Journal of Soft Computing and Information Technology

Journal of Soft Computing and Information Technology

Segmentation of Brain Tissues in MRI Images Using Improved Gustafson-Kessel Clustering Algorithm

Document Type : Persian Original Article

Authors
1 Department of Engineering Sciences, Faculty of Advanced Technologies, University of Mohaghegh Ardabili, Namin, Iran.
2 Department of Bioelectric, Faculty of Biomedical Engineering, Sahand University of Technology, Tabriz, Iran.
Abstract
Magnetic Resonance Imaging (MRI) often suffers from noise and intensity non-uniformity (INU), making image segmentation a challenging task. The fuzzy c-means (FCM) algorithm is a popular clustering-based method for image segmentation, but it is sensitive to noise, and its convergence rate is influenced by data distribution. Traditional FCM approaches use the Euclidean distance, which does not account for the variation in data point distances within similar and compact clusters. To address these limitations, a new cost function is proposed for the Gustafson-Kessel (GK) clustering algorithm that utilizes the Mahalanobis distance for similarity measurement. This approach enhances robustness to noise and INU conditions compared to other FCM-based methods. Additionally, information theory is incorporated to further improve noise robustness and segmentation accuracy. Conventional GK clustering is typically affected by the choice of fuzziness value; hence, a membership function entropy is introduced to mitigate this issue. In the proposed algorithm, morphological reconstruction is used as a pre-processing step to reduce noise while preserving object contours. Experimental results on various MRI datasets demonstrate that the proposed algorithm performs well in segmenting multiple tissues under different noise and INU conditions.
Keywords

