Improved Intensity Inhomogeneity Correction Techniques in MR Brain Image Segmentation

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Proeeds of the 17th World Coress The Iteratoal Federato of Atoat Cotrol Seol, Korea, l 6-11, 008 Iproved Itest Ihooeet Correto Tehqes MR Bra Iae Seetato László Szlá*, László Dávd*, Sádor M.

1 Proeeds of the 17th World Coress The Iteratoal Federato of Atoat Cotrol Seol, Korea, l 6-11, 008 Iproved Itest Ihooeet Correto Tehqes MR Bra Iae Seetato László Szlá*, László Dávd*, Sádor M. Szlá*, Balázs Beó**, Zoltá Beó** *Falt of Tehal ad Ha Sees, Sapeta Hara See Uverst of Târ-Mreş, Roaa (Tel: ; e-al: {lalo,ldavd,szs}@ sapeta.ro). **Departet of Cotrol Eeer ad Iforato Teholo, Bdapest Uverst of Teholo ad Eoos, Bdapest, Har (e-al: beo@t.be.h, beo@t.be.h) Abstrat: Itest hooeet or test o-fort (INU) s a desred pheoeo that represets the a obstale for MR ae seetato ad restrato ethods. Varos tehqes have bee proposed to elate or opesate the INU, ost of whh are ebedded to lster alorths. Ths paper proposes a pre-flter tehqe for Gassa ad plse ose elato, ad a soothe flter that asssts the fzz -eas (FCM) alorth at the estato of hooeet as a slowl var addtve or ltplatve ose. The seetato s proded b FCM alorth toether wth the INU estato. The slowl var behavor of the bas or a feld s assred b a soothe flter that perfors a otext depedet avera, based o a orpholoal rtero. The experets s -D sthet phatos ad real MR aes show, that the proposed ethod provdes arate seetato. The proded seetato ad fzz ebershp vales a serve as exellet spport for 3-D restrato ad seetato tehqes. 1. INTRODUCTION Maet resoae a (MRI) s a ver poplar edal a tehqe, al bease of ts hh resolto ad otrast, whh represet reat advatae above other daost a odaltes. Besdes all these ood propertes, MRI also sffers fro three osderable obstales: oses (xtre of Gassa ad plse oses), partal vole artefats (pxels ota at least two tpes of tsses), ad test hooeet (Sal ad Y, 005). Ths latter oe, also ow as test ofort (or INU artefat), afests as a spatall slowl var fto, that aes pxels belo to the sae tsse be observed hav dfferet testes. I order to prode a orret seetato or restrato of MR aes, the INU artefat eeds to be odelled ad opesated. INU has two dfferet tpes of sores: those related to the MRI deve, ad those related to the aed patet s shape, posto ad oretato. Whle the frst tpe of sore has effet opesato ad albrato ethods, the seod tpe of INU artefats are h ore dfflt to hadle (Vov et al., 007). A wdel sed tehqe, hadl ostl the frst tpe of INU, ossts of the sae of a for phato to prode pror forato (Axel et al., 1987). Hooorph flter represets a poplar opesato ethod (ohsto et al., 1996; Bra et al., 1998), blt o the theoretal asspto, that the freqe spetra of the ae strtres ad of the INU artefat are ooverlapp eah other. The effe of sh ethods are lted bease the tal asspto does ot hold. Althoh several INU opesato approahes exst (Leept et al., 1999; Pha ad Pre, 1999b; Zha et al., 001), oe of the ost wdel sed ethods s the adaptato of the fzz -eas (FCM) lster alorth to teratvel approxate the INU as a sooth var bas or a feld. I ths order, Pha ad Pre (1999a, 1999b) troded a odfed objetve fto prod bas feld estato ad ota extra ters that fore ths artefat var soothl. The also provded a ltrd tehqe to speed p the optatoall heav alorth, bt eve ths wa, the alorth perfors slowl. A probablst approah lead to the sae objetve fto was ve (L et al., 005). Lew ad Ho (003) reated a lo bas feld estato tehqe that odels the INU wth sooth B- sple srfaes. Frther FCM-based bas feld estato tehqes were troded reetl b Ahed et al. (00) ad Sal ad Y (005). The odfato troded b Ahed et al. allows the labell of a voxel to be fleed b ts edate ehbors. Ths approah has reded soe of the oplext of ts aestors, bt the zero radet odto that was sed for bas feld estato leads to several slassfatos (Sal ad Y, 005). The other approah provded a ea spread flter ethod to soothe the estated bas feld ever le of the FCM alorth. Ths approah redes the aot of eessar optatos, bt the reslt of the seetato s ot deterst de to the atre of the sooth flter. I ths paper we propose two flter tehqes to aopa the FCM-based bas- or a feld estato of the test hooeet, ad show ther effe MR /08/$ IFAC / KR

