A Fuzzy Consensus Clustering Algorithm for MRI Brain Tissue Segmentation
Abstract
:1. Introduction
 Proposed a consensus clustering method for MRI brain tissue segmentation.
 The results of four variants of fuzzy clustering methods are combined to achieve better results.
 To check the efficacy of the proposed method, we conducted experiments on two standard brain segmentation datasets.
2. Methodology
2.1. PreProcessing
2.2. Segmentation
2.2.1. Robust Spatial Kernel FCM (RSKFCM)
2.2.2. Generalized Spatial Kernel FCM (GSKFCM)
2.2.3. Modified Intuitionistic Fuzzy CMeans (MIFCM)
2.2.4. Consensus Clustering Using Voting Schema
Algorithm 1: Consensus Clustering using voting scheme 
Data: Input image $X=\{{x}_{1},\cdots ,{x}_{j},\cdots ,{x}_{n}\}$, Stopping criteria $\left(\epsilon \right)$, m, number of clusters C Result: Segmentation results, Cluster centers

3. Experimental Results
3.1. Datasets
3.1.1. OASIS
3.1.2. IBSR18
3.2. Evaluation Metrics
3.3. Experimental Setup
3.4. Results
 HMRFEM [8]: This method combines hidden Markov random field (HMRF) with an EM algorithm for MRI image segmentation. The main advantage of this method is it derives how the spatial information is encoded through the mutual influences of neighboring sites.
 FASTPVE [41]: This method uses Markov random field(MRF) for brain tissue segmentation. To increase the speed, this method uses fast iterated conditional modes to solve MRFs.
 MSSEG [42]: This method deal with images in the presence of WM lesions. This approach integrates a robust partial volume tissue segmentation with WM outlier rejection and filling, combining intensity and probabilistic and morphological prior maps.
 RFCM [43]: This method models the intensity inhomogeneities as a gain field that causes image intensities to smoothly and slowly vary through the image space. It iteratively adapts to the intensity inhomogeneities and is completely automated.
 SFCM [44]: This method generalizes the objective function of a conventional FCM by incorporating a spatial penalty on the membership function.
 FANTASM [45]: This method is the extension of an adaptive FCM. In this method, an additional constraint is placed on the membership functions that force them to be spatially smooth.
 PVC [31]: This method uses a partial volume model for MRI brain tissue segmentation. First, it classifies nonbrain tissue using a combination of anisotropic diffusion filtering, edge detection, and mathematical morphology. Further, the local estimates are computed by fitting a partial volume tissue measurement model to histograms of neighborhoods about each estimate point. Voxels in the intensitynormalized image are then classified into six tissue types using a maximum a posteriori classifier.
 SPM5 [46]: This method is based on a mixture of Gaussians. In addition, it is extended to incorporate a smooth intensity variation and nonlinear registration with tissue probability maps.
 GAMIXTURE [47]: This method employs finite mixture models (FMMs) for brain tissue segmentation. To deal with FMM complex optimization, this method employs a global optimization algorithm that uses blended crossover and a new permutation operator.
 ANN [48]: This method is based on a selforganizing map (SOM). Initially, the feature vector is extracted from the intensity of the pixel and its n nearest neighbors. Further, to improve the robustness, statistical transformation is applied to the extracted feature vector. Finally, each pixel is classified using SOM.
 KNN [49]: This method uses KNN for brain tissue segmentation.
 BrainSuit09 [50]: This is an automatic brain image analysis tool. The tool provides a sequence of lowlevel operations in a single package that can produce accurate brain segmentation in clinical time.
 SVPASEG [51]: This method uses local image models for brain tissue segmentation. This model combines the local models for tissue intensities and Markov Random Field (MRF) into a global probabilistic image model. Finally, the parameters for the local intensity models are obtained without supervision by maximizing the weighted likelihood of a certain finite mixture model.
 EGCSOM [52]: This method uses selforganizing maps (SOM) for brain tissue segmentation. Initially, first and secondorder features are extracted using overlapping windows. Further, evolutionary computing is used for feature selection. Finally, map units are grouped using SOM.
 RFCRF [53]: This method uses a conditional random field with a random forest for brain tissue segmentation. This method uses intensities, gradients, probability maps, and locations as features.
3.4.1. Results on OASIS Dataset
3.4.2. Results on IBSR18 Dataset
3.5. Autism Spectrum Disorder Detection Using Proposed Method
3.6. Discussion
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Method  CSF  GM  WM  

