Document Type : Original Article

Authors

1 Department of Engineering Sciences, Faculty of Advanced Technologies, University of Mohaghegh Ardabili, Namin, Iran

2 Faculty of Biomedical Engineering, Sahand University of Technology, Tabriz, Iran

Abstract

The fuzzy c-means (FCM) algorithm is widely used for image segmentation based on clustering. However, it is sensitive to noise, and its convergence is affected by the data distribution. FCM relies on the Euclidean distance metric, which fails to account for variations in the distances within similar and compact clusters. Moreover, the distance metric is not locally adaptive to the shape of clusters. This paper introduces a robust Gustafson-Kessel (RGK) clustering algorithm to address these limitations for brain tissue segmentation using MRI images. To achieve accurate segmentation under varying noise levels and intensity non-uniformity (INU), a Wiener filter integrated with wavelet transform (WFWT) is employed as a preprocessing step to enhance image quality while preserving object edges. The Mahalanobis distance is used for clustering to better adapt to the shape of the clusters. Additionally, the RGK algorithm incorporates membership matrix filtering to exploit the local spatial constraint. The proposed RGK algorithm was evaluated using two datasets: the BrainWeb simulated dataset and MRI scans from 10 healthy individuals at the Golghasht Medical Imaging Center in Tabriz (GMICT), Iran. In RGK, it is not necessary to compute the distance between pixels within local spatial neighbors and clusters. Experimental results demonstrate that the RGK algorithm outperforms traditional FCM-based methods in the segmentation of brain tissues.

