Optimized Fuzzy Logic Based Segmentation for Abnormal MRI Brain Images Analysis

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1 207 Optimized Fzzy Logic Based Segmentation for Abnormal MRI Brain Images Analysis Indah Soesanti 1, Adhi Ssanto 2, Thomas Sri Widodo 2 and Maesadi Tokronagoro 3 1 Department of Electrical Engineering and Information Technology, Gadah Mada University, Yogyakarta, Indonesia 2 Department of Electrical Engineering and Information Technology, Gadah Mada University, Yogyakarta, Indonesia 3 Faclty of Medicine, Gadah Mada University, Yogyakarta, Indonesia Abstract In this paper an optimized fzzy logic based segmentation for abnormal MRI brain images analysis is presented. A conventional fzzy c-means (FCM) techniqe does not se the spatial information in the image. In this research, we se a FCM algorithm that incorporates spatial information into the membership fnction for clstering. The FCM algorithm that incorporates spatial information into the membership fnction is sed for clstering, while a conventional FCM algorithm does not flly tilize the spatial information in the image.the advantage of the techniqe is less sensitive to noise than the others. Originality of this research is focsed in application of the techniqe on a normal and a glioma MRI brain images, and analysis of the area of abnormal mass from segmented images. The reslts show that the method effectively segmented MRI brain images, and the segmented normal and glioma MRI brain images can be analyzed for diagnosis prpose. The area of abnormal mass is identified from 7.15 to cm 2. Keywords: Adaptive image segmentation, FCM clstering, abnormal MRI brain image, fzzy membership fnction. 1. Introdction Image segmentation is one of the most important step to extract information in image processing. Segmentation has wide application in medicine area. The main obective of segmentation of medical image is to partition the image into mtally exclsive and exhasted regions sch that each region of interest is spatially contigos and the pixels within the region are homogeneos with respect to a predefined criterion. Magnetic Resonance Imaging (MRI) is the state-of-the-art medical imaging technology which allows cross sectional view of the body with nprecedented tisse contrast. MRI provides a digital representation of tisse characteristic that can be obtained in any tisse plane. The images prodced by an MRI scanner are best described as slices throgh the brain. MRI has the added advantage of being able to prodce images which slice throgh the brain in both horizontal and vertical planes. The obective of segmenting different types of soft-tisse in MRI brain images is to label complex strctres with complicated shapes, as white matter, grey matter, CSF and other types of tisses in nerological conditions. A variety of segmentation methods have been developed to satisfy increasing reqirement of image segmentation over past several years. FCM (Fzzy c-means) is nspervised techniqe that has been sccessflly applied to ftre analysis, clstering, and classifier designs in the fields sch as astronomy, geology, medical imaging, target recognition, and image segmentation. An image can be represented in varios featre spaces, and the FCM method classifies the image by groping similar data points in the featre space into clsters. Dring the past many researchers in the field of medical imaging and soft compting have made significant srvey in the field of image segmentation. There has been considerable interest recently in the se of segmentation methods based on fzzy logic, which retain more information from the original medical image than hard segmentation methods (e.g. Bezdek et al. [1], Udpa et al. [2], Pham [3], Masoole and Moosavi [4]). The fzzy C- means (FCM) clstering, in particlar, can be sed to obtain a accrate segmentation via fzzy pixel classification. Unlike hard clstering methods which force pixels to belong exclsively to one class, FCM allows pixels to belong to mltiple classes with varying degrees of membership fnctions. This approach allows additional flexibility in many applications and has recently been sed in processing of medical images [5]. For example, in their segmentation of MRI brain images, Pham et al. [5] thresholded the FCM memberships in order to extract pixels which a high confidence of correct classification. X et al. [6] sed deformable srfaces that converged to the peaks of the memberships. The FCM method, however, does not address the intensity inhomogeneity

