for occult tumor detection. Biomed Signal Process Control 55:101633

    Google Scholar 

  • Li G, Han X (2021) A color image encryption algorithm with cat map and chaos map embedded. Int J Uncertain Fuzziness Knowl Based Syst 29(Supp01):73–87

    MathSciNet  MATH  Google Scholar 

  • Li Q, Wang H, Li B-Y, Yanghua T, Li J (2021) Iie-segnet: deep semantic segmentation network with enhanced boundary based on image information entropy. IEEE Access 9:40612–40622

    Google Scholar 

  • Lin X, Xianxing Yu, Li W (2022) A heuristic whale optimization algorithm with niching strategy for global multi-dimensional engineering optimization. Comput Ind Eng 171:108361

    Google Scholar 

  • Liu G, Zhou B, Huang Y, Wang L, Wang W, Zhao E (2021) Video image scaling technology based on adaptive interpolation algorithm and tts fpga implementation. Comput Stand Interfaces 76:103516

    Google Scholar 

  • Mohammad S, Laith A (2021) Opposition-based learning multi-verse optimizer with disruption operator for optimization problems. Soft Comput 26(21):11669–93

    Google Scholar 

  • Nafi ÖB, Berkan AS, Timur D, Bilal Ö (2022) A novel version of slime mould algorithm for global optimization and real world engineering problems: enhanced slime mould algorithm. Math Comput Simul 198:253–288

    MathSciNet  MATH  Google Scholar 

  • Narain KJ, Sahoo Prasanna K, Wong Andrew KC (1985) A new method for gray-level picture thresholding using the entropy of the histogram. Comput Vis Graph Image Process 29(3):273–285

    Google Scholar 

  • Niu Y, Zheng X, Zhao T, Chen J (2019) Visually consistent color correction for stereoscopic images and videos. IEEE Trans Circuits Syst Video Technol 30(3):697–710

    Google Scholar 

  • Priti B, Abhishek S, Kshitiz G (2022) Osteosarcoma detection from whole slide images using multi-feature non-seed-based region growing segmentation and feature extraction. Neural Process Lett. https://doi.org/10.1007/s11063-022-10914-6

    Article  Google Scholar 

  • Renugambal A, Selva BK (2021) Kapur’s entropy based hybridised wcmfo algorithm for brain mr image segmentation. IETE J Res. https://doi.org/10.1080/03772063.2021.1906765

    Article  Google Scholar 

  • Seydali F, Hegazy R, Ali AM, Olabi AG (2022) Optimal techno-economic energy management strategy for building’s microgrids based bald eagle search optimization algorithm. Appl Energy 306:118069

    Google Scholar 

  • Shang X, Liang J, Wang G, Zhao H, Chengjia W, Lin C (2018) Color-sensitivity-based combined psnr for objective video quality assessment. IEEE Trans Circuits Syst Video Technol 29(5):1239–1250

    Google Scholar 

  • Shen X, Chang Z, Xie X, Niu S (2022) Task offloading strategy of vehicular networks based on improved bald eagle search optimization algorithm. Appl Sci 12(18):9308

    Google Scholar 

  • Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713

    Google Scholar 

  • Singh P (2020) A neutrosophic-entropy based clustering algorithm (nebca) with hsv color system: a special application in segmentation of parkinson’s disease (pd) mr images. Comput Methods Programs Biomed 189:105317

    Google Scholar 

  • Taghian M, Asadi A, Safabakhsh R (2022) Learning financial asset-specific trading rules via deep reinforcement learning. Expert Syst Appl 195:116523

    Google Scholar 

  • Tuerxun W, Chang X, Guo H, Guo L, Zeng N, Gao Y (2022) A wind power forecasting model using lstm optimized by the modified bald eagle search algorithm. Energies 15(6):2031

    Google Scholar 

  • Wang P, Zhang Y, Jiang B, Hou J (2020) An maize leaf segmentation algorithm based on image repairing technology. Comput Electron Agric 172:105349

    Google Scholar 

  • Wang X, Wang L, Li G, Xie X (2021) A robust and fast method for sidescan sonar image segmentation based on region growing. Sensors 21(21):6960

  • Wang R, Cao S, Ma K, Zheng Y, Meng D (2021) Pairwise learning for medical image segmentation. Med Image Anal 67:101876

    Google Scholar 

  • Wang J, Lin D, Zhang Y, Huang S (2022) An adaptively balanced grey wolf optimization algorithm for feature selection on high-dimensional classification. Eng Appl Artif Intell 114:105088

    Google Scholar 

  • Wei D, Wang Z, Si L, Tan C (2021) Preaching-inspired swarm intelligence algorithm and its applications. Knowl Based Syst 211:106552

    Google Scholar 

  • Yeung M, Sala E, Schönlieb C-B, Rundo L (2022) Unified focal loss: generalising dice and cross entropy-based losses to handle class imbalanced medical image segmentation. Comput Med Imaging Graph 95:102026

    Google Scholar 

  • Zhang Y, Zhou Y, Zhou G, Luo Q, Zhu B (2022) A curve approximation approach using bio-inspired polar coordinate bald eagle search algorithm. Int J Comput Intell Syst 15(1):1–25

    Google Scholar 

  • Zhou Z, Dai M, Guo Y, Li X (2021) Global-to-local region-based indicator embedded in edge-based level set model for segmentation. Digit Signal Process 114:103061

    Google Scholar 

  • Zouaoui H, Moussaoui A et al (2021) Bioinspired inference system for mr image segmentation and multiple sclerosis detection. Int J Swarm Intell Res (IJSIR) 12(3):37–57

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical and Electrical Engineering, Changchun University of Technology, Changchun, 130012, People’s Republic of China

    Guoyuan Ma, Xiaofeng Yue & Juan Zhu

Authors
  1. Guoyuan Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaofeng Yue
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Juan Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaofeng Yue.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The work is supported in part by Science and Technology Department of Jilin Province (20220203091SF) and Jilin Province Development and Reform Commission (2020C018-3).

Appendix A: Basic BES algorithm

Appendix A: Basic BES algorithm

See Table 15.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ma, G., Yue, X. & Zhu, J. Multi-threshold segmentation of grayscale and color images based on Kapur entropy by bald eagle search optimization algorithm with horizontal crossover and vertical crossover. Soft Comput 27, 14759–14790 (2023). https://doi.org/10.1007/s00500-023-08513-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-023-08513-1

Keywords

Search

Navigation