Keywords

[1] Kouhi, A et al, “Robust FCM clustering algorithm with combined spatial constraint and membership matrix local information for brain MRI segmentation,” Expert Systems with Applications, vol. 146, pp. 113159, 2020.
[2] Emam, M. M et al, “A modified reptile search algorithm for global optimization and image segmentation: Case study brain MRI images,” Computers in biology and medicine, vol. 152, pp. 106404, 2023.
[3] Bandyopadhyay, R et al, “Segmentation of brain MRI using an altruistic Harris Hawks’ Optimization algorithm,” Knowledge-Based Systems, vol. 232, pp. 107468, 2021.
[4] Li, C et al, “Multiplicative intrinsic component optimization (MICO) for MRI bias field estimation and tissue segmentation,” Magnetic resonance imaging, vol. 32, no. 7, pp. 913-923, 2014.
[5] Hassan, M et al, “Robust spatial fuzzy GMM based MRI segmentation and carotid artery plaque detection in ultrasound images,” Computer methods and programs in biomedicine, vol. 175, pp. 179-192, 2019.
[6] Singh, C et al, “An Intuitionistic Fuzzy C-Means and Local Information-Based DCT Filtering for Fast Brain MRI Segmentation,” Journal of Imaging Informatics in Medicine, pp. 1-24., 2024.
[7] Jafrasteh, B et al, “Enhanced Spatial Fuzzy C-Means Algorithm for Brain Tissue Segmentation in T1 Images,” Neuroinformatics, pp. 1-14, 2024.
[8] Singh, C et al, “A novel approach for brain MRI segmentation and image restoration under intensity inhomogeneity and noisy conditions,” Biomedical Signal Processing and Control, vol. 87, pp. 105348, 2024.
[9] Natarajan, S et al, “Minimally parametrized segmentation framework with dual metaheuristic optimisation algorithms and FCM for detection of anomalies in MR brain images,” Biomedical Signal Processing and Control, vol. 78, pp. 103866, 2022.
[10] Houssein, E. H et al, “Accurate multilevel thresholding image segmentation via oppositional Snake Optimization algorithm: Real cases with liver disease,” Computers in Biology and Medicine, vol. 169, pp. 107922, 2024.
[11] H. Essam et al, “An efficient multilevel thresholding segmentation method for thermography breast cancer imaging based on improved chimp optimization algorithm,” Expert Systems with Applications, vol. 185, pp. 115651, 2021.
[12] M. Guoyuan and X. Yue, “An improved whale optimization algorithm based on multilevel threshold image segmentation using the Otsu method,” Engineering Applications of Artificial Intelligence, vol. 113, pp. 104960, 2022.
[13] Lang, T and Sauer, T, “Feature-Adaptive Interactive Thresholding of Large 3D Volumes. arXiv preprint arXiv:2210.06961, 2022.
[14] D. Bin et al, “An active contour model based on shadow image and reflection edge for image segmentation,” Expert Systems with Applications, vol. 238, pp. 122330, 2024.
[15] C. Yiyang et al, “An active contour model for image segmentation using morphology and nonlinear Poisson’s equation,” Optik, vol. 287, pp. 170997, 2023.
[16] Zia, H et al, “Active Contour Model for Image Segmentation,” Asia Conference on Advanced Robotics, Automation, and Control Engineering (ARACE), pp. 13-17, 2022.
[17] Adhikari, S. K et al, “Conditional spatial fuzzy C-means clustering algorithm for segmentation of MRI images,” Applied soft computing, vol. 34, pp. 758-769, 2015.
[18] Elazab, A et al, “Segmentation of brain tissues from magnetic resonance images using adaptively regularized kernel‐based fuzzy C‐means clustering,” Computational and mathematical methods in medicine, vol. 2015, no. 1, pp. 485495, 2015.
[19] Bakhshali, M. A, “Segmentation and enhancement of brain MR images using fuzzy clustering based on information theory,” Soft Computing, vol. 21, pp. 6633-6640., 2017.
[20] Moeskops, P et al, “Automatic segmentation of MR brain images with a convolutional neural network,” IEEE transactions on medical imaging, vol. 35, no. 5, pp. 1252-1261, 2016.
[21] Ghosh, P et al, “Chaotic firefly algorithm-based fuzzy C-means algorithm for segmentation of brain tissues in magnetic resonance images,” Journal of Visual Communication and Image Representation, vol. 54, pp. 63-79., 2018.
[22] Verma, H et al, “A population-based hybrid FCM-PSO algorithm for clustering analysis and segmentation of brain image,” Expert systems with applications, vol. 167, pp. 114121, 2021.
[23] Tongbram, S and et al, “A novel image segmentation approach using fcm and whale optimization algorithm,” Journal of ambient intelligence and humanized computing, pp. 1-15., 2021.
[24] Chighoub, F and Saouli, R, “Fully integrated spatial information to improve FCM algorithm for brain MRI Image segmentation,” Automatic Control and Computer Sciences, vol. 56, no. 1, pp. 67-82., 2022.
[25] Kumar, D et al, “Kernel picture fuzzy clustering with spatial neighborhood information for MRI image segmentation,” Soft Computing, vol. 26, no. 22, pp. 12717-12740, 2022.
[26] Khaled, A et al, “Learning to detect boundary information for brain image segmentation,” BMC bioinformatics, vol. 23, no. 1, pp. 332, 2022.
[27] Khatri, I et al, “A noise robust kernel fuzzy clustering based on picture fuzzy sets and KL divergence measure for MRI image segmentation,” Applied Intelligence, vol. 53, no. 13, pp. 16487-16518, 2023.
[28] Kumar, D et al, “Bias-corrected intuitionistic fuzzy c-means with spatial neighborhood information approach for human brain MRI image segmentation,” IEEE Transactions on Fuzzy Systems, vol. 30, no. 3, pp. 687-700, 2020.
