Fuzzy farthest point first method for MRI brain image clustering

IET Image ProcessingVolume 13, Issue 13 p. 2395-2400 Research ArticleFree Access Fuzzy farthest point first method for MRI brain image clustering Mohammed Debakla, Corresponding Author Mohammed Debakla debakla_med@univ-mascara.dz Faculty of Science Exact, University of Mustapha Stambouli Mascara, Mascara, AlgeriaSearch for more papers by this authorMohamed Salem, Mohamed Salem Faculty of Science Exact, University of Mustapha Stambouli Mascara, Mascara, AlgeriaSearch for more papers by this authorKhalifa Djemal, Khalifa Djemal IBISC Laboratory, Evry Val d'Essone University, Evry, FranceSearch for more papers by this authorKhaled Benmeriem, Khaled Benmeriem Faculty of Science Exact, University of Mustapha Stambouli Mascara, Mascara, AlgeriaSearch for more papers by this author Mohammed Debakla, Corresponding Author Mohammed Debakla debakla_med@univ-mascara.dz Faculty of Science Exact, University of Mustapha Stambouli Mascara, Mascara, AlgeriaSearch for more papers by this authorMohamed Salem, Mohamed Salem Faculty of Science Exact, University of Mustapha Stambouli Mascara, Mascara, AlgeriaSearch for more papers by this authorKhalifa Djemal, Khalifa Djemal IBISC Laboratory, Evry Val d'Essone University, Evry, FranceSearch for more papers by this authorKhaled Benmeriem, Khaled Benmeriem Faculty of Science Exact, University of Mustapha Stambouli Mascara, Mascara, AlgeriaSearch for more papers by this author First published: 10 October 2019 https://doi.org/10.1049/iet-ipr.2018.6618Citations: 2AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Image clustering is considered amongst the most important tasks in medical image analysis and it is regularly required as a starter and vital stage in the computer-aided medical image process. In brain magnetic resonance imaging (MRI) analysis, image clustering is regularly used for estimating and visualising the brain anatomical structures, to detect pathological regions and to guide surgical procedures. This study presents a new method for MRI brain images clustering based on the farthest point first algorithm and fuzzy clustering techniques without using any a priori information about the clusters number. The algorithm has been approved against both simulated and clinical magnetic resonance images and it has been compared with the fourth clustered algorithms. Results demonstrate that the proposed algorithm has given reasonable segmentation of white matter, grey matter and cerebrospinal fluid from MRI data, which is superior in preserving image details and segmentation accuracy compared with the other four algorithms giving more than 91% in Jaccard similarity. 1 Introduction Magnetic resonance imaging (MRI) of various parts of the human body such as the brain and spinal is a sheltered and painless test that uses a magnetic field and radio waves to produce images with more details. In the case of MRI brain, these images are extremely useful to recognise brain stem diseases and tumours using a strong magnetic field, radio frequency pulses and a computer to produce accurate information [1]. Segmentation is the main part of the brain MRI image processing. It is used to recognise any abnormalities occurring (particularly) in the brain. Although a lot of works seek to identify the whole image sub-districts such as white matter (WM), grey matter (GM) and cerebrospinal fluid spaces (CFSs), others are expected to extract one particular structure, for example, brain tumour, multiple sclerosis lesion or sub-cortical structure. Many techniques for MRI segmentation have been developed throughout the years. The clustering algorithm is among the most used methods in the process of segmenting medical images. It is the way toward isolating image pixels into similar groups [2, 3], whose objective is to identify structures or existing clusters in a group of unlabelled information. Clustering algorithms are usually used in the brain MRI images field [4-6]. Clustering methods could be divided into two primary classes [7], the