Efficiency of Fuzzy C Means algorithm for Brain Tumor segmentation in MR Brain Images

: Background and Objective: Image processing is a technique or set of operations to get meaningful information from an image for the usefulness and effectiveness of images. Image segmentation is an efficient technique in extracting and separating some of the features in the images. Methods: The main objective of this research work is to find the best fit of FCM algorithm over finding the axial and coronal plane of MRI brain imagesvia its accuracy and computational time.In the preprocessing, brain images of MRI have been converted from the DICOM format into standard image. Preprocessing is carried out by Gaussian filter technique to remove the noises in the images. The Fuzzy C Means (FCM) algorithm is implemented to segment the tumor affected region in the MR images. Results: By comparing the histogram values of the images (before and after segmentation) with the cluster center values by the FCM algorithm, the efficiency and accuracy of the algorithm is evaluated. Conclusion: The best fit of FCM algorithm into the axial and coronal plane is identified based on the computational time in this work.

therapy in automatic segmentation of medical images [8]. The segmentation is based on the measurements taken from the images based on the texture, color, depth, motion or intensity values of an image. In general, image segmentation is a step by step process to study all the image regions in depth. One of the major applications of image segmentation is to identify the objects in the scene and measuring its shape and size. In this research work, the MRI brain images are analyzed with the FCM algorithm and the results are verified with the histograms values of the images to evaluate the accuracy of the results. This article is organized as follows.Section II deals with the literature review of the variousrelated works, section III discusses about the materials and methods applied in this research work.The results and its discussion are explained in section IV and finally section V concludes the research work.
2. Literature Survey There are many researchers performing research to find the efficiency of tumor affected region to help the radiologists. In particularly, MRI brain image the performance of the FCM is highly important clustering algorithm for its efficiency and effectiveness. Some of the research works for different persons are discussed here from which gives a different perspective of FCM. 3D brain tumor segmentation in MRI using fuzzy classification, symmetry analysis and spatially constrained deformable models discussed about the segmentation of brain tumor. Fuzzy classification and approximate brain asymmetry plane based on these two different approaches the tumor detection is carried out and its effective for all different types of tumor [10]. M.N. Ahmed etal. are carried out in their research work in bias field estimation and adaptive segmentation of MRI data using a modified fuzzy c-means algorithm. They proposes a novel algorithm to segment the MRI data and evaluate the inhomogeneities intensity of fuzzy logic [1]. Current Methods in the Automatic Tissue Segmentation of 3D Magnetic Resonance Brain Images they provide the current methods in the tissue segmentation with the detailed study of each method with the mathematical representation and advantages and disadvantages of the methods. They provide the conventional fuzzy c-means with the two ideas intensity nonuniformity INU and spatial context with the pixel values in clustering process [12].
Automatic Tumor Segmentation Using Knowledge-Based Techniques is research work done by Matthew C. Clarkand etal. The suspected tumor is identified by multispectral histogram analysis and region analysis is used for the intracranial region. They generated a system that automatically identifies tumor segments and labels of glioblastoma-multiforme tumors in the human brain with the help of magnetic resonance images [6]. Discrete dynamic contour model with adjacent vertices consists of vertices and edges is the main evaluation criteria to segment thalamus from MRI brain images which is an important neuro-anatomic structure in brain is the research work discussed by LadanAmini and et.al [4]. Intensity space map(ISM) is combined with the fuzzy c-means clustering algorithm to segment the color MRI images for tumor detection work. Though the manual segmentation of MRI data is possible, this algorithm segments the muscle regions and its time consuming [19].
Keh-Shih Chuang, Hong-Long Tzeng, Sharon Chen, Jay Wu and Tzong-Jer Chen carried their research work in Fuzzy c-means clustering with spatial information for image segmentation. The spatial information incorporates with the fuzzy c-means algorithm for clustering into the membership function. Each pixel is taken consideration with the summation of spatial function with the neighborhood membership function [5]. Another research work proposes a new automatic clustering approach with a hybrid algorithm in the combination of Artificial Bee colony with fuzzy c-means to determine the tumor region. The hybridization of (FCMAB), to segment the MRI brain image extracts abnormal cell growth with the cluster centers [3]. The log bias field is stack of spline surfaces, that reduces the spline coefficients of 3-bias field reduces in finding the spline coefficients is effective two-stage algorithm. They proposed algorithm inorder to account the spatial continuity constraints between image volume element. The MR imaging signal is formulated by a multiplicative bias field with INU artifact [11].A Modified Fuzzy C-Means Algorithm for Bias Field Estimation and Segmentation of MRI Data is a research work carried by Mohamed N. Ahmed. The objectivefunctions of the standard fuzzy cmeans algorithm for inhomogeneities and allow voxel the volume element of an image is influences the adjacent neighborhood. Theregularize and biases of the neighborhood pixels leads towards the homogeneous labeling in the piecewise information [2].
Brain Tumor Detection Using MRI Images is done by the research authors of PranitaBalaji Kanade1 and P.P Gumaste. They proposed algorithm which consists of six stage process which includes test images,preprocessing, denoising and SWT, segmentation, feature extraction and SVM/PNN. The algorithm is have higher accuracy and low error rates. The image segmentation algorithm will have following features accuracy, reliability, repeatability, robustness and least dependency [8]. Ming Zhao and etal.carried their research work titled as Automatic Threshold Level Set Model Applied on MRI Image Segmentation of Brain Tissue [20]. A mathematical representation and proof for Chan and Vese model for the different mean and variance for automatic threshold level set for the image segmentation. The extraction of MR images was developed by threshold level set without edges for the tissues in brain.Dzung L. Pham and Jerry L. Prince evaluated a novel algorithm with the multiplicative intensity inhomogeneities for the obtaining the fuzzy segmentation of images. An iterative algorithm is developed to minimize the objective function of fuzzy c-means [13].

