# A Fuzzy Consensus Clustering Algorithm for MRI Brain Tissue Segmentation
## 1 Introduction  
Segmenting brain tissue is the process of subdividing the image of the brain into major components such as Cerebrospinal Fluid (CSF), Gray Matter (GM), and White Matter (WM). The step of brain tissue segmentation is fundamental in diagnosing and monitoring a wide range of neurological diseases. Several researchers have strived to develop automatic brain tissue segmentation in the last two decades [1; 2; 3; 4]. Brain tissue segmentation has been developed by many unsupervised methods in the literature. The most commonly used unsupervised methods are: K-Means [5; 6; 7], Expectation-Maximization [8], and Fuzzy Clustering [9; 10]. Fuzzy clustering methods offer considerable benefits compared with the aforementioned methods as they are capable of handling brain images that are complex, largely uncertain, and imprecise. Even though, traditional Fuzzy C-Means (FCM) showcases outstanding results on brain image segmentation, it has some limitation such as being sensitive to noise due to the use of the Euclidean distance metric and neighbourhood information ignorance. The FCM computes the distance between cluster center and voxels using a Euclidean distance measure. Euclidean distance is very sensitive to noise which results in the deterioration of segmentation results. In the literature, we found many variants of FCM methods thatare developed to address the aforementioned shortcomings. To address the noise sensitivity, researchers added the spatial information into the FCM objective function [11; 12]. The addition of a spatial function to an objective function helps to reduce the impact of noise and also helps to enhance performance. The spatial information may be local or global [13]. On the other hand, to address the limitations of Euclidean distance, many researchers developed a kernel version of FCM and named it Kernel FCM (KFCM) [14; 15]. KFCM adopts kernel function as a distance measure. The kernel function transfers the input data to higher dimensional kernel space and makes the clustering task easier. The aforementioned FCM variant methods are based on a traditional fuzzy set. In a fuzzy set, the non-membership value is always the complement of the membership value. However, in real time, this assumption fails due to hesitation. The hesitation arises due to uncertainty in defining the membership function. To handle this hesitation, [PERSON] [16] developed an advanced fuzzy set called Intuitionistic Fuzzy Set (IFS). In IPS, the non-membership value is computed using the fuzzy complement generator functions. In recent times, researchers have given more attention in developing IFS-based clustering methods [17; 18; 19; 20]. [PERSON] [18] developed an Intuitionistic Fuzzy C-Means (IFCM) where the intuitionistic fuzzy entropy is added to the conventional FCM objective function. The intuitionistic fuzzy set handles the uncertainty which originates while defining a membership function by considering the hesitation degree. To handle noise and uncertainty during segmentation, [PERSON] et al. [21] considered both the pixel and local neighborhood information. The main benefit of this method is that it is non-parametric. Recently, researchers have come to realize that a single clustering method might fail to produce good results with complex data. Hence, they are concentrating on developing consensus clustering methods [22; 23]. Consensus clustering is also known as cluster ensemble, and its main aim is to find a single partition of data with overlapping clusters. In the literature, it has been widely agreed that consensus clustering can generate robust results [24; 25; 26; 27]. Motivated by the advantages of consensus clustering, in this paper we are proposing a brain tissue segmentation method based on consensus clustering. The proposed method consists of two steps: Pre-processing and Segmentation. In pre-processing, the brain images are pre-processed by employing registration, skull stripping, and bias field correction.