[29] Kollem, S et al, “Brain tumor MRI image segmentation using an optimized multi-kernel FCM method with a pre-processing stage,” Multimedia Tools and Applications, vol. 82, no. 14, pp. 20741-20770, 2023.
[30] Solanki, R and Kumar, D, “Probabilistic intuitionistic fuzzy c-means algorithm with spatial constraint for human brain MRI segmentation,” Multimedia Tools and Applications, vol. 82, no. 22, pp. 33663-33692, 2023.
[31] Alagarsamy, S and et al, “Automated brain tumor segmentation for MR brain images using artificial bee colony combined with interval type-II fuzzy technique,” IEEE Transactions on Industrial Informatics, vol. 19, no. 11, pp. 11150-11159, 2023.
[32] Kalti, K and Touil, A, “A Robust Contextual Fuzzy C-Means Clustering Algorithm for Noisy Image Segmentation,” Journal of Classification, vol. 40, no. 3, pp. 488-512, 2023.
[33] Mohammadi, S et al, “Automated segmentation of meningioma from contrast-enhanced T1-weighted MRI images in a case series using a marker-controlled watershed segmentation and fuzzy C-means clustering machine learning algorithm,” International Journal of Surgery Case Reports, vol. 111, pp. 108818, 2023.
[34] Shekari, M and Rostamian, M, “Brain tumor segmentation from MRI using FCM clustering, morphological reconstruction, and active contour,” Multimedia Tools and Applications, vol. 83, no. 14, pp. 42973-42998, 2024.
[35] Tian, Z and Wang, S, “A level set model with shape prior constraint for intervertebral disc MRI image segmentation,” Multimedia Tools and Applications, pp. 1-29, 2024.
[36] Dunning, P. D and Kim, H. A, “Introducing the sequential linear programming level-set method for topology optimization,” Structural and Multidisciplinary Optimization, vol. 51, pp. 631-643, 2015.
[37] Jafargholkhanloo, A. F. and Shamsi, M, “Cephalometry analysis of facial soft tissue based on two orthogonal views applicable for facial plastic surgeries,” Multimedia Tools and Applications, vol. 82, no. 20, pp. 30643-30668, 2023.
[38] J. C. Bezdek et al, “FCM: The fuzzy c-means clustering algorithm,” Comput. Geosci, vol. 10, no. 2-3, pp. 191-203, 1984.
[39] K. Raghu and J. Kim, “A note on the Gustafson-Kessel and adaptive fuzzy clustering algorithms,” IEEE Transactions on Fuzzy systems, vol. 7, no. 4, pp. 453-461, 1999.
[40] D. Dejan and I. Škrjanc, “Recursive clustering based on a Gustafson–Kessel algorithm,” Evolving systems, vol. 2, no. 1, pp. 15-24, 2011.
[41] B. R. P. J. Veen and U. Kaymak, “Improved covariance estimation for Gustafson-Kessel clustering,” IEEE International Conference on Fuzzy Systems, vol. 2, 2002.
[42] G. Donald and W. C. Kessel, “Fuzzy clustering with a fuzzy covariance matrix,” IEEE conference on decision and control including the 17th symposium on adaptive processes, 1979.
[43] S. László et al, “MR brain image segmentation using an enhanced fuzzy c-means algorithm,” Proceedings of the 25th annual international conference of the IEEE engineering in medicine and biology society, vol. 1, 2003.
[44] L. Tao et al, “Significantly fast and robust fuzzy c-means clustering algorithm based on morphological reconstruction and membership filtering,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 5, pp. 3027-3041, 2018.
[45] Göreke, V, “A novel method based on Wiener filter for denoising Poisson noise from medical X-Ray images,” Biomedical Signal Processing and Control, vol. 79, pp. 104031, 2023.
[46] Shreyamsha Kumar, B. K, “Image denoising based on non-local means filter and its method noise thresholding,” Signal, image and video processing, vol. 7, pp. 1211-1227, 2013.
[47] W. Cong et al, “Residual-driven fuzzy C-means clustering for image segmentation,” IEEE/CAA Journal of Automatica Sinica, vol. 8, no. 4, pp. 876-889, 2020.
[48] Jafargholkhanloo, A. F and Shamsi, M, “Quantitative analysis of facial soft tissue using weighted cascade regression model applicable for facial plastic surgery,” Signal Processing: Image Communication, 121, 117086, 2024.
[49] https://brainweb.bic.mni.mcgill.ca/cgi/brainweb1
[50] M. Shah et al., “Evaluating intensity normalization on MRIs of human brain with multiple sclerosis,” Med. Image Anal, vol. 15, no. 2, pp. 267–282, 2011.
[51] R. T. Shinohara et al., “Statistical normalization techniques for magnetic resonance imaging,” NeuroImage Clin, vol. 6, pp. 9–19, 2014.
[52] Fortin, Jean-Philippe et al, “Harmonization of cortical thickness measurements across scanners and sites,” Neuroimage, vol. 167, pp. 104-120, 2018.  
[53] M. Jenkinson et al, “FSL,” Neuroimage, vol. 62, no. 2, pp. 782–790, 2012.
[54] R. R. Edelman, J. R. Hesselink, M. B. Zlatkin, and J. V. Crues, Clinical magnetic resonance imaging, vol. 1, WB Saunders, 2006.
[55] C. Westbrook, C. K. Roth, and J. Talbot, MRI in Practice, 4th ed. Chichester, England: Wiley-Blackwell, 2011.
[56] R. Wang et al, “Medical image segmentation using deep learning: A survey,” IET Image Process, vol. 16, no. 5, pp. 1243–1267, 2022.
[57] B. Billot et al, “SynthSeg: Segmentation of brain MRI scans of any contrast and resolution without retraining,” Med. Image Anal, vol. 86, no. 102789, p. 102789, 2023.
[58] B. Billot et al, “Robust machine learning segmentation for large-scale analysis of heterogeneous clinical brain MRI datasets,” Proc. Natl. Acad. Sci. U. S. A, vol. 120, no. 9, p. e2216399120, 2023.