2 208 artifact that occrs in nearly all MRI [7]-[8]. Originality of this research is the method applied on a normal MRI brain image and a glioma MRI brain images, and analyze the area of abnormal mass from segmented images. 2. Fndamental Theory 2.1 Magnetic Resonance Imaging Magnetic Resonance Imaging (MRI) is an imaging sed primarily in medical settings to prodce high qality medical images of the soft tisses. MRI is an imaging techniqe sed primarily in medical settings to prodce high qality images of the inside of the hman body. In this section we give a brief description of the principles of MRI which are refered to [9]. In MRI, the image is a map of the local transverse magnetization of the hydrogen nclei. This transverse magnetization in trn depends on several intrinsic properties of the tisse. MRI is based on the principles of nclear magnetic resonance (NMR). The NMR phenomenon relies on the fndamental property that protons and netrons that make p a ncles possess an intrinsic anglar momentm called spin. When protons and netrons combine to form ncles, they combine with oppositely oriented spins. Ths, nclei with an even nmber of protons and netrons have no net spin, whereas nclei with an odd nmber of protons or netrons possess a net spin. Hydrogen nclei have an NMR signal since its ncles is made p of only a single proton and possess a net spin. The hman body is primarily fat and water, which have many hydrogen atoms. Medical MRI primarily images the NMR signal from the hydrogen nclei in the body tisses. The net spin of the ncles arond its axis gives it an anglar moment. Since the proton is a positive charge, a crrent loop perpendiclar to the rotation axis is also created, and as a reslt the proton generates a magnetic field. The oint effect of the anglar moment and the self generated magnetic field gives the proton a magnetic dipole moment parallel to the rotation axis. Under normal condition, one will not experience any net magnetic field from the volme since the magnetic dipole moments are oriented randomly and on average eqalize one another. When placed in a magnetic field, a proton with its magnetic dipole moment processes arond the field axis. The freqency of this precession, v 0, is the resonant freqency of NMR and is called the Larmor freqency. The precession freqency is directly proportional to the strength of the magnetic field, i.e. v 0 = gb 0 (1) where B 0 is the main magnetic field strength, and g is a constant called gyromagnetic ratio which is different for each ncles (42.56 MHz/Tesla for protons). Given a specimen, the application of a magnetic field B 0 wold create a net eqilibrim magnetization M 0 per cbic centimeter, which is aligned to the B 0 field. The M 0 is the net reslt of smming p the magnetic fields de to each of the H nclei and is directly proportional to the local proton density (or spin density). However, M 0 is many orders of magnitde weaker than B 0 and is not directly observable. By tipping M 0 away from the B 0 field axis with an appropriate RF plse having a freqency eqals to the Larmor freqency, a longitdinal magnetization component ML and a transverse magnetization component MT is prodced. When the RF plse is trned off, the longitdinal magnetization component ML recovers to M 0 with a relaxation time T1, and the transverse magnetization component MT dephases and decays to zero with a relaxation time T2 1. Dring relaxation, the protons lose energy by emitting their own RF signal with the amplitde proportional to MT. which is referred to as the free-indction decay (FID) response signal. T2 indicates the time constant reqired from a given tisse type to decay for the FID response signal. The FID response signal is measred by an RF coil placed arond the obect being imaged. In MR imaging, the RF plse is repeated at a predetermined rate. The repetition time, TR, is the period of the RF plse seqence is. The FID response signals can be observed at varios times within the TR interval. echo delay time, TE is the time between which the RF plse is applied and the response signal is measred. The TE is the time when the spin echo occrs de to the refocsing effects of the 180 degree refocsing plse applied after a delay of TE/2 from the RF plse. The TR and TE control how strongly the local tisse relaxation times, T1 and T2, affect the signal. By adsting TR and TE the acqired MR image can be made to contrast different tisse types. 2.2 Image Segmentation The aim of medical image segmentation on hman graphical interaction is to define regions, sing methods sch as manal slice editing, region painting and interactive thresholding. Raapakse [13] had classified the different methods of image segmentation as for categories. (1) Thresholding region growing and edge based techniqes. (2) The maximm-likelihood-classifier (MLC). These methods are basically depend on the prior model and its parameters. Vannier et al. [14] reported satisfactory preliminary reslts with Bayesian MLC. Ozkan et al. [15] researched abot the MLC and the neral