2 17th IFAC World Coress (IFAC'08) Seol, Korea, l 6-11, 008 bra ae seetato s real MR sles ad artfal phatos. The rest of the paper s orazed as follows: seto desrbes the proposed flter tehqes ad the FCMbased bas- ad a feld estato approahes. Seto 3 provdes a qaltatve aalss ad short dssso of seetato reslts. I seto 4 the olsos are forlated.. METHODS.1. Cotext depedet pre-flter Iplse ad Gassa ose s reoved fro the oral MR ae s a otext depedet loal flter, whh obes avera ad eda flter effets based o phsal dstaes ad re level dfferees betwee ehbor pxels. The proposed tehqe ats le a low-pass as, bt the as wehts are separatel opted for eah pxel, based o the dstaes ad re level dfferees eotered wth a ehborhood. The weht of eah ehbor pxel s the prodt of two ters: a dstae ter that dereases expoetall wth Eldea dstae easred fro the ddle pxel; ad a re level ter, whh s hh for pxels that have slar testes wth the ddle pxel ad low f the dffer sfatl. The ddle pxel ets ts weht based o the relablt of ts re level test. Detals of sh tehqes are desrbed (Ca et al., 007; Szlá et al., 007)... Covetoal FCM lster ad dervatos The ovetoal FCM alorth has bee appled sessfll a wde varet of lster probles. Ths alorth optall parttos a set of objet data to a prevosl set ber of lsters based o the teratve zato of a qadrat objetve fto. Whe appled to seet resale aes, FCM lsters the test vale of eah pxel x, 1K. The objetve fto to be zed s ve as follows: FCM 1 1 x v, (1) where > 1 s the fzz expoet or fzzfato paraeter, v represets the etrod or prototpe of the th lster, ad [0,1] s the fzz ebershp fto dat the deree to whh pxel belos to lster. The defto of fzz lo ples, that 1 1. The ostraed optzato of the objetve fto s aheved s Larae ltplers. I ths order, we eed to ze the follow fto: F FCM x v λ, () whh we obtaed b add a zero ter to the objetve fto. The zato s reahed b alteratel appl the optzato of FFCM over { } wth v fxed, 1K, ad the optzato of F FCM over { v } wth fxed, 1K, 1K (Bezde ad Pal, 1991). I eah le, optal fzz ebershp ad optal etrod vales are opted s the forlas: ad v x j 1 /( 1) v /( 1) v j x x 1 (3) 1. (4) for a 1K ad 1K. After adeqate talzato of lster prototpe vales v, (3) ad (4) are alteratel appled tl the or of the varato of the vetor v, oposed of the etrod vales, stas wth a prevosl set bod ε. The above preseted alorth lsters the set of data { x }, whh was reorded ao deal rstaes, ota o ose. However, the real ase, the observed data { } dffers fro the atal oe { x } : there are plse ad Gassa oses, whh were treated the prevos sbseto, ad there s the test o-fort (INU) artefat, whh wll be hadled here. Lteratre reoeds two dfferet data varato odels for test hooeet: the bas ad the a feld odel. If we osder the INU as a bas feld, for eah pxel we wll have x + b, where b represets the bas vale at pxel. I ase of a feld odell, there wll be a a vale for eah pxel, sh that x. I ase of both odels, the varato of the test betwee ehbor pxels has to be slow. Ths s assred b the sooth flter preseted the ext seto. I ase of odell INU as a bas feld, the objetve fto beoes: b 1 1 b v. (5) Ta the dervatves of the Larae ltpler forla that orrespods to b, wth respet to, v ad b, respetvel, ad eqall the to zero, we obta the follow optzato forlas: v j 1 1 b b /( 1) v /( 1) v j ( 1, (6) b ), (7) 966