crisp clustering (or hard clustering) and the other is fuzzy clustering. In the first, the limit between clusters is completely defined. However, in many cases, these limits cannot be clearly defined where some patterns may appertain to several clusters. In such cases, the fuzzy clustering is the practical and more valuable method to classify these patterns. For most of the fuzzy clustering methods, the clusters number must be provided to achieve the clustering process. In this paper, we propose a new clustering algorithm which is able to perform image segmentation without having any information about the cluster number. This proposed clustering method is based on the improvement of the farthest point first (FPF) algorithm [8, 9] by introducing fuzzy logic in its new formulation. Indeed, the fuzzy FPF (FFPF) method determines the clusters centres regarding the farthest point as the FPF algorithm does. Furthermore, the FFPF considers the fuzzy membership degrees as the distance between a pixel and the centre of its cluster. It starts by one cluster and tries to create a new one at every iteration from the farthest point and so on until a stop criterion is reached. The proposed fuzzy-based segmentation algorithm is evaluated using normal and pathological brain MRIs, where it is used to detect some significant regions in the brain such as WM, GM and CFS. Our algorithm is compared with other known algorithms of segmentation such as fuzzy c-means (FCM) and kernelised FCM using misclassification rate (MCR) and the Jaccard similarity (JS) metrics. The remainder of this paper is organised as follows: we will start by citing and presenting some fuzzy MRI brain clustering and segmentation approaches from the literature. Section 3 s dedicated to detail our proposed approach where the FPF algorithm is enhanced by introducing fuzzy clustering. Experimental results and evaluation of the FFPF method are presented in Section 4. 2 FCM clustering approaches Fuzzy theory-based intelligent techniques are broadly favoured for medical applications especially for MR brain image segmentation because of high accuracy. Numerous fuzzy techniques for MRI segmentation have been developed throughout the years. One of the clustering algorithms that have got considerable success in image clustering and segmentation is the notable FCM. Since the introduction of FCM algorithm by Dunn [10] and Bezdek [11] in image segmentation, many authors have focused their researches over the development of new fuzzy-based intelligent techniques or the enhancement of the FCM in order to improve the performance of MRI segmentation. Zanaty in [4] has implemented a kernelised FCM to find the suitable validity criterion of kernelised FCM and kernelised FCM with spatial constraints for automatic segmentation of MRI, so they replaced the original Euclidean distance in the FCM by a Gaussian radial basis function classifier. In [12], Elazab et al. proposed an adaptively regularised kernel-based FCM (ARKFCM) clustering approach for segmentation of brain magnetic resonance images. The proposed approach is based on three algorithms: the grey scale of the average filter, median filter and devised weighted images. In [5], Ji et al. have included a possibilistic approach within FCM. In their paper, the authors try to improve the feasibility of FCM for bias field estimation. To estimate the intensity in homogeneity, the global intensity is introduced into the coherent local intensity clustering algorithm and takes the local and global intensity information into account. Another interesting enhancement of the FCM algorithm has been presented by Kim [13]. The new proposed approach is called generalised spatial FCM (SFCM) algorithm, which uses both pixel attributes and the spatial local information. In [14], Ji et al. have proposed the generalised rough-FCM algorithm for brain MR image segmentation. In this algorithm, each cluster is defined by three-determined rough-fuzzy regions, so the membership of each pixel is estimated with respect to the region it is located in. They