3 209 network classifier which showed the speriority of the neral network. Some new methods of image segmentation that cold be classified as statistical methods have been introdced in the past few years. Hansen [16] sed a probabilistic spervised relaxation techniqe for segmenting 3D medical images. The method introdced the se of ces to gide the medical image segmentation. Those ces marked by the ser have the mean and standard deviation as description parameters. (3) The neral networks methods one example of which is the work of Ahmed et al. [14] who sed a two stages neral network system for CT/MRI image segmentation. The first stage is a self-organized principal component analysis (SOPCA) network and the second stage consists of a self-organizing featre map (SOFM). The reslts obtained compare favorably with the classical and statistical methods. (4) The Fzzy Clstering methods. In [18] a comparison between the fzzy logic and artificial neral network techniqes in segmenting magnetic resonance images debated for the need of nspervised techniqe in segmentation which was provided sing the nspervised fzzy c-mean algorithm. 3. Fzzy C-Means Clstering The FCM method assigns pixels to each clster by sing fzzy membership fnctions. Let X=(x 1, x 2,.,x N ) denotes an image with N pixels to be partitioned into c clsters, where x i represents mltispectral (featres) data. The algorithm is an iterative optimization that minimizes the cost fnction defined as follows [16]: J N c 1 i1 m x vi where represents the membership fnction of pixel x in the ith clster, v i is the ith clster center, and m is a constant. The parameter m controls the fzziness of the reslting partition, and m = 2 is sed in this stdy. The cost fnction is minimized when pixel close to the centroid of their clsters are assigned high membership vales, and low membership vales are assigned to pixels with data far from the centroid. The fzzy membership fnction represents the probability that a pixel belongs to a specific class. In the FCM algorithm, the probability is dependent solely on the distance between the pixel and each individal clster center in the featre domain. The membership fnctions and clster centers are pdated by the following: 2 (2) and v i c k 1 N 1 where [0, 1]. N 1 x x m x m 1 v v i k 2 /( m1) Starting with an initial gess for each clster center, the FCM converges to a soltion for v i representing the local minimm or a saddle point of the cost fnction. Convergence can be detected by comparing the changes in the membership fnction or the clster center at two sccessive iteration steps. One of the important characteristics of an image is that neighboring pixels possess similar featre vales, and the probability that they belong to the same clster is great. This spatial relationship is important, bt it is not tilized in a konvensional FCM algorithm. To exploit the spatial information, a spatial fnction is defined as. ik knb( x ) (3) (4) h (5) In this formla, NB(x ) represents a sqare window centered on pixel x in the spatial domain. A 3 x 3 window was sed throghot this work. Jst like the membership fnction, the spatial fnction h represents the probability that pixel x belongs to ith clster. The spatial fnction of a pixel for a clster is large if the maority of its neighborhood belongs to the same clster. The spatial fnction in incorporated into membership fnction as follows: ' c k 1 p h p k q h q k In this formla, p and q are parameters to control the relative importance of both fnctions. In a homogenos region, the spatial fnctions fortify the original membership, and the clstering reslt remains nchanged. However, for a noisy pixel, this formla redces the weighting of a noisy clster by the labels of its (6)

4 210 neighboring pixels. As a reslt, misclassified pixels from noisy regions or sprios blobs can easily be corrected. The spatial FCM with parameter p and q is denoted sfcm p,q. Note that sfcm 1,0 is identical to the conventional FCM. The clstering is a two-pass process at each iteration. The first pass is the same as that in standard FCM to calclate the membership fnction in the spectral domain. In the second pass, the membership information of each pixel is mapped to the spatial domain, and the spatial fnction is compted from that. The FCM iteration proceeds with the new membership that is incorporated with the spatial fnction. The iteration is stopped when the maximm difference between two clster centers at