3.Materials and Methods
Dunn was the first person to introduce the Fuzzy C-Means clustering algorithm and it's extended by Bezdek.Duun Clustering is a widely used technique to classify images, that pixels of same group are belongs to one group and differentiated pixels are belongs to some other groups [15].The MRI scans has been taken for the patients for many reasons. To detect and identify bleeding, injury, blood vessels, tumors in brain area. MRI also diagnoses more problem than on X-ray, ultrasound scan or CT scan. Brain is the main central nervous unit which connects all the nerves of the body. It's very important for the patients to diagnose the various problems in the brain. So the detection and prediction of the brain tumor affected region is must and it should be precise for the radiologists to produce accurate results to the physicians. Fuzzy c-means (FCM) clustering algorithm is a commonly used in image segmentation, to assigns pixels of the images into distinct classes based on the features of the image.One of the important domains of Fuzzy C Means is medical image analysis. This paper analysis and detect brain tumor affected region separately with the help of the FCM in the coordination of histogram values of the image. The MRI scanner scans the brain and produces the resultant image in three different planes for the detailed description. The magnetic resonance scanner provides various scanning images of the brain from different directions. Figure 1 shows the different planes of the MRI brain images. One is axial plane which slices the brain and provides the information, the second one is the coronal plane shows the information from the back with the spinal cord and the last one is the sagittal plane. The sagittal plane describes the brain image from the left and right side of the brain anatomy shows in the Fig. 1. The FCM clustering algorithm is an iterative process to produce the cluster centers partition by minimizing the weighted group of squared error objective functions summation. The MRI brain image is segmented by FCM algorithm is carried by many researchers. In this paper, the segmented region pixel values is verified with the histogram of the resultant images. The histogram values of the resultant image is been analyzed. The research methodology of this research work includes four modules. The first module is converting the DICOM images in to some real world images which can be easily handled by any software. The second module is preprocessing the input image by removing noise. The third module is applying the traditional FCM algorithm to the preprocessed images and finding the cluster values to the resultant images and the last module is generation of histogram values and cross examining with the results from the third module to find the accuracy with the coordination of pixels intensity. The resultant images produce the segmented region of the input MRI brain images based on the evaluation of the intensity values of the images. By segmenting the image the cluster center values are been recorded with the help of FCM algorithm.

Gaussian filter
The MRI input brain imagenoises areremoved with the Gaussian filter in the preprocessing stage. The Gaussian noise is an form of white noise. It is caused due to the signals random fluctuations. The white noise is a random signal with spectral densities flat power and it is also called as additive noise [9]. An simple and important filtering techniques for images is the Gaussian filtering which is a subtitle of bilateral filtering. In the Gaussian filtering function both the closeness function and similarity function are the Gaussian function arguments of the Euclidean distance. The closeness function is described in the equation 5 and the similarity function is illustrated in the equation 6 [14].
‖is a suitable measure of distance between the intensity values of ∅ and f. The geometric spread d is the domain is chosen based on the desired amount of low-pass filtering. The Gaussian range filter is insensitive to the overall filters and additives changes are subjected to image intensity.

