FCM Clustering Algorithms for Segmentation of Brain MR Images

Table 1

Comparison of the algorithms used for segmentation for brain MR images with intensity in homogeneity correction in terms of advantages and limitations.

Algorithm	Advantages	Limitations	Quantitative evaluation
Bias corrected FCM (BCFCM) [14]	BCFCM compensate for the gray (intensity) levels inhomogeneity and allow the labelling of a pixel to be influenced by the labels in its immediate neighbourhood	BCFCM computes the neighbourhood term in each iteration step, which is very computationally time-consuming and lacks enough robustness to noise and outliers and is difficult to cluster non-Euclidean structure data	Segmentation accuracy (SA)
Spatially constrained kernelized FCM (FCM_S1, FCM_S2 and KFCM_S1, KFCM_S2) [21]	Clusters the non-Euclidean structures in data. Robustness of the original clustering algorithms to noise and outliers while retaining computational simplicity	KFCM_S1 and KFCM_S2 are heavily affected by their parameters	Segmentation accuracy and similarity measure
Improved FCM (IFCM) [26]	IFCM performs better than the traditional FCM	Sensitive to algorithmic parameter value selection	Undersegmentation (UnS), oversegmentation (OvS), incorrect segmentation (InS), and comparison score
Fast generalized FCM (FGFCM) [68]	FGFCM lessens the disadvantages of fuzzy -means (FCM) algorithms with spatial constraints (FCM_S) and at the same time enhances the clustering performance. The introduction of local spatial information to the corresponding objective functions enhances their insensitiveness to noise	Lack enough robustness to noise and outliers, especially in absence of prior knowledge of the noise. The time of segmenting an image is dependent on the image size, and hence the larger the size of the image, the more the segmentation time	Segmentation accuracy and similarity measure
Gaussian Kernelized FCM (GKFCM) [27]	It is a generalized type of FCM, BCFCM, KFCM_S1, and KFCM_S2 algorithms and is more efficient and robust with good parameter learning scheme in comparison with FCM and its variant	For the case of Gaussian noise of 10% level, KFCM_S has better result than GKFCM	Segmentation accuracy
Modified FCM classification method using multiscale Fuzzy -means (MsFCM) [44]	The method is robust for noise and low contrast MR images because of its multiscale diffusion filtering scheme	The threshold value of parameter used in the algorithm may need to be adjusted when this method is applied to other images with a different noise level	Dice coefficient and overlap ratio
Modified fast FCM (MFCM) for brain MR images segmentation [15]	Intensity inhomogeneity, noise, and partial volume (PV) effects are taken into account for image segmentation. Automated method to determine the initial values of the centroids and adaptive method to incorporate the local spatial continuity to overcome the noise effectively and prevent the edge from blurring	Quantitative accuracy decreases when the noise level in brain MR images increases. Larger radius of neighbourhood leads to the loss of texture, so CSF cannot be segmented accurately	Jaccard similarity and Dice coefficient
Modified robust FCM algorithm with weighted bias estimation (MRFCM-wBE) [19]	Initializes the centroids using dist-max initialization algorithm to reduce the number of iterations	The algorithm was tested on T1-T2 weighted images and simulated brain images corrupted by Gaussian noise only	Silhouette value