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Archimedes optimizer-based fast and robust fuzzy clustering for noisy image segmentation

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Abstract

Fuzzy C-means (FCM) is one of the prominent and effective cluster-based image segmentation techniques exceedingly susceptible to noise and initial cluster centers, thereby effortlessly converging toward local optima. However, FCM consumes exceptionally high computation time due to the repetitive computation of the distance amid cluster centers and pixels. To resolve this apprehension, this paper aims to consider a histogram-based fast fuzzy image clustering (HBFFIC) procedure that primarily tends to carry out morphological reconstruction (MR) operation over the image to assure noise immunity and safeguard details of the imagery. Further, as a replacement for pixels of a summed image, clustering is carried out based on gray-level histogram. This with no qualm radically trims down the computational time as the number of gray levels in an image is normally to a great extent lesser than that of the number of its pixels. Though HBFFIC is a proficient local optimizer however, owing to arbitrary initialization that is carried out in FCM, HBFFIC has the utmost possibility to get effortlessly wedge into local optima. Consequently, this is where the role of nature-inspired optimization algorithms (NIOA) comes into picture. For that reason, this paper successfully makes use of NIOA to prevail over the dilemma using Archimedes optimizer (AO) to discover the most favorable cluster centers. The real-world images particularly synthetic, grayscale, and color pathology images are exercised to perform the experimental study. The experimental study clearly highlights that the proposed hybrid algorithm (HBFFIC-AO) for noisy image segmentation outperforms the other state-of-art algorithms in terms of segmentation accuracy (SA), comparison score (CS), MSE, and PSNR. The visual along with numerical outcomes projected in the experimental study point toward the pre-eminence of the proposed algorithm as compared with the prevailing leading-edge image segmentation algorithms.

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References

  1. Bong CW, Rajeswari M (2012) Multiobjective clustering with metaheuristic: current trends and methods in image segmentation. IET Image Proc 6(1):1–10. https://doi.org/10.1049/iet-ipr.2010.0122

    Article  Google Scholar 

  2. Dhal KG, Das A, Ray S, Gálvez J, Das S (2019) Nature-inspired optimization algorithms and their application in multi-thresholding image segmentation. Archiv Comput Method Eng. https://doi.org/10.1007/s11831-019-09334-y

    Article  Google Scholar 

  3. Dhal KG, Ray S, Das S, Biswas A, Ghosh S (2019) Hue-preserving and gamut problem-free histopathology image enhancement. Iranian J Sci Technol, Trans Electr Eng 43(3):645–672. https://doi.org/10.1007/s40998-019-00175-w

    Article  Google Scholar 

  4. Bezdek JC, Ehrlich R, Full W (1984) FCM: The fuzzy c-means clustering algorithm. Comput Geosci 10(2–3):191–203. https://doi.org/10.1016/0098-3004(84)90020-7

    Article  Google Scholar 

  5. Das S, Konar A, Chakraborty UK (2006) Automatic fuzzy segmentation of images with differential evolution. IEEE Congres Evolut Comput 2006:2026–2033. https://doi.org/10.1109/CEC.2006.1688556

    Article  Google Scholar 

  6. Ahmed MN, Yamany SM, Mohamed N, Farag AA, Moriarty T (2002) A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data. IEEE Trans Med Imaging 21(3):193–199. https://doi.org/10.1109/42.996338

    Article  Google Scholar 

  7. Chen S, Zhang D (2004) Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure. IEEE Transact Syst Man Cybern Part B (Cybernetics) 34(4):1907–1916. https://doi.org/10.1109/TSMCB.2004.831165

    Article  Google Scholar 

  8. Szilagyi, L., Benyo, Z., Szilágyi, S. M., & Adam, H. S. (2003) . MR brain image segmentation using an enhanced fuzzy c-means algorithm. In Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE Cat No 03CH37439) 1pp.724-726 https://doi.org/10.1109/IEMBS.2003.1279866.