two sccessive iterations is less than a threshold (=0,02). After the convergence, defzzification is applied to assign each pixel to a specific clster for which the membership is maximal is extensive edema extending anteriorly and posteriorly and involving the basal ganglia. The shift and mass effect on the ventricle have reslted in compromise of the foramen of Monro, and there is evidence of active hydrocephals, as shown by both the ventriclar enlargement and a homogeneos increase throgh the periventriclar region. An additional area of increased signal, separated from the right hemisphere in the left side, sggest that there may even be a metastatic focs or evidence of distant extension of tmor into the left hemisphere. All these featres sggest a very high Grade IV glioma or glioblastoma. 4. Experimental Reslts 4.1 Normal MRI Brain Image (a) Original MRI2 Brain image (b) Segmented MRI2 Brain image In this research, MRI image is segmented sing FCM method incorporated into the spatial information. Figre 1(a) shows the 256x256 grayscale original T2-weighted MRI1 brain image. Fig. 1(b) shows the reslt of the FCM incorporated into the spatial information with parameters p=1 and q=2. Figre 2. MRI2 Brain image 4.3 Analysis of the Area of Abnormal Mass In this stdy, we also apply the FCM method to segment for 256x256 MRI brain images with abnormal mass (i.e. MRI3, MRI4, MRI5, MRI6, MRI7, and MRI8), as shown in Figre 3 [17]. Application of the FCM method in segmentation of the images is in order to analysis of the area of abnormal mass Figre 4 shows the 256x256 segmented MRI3-MRI8 images. (a) Original MRI1 Brain image (b) Segmented MRI1 Brain image Figre 1. MRI1 Brain image As can be seen in the segmented images in Fig. 2, lesion or abnormal mass is not identified, and the ventriclar system is not extensive and it is a median. So, the image is normal brain MRI image. 4.2 Glioma MRI Brain Images Figre 2(a) shows the 256x256 original MRI2 image [17]. As can be seen in the segmented image in Fig. 2(b), there Table 1 shows area of abnormal mass of segmented MRI images. The reslts are MRI images identified tmors of 2.66% to 7.22% or 7.15 to cm 2. In the brain tmor, glioma, the bigger area of tmor the higher grade of glioma. Table 1. Area of abnormal mass Images Areas in % Areas in cm 2 MRI MRI MRI MRI

5 211 MRI MRI (a) (b) (c) (d) (e) (f) Figre 3. Original abnormal mass MRI brain images: (a) MRI3, (b) MRI4, (c) MRI5, (d) MRI6, (e) MRI7, (f) MRI8. (a) (b) (c) (d) (e) (f) Figre 4.(a) Segmented MRI3, (b) segmented MRI4, (c) segmented MRI5, (d) segmented MRI6, (e) segmented MRI7, (f) segmented MRI8.

6 Conclsions In this paper we apply an extended FCM method that incorporates the spatial information into the membership fnction to improve the reslts of MRI brain image segmentation. The membership fnctions of the neighbors centered on a pixel of MRI brain image in the spatial domain are enmerated to obtain the clster distribtion statistics. These statistics are transformed into a weighting fnction and incorporated into the membership fnction. This neighboring effect redces the nmber of sprios blobs and biases the soltion toward piecewise homogeneos labeling. The techniqe was sed to analyze a normal MRI brain image and glioma MRI brain images. We applied the techniqe on a normal MRI brain image and on a glioma MRI brain image. The reslts show that the method effectively segmented Magnetic Resonance Imaging (MRI) brain images with spatial information, and the segmented normal and glioma MRI brain images can be analyzed for diagnosis prpose. The reslts are MRI images identified tmors of 7.15 to cm 2. References [1] J. Bezdek. L. Hall. and L. Clarke. Review of MR image segmentation sing pattern recognition. Medical Physics. vol pp [2] J. K. Udpa. L. Wei. S. Samarasekera. Y. Miki. M. A. van Bchem. and R. I. Grossman. "Mltiple sclerosis lesion qantification sing fzzy-connectedness principles." IEEE Transactions on Medical Imaging. vol pp [3] D.L. Pham. Unspervised Tisse Classification in Medical Images sing Edge-Adaptive Clstering. Proceedings of the 25 th Annal International Conference of the IEEE EMBS. Cancn. Mexico. Sep [4] L. Jiang and W. Yang. A Modified Fzzy C-Means Algorithm for Segmentation of Magnetic Resonance Images. Proc. VIIth Digital Image Compting: Techniqes and Applications. Sydney Dec [5] D.L. Pham and J.l. Prince. Adaptive fzzy segmentation of magnetic resonance images. IEEE Trans. in Medical Imaging Vol. 18. pp [6] C. X. D.L Pham. and J.L. Prince. Finding the brain cortex sing fzzy segmentation. isosrfaces. and deformable srfaces. In Proc. XVth Int. Conf. on Inform. Processing in Medical Imaging. (IPMI 1997). pp [7] S.R. Kannan. Segmentation of MRI Using New Unspervised Fzzy C Mean Algorithm. ICGST-GVIP Jornal. Vol. 5. No.2. Jan [8] S. Alizadeh. M. Ghazanfari. and M. Fathian. Using Data Mining for Learning and Clstering FCM. International Jornal of Comptational Intelligence. Vol. 4. No. 2. Spring [9] A. Wee, C. Liew, and H. Yan. Crrent Methods in the Atomatic Tisse Segmentation of 3D Magnetic Resonance Brain Images. Crrent Medical Imaging Reviews, Vol. 2, No. 1, 2006, pp [10] J.C. Raapakse. J.N. Giedd. and J.L. Rapoport. Statistical Approach to Segmentation of Single Channel Cerebral MR Images. IEEE Trans. on Medical Imaging. Vol.16. No.2. April [11] M.W. Vannier. C.M. Speidel. and D.L. Rickman. Magnetic resonance imaging mlti spectral tisse classication. Jornal of NIPS. vol.3. Ag [12] M. Ozkan. B.M. Dawant. and R.J. Macinas. Neral Network_Based Segmentation of Mlti_Modal Medical Images. A Comparative and Prospective Stdy. IEEE Transactions on Medical Imaging. Vol. 12. No.3. Sep pp [13] M.W. Hansen and W.E. Higgins. Relaxation Methods for Spervised Image Segmentation. IEEE Trans. on Pattern Analysis and Machine Intelligence. Vol. 19. No. 9. Sep [14] M.N. Ahmed and A.A. Farag. Two stages Neral Network for Medical Volme Segmentation. Accepted for Pblication in the Jornal of Pattern Recognition Letters [15] L.O. Hall. A.M. Bensaid. L.P. Clarke. R.P. Velthizen. M.S. Silbger. and J.C. Bezdek. A Comparison of Neral Network and Fzzy Clstering Techniqes in Segmenting Magnetic Resonance Images of the Brain. IEEE Transactions on Neral Networks. Vol. 3. No. 5. Sep pp [16] K.S. Chang. H.L. Tzeng. S. Chen. J. W. and T.J. Chen. Fzzy C-Means Clstering with Spatial Information for Image Segmentation. Compterized Medical Imaging and Graphics. Vol. 30 (2006). Elsevier. pp [17] J.H. Besese. Cranial MRI. A Teaching File Approach. McGraw-Hill. International Edition. Medical Series Indah Soesanti is with the Department of Electrical Engineering and Information Technology. Gadah Mada University. Yogyakarta. Indonesia. She received B.S. and M.Eng. from Gadah Mada University. Yogyakarta. Indonesia in 1998 and respectively. He is crrently a Ph.D. stdent at the Electrical Engineering. Gadah Mada University. She has more than 7 years of experience in teaching. Her research interests inclde image processing. signal processing. fzzy logiz and its application. optimization. and information system. She has pblished more than five papers in national ornals. She has also presented more than ten research articles in national and international conferences. Adhi Ssanto is a Professor in the Department of Electrical Engineering and Information Technology. Gadah Mada University. Yogyakarta. Indonesia. He received M.Sc. and Ph.D. from University of California. Davis. US in 1966 and respectively. He has more than 40 years of experience in teaching and research. His crrent area of research incldes image processing. signal processing. neral networks. wavelets. fzzy logiz and its application. optimization and control. instrmentation. and information system. He has pblished more than ten papers in referred international ornals. He has also presented more than twenty research articles in national and international conferences. He has written few books related to his research work.

7 213 Thomas Sri Widodo is a Professor in the Department of Electrical Engineering and Information Technology. Gadah Mada University. Yogyakarta. Indonesia. He received DEA. and Ph.D. from Universite des Sciences et Techniqes d Langedoc. Montpellier 2. France in 1986 and respectively. He has more than 30 years of experience in teaching and research. His crrent area of research incldes electronics. telecommnication. image processing. signal processing. neral networks. wavelets. fzzy logiz and its application. instrmentation and control. biomedical engineering. and hypertermia. He has pblished more than ten papers in referred international ornals. He has also presented more than forty research articles in national and international conferences. He has written few books related to his research work. He is crrently dealing with few proects sponsored by government of Indonesia (the Ministry of Edcation and the State Ministry of Research and Technology). Maesadi Tokronagoro is a Professor in the Faclty of Medicine. Gadah Mada University. Yogyakarta. Indonesia. He received M.S. and Ph.D. from Gadah Mada University. Yogyakarta. Indonesia in 1981 and respectively. He has more than 30 years of experience in teaching and research. His crrent area of research incldes radiology. radiotherapy. medical image processing. biomedical engineering. and hypertermia.