3 17th IFAC World Coress (IFAC'08) Seol, Korea, l 6-11, 008 b v 1. (8) 1 If we approxate the INU artefat as a a feld, the objetve fto shold be: 1 1 / v. (9) Bease the dervatves of ths fto are hard to hadle, we slhtl odf ths objetve fto the follow wa: 1 1 v. (10) Ths approah dstorts the fto sh a wa, that t ves hher pat to lhter pxels (as ther a feld vale wll probabl be over t). Ta the dervatves of the Larae ltpler that orrespods to, wth respet to, v ad, respetvel, ad eqall the to zero, we obta the follow optzato forlas: v j 1 1 v /( 1) /( 1) v j, (11) 1, (1) 1 v 1 v. (13) Slarl to the ovetoal FCM, these optzato forlas are appled alteratvel eah terato..3. Soothe flter The test hooeet artefat vares slowl alo the ae. Ths propert s ored b both the bas or a feld approahes preseted above. To avod ths proble, a flter tehqe s appled eah optato le, to soothe the bas or a feld. Ths flter trodes a extra step to eah optzato le, after proeed wth (8) or (13). Several, ot ol FCM-based INU opesato approahes appl lare szed, pxels wde avera flters perfored oe or several tes eah le (Wells et al., 1996; Zhao et al., 007). These flters effetl hde tsse detals, whh a appear the estated b or vales, bt also trasfer bas or a opoets to dstatl stated pxels. Us larer avera wdows aplfes ths latter desred effet. I order to rede the trasfer of bas data to dstat pxels, we eed to he the eesst of avera at all loatos, ad dede to proeed or sp the avera aordl. Avera s delared eessar or ot, based o the ax test dfferee eotered wth a sall ehborhood of the pxel. The optato of the ax dfferee s aoplshed b a orpholoal radet operato s a 3 3 sqare or slhtl larer rossshaped strtr eleet. Wherever the orpholoal radet vale exeeds the prevosl set threshold vale θ, the averaed bas or a vale wll be sed; otherwse the estated vale s valdated. The proposed flter a be easl pleeted ad effetl perfored b bath-tpe ae proess operatos..4. Mlt-stae bas ad a feld estato Bas or a feld estato s the prevos FCM-based approahes (Ahed et al., 00; Sal ad Y, 005; Zhao et al., 007) a ol hadle the INU artefat to a lted apltde. For a pxel, the FCM alorth asss the hhest fzz ebershp to the losest lster. Coseqetl, whe the INU apltde s oparable wth the dstae betwee lsters, these pxels wll be attrated b the wro lster, ad the bas or a feld wll be estated aordl. The soothe of the bas ad a feld a repar ths d of slassfatos, bt the larer these wrol labelled spots are, the harder wll be to elate the va sooth. I order to deal wth hh-apltde INU artefats, we propose perfor the bas or a feld estato ltple staes. Whe the FCM-based alorth ve b (6)-(8) of (11)-(13) has overed, we odf the pt (observed) ae aord to the estated bas or a feld: ( old ) ( old ) b, or /, (14) ad the restart the alorth fro the be, s the odfed pt ae..5. Alorth The preseted alorth a be sarzed as follows: 1. Reove the Gassa ad plse oses fro the MR ae s the otext depedet pre-flter tehqe.. Italze lster prototpes v wth rado vales that dffer fro eah other. 3. Italze the bas (a) feld vales wth 0-ea (1-ea) rado bers hav reded varae, or spl set b 0 ( 1 ) for a pxel. 4. Copte ew fzz ebershp fto vales, 1K, 1K, s (6) or (11),. 5. Copte ew lster prototpe vales v, (7) or (1). 1K, s 6. Perfor ew bas or a feld estato for eah pxel s (8) or (13). 7. Soothe the bas or a feld s the proposed sooth flter. 967