The Fuzzy C-Means Algorithm
Fuzzy c-means is clustering algorithm to classify the pixels into two or more groups. FCM is mainly used to segment the images. Though, several approaches are exists in the real world for MRI brain image the FCM produces more efficient and effective results than the others. The FCM clustering algorithm works on the image based on some features like intensity values, texture, and pixels regions etc. In this approach, we cluster the image by taking the intensity of the pixels. The merely same intensity values of the pixels will belongs to one cluster and other pixels which may have the same intensity values form the next cluster. FCM clustering algorithm is based on minimizing the weighted square mean error of the objective function The above equation is the weighting function of the FCM clustering algorithm. Centroids cluster of I is in C i and the u value is the range of between 0 and 1; Euclidean distance between the i th centroids and j th data joint is represented by d ij and weighting function is m£(1,∞) [7].

Objective function of FCM
The procedure convergesthe saddle point of Y m or minimizes the local minima.The fuzzy segmentation of image data is done by the iterative process by optimizing the objective function is carried as follows 1. C and q values are to be set.
This iteration process is stop when it meets the following condition. The termination criterion with the range between 0 and 1, and k is the number of iteration steps. In the above equations m>1 and x i is data measured in d-dimensional, M ij is the X membership degree in the j cluster and center of the cluster is in the d dimension of R j [7]. The‖ * ‖ is expressing the similarity between center and the measured data. The optimization of the objective function is carried out in the segmentation of fuzzy, with the update of the cluster centers and objective functions of the equation(1) [17].The above equations 2 and 3 are the FCM to create clusters of the MRI brain image to segment and separated the tumor affected region based on the intensity values of the image.In the, FCM the C represents the clustering which means creating group of objects which are similar belongs to one group and dissimilar are belongs to different group.

Application Areas of FCM
The applications of clustering techniques are document categorization, customer/market segmentation, scientific data analysis, city planning, land use and in earthquake studies [16]. Fuzzy, hard, remote sensing, satellite signal receiving, are the broad classification area of clustering algorithms. The clustering is widely used in many research areas such as data mining, artificial intelligence, fuzzy systems, pattern recognition, machine learning etc. The application of cluster analysis is widely used in chemistry, the systematize chemical and physical properties are analyzed and give detailed report in the field of analytical chemistry. The FCM is been applied in the data mining domain widely. The comparative analysis of FCM with k Medoids for the statistical data points are analysis in the research work and the results are discussed. The experimental results are discussed and effectiveness of the FCM is shown clearly for the distributed data points [18].

