Segmentation Method of MRI Using Fuzzy Gaussian Basis Neural Network

Transcription

1 Neural Informaton Processng - Letters and Revews Vol.8, No., August 005 LETTER Segmentaton Method of MRI Usng Fuzzy Gaussan Bass Neural Networ We Sun College of Electrcal and Informaton Engneerng, Hunan Unversty, Changsha, 41008, Chna E-mal: we_sun@hnu.cn Yaonan Wang College of Electrcal and Informaton Engneerng, Hunan Unversty, Changsha, 41008, Chna E-mal: yaonan@mal.hunu.edu.cn (Submtted on Arl 8, 005) Abstract Consderng the features of magnetc resonance magng (MRI), a segmentaton method of MRI based on fuzzy Gaussan bass neural networ (FGBNN) s roosed. In roosed method, the fuzzy nference s realzed by neural networ. Gaussan bass functon s used as fuzzy membersh functon, and error bacroagaton (BP) algorthm s used to tran the neural networ. The exermental results show that the roosed method has hgher segmentaton recson and faster networ learnng seed than the segmentaton method based on tradtonal radal bass functon neural networ (RBFNN). Keywords Fuzzy neural networ, magnetc resonance mage, mage segmentaton 1. Introducton Wth the develoment of modern medcal scence and nformaton technque, the magnetc resonance magng (MRI) s more and more wdely used n clncal medcne. Comared wth the comuterzed tomograhy (CT), MRI does less harm to human health and ts magng effect s better for arenchyma whch contans more water, such as bran, breast and belly, etc. In MRI rocess, mage segmentaton s very mortant for decdng the satal locaton, shae and sze of the focus, establshng and amendng theraeutc roject, selectng oeraton ath and evaluatng theraeutc effect. And t s also the foundaton of three-dmensonal reconstructon and vsualzaton [1]. So t s a hot tas to fnd the arorate MRI segmentaton method for modern medcne mage feld. Snce the end of 1970s when MRI was used n clncal examnng, many MRI segmental methods have been develoed []. In these methods, neural networ attracted more and more researchers for ts abltes of selflearnng, fault tolerance, and otmum search. It can counteract the uncertantes n MRI such as temerature and electrcal nose, magnetc feld nhomogenety, ndvdual dfferences, and dsordered sueroston of tssue [3], [4], [5]. But t can not exress human exert s nowledge and exerence, and the constructon of ts toologcal structure lacs of theoretcal methods. Moreover the hyscal meanng of ts jont weght s not clear. All these can mae the segmentaton method of neural networs unstable. Fortunately, these roblems can be solved by usng fuzzy neural networ (FNN) technology, whch combnes fuzzy technque wth neural networs together by usng neural networs to rocess fuzzy nformaton. It rovdes neural networs the ablty to exress qualtatve nowledge, and networ toologcal structure and jont weght have clear hyscal meanng. Also, t can mae the ntalzaton of networ easer, avod the local otmzaton of networ tranng, and ensure the stablty of networs [6],[7]. Ths aer roosed an MRI segmental method based on fuzzy Gaussan bass neural networs (FGBNN). Ths method not only has good ablty of exressng qualtatve nowledge and self-learnng, but also ntegrates the excellent local erformance of Gaussan bass functon. It enhances the recson of the MRI segmentaton. 19

2 Segmentaton Method of MRI Usng Fuzzy Gaussan Bass Neural Networ W. Sun and Y. Wang The structure of ths aer s arranged as follows. In Secton, the structure and learnng algorthm of the roosed FGBNN are descrbed. In Secton 3, the segmentaton method of MRI usng roosed FGBNN s ntroduced. Exermental results are gven and analyzed n Secton 4. Fnally, n Secton 5, some conclusons are drawn.. FGBNN The roosed FGBNN uses neural networs to realze fuzzy nference, uses Gaussan bass functon as fuzzy membersh functon, and uses BP algorthm to tran the networ. Its structure and learnng algorthm are develoed n ths secton..1 The structure of FGBNN The structure of the roosed FGBNN s shown as Fg.1. The networ conssts of four layers, Usng I ( j) ( j) and O to reresent the nut and outut of the th neuron n the jth layer, resectvely, the relatonsh between the nut and outut of each layer can be descrbed as follows. O O w O x 1 O 1 y 1 x n O m y m Fgure 1. The structure of FGBNN The frst layer s the nut layer, whch ntroduce nut varables { x, x,, } oututs of the frst layer can be formulated as 1 L x n nto the networ. The O = x = 1,, n The second layer s the fuzzfcaton layer, whch fuzzfes nut varables. Every nut varable s fuzzfed nto three fuzzy lngustc terms,.e., small(s), medum (M), and large(l). We use Gaussan bass functon as the fuzzy membersh functon. The oututs of second layer can be descrbed as 0