also estimated a weighting parameter which determines the importance of each region. Kang et al. [15] have improved the original FCM by including an adaptive weighted average filter, whereas Ahmed et al. [16] have proposed a very time-consuming improvement of the objective function of FCM, its idea was to use the labels in the neighbourhood of a pixel to compute its label. This drawback was treated in [17], where Chen and Zhang have proposed two variants of algorithms to simplify the neighbourhood term of the objective function of [16]. Chuang et al. [18] have proposed SFCM that make a modification of the standard FCM algorithm by using spatial information in the membership function. Cai et al. [19] proposed a fast generalised-FCM algorithm which incorporates the spatial information, the intensity of the local pixel neighbourhood and the number of grey levels in an image. Xiao et al. [6] have proposed the weighted Gaussian FCM, where they considered a weighted clustering scheme applied to a Gaussian smoothed image using a bootstrapping approach of feature weighting. El-Melegy and Mokhtar in [20] improved the FCM algorithm to deal with any prior information about the class centre. Hemanth et al. [21] have proposed a fast and accurate FCM algorithm for MR brain image segmentation. They extend the FCM by adding a data reduction approach (pre-clustering) to reduce the computational complexity and the convergence rate. Other researchers have used hybrid clustering methods. Indeed, Harsimranjot and Reecha [22] have proposed a new approach to detect automatically the tumour in MR images using FCM and seeded region growing while Rajendrana and Dhanasekaran in [23] have developed a fuzzy clustering and deformable model for tumour segmentation on MRI brain image. Parveen Singh [24] have used enhancement techniques such as contrast improvement and mid-range stretch to enhance the image. Double thresholding and morphological operations are used for skull striping while FCM clustering is used for the segmentation of the image to detect the suspicious region in brain MRI image. Malakooti et al. [25] have used fuzzy logic and neural networks as a tumour segmentation technique to extract the boundary taking into account the level set method. Deshmukh and Khule [26] presented an automated recognition system for the MRI image using the neuro-fuzzy logic taking into account that manual analysis of brain tumour is time annihilating and produces inaccurate results. Ortiz et al. [27] proposed a segmentation technique using three-dimensional statistical features extracted from the volume image. The method is based on unsupervised vector quantisation and fuzzy clustering techniques. Recently in [28] Guo et al. present a novel fuzzy clustering algorithm to segment brain MRI by adding a new term to the objective function of FCM. The new term comes from guided filter for its capability in noise suppression and edge-preserving smoothing. Most of these approaches need prior information to achieve the clustering process. This information concerns the initial cluster number to start with. While some approaches have given this number as input, others use heuristic methods to determine this initial cluster number. This major drawback will affect the clustering approach in terms of precision or time-consuming. In our proposed method that aims to improve the clustering, we will enhance the FPF approach with fuzzy logic. This method is of a significant advantage since it does not require a prior cluster number. Instead, it starts with one cluster and tries to get the right clusters number. 3 FFPF approach In this section, we will recall the FPF principle and we will detail the proposed FFPF approach. 