Histograms
Histogram is a graphical representation of an image based on the intensity distribution of an image and quantifies the each intensity values based on the number of pixels considered. In this work the detection of affected region is identified based on the intensity level of images using FCM [10]. If f be a image it is been represented by m r and m c matrix of pixel integer intensities ranging from 0 to L-1. The set of possible intensity value is 0 to 255. pixels) of number n)/(total intensity with the pixels of (number  n p (4) The second step is preprocessing starts with 3 MRI image for three different persons AXI_IMG_01 by removing the noise. The noises in the images are removed with the gaussian filtering techniques. Some of the pixels could be affected some form of white or some other noise so the removal of noise by gaussian technique will produce more standard resultant image. Since, the MRI images are black and white the gaussian filterin gtechnique might be correct choice inorder to get a clartity of the image. The results of the preprocessing module is shown in the Fig. 3. The third step is implementing the fuzzy c-means algorithm with the steps are evaluated as in the objective function of FCM. The equations of the FCM are implemented IBM machine with intel®core @ Duo processor and 8 GB RAM, running Windows7 operating system. The algorithm was developed via Matlab (R2008a). In this work, the segmentation of images is based on the intensity values of pixels in the imaging plane. The FCM is a clustering algorithm which gives the resultant images or values based on the cluster center of the pixels. The default segmentation level of the FCM algorithm set as n=2 are shown in the Fig. 3(b) and 3(c). The images are been segmented based on the intensity values of pixels; however the cluster center produces the highest point of intensity values of the image. The last level, separate the brain tumour affected region shown in the Fig. 3(d). The last step in this research work is cross-examing the cluster centers of FCM algorithm with the intesnity values of the resultant image with the histogram graph. The diagnoziation of brain tumor is highly important. We are segmenting the MRI brain images based on the pixels intensity values, so on reexaming the resultant values with the histogram graph give more adequate results. The resultant image of the FCM is compared with the histogram values of the image before and after segmentation. Since, the segmentation is based on the intensity values, the cluster values gives the intensity range of the image. With this, the histogram graph are been compared to achieve the correctness of the image. the validation of the resultant image is been analysed with the histogram graph vlaues for more accuracy. The cluster centers of the AXI_IMG_01 are c1=101.2571 and c2=6.6779.
The cluster center values obtained in the FCM algorithm is matches with the histogram graph values which shows its efficiency and correctness of the algorithm. The segmentation of images through the FCM algorithm is achieved by the intensity values of the images. The FCM algorithm segments the images and produces the cluster center values of the images and resultant images. However, in the first level of segmentation the cluster center values produces the highest intensity values of the images and in the next level it again segments the image and produces the cluster center values.After receiving the resultant images the histogram graph for both the image i.e. before and after segmentation is been analyzed with the cluster center values of the images. The segmentation is based on the intensity values of the pixels it has been cross examined with the histogram graph of the images. Fig. 4(a) shows the histogram value of AXI_IMG_01 before FCM, and its value is peaks at 100 which are same as the cluster center c1 of the image in the FCM clustering algorithm and the Fig. 4(b)depicts the tumor affected region separately with the same histogram values as with cluster center c2 of the AXI_IMG_01. The axial plane image AXI_IMG_02 sample data is implemented as same as the AXI_IMG_01. The FCM clustering algorithm produces the same result as with the coordination of histogram. The cluster center values of AXI_IMG_02 is c1=109.0320 and c2=10.330. Fig. 5 shows the preprocessing and various steps of AXI_IMG_02 and separated brain tumor affected region separately. Cluster center values are compared with the histogram graph intensity of the AXI_IMG_02 before and after segmentation are shown in the Fig. 6. The process is implemented for AXI_IMG_03 with the cluster centers c1=128.5591 and c2=13.4650 and the results are shown in the Fig. 7. andFig. 8.   The table I shows the computation time values of AXI_IMG_01, AXI_IMG_02 and AXI_IMG_03. The computation time is the CPU execution time of FCM algorithm which not includes the preprocessing time. The computation time is calculated in seconds. Fig. 4(a) shows before segmentation with the full intensity value is peak at the somewhere between 120 and 130. The value is equal to cluster center c1=128.559. After the segmentation the histogram value is peak at the point 10. Fig. 4(b) segmented region intensity value is equal to the cluster center value c2=10.330 of FCM algorithm which shows the accuracy of the segmented region.
The cluster centers of c1 and c2 of the sample data are shown in the table. The table shows the cluster center values of the image before and after segmentation of images. This value is approximately equal to the histogram peak point values for the corresponding images to maintain the accuracy and to achieve adequate results. Diagnosing tumor plays an important role in patients to produce accurate results is a highly an important criteria. The coronal plane is another plane in the MRI brain image which shows some tumor affected region with the back plane of the human. In the axial plane we can detect some types of tumor. The coronal plane sample MRI data set is shown in the Fig. 9. COR_IMG_01 data is also preprocessed with the Gaussian filter technique. The cluster values of COR_IMG_02 is c1=40.0859 and c2=182.6475 and the results are shown in the Fig. 10.and histogram graph of the image are shown in the Fig. 11.  In the coronal plane nearly 20 images are taken as input among that 3 image with their results are discussed here. The COR_IMG_02 is done with the preprocessing module and the traditional fuzzy c-means clustering algorithm is applied and the results are compared with the histogram values which are shown in the figures Fig. 12and Fig. 13 with the two cluster center values as c1= 26.7629 and c2=138.3620. The COR_IMG_03 has undergone the same step of process as in the structured approach and produces the results as shown in the Fig. 14. and Fig. 15. With the cluster center values in the coordination of the histogram. The computation time for the three image of the coronal plane with their cluster center values obtained from the proposed approach is shown in the Table II.

Conclusion
The prediction of brain tumor is a critical problem in the medical field. The tumor affected region is separated from the MRI brain images by comparing the computational time of the axial and coronal plane and also finding the best fit of the FCM algorithm over the two planes. The structured approach discusses so far will help the physicians to detect the tumor affected region very easily. The preprocessing of images is carried out byGaussian filter method to remove the noisesfrom the images. After preprocessing, the traditional FCM is applied to segment the tumor affected region. The affected region is cross examined with the cluster center values of FCM. A physician can detect the tumor affected region very straightforwardly with the help of result of FCM algorithm. But, the FCM algorithm alone cannot diagnose the tumor for some type brain images. It helps the doctors or radiologists in finding the affected region perfectly to detect the tumor. The proposed approach is more suitable and robust for the coronal plane rather than the axial plane based on the computational time when comparing with the axial plane. The future work is to calculate the area of the tumor affected region by means of intensity based pixel values.