  9. Cai W, Chen S, Zhang D (2007) Fast and robust fuzzy c-means clustering algorithms incorporating local information for image segmentation. Pattern Recogn 40(3):825–838. https://doi.org/10.1016/j.patcog.2006.07.011

    Article  MATH  Google Scholar 

  10. Krinidis S, Chatzis V (2010) A robust fuzzy local information C-means clustering algorithm. IEEE Trans Image Process 19(5):1328–1337. https://doi.org/10.1109/TIP.2010.2040763

    Article  MATH  Google Scholar 

  11. Gong M, Zhou Z, Ma J (2011) Change detection in synthetic aperture radar images based on image fusion and fuzzy clustering. IEEE Trans Image Process 21(4):2141–2151. https://doi.org/10.1109/TIP.2011.2170702

    Article  MATH  Google Scholar 

  12. Gong M, Liang Y, Shi J, Ma W, Ma J (2012) Fuzzy c-means clustering with local information and kernel metric for image segmentation. IEEE Trans Image Process 22(2):573–584. https://doi.org/10.1109/TIP.2012.2219547

    Article  MATH  Google Scholar 

  13. May V, Keller Y, Sharon N, Shkolnisky Y (2016) An algorithm for improving non-local means operators via low-rank approximation. IEEE Trans Image Process 25(3):1340–1353. https://doi.org/10.1109/TIP.2016.2518805

    Article  MATH  Google Scholar 

  14. Nguyen MP, Chun SY (2017) Bounded self-weights estimation method for non-local means image denoising using minimax estimators. IEEE Transact Image Process 26(4):1637–1649. https://doi.org/10.1109/TIP.2017.2658941

    Article  MATH  Google Scholar 

  15. Saranathan AM, Parente M (2015) Uniformity-based superpixel segmentation of hyperspectral images. IEEE Trans Geosci Remote Sens 54(3):1419–1430. https://doi.org/10.1109/TGRS.2015.2480863

    Article  Google Scholar 

  16. Zaixin Z, Lizhi C, Guangquan C (2013) Neighbourhood weighted fuzzy c-means clustering algorithm for image segmentation. IET Image Proc 8(3):150–161. https://doi.org/10.1049/iet-ipr.2011.0128

    Article  Google Scholar 

  17. Guo FF, Wang XX, Shen J (2016) Adaptive fuzzy c-means algorithm based on local noise detecting for image segmentation. IET Image Proc 10(4):272–279. https://doi.org/10.1049/iet-ipr.2015.0236

    Article  Google Scholar 

  18. Lei T, Jia X, Zhang Y, He L, Meng H, Nandi AK (2018) Significantly fast and robust fuzzy c-means clustering algorithm based on morphological reconstruction and membership filtering. IEEE Trans Fuzzy Syst 26(5):3027–3041. https://doi.org/10.1109/TFUZZ.2018.2796074

    Article  Google Scholar 

  19. Khan W (2013) Image segmentation techniques: a survey. J Image Graphic 1(4):166–170

    Google Scholar 

  20. Dhal KG, Ray S, Das A, Das S (2019) A survey on nature-inspired optimization algorithms and their application in image enhancement domain. Arch Comput Method Eng 26(5):1607–1638. https://doi.org/10.1007/s11831-018-9289-9

    Article  Google Scholar 

  21. Dhal KG, Gálvez J, Ray S, Das A, Das S (2020) Acute lymphoblastic leukemia image segmentation driven by stochastic fractal search. Multimed Tools Appl. https://doi.org/10.1007/s11042-019-08417-z

    Article  Google Scholar 

  22. Dhal KG, Gálvez J, Das S (2019) Toward the modification of flower pollination algorithm in clustering-based image segmentation. Neural Comput Appl 32:3059–3077. https://doi.org/10.1007/s00521-019-04585-z

    Article  Google Scholar 

  23. Dhal KG, Das A, Ray S, Das S (2019) A clustering based classification approach based on modified cuckoo search algorithm. Pattern Recognit Image Anal 29(3):344–359. https://doi.org/10.1134/S1054661819030052

    Article  Google Scholar 

  24. Dhal, K. G., Fister Jr., I., Das, A., Ray, S., and Das, S. (2018). Breast Histopathology Image Clustering using Cuckoo Search Algorithm. 5th Student Computer Science Research Conference University of Maribor, Slovenia https://doi.org/10.26493/978-961-7055-26-9.47-54

  25. Dhanachandra N, Chanu YJ (2020) An image segmentation approach based on fuzzy c-means and dynamic particle swarm optimization algorithm. Multimed Tools Appl. https://doi.org/10.1007/s11042-020-08699-8

    Article  Google Scholar 

  26. Xiong L, Tang G, Chen YC, Hu YX, Chen RS (2020) Color disease spot image segmentation algorithm based on chaotic particle swarm optimization and FCM. J Supercomput. https://doi.org/10.1007/s11227-020-03171-8