3.1 FPF algorithm The FPF algorithm is a polynomial algorithm for clustering purpose introduced by Gonzalez [8]. The FPF algorithm increasingly computes the set of clusters' centres C1⊂C2⊂…⊂Ck, where Ck is the final solution to the problem. In difference with the known k-means algorithm [29], FPF starts the image clustering process by considering the whole input image as a unique cluster with the randomly chosen centroid. In each iteration, it chooses the farthest pixel from all the existing centres as a new centroid. Then, a new cluster will be created by the nearest pixels to this new centroid. When the desired clusters number k is reached, the FPF clustering process stops giving the set Ck as result. The FPF algorithm is presented as Fig. 1. Fig. 1Open in figure viewerPowerPoint Algorithm 1: FPF algorithm 3.2 FFPF algorithm We define the FFPF as clustering algorithm derived from the FPF algorithm considering that each pixel may belong to more than one cluster, where the degree of membership for each item is given by a probability distribution over the clusters. The FFPF algorithm assigns pixels to each class using fuzzy memberships. Let X = (x1, x2,. .., xN) denote an image with N pixels to be partitioned into k clusters, where xi represents multispectral (features) data. The algorithm is an embedded iterative optimisation process that tries to find the optimal clusters number starting from one cluster. It added the farthest pixel as a new cluster centre and minimises the objective function JFFPF (U, C), where U is the memberships degrees matrix and C = {C1, C2,. .., Ck} is a vector of cluster centres which have to be determined. The processes of the proposed approach are depicted in Fig. 2. Fig. 2Open in figure viewerPowerPoint Proposed approach: the FFPF algorithm assigns pixels to each class using fuzzy memberships For a given cluster number k, the objective function is defined as follows: (1)The membership's degrees matrix U must satisfy the following constraints [30]: (2)where µij is the membership function of pixel xj in the ith cluster ci and m∈[1,∞ [is a fuzziness coefficient and d(xj, ci) is a distance measure between pixel xj and cluster centre ci (we can use the Euclidean distance). JFFPF is optimised by introducing the Lagrange multipliers λi [10] to incorporate the constraint in (2). This yields function to be minimised (3)JFFPF is alternately optimised in two steps: Step 1: Optimising membership degrees U is an optimal value of if and , which lead to (4) (5) From (5), we obtain (6) By combining (4) and (6), we get (7) (8) The new membership values are obtained by inserting into (6) yields (9) (10) Step 2: Optimising the cluster centres: The obtained membership values are used to optimise clusters centres by deriving of JFFPF with respect to centres. Thus, the cluster centres are updated by (11) In each iteration, matrix U is computed using (10) and the associated cluster centres are computed by (11) until we obtain a neglected variation of the objective function. After minimising JFFPF value, the algorithm selects the farthest pixel to be the new cluster centre and redo the two steps minimisation process. It stops when the inter-clusters inertia change is below a certain threshold. This inertia is based on the Ward criteria [31] that computes the distance between two clusters centres as follows: (12)where and are, respectively, the weights of the two clusters ci and cj, ci and cj are the centres of the two clusters I and j. Thus the total inertia is given by (13)Clustering result of each pixel is obtained by U = {μij}. A detailed description of the FFPF algorithm is presented as Fig. 3. Fig. 3Open in figure viewerPowerPoint Algorithm 2: FFPF algorithm 4 Experimental results In this section, we present some experimental results that evaluate the performance of the FFPF algorithm. Our experiments are coded in MATLAB and run on a TM i5-8400 T computer with 3.30 GHz (CPU) and 8 GB RAM. A comparative study is conducted on the proposed method, FFPF, with the original FPF algorithm [8] and some other fuzzy clustering-based image segmentation approaches which are FCM [11], KFCM [4], ARKFCM [12] for simulated and clinical brain magnetic resonance images. To quantitatively analyse the FFPF segmentation accuracy and performance, we have used two metrics, the MCR and the JS metric [32] which are defined as follows: (14) (15)where Ai denotes the set