[1] S. Kollem, C. R. Prasad, J. Ajayan, V. Malathy, A. Subbarao, “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.
[2] S. Alagarsamy, V. Govindaraj, A. Senthilkumar, “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.
[3] C. Singh, S. K. Ranade, D. Kaur, A. Bala, “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.
[4] J. Lyu, X. Chen, S. A. AlQahtani, M. S. Hossain, “Multi-modality MRI fusion with patch complementary pre-training for internet of medical things-based smart healthcare,” Information Fusion, vol. 107, pp. 102342, 2024.
[5] N. Aboubakr, M. Popova, J. L. Crowley, “Color-based fusion of mri modalities for brain tumor segmentation,” In Proceedings of International Conference on Medical Imaging and Computer-Aided Diagnosis Medical Imaging and Computer-Aided Diagnosis, pp. 89-97, 2021.
[6] Y. Fei, G. Wei, S. Zongxi, “Medical image fusion based on feature extraction and sparse representation,” International journal of biomedical imaging, vol. 1, pp. 3020461, 2017.
[7] M. Hassan, I. Murtza, A. Hira, S. Ali, S, K. Kifayat, “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.
[8] S. Natarajan, V. Govindaraj, Y. Zhang, P. R. Murugan, K. Balasubramanian, K. Kandasamy, K. Ejaz, “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.
[9] I. Khatri, D. Kumar, A. Gupta, A, “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.
[10] E. H. Houssein, N. Abdalkarim, K. Hussain, E. Mohamed, E, “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] E. H. Houssein, M. M. Emam, A. A. Ali, A. A, “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] G. Ma, 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] T. Lang, T. Sauer, “Feature-Adaptive Interactive Thresholding of Large 3D Volumes,” arXiv preprint arXiv:2210.06961, 2022.
[14] B. Dong, G. Weng, Q. Bu, Z. Zhu, J. Ni, “An active contour model based on shadow image and reflection edge for image segmentation,” Expert Systems with Applications, vol. 238, pp. 122330, 2024.
[15] Y. Chen, L. Wu, G. Wang, H. He, G. Weng, H. Chen, H, “An active contour model for image segmentation using morphology and nonlinear Poisson’s equation,” Optik, vol. 287, pp. 170997, 2023.
[16] H. Zia, A. Niaz, K. N. Choi, K. N, “Active Contour Model for Image Segmentation,” In Asia Conference on Advanced Robotics, Automation, and Control Engineering (ARACE), 2022.
[17] C. Li, J. C. Gore, C. Davatzikos, “Multiplicative intrinsic component optimization (MICO) for MRI bias field estimation and tissue segmentation,” Magnetic resonance imaging, vol. 32, no. 7, pp. 913-923, 2014.
[18] P. D. Dunning, H. A. Kim, “Introducing the sequential linear programming level-set method for topology optimization,” Structural and Multidisciplinary Optimization, vol. 51, pp. 631-643, 2015.
[19] S. K. Adhikari, J. K. Sing, D. K. Basu, M. Nasipuri, “Conditional spatial fuzzy C-means clustering algorithm for segmentation of MRI images,” Applied soft computing, vol. 34, pp. 758-769, 2015.
[20] A. Elazab, C. Wang, F. Jia, J. Wu, G. Li, Q. Hu, “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.
[21] J. Song, Z. Zhang, Z, “A modified robust FCM model with spatial constraints for brain MR image segmentation,” Information, vol. 10, no. 2, pp. 74, 2019.
[22] J. Qiao, X. Cai, Q. Xiao, Z. Chen, P. Kulkarni, C. Ferris, ... S. Sridhar, “Data on MRI brain lesion segmentation using K-means and Gaussian Mixture Model-Expectation Maximization,” Data in brief, vol. 27, pp. 104628, 2019.
[23] R. Meena Prakash, R. Shantha Selva Kumari, “Spatial fuzzy C means and expectation maximization algorithms with bias correction for segmentation of MR brain images,” Journal of medical systems, vol. 41, pp. 1-9, 2017.
[24] M. Singh, A. Verma, N. Sharma, “Multi-objective noise estimator for the applications of de-noising and segmentation of MRI data,” Biomedical Signal Processing and Control, vol. 46, pp. 249-259, 2018.
[25] P. Ghosh, K. Mali, S. K.  Das, “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.
[26] A. F. Jafargholkhanloo, M. Shamsi, “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.
[27] H. Verma, D. Verma, P. K. Tiwari, “A population-based hybrid FCM-PSO algorithm for clustering analysis and segmentation of brain image,” Expert systems with applications, vol. 167, pp. 114121, 2021.
[28] S. Tongbram, B. A. Shimray, L. S. Singh, N. Dhanachandra, “A novel image segmentation approach using fcm and whale optimization algorithm,” Journal of ambient intelligence and humanized computing, pp. 1-15, 2021.
[29] R. Bandyopadhyay, R. Kundu, D. Oliva, R. Sarkar, “Segmentation of brain MRI using an altruistic Harris Hawks’ Optimization algorithm,” Knowledge-Based Systems, vol. 232, pp. 107468, 2021.
[30] A. Kouhi, H. Seyedarabi, A. Aghagolzadeh, “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.
[31] M. Tavakoli-Zaniani, Z. Sedighi-Maman, M. H. F. Zarandi, “Segmentation of white matter, grey matter and cerebrospinal fluid from brain MR images using a modified FCM based on double estimation,” Biomedical Signal Processing and Control, vol. 68, pp. 102615, 2021.
[32] D. Kumar, I. Khatri, A. Gupta, R. Gusain, “Kernel picture fuzzy clustering with spatial neighborhood information for MRI image segmentation,” Soft Computing, vol. 26, no. 22, pp. 12717-12740, 2022.
[33] S. Vinurajkumar, S. Anandhavelu, “An Enhanced Fuzzy Segmentation Framework for extracting white matter from T1-weighted MR images,” Biomedical Signal Processing and Control, vol. 71, pp. 103093, 2022.
[34] D. Kumar, R. K. Agrawal, P. Kumar, “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.
[35] R. Solanki, D. Kumar, “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.
[36] P. Kumar, R. K. Agrawal, D. Kumar, “Fast and robust spatial fuzzy bounded k-plane clustering method for human brain MRI image segmentation,” Applied Soft Computing, vol. 133, pp. 109939, 2023.
[37] S. Mohammadi, S. Ghaderi, K. Ghaderi, M. Mohammadi, M. H. Pourasl, “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.
[38] J. C. Bezdek, R. Ehrlich, W. Full, “FCM: The fuzzy c-means clustering algorithm,” Computers & geosciences, vol. 10, no. 2, pp. 191-203, 1984.
[39] R. Krishnapuram, 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. Dovžan, I. Škrjanc, “Recursive clustering based on a Gustafson–Kessel algorithm,” Evolving systems, vol. 2, no. 1, pp. 15-24, 2011.
[41] R. Babuka, P. J. Van der Veen, U. Kaymak, “Improved covariance estimation for Gustafson-Kessel clustering,” In IEEE World Congress on Computational Intelligence, vol. 2, pp. 1081-1085, 2022.
[42] D. E. Gustafson, W. C. Kessel, “Fuzzy clustering with a fuzzy covariance matrix,” In IEEE conference on decision and control including the 17th symposium on adaptive processes, pp. 761-766, 1979.
[43] Z. Wang, Q. Song, Y. C. Soh, K. Sim, “An adaptive spatial information-theoretic fuzzy clustering algorithm for image segmentation,” Computer Vision and Image Understanding, vol. 117, no. 10, pp. 1412-1420, 2013.
[44] L. Tao et al, “Adaptive morphological reconstruction for seeded image segmentation,” IEEE Transactions on Image Processing, vol. 28, no. 11, pp. 5510-5523, 2019.
[45] 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.
[46] V. Luc, “Morphological grayscale reconstruction in image analysis: applications and efficient algorithms,” IEEE transactions on image processing, vol. 2, no. 2, pp. 176-201, 1993.
[47] http://www.bic.mni.mcgill.ca/brainweb/ (Brainweb Simulated Brain Database)
[48] A. F. Jafargholkhanloo, M. Shamsi, “Quantitative analysis of facial soft tissue using weighted cascade regression model applicable for facial plastic surgery,” Signal Processing: Image Communication, vol. 121, pp. 117086, 2024.
[49] C. Wang, W. Pedrycz, Z. Li, M. Zhou, “Residual-driven fuzzy C-means clustering for image segmentation,” IEEE/CAA Journal of Automatica Sinica, vol. 8, no. 4, pp. 876-889, 2020.
[50] R. Wang et al, “Medical image segmentation using deep learning: A survey,” IET Image Process, vol. 16, no. 5, pp. 1243–1267, 2022.
[51] 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.
[52] 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.