    Article  Google Scholar 

  27. Das, R. (2020). Color image segmentation using adaptive particle swarm optimization and fuzzy C-means. arXiv preprint arXiv:2004.08547. https://doi.org/10.48550/arXiv.2004.08547

  28. Zhang J, Ma Z (2020) Hybrid fuzzy clustering method based on fcm and enhanced logarithmical PSO (ELPSO). Comput Intell Neurosci. https://doi.org/10.1155/2020/1386839

    Article  Google Scholar 

  29. Halder A, Maity A, Sarkar A, Das A (2019) A Dynamic Spatial Fuzzy C-Means Clustering-Based Medical Image Segmentation. In: Abraham Ajith, Dutta Paramartha, Mandal Jyotsna Kumar, Bhattacharya Abhishek, Dutta Soumi (eds) Emerging Technologies in Data Mining and Information Security: Proceedings of IEMIS 2018, Volume 2. Springer Singapore, Singapore, pp 829–836. https://doi.org/10.1007/978-981-13-1498-8_73

    Chapter  Google Scholar 

  30. Wang, M., Wan, Y., Gao, X., Ye, Z., & Chen, M. (2018). An image segmentation method based on fuzzy C-means clustering and Cuckoo search algorithm. In Ninth International Conference on Graphic and Image Processing (ICGIP 2017) International Society for Optics and Photonics 10615: 1061525 https://doi.org/10.1117/12.2302922

  31. Li MQ, Xu LP, Xu N, Huang T, Yan B (2018) SAR image segmentation based on improved grey wolf optimization algorithm and fuzzy c-means. Math Problems Eng. https://doi.org/10.1155/2018/4576015

    Article  Google Scholar 

  32. Zhang M, Jiang W, Zhou X, Xue Y, Chen S (2019) A hybrid biogeography-based optimization and fuzzy C-means algorithm for image segmentation. Soft Comput 23(6):2033–2046. https://doi.org/10.1007/s00500-017-2916-9

    Article  Google Scholar 

  33. Toz G, Yücedağ İ, Erdoğmuş P (2019) A fuzzy image clustering method based on an improved backtracking search optimization algorithm with an inertia weight parameter. J King Saud Univ Comput Inf Sci 31(3):295–303. https://doi.org/10.1016/j.jksuci.2018.02.011

    Article  Google Scholar 

  34. Singh, T. I., Laishram, R., & Roy, S. (2019). Comparative study of combination of swarm intelligence and fuzzy C means clustering for medical image segmentation. In Smart Computational Strategies: Theoretical and Practical Aspects: 69–80 Springer, Singapore https://doi.org/10.1007/978-981-13-6295-8_7

  35. Zhi H, Liu S (2020) Gray image segmentation based on fuzzy c-means and artificial bee colony optimization. J Intell Fuzzy Syst 38(4):3647–3655. https://doi.org/10.3390/electronics10243116

    Article  Google Scholar 

  36. Tongbram S, Shimray BA, Singh LS, Dhanachandra N (2021) A novel image segmentation approach using fcm and whale optimization algorithm. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-020-02762-w

    Article  Google Scholar 

  37. Vishnoi S, Jain AK, Sharma PK (2019) An efficient nuclei segmentation method based on roulette wheel whale optimization and fuzzy clustering. Evol Intel. https://doi.org/10.1007/s12065-019-00288-5

    Article  Google Scholar 

  38. Narmatha C, Eljack SM, Tuka AARM, Manimurugan S, Mustafa M (2020) A hybrid fuzzy brain-storm optimization algorithm for the classification of brain tumor MRI images. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-020-02470-5

    Article  Google Scholar 

  39. Tiwari V, Jain SC (2020) Histopathological cells segmentation using exponential grasshopper optimisation algorithm-based fuzzy clustering method. Int J Intell Inf Database Syst 13(2–4):118–138

    Google Scholar 

  40. Fred AL, Kumar SN, Padmanaban P, Balazs Gulyas H, Kumar Ajay (2020) Fuzzy-Crow Search Optimization For Medical Image Segmentation. In: Oliva Diego, Hinojosa Salvador (eds) Applications of Hybrid Metaheuristic Algorithms for Image Processing. Springer International Publishing, Cham, pp 413–439. https://doi.org/10.1007/978-3-030-40977-7_18

    Chapter  Google Scholar 

  41. Dash M, Londhe ND, Ghosh S, Shrivastava VK, Sonawane RS (2020) Swarm intelligence based clustering technique for automated lesion detection and diagnosis of psoriasis. Comput Biol Chem 86:107247. https://doi.org/10.1007/s42452-020-04110-1