of pixels belonging to the ith class identified by the clustering algorithm, whereas Bi denotes the set of pixels belonging to the ith class of the ground truth. As a fuzzy similarity measure, the larger the JS value, the better the clustering performance is. 4.1 Experimental results on simulated brain MR images The following experiments are carried out using simulated brain database [33] which contains a set of realistic MR volumes produced by an MR imaging simulator with available ground truths tissues of CFSs, GM and WM. The proposed FFPF algorithm is first applied to segment a T1-weighted brain MR image with 217 × 181 px2 and 20% grey-scale non-uniformity in order to identify important regions in brain such as WM, GM and CFS. These regions are significant for the physician radiographer to analyse and diagnose the diseases. The results are given in Figs. 4-7. The original brain image shown in Fig. 4a. Figs. 4b–d show the ground truths of Fig. 4a (WM, GM and CFS, respectively). The experimental results of the segmented image by FCM, KFCM, ARKFCM, FPF and our proposed method can be seen in Figs. 5-7. It can be observed from Figs. 7d–f that the FFPF algorithm is more superior to other algorithms on the extraction of brain tissue. Fig. 4Open in figure viewerPowerPoint Original image (a) Original MR image, (b)–(d) Ground truth images (WM, GM and CFS, respectively) Fig. 5Open in figure viewerPowerPoint Segmentation results of MR image with FCM algorithm (a) WM region, (b) GM region, (c) CFS region Fig. 6Open in figure viewerPowerPoint Segmentation results of MR image (a)–(c) KFCM algorithm, (d)–(f) ARKFCM algorithm Fig. 7Open in figure viewerPowerPoint Segmentation results of MR image (a)–(c) FPF algorithm, (d)–(f) Proposed FFPF algorithm Furthermore, the statistical results of the JS values of WM, GM and CFS for the five algorithms are shown in Table 1. Table 1. JS values of simulated MR image Tissues FCM KFCM ARKFCM FPF FFPF WM 0.8872 0.9002 0.9075 0.8701 0.9123 GM 0.8021 0.8042 0.8419 0.7624 0.8517 CFS 0.9042 0.9056 0.9104 0.8661 0.9114 average 0.8645 0.8700 0.8866 0.8328 0.8978 Bold values indicate the best values of the proposed algorithm It can be seen from the experimental results in Table 1 that FFPF algorithm has higher values than the other four algorithms; the average JS of FFPF is 0.8978 for the axial slice as shown in Fig. 4, which is better than the other four algorithms within a range of 1.12–6.50%. It is also shown from the experimental data in Table 2 that MCR values of FFPF algorithm are minimum compared with the other segmentation algorithms. Table 2. MCR values of simulated MR image Tissues FCM KFCM ARKFCM FPF FFPF WM 0.0182 0.0081 0.0047 0.0196 0.0017 GM 0.0492 0.0161 0.0124 0.0687 0.0082 CFS 0.0291 0.0172 0.0095 0.0367 0.0061 average 0.0321 0.0139 0.0089 0.0416 0.0053 Bold values indicate the best values of the proposed algorithm It can also be noted for this experiment that we have improved the clustering rates with respect to the FPF algorithm taking into account the values of the two metrics JS and MCR, where JS is increased from 0.8328 to 0.8978 and MCR is decreased from 0.0416 to 0.0053. The data in Tables 1 and 2 illustrate that the proposed algorithm has better and higher segmentation accuracy. The second experiment is to segment a T1-weighted axial slice with 181 × 217 px2 corrupted with 9% noise and 20% grey-scale non-uniformity. The segmentation results are presented in Figs. 8-10. The original brain image is shown in Fig. 8a, the experimental results of the segmented image by FCM is shown in Figs. 6b–d, whereas the results of KFCM, ARKFCM, FPF and FFPF methods are shown in Figs. 9 and 10. Fig. 8Open in figure viewerPowerPoint Segmentation results of MR noisy image (a) Original MR image with 9% noise, (b)–(d) FCM algorithm (WM, GM and CFS, respectively) Fig. 9Open in figure viewerPowerPoint Segmentation results of MR noisy image (a)–(c) KFCM algorithm, (d)–(f) ARKFCM algorithm Fig. 10Open in figure viewerPowerPoint Segmentation results of MR noisy image (a)–(c) FPF algorithm, (d)–(f) Proposed