17th IFAC World Coress (IFAC'08) Seol, Korea, l 6-11, 008 8. Repeat steps 4-7 tl there s o relevat hae the lster prototpes.

Modf the pt ae aord to the estated bas or a feld s (14), ad repeat steps -8 tl the INU artefat s opesated. The alorth sall reqres a sle repetto.

RESULTS AND DISCUSSION We appled the preseted flter ad seetato tehqes to several T1-wehted real MR aes, artfall otaated wth dfferet ds of oses. F. 1.

Ihooeet orreto deostrated o a artfall otaated real MR ae: (a) oral, (b) FCM seetato wthot orreto, () reslt of FCMbased seetato wth o pre-flter, (d) reslt of FCMbased seetato wth otext sestve

. Ihooeet orreto s a phato: (a) oral, (b) FCM seetato reslt wthot orreto, () estated bas feld, (d) seetato reslt based o bas feld estato, (e) estated a feld, (d) seetato reslt based o a feld estato

4 17th IFAC World Coress (IFAC'08) Seol, Korea, l 6-11, Repeat steps 4-7 tl there s o relevat hae the lster prototpes. Ths s tested b opar a or of the dfferee betwee the ew ad the old vetor v wth a preset sall ostat ε. 9. Modf the pt ae aord to the estated bas or a feld s (14), ad repeat steps -8 tl the INU artefat s opesated. The alorth sall reqres a sle repetto. ara ad effe of the proposed seetato tehqe, s a real T1-wehted MR bra sle. The presee of the soothe flter spports the arate seetato, whle the pre-flter has a relarzer effet o the fal reslt. 3. RESULTS AND DISCUSSION We appled the preseted flter ad seetato tehqes to several T1-wehted real MR aes, artfall otaated wth dfferet ds of oses. F. 1. deostrates the effe of the pre-flter tehqe o a real MR sle tae fro Iteret Bra Seetato Repostor (Worth, 000). F. 3. Ihooeet orreto deostrated o a artfall otaated real MR ae: (a) oral, (b) FCM seetato wthot orreto, () reslt of FCMbased seetato wth o pre-flter, (d) reslt of FCMbased seetato wth otext sestve pre-flter F. 1. Elato of plse ad Gassa oses deostrated wth a real T1-wehted MR bra ae otaated wth artfal ose: (a) oral, (b) fltered, () FCM seetato after orreto F.. Ihooeet orreto s a phato: (a) oral, (b) FCM seetato reslt wthot orreto, () estated bas feld, (d) seetato reslt based o bas feld estato, (e) estated a feld, (d) seetato reslt based o a feld estato The reslts of bas ad a feld estato perfored o a phato ae are show F.. Covetoal FCM s able to opesate the INU artefat, bt wth the se of soothed bas or a feld, ths pheoeo s effetl overoe. I ase of low-apltde hooeet, a sle stae of bas or a feld estato s sffet. F. 3. shows the F. 4. Seetato of a heavl hooeeos real MR ae: (a) oral, (b) seetato wthot opesato, () bas feld estated the frst stae, (d) opesated MR ae after frst stae, (e) FCM-based seetato after frst stae, stll sable, (f) bas feld estated the seod stae, () fal