    Article  Google Scholar 

  42. Rapaka S, Kumar PR, Katta M, Lakshminarayana K, Kumar NB (2021) A new segmentation method for non-ideal iris images using morphological reconstruction FCM based on improved DSA. SN Appl Sci 3(1):1–15. https://doi.org/10.1007/s42452-020-04110-1

    Article  Google Scholar 

  43. Abdellahoum H, Mokhtari N, Brahimi A, Boukra A (2021) CSFCM: an improved fuzzy c-means image segmentation algorithm using a cooperative approach. Expert Syst Appl 166:114063. https://doi.org/10.1016/j.eswa.2020.114063

    Article  Google Scholar 

  44. Salcedo-Sanz S (2016) Modern meta-heuristics based on nonlinear physics processes: a review of models and design procedures. Phys Rep 655:1–70. https://doi.org/10.1016/j.physrep.2016.08.001

    Article  Google Scholar 

  45. Hashim FA, Hussain K, Houssein EH, Mabrouk MS, Al-Atabany W (2021) Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems. Appl Intell 51(3):1531–1551. https://doi.org/10.1007/s10489-020-01893-z

    Article  MATH  Google Scholar 

  46. Mittal H, Saraswat M (2018) An optimum multi-level image thresholding segmentation using non-local means 2D histogram and exponential Kbest gravitational search algorithm. Eng Appl Artif Intell 71:226–235. https://doi.org/10.1016/j.engappai.2018.03.001

    Article  Google Scholar 

  47. Labati R D Piuri V and Scotti F (2011) All-IDB: The acute lymphoblastic leukemia image database for image processing, In 2011 18th IEEE international conference on image processing 2045–2048 https://doi.org/10.1109/ICIP.2011.6115881

  48. Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S (2020) Equilibrium optimizer: a novel optimization algorithm. Knowl-Based Syst 191:105190. https://doi.org/10.1016/j.knosys.2019.105190

    Article  Google Scholar 

  49. Karami H, Anaraki MV, Farzin S, Mirjalili S (2021) Flow direction algorithm (fda): a novel optimization approach for solving optimization problems. Comput Ind Eng 156:107224. https://doi.org/10.1016/j.cie.2021.107224

    Article  Google Scholar 

  50. Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. In Proceedings of ICNN'95-International Conference on Neural Networks https://doi.org/10.1109/ICNN.1995.488968

  51. Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133. https://doi.org/10.1016/j.knosys.2015.12.022

    Article  Google Scholar 

  52. García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J Heuristics 15(6):617–644. https://doi.org/10.1007/s10732-008-9080-4

    Article  MATH  Google Scholar 

  53. Das A, Namtirtha A, Dutta A (2021) Fuzzy clustering of acute lymphoblastic leukemia images assisted by eagle strategy and morphological reconstruction. Knowl-Based Syst. https://doi.org/10.1016/j.knosys.2021.108008

    Article  Google Scholar 

  54. Dhal KG, Das A, Ray S, Gálvez J (2021) Randomly attracted rough firefly algorithm for histogram based fuzzy image clustering. Knowl-Based Syst 216:106814. https://doi.org/10.1016/j.knosys.2021.106814

    Article  Google Scholar 

  55. Das A, Dhal KG, Ray S, Gálvez J (2021) Histogram-based fast and robust image clustering using stochastic fractal search and morphological reconstruction. Neural Comput Appl. https://doi.org/10.1007/s00521-021-06610-6

    Article  Google Scholar 

  56. Vincent L (1993) Morphological grayscale reconstruction in image analysis: applications and efficient algorithms. IEEE transact image process 2(2):176–201. https://doi.org/10.1109/83.217222

    Article  Google Scholar 

  57. Junwei, T., & Yongxuan, H. (2007). Histogram constraint based fast FCM cluster image segmentation. In 2007 IEEE International Symposium on Industrial Electronics: 1623–1627 IEEE

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This work has been partially supported by the grant received in the research project under RUSA 2.0 component 8, Government of India, New Delhi.

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Correspondence to Rebika Rai.

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Dhal, K.G., Das, A., Ray, S. et al. Archimedes optimizer-based fast and robust fuzzy clustering for noisy image segmentation. J Supercomput 79, 3691–3730 (2023). https://doi.org/10.1007/s11227-022-04769-w

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