FFPF algorithm From the results, a better segmentation is obtained in Figs. 10d–f, which is less affected by noise compared with the other results. The FFPF algorithm has proved its robustness to noise, without going through a pre-processing step. Overall, the three classes (WM, GM and CFS) were well-detected despite the presence of noise. It can be seen from Table 3 that JS values of all algorithms have decreased compared with Table 1 due to the presence of noise in the original image. However, FFPF algorithm has obtained higher values than FCM, KFCM and FPF algorithms, but it has a slightly lower value compared with the ARKFCM, which could be explained by the filter included in ARKFCM algorithm. Similarly, it can be shown from Table 4 that the MCR values of the five algorithms are increased, but those of the FFPF algorithm are still less. Table 3. Comparison of JS on simulated MR images Tissues FCM KFCM ARKFCM FPF FFPF WM 0.8584 0.8712 0.9075 0.8532 0.8964 GM 0.7635 0.7813 0.8409 0.7742 0.8379 CFS 0.8812 0.8957 0.9052 0.8924 0.9031 average 0.8343 0.8494 0.8845 0.8399 0.8791 Bold values indicate the best values of the proposed algorithm Table 4. Comparison of MCR on simulated MR images Tissues FCM KFCM ARKFCM FPF FFPF WM 0.0256 0.0156 0.0082 0.0224 0.0037 GM 0.0671 0.0234 0.0206 0.0586 0.0096 CFS 0.0386 0.0268 0.0125 0.0317 0.0088 average 0.0437 0.0219 0.0137 0.0375 0.0073 Bold values indicate the best values of the proposed algorithm These values illustrate that both algorithms (FFPF and ARKFCM) have a better anti-noise ability and higher segmentation accuracy. However, we can improve the performance of the FFPF algorithm by introducing a filtering step. 4.2 Experimental results on clinical brain MR image To further verify the performance of the algorithm, a real clinical normal MR image was selected from the IXI dataset (https://brain-development.org). This dataset contains nearly 600 MR images from normal, healthy subjects. The data have been collected at three different hospitals in London: Hammersmith Hospital uses a Philips 3T system; Guy's Hospital uses a Philips 1.5T system; and Institute of Psychiatry uses a GE 1.5T system. The segmentation results of a normal T1-weighted real MR image are shown in Figs. 11 and 12. The original brain image is shown in Fig. 11a, the experimental results segmented by FCM, KFCM, ARKFCM, FPF and FFPF are shown in Figs. 11b–f, respectively. The segmented tissues of the brain image (WM, GM and CFS) by the proposed method are shown in Figs. 12a–c, respectively. Fig. 11Open in figure viewerPowerPoint Segmentation results on real MR image (a) Original real MR image, (b) FCM, (c) KFCM, (d) ARKFCM, (e) FPF, (f) FFPF Fig. 12Open in figure viewerPowerPoint Segmented tissues of the brain image using the FFPF method (a) WM, (b) GM, (c) CFS We can clearly see that the proposed algorithm can effectively maintain the regions' homogeneity, and it preserves more detailed information about the original MR image. We can also note that the ARKFCM algorithm gives nearly the same results as ours. While for the FCM, KFCM and FPF algorithms there exists some misclassification in the segmented image, where a small part of WM was processed as a part of the GM. We can deduce from Fig. 8 that the FFPF method tends to better mark out WM, GM and also delineate correctly the CFS. The last series of our experiments are carried out to evaluate the proposed algorithm's performance in detecting tumours from pathological brain MRI datasets. A real clinical normal MR image was selected from the Whole Brain Atlas clinical MR image database [34]. Fig. 13a shows a T1-weighted MR image, the segmentation result of the MR image shown in Figs. 13b and c shows the affected tissue by the tumour; in this case, the GM class. The tumour class is shown in Fig. 13d. Fig. 13Open in figure viewerPowerPoint Segmentation results of real MRI image with tumour using the FFPF algorithm (a) Original image, (b) Segmentedimage, (c) Affected tissue by thetumour, (d) Tumour class Brain tumour segmentation aims to