DC  HD  AVD  DC  HD  AVD  DC  HD  AVD  
HMRFEM [8]  61.47$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.32$  7.17$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.62$  12.51$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}8.57$  79.65$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}4.26$  5.14$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.62$  4.11$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}8.04$  83.82$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}4.02$  5.09$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.31$  3.33$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}8.64$ 
FASTPVE [41]  54.08$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}3.61$  7.17$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.51$  12.51$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}7.28$  78.97$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.24$  5.14$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}0.92$  4.11$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}6.34$  85.11$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.61$  5.09$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.11$  3.33$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}6.24$ 
FSL [38]  79.72 ± 3.64  4.78$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.92$  9.36$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}5.32$  87.84$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.37$  5.33$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}0.81$  5.37$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}6.57$  88.51$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.31$  5.13$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.34$  8.18$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}4.95$ 
SPM12 [39]  80.46$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}4.02$  6.71$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.01$  20.77$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}6.04$  89.52$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.52$  3.91$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}0.76$  3.67$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}4.82$  88.11$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.42$  4.54$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}0.95$  2.7$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}5.24$ 
FreeSurfer [40]  84.33$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}3.96$  4.4$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.04$  4.33$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}4.06$  91.47$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.44$  4.18$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}0.59$  2.63$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}4.91$  90.48$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.31$  3.8$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}0.59$  2.77$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}5.64$ 
MSSEG [42]  89.95$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.62$  4.18$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.62$  4.71$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.62$  91.24$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.62$  4.31$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.62$  2.87$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.62$  89.58$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.62$  4.39$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.62$  2.91$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.62$ 
RSKFCM [28]  90.06 $\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.79$  4.06$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.61$  4.31$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}4.52$  92.31$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.61$  4.21$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}0.46$  2.31$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}3.42$  90.51$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.52$  4.31$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}0.42$  2.81$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}5.29$ 
GSKFCM [29]  91.23$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.82$  4.08$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.53$  4.28$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}3.26$  92.51$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.32$  4.13$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}0.42$  2.11$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}3.61$  90.62$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.61$  4.28$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}0.68$  2.71$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}5.41$ 
MIFCM_S [20]  89.21$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}3.02$  4.23$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.42$  4.51$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}3.14$  89.81$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.41$  4.41$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}0.31$  2.97$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}3.59$  87.28$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.71$  4.59$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}0.82$  3.01$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}5.16$ 
MIFCM_Y [20]  92.65$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}3.06$  3.96$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.46$  3.91$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}3.02$  93.64$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.51$  4.23$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}0.32$  2.16$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}3.42$  92.61$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.68$  4.31$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}0.84$  2.17$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}5.24$ 
Proposed Method (consensus clustering)  93.64$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.15$  3.16$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.31$  3.85$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.06$  94.71$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.30$  4.01$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}0.21$  2.06$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}2.96$  93.17$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}1.32$  4.26$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}0.81$  2.07$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}4.21$ 
Method  GM  WM  CSF  

mean  std  mean  std  mean  std  
RFCM [43]  65.00  0.05  75.00  0.05  NA  NA 
NLFCM [43]  72.00  0.05  74.00  0.05  NA  NA 
FCM [43]  74.00  0.05  72.00  0.05  NA  NA 
HMRFEM [8]  74.60  0.04  89.60  0.02  12.60  0.05 
SFCM [44]  70.60  0.06  86.60  0.03  16.60  0.07 
FANTASM [45]  71.60  0.06  88.60  0.03  11.60  0.06 
PVC [31]  70.60  0.08  83.60  0.07  13.60  0.06 
SPM5 [46]  68.60  0.07  86.60  0.02  10.60  0.05 
GAMIXTURE [47]  78.60  0.08  87.60  0.02  15.60  0.09 
ANN [48]  70.60  0.07  87.60  0.03  11.60  0.06 
KNN [49]  79.60  0.03  86.60  0.03  16.60  0.07 
BrainSuit09 [50]  72.00  0.09  83.00  0.08  NA  NA 
SVPASEG [51]  81.60  0.03  88.60  0.02  16.60  0.07 
SPM8 [39]  81.60  0.02  88.60  0.01  17.60  0.08 
EGCSOM [52]  73.00  0.05  76.00  0.04  NA  NA 
HFSSOM [52]  60.00  0.09  60.00  0.08  NA  NA 
FASTPVE [41]  78.00  0.08  86.00  0.04  NA  NA 
FASTPVE(SICM) [41]  78.00  0.08  86.00  0.04  NA  NA 
RFCRF [53]  96.10  0.01  92.00  0.02  92.00  0.03 
RFCRF1 [53]  94.00  0.01  89.00  0.02  88.00  0.03 
FSL [38]  78.13  0.04  85.94  0.13  75.02  0.04 
FreeSurfer [40]  79.62  0.06  86.17  0.12  76.42  0.06 
SPM12 [39]  82.30  0.04  89.82  0.02  78.62  0.14 
RSKFCM [28]  96.68  0.09  93.55  0.10  93.41  0.08 
GSKFCM [29]  96.72  0.03  93.58  0.02  93.43  0.02 
MIFCM_S [20]  96.74  0.41  93.62  0.43  93.86  0.71 
MIFCM_Y [20]  96.82  0.15  93.64  0.15  94.02  0.15 
Proposed Method (consensus clustering)  97.31  0.01  94.50  0.04  95.68  0.02 
Method  Accuracy  Precision  Recall 

KMeans  52.28 $\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$2.35  0.531$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$0.098  0.542$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$0.077 
FCM  52.36$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$2.05  0.534$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$0.081  0.546$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$0.079 
RSKFCM [28]  54.06$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$1.21  0.548$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$0.074  0.556$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$0.068 
GSKFCM [29]  54.61$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$1.61  0.550$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$0.061  0.557$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$0.073 
MIFCM_S [20]  55.08$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$1.34  0.551$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$0.067  0.559$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$0.085 
MIFCM_Y [20]  55.18$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$1.27  0.556$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$0.058  0.560 $\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$0.054 
Proposed Method (consensus clustering)  56.84$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$1.09  0.565$\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$0.047  0.570 $\phantom{\rule{3.33333pt}{0ex}}\pm \phantom{\rule{3.33333pt}{0ex}}$0.049 
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Aruna Kumar, S.V.; Yaghoubi, E.; Proença, H. A Fuzzy Consensus Clustering Algorithm for MRI Brain Tissue Segmentation. Appl. Sci. 2022, 12, 7385. https://doi.org/10.3390/app12157385
Aruna Kumar SV, Yaghoubi E, Proença H. A Fuzzy Consensus Clustering Algorithm for MRI Brain Tissue Segmentation. Applied Sciences. 2022; 12(15):7385. https://doi.org/10.3390/app12157385
Chicago/Turabian StyleAruna Kumar, S. V., Ehsan Yaghoubi, and Hugo Proença. 2022. "A Fuzzy Consensus Clustering Algorithm for MRI Brain Tissue Segmentation" Applied Sciences 12, no. 15: 7385. https://doi.org/10.3390/app12157385