3 Neural Informaton Processng - Letters and Revews Vol.8, No., August 005 O = µ ~ ( O ) = ex[ ( O a ) / b ], = 1,, n ; j = 1,, 3 A where A ~ s the jth lngustc term corresondng to the th nut, A {S,M,L}, a and b are translaton and dlaton arameter of Gaussan membersh functon corresondng to A. The thrd layer s fuzzy nference layer. Every node n ths layer corresonds to a fuzzy nference rule. ~ Suosng A q, q s the lngustc term corresondng to qth nut n the th fuzzy rule, and usng multlcaton sgn * substtute the oeraton AND, the outut of the th node n ths layer can be descrbed as O = O 1 1 O n L O = O, = 1,, 9 where Oq denotes the membersh of qth nut to A q q, q, q = 1,, 3 ; q = 1,, n. The forth layer s the defuzzfcaton layer. Its functonal relatonsh can be formulated as where y = O ~ n O w = O n n q= 1 w s the weght of networ, y s th outut of networ.. The learnng algorthm of FGBNN q q, = 1,, m. The BP algorthm was used to tran the roosed FGBNN. The arameters to be traned nclude a and b. The learnng error functon s defned as 1 Jc = ( yˆ where ŷ s the th desred outut of the networ, and Then, the teratve learnng algorthm of where η w s the learnng rate of w w, and y ) y s the th actual outut of the networ. w can be formulated as w, ( t + 1) = w η w (6) w Jc J y c w = = = ( yˆ y ) O (7) w y w In the same way, we can get the teratve learnng algorthm of a and b as where ηa and η b are learnng rate of a and b, resectvely, and a ( t + 1) = a η a (8) a b ( t + 1) = b η b (9) b (5) a O t J c Jc ( ) O O = = ( 4) a, O O O a = {[ y ˆ y ] w O [ O a ]/ b } J b = b = j c =, O t J c ( ) O O ( 4) O O O b (10) 1

4 Segmentaton Method of MRI Usng Fuzzy Gaussan Bass Neural Networ W. Sun and Y. Wang 3 = {[ y ˆ y ] w O [ O a ] / b } = j (11) 3. Segmentaton of MRI based on FGBNN The MRI s mult-sectrum mage consstng of T1 mage, T mage, and PD mage. These three mages resectvely dect the characterstcs of dfferent tssues. Segmentaton by analyzng these three mages together has hgher recson than just analyzng one of them. For each xel of MRI, we tae ts three gray values n T1 mage, T mage and PD mage as nut varables of the FGBNN. The oututs of the FGBNN corresond to the classes of the xels n the mage. For examle, all xels n the bran MRI belong to fve classes,.e., gray matter, whte matter, cortex, CSF (cerebrosnal flud), and bacground. Therefore the FGBNN for the segmentaton of bran MRI has 5 outut nodes. When segmentng an MRI, we ut the three gray values of a xel nto the FGBNN, and can get the networ oututs of whch values reresent the membersh degrees of ths xel to all classes. We regard the class whch has largest membersh degree as the class of ths xel. For obtanng the learnng samle to tran the FGBNN, these mages are frst read and segmented by human exerts, and referenced segmented mages can be obtaned. Accordng to these referenced segmented mages, each xel s gray values of T1 mage, T mage, PD mage, and membersh degrees to all classes consttute a learnng samle. All xels learnng samles form a samle set. After tranng the FGBNN usng ths samle set, the networ can aroxmate the level of exerts segmentaton. In order to mrove the segmental recson, we can choose more mages and consttute more samle set to tran the networ. 4. Exerments In order to test the erformance of the roosed segmentaton method, a bran MRI s segmented n ths aer. Fg. gves three orgnal mages of T1, T and PD. Fg.3 shows the segmentaton result of the roosed FGBNN. Fg.4 s the segmentaton result of the three-layer RBFNN, whch uses comettve learnng algorthm at the frst layer and the gradent-descent learnng algorthm at the second layer. Table 1 comares the learnng tme of two neural networs, and Table comares the segmentaton accuracy of the two methods. Fgure. Orgnal mages of T1, T, and PD Fgure 3. Segmentaton result of the FGBNN Fgure 4. Segmentaton result of the three-layer RBFNN

5 Neural Informaton Processng - Letters and Revews Vol.8, No., August 005 Table 1. Comarson of learnng tme between two neural networs Class of networ FGBNN three-layer RBFNN Learnng tme(s) 34.3± ±6.16 Table. Comarson of accuracy between two segmentaton methods Methods Segmentaton Accuracy Gray matter Whte matter Cortex CSF Bacground FGBNN 94.% 93.1% 95.6% 91.4% 97.8% three-layer RBFNN 81.7% 86.4% 78.7% 73.6% 94.3% From the results of Table 1, we can see that the learnng seed of the FGBNN s faster than that of the three-layer RBFNN. From the results of Table, we can also conclude that the segmentaton accuracy of the FGBNN s hgher than that of the three-layer RBFNN. 5. Conclusons In ths aer, a segmentaton method of MRI based on fuzzy Gaussan bass neural networ s roosed. Fuzzy technque and neural networ technque are combned by usng neural networ to realze fuzzy nference. Gaussan bass functon s taen as fuzzy membersh functon. The results of exerments show that the erformance of the roosed method s better than the method based on three-layer RBFNN. Reference [1] M. I. Kohn, N. K. Tanna, and G. T. Herman, Analyss of bran and cerebrosnal flud volumes wth MR magng, Radology, Vol. 178, No. 1, , [] J. C. Bezde, L. O. Hall, L. P. Clare, Revew of MR mage segmentaton technques usng attern recognton, MedPhys, Vol. 0, No. 4, , [3] R. Ulrch, Quantzaton of greymatter, whtematter, and cerebrosnal flud from sn-echo magnetc resonance mages usng an artfcal neural networ technque, MedPhys, Vol. 1, No., , [4] V. C. Raquel, M. B. Verónca, and Y. S. Oscar, Coulng of Radal-Bass Networ and Actve Contour Model for Multsectral Bran MRI segmentaton, IEEE Trans on Bomedcal Engneerng, Vol. 51, No. 3, , 004. [5] J. Alrezae, M.E. Jerngan, and C. Nahmas, Automatc segmentaton of cerebral MR mages usng artfcal neural networs, IEEE Trans on Nuclear Scence, Vol. 45, No. 4, , [6] S. Horawa, T. Furuhash, and Y. Uchawa, On fuzzy modelng usng neural networs wth the bac roagaton algorthm, IEEE Trans. on Neural Networs, Vol. 3, No. 5, , 199. [7] D. K. Araun, Neural fuzzy models for multsectral mage analyss, Aled Intellgence, Vol. 8, No., , We Sun got hs Ph. D degree from Hunan Unversty n 003, and currently wors as an Assocate Professor n Electrcal and Informaton Engneerng College, Hunan Unversty. Hs research nterest ncludes neural nformaton rocessng, bomedcal mage, ntellgent control, and robotc control. 3

6 Segmentaton Method of MRI Usng Fuzzy Gaussan Bass Neural Networ W. Sun and Y. Wang Yaonan Wang got hs Ph. D degree from Hunan Unversty n 1995, and currently wors as a Professor n Electrcal and Informaton Engneerng College, Hunan Unversty. Hs research nterest ncludes ntellgent nformaton rocessng, mage rocessng, ntellgent control, and robotc control. 4