separate the different tumour tissues such as active cells, oedema and necrosis from normal brain tissues (WM, GM and CFS). It can be seen from the segmented image shown in Fig. 13b that the proposed method has detected the tumour part clearly from the given MRI brain image without having any prior knowledge about its existence. We can also note from Fig. 13d that the tumour region is well-extracted by the FFPF algorithm so it is possible to get tumour information such as location and size. These improvements of the results in all experimentations compared with the other algorithms can be explained by the two strength points of our proposed algorithm which are the absence of the initialisation step which causes local minima problem and no need of prior information about the clusters' number. 5 Conclusion In this work, we have proposed a FFPF clustering for unsupervised MR image segmentation. We have improved the FPF clustering by introducing fuzzy logic in its new formulation. The main advantage of the proposed approach is that it is able to perform image segmentation without using any prior information about the clusters number of the image. In experiments, we have carried out quantitative and qualitative comparison and analyses between the proposed algorithm and other four algorithms (FCM, KFCM, ARKFCM and FPF) for simulated and real brain MRI images, where all experimental results indicate that the proposed approach produces more accurate and reasonable segmentations of WM, GM and CFS from MRI data, and can effectively resist to noises and artefacts. FFPF algorithm also yields a higher JS measurement and a lower MCR value than other algorithms and could retain the details of the image. These results are explained by the fact that this algorithm is a hybridisation of two clustering algorithms: the FPF and the FCM where we take advantage of the strong points of each one. The absence of initialisation in FPF, to avoid local minima, which penalises the FCM and, on the other hand, the fuzziness of the clusters membership that characterises the FCM, this property gives flexibility to the new clustering algorithm regarding the assignment of clusters members. The proposed algorithm could be improved by optimising the clustering criterion by the bio-inspired algorithm or other intelligent techniques. 6 References 1Chetih N., Messali Z., and Serir A. et al: 'Robust fuzzy c-means clustering algorithm using non-parametric Bayesian estimation in wavelet transform domain for noisy MR brain image segmentation', IET Image Process., 2018, 12, (5), pp. 652– 660 2Hartigan J.A.: ' Clustering algorithms' ( John Wiley & Sons, Inc., NY, USA, 1975) 3Gao W.: 'Improved ant colony clustering algorithm and its performance study', Comput. Intell. Neurosci., 2016, 2016, p. 14 4Zanaty E.A.: 'Determining the number of clusters for kernelized fuzzy c-means algorithms for automatic medical image segmentation', Egypt. Inf. J., 2012, 13, (1), pp. 39– 58 5Ji Z.X., Sun Q., and Xia D.: 'A modified possibilistic fuzzy c-means clustering algorithm for bias field estimation and segmentation of brain MR image', Comput. Med. Imaging Graph., 2011, 35, (5), pp. 383– 397 6Xiao K., Hock S., and Bargiela A.: 'Automatic brain MRI segmentation scheme based on feature weighting factors selection on fuzzy c-means clustering algorithms with Gaussian smoothing', Int. J. Comput. Intell. Bioinf. Syst. Biol., 2010, 1, (3), pp. 316– 331 7Ulutagay G., and Nasibov E.: 'Fuzzy and crisp clustering methods based on the neighborhood concept: a comprehensive review 1', J. Intell. Fuzzy Syst., 2012, 23, (6), pp. 271– 281 8Gonzalez T.F.: 'Clustering to minimize the maximum intercluster distance', Theor. Comput. Sci., 1985, 38, (3), pp. 293– 306 9Dharmarajan A., and Velmurugan T.: 'Lung cancer data analysis by k-means and farthest first clustering algorithms', Indian J. Sci. Technol., 2015, 8, (15), pp. 1– 8 10Dunn J.C.: 'A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters', J. Cybern., 1974, 3, (3), pp. 32– 57 11Bezdek J.C.: ' Pattern recognition with fuzzy objective function algorithms' ( Plenum Press, New York, 1982) 12Elazab A., Wang C., and Jia F. et al: 'Segmentation of brain tissues from magnetic resonance images using adaptively regularized kernel-based fuzzy C-means clustering', Comput. Math. Methods Med., 2015, 2015, Article ID 485495 13Lung H.V., and Kim J.M.: ' A generalized spatial fuzzy C-means algorithm for medical image segmentation'. Proc. IEEE Int. Conf. Fuzzy Systems, Korea, 2009, pp. 20– 24 14Ji Z., Sun Q., and Xia Y. et al: 'Generalized rough fuzzy c-means algorithm for brain MR image segmentation', Comput. Method Program Biomed., 2012, 108, (2), pp. 644– 655 15Kang J., Min Y.L.Q., and Luan Q.X. et al: 'Novel modified fuzzy c-means algorithm with applications', Digit. Signal Process., 2009, 19, (2), pp. 309– 319 16Ahmed M.N., Yamany S.M., and Mohamed N. et al: 'A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data', IEEE Trans. Med. Imaging, 2002, 21, (3), pp. 193– 199 17Chen S., and Zhang D.: 'Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure', IEEE Trans. Syst. Man Cybern., 2004, 34, (4), pp. 1907– 1916 18Chuang K.S., Tzeng H.L., and Chen S. et al: 'Fuzzy c-means clustering with spatial information for image segmentation', Comput. Med. Imaging. Graph, 2006, 30, (1), pp. 9– 15 19Cai W., Chen S., and Zhang D.: 'Fast and robust fuzzy C-means clustering algorithms incorporating local information for image segmentation', Pattern Recognit., 2007, 40, (3), pp. 825– 838 20El-Melegy M., and Mokhtar H.: 'Tumor segmentation in brain MRI using a fuzzy approach with class center priors', EURASIP J. Image Video Process., 2014, 2014, (1), pp. 1– 14 21Hemanth D., Anitha J.J., and Balas V.: 'Fast and accurate fuzzy C-means algorithm for MR brain image segmentation', Wiley Periodicals, Int. J. Imaging Syst. Technol., 2006, 26, (3), pp. 188– 195 22Harsimranjot K., and Reecha S.: 'Segmentation of tumor region from brain MRI images using fuzzy C-means clustering and seeded region growing', J. Comput. Eng. (IOSR-JCE), 2016, 18, (5), pp. 20– 24 23Rajendrana A., and Dhanasekaran R.: ' Fuzzy clustering and deformable model for tumor segmentation on MRI brain image: a combined approach'. Proc. Int. Conf. Communication Technology and System Design, Procedia Engineering, Coimbatore, India, 2012, pp. 327– 333 24Parveen Singh A.: ' Detection of brain tumor in MRI images, using combination of fuzzy c-means and SVM'. Proc. IEEE Second Int. Conf. Signal Processing and Integrated Networks (SPIN), Noida, India, 2015 25Malakooti M.V., Mousavi S.A., and Taba N.H.: 'MRI brain image segmentation using combined fuzzy logic and neural networks for the tumor detection', J. Acad. Appl. Stud., 2013, 3, (5) 26Deshmukh R.J., and Khule R.S.: 'Brain tumor detection using artificial neural network fuzzy inference system (ANFIS)', Int. J. Comput. Appl. Technol. Res., 2014, 3, (3), pp. 50– 154 27Ortiz A., Palacio A.A., and Górriz J.M.: 'Segmentation of brain MRI using SOM-FCM-based method and 3D statistical descriptors', Comput. Math. Methods Med., 2013, 2013 28Guo L., Chen L., and Wu Y. et al: 'Image guided fuzzy C-means for image segmentation', Int. J. Fuzzy Syst., 2017, 19, (6), pp. 1660– 1669 29MacQueen J.B.: ' Some methods for classification and analysis of multivariate observations'. Proc. Fifth Berkeley Symp. Mathematical Statistics and Probability, Berkeley, 1967, pp. 281– 297 30Ruspini E.H.: 'A new approach to clustering', Inf. Control, 1969, 15, (1), pp. 22– 32 31Ward J.: 'Hierarchical grouping to optimize an objective function', J. Am. Stat. Assoc., 1963, 58, (301), pp. 236– 244 32Vovk U., Pernus F., and Likar B.A.: 'Review of methods for correction of intensity inhomogeneity in MRI', IEEE Trans. Med. Imaging, 2007, 26, (3), pp. 405– 421 33 Brain Web.: Simulated Brain Database. Available at http://brainweb.bic.mni.mcgill.ca/brainweb/, accessed 25 February 2018 34 Whole Brain Atlas clinical MR image database. Available at http://www.med.harvard.edu/aanlib/, accessed 25 February 2018 Citing Literature Volume13, Issue13November 2019Pages 2395-2400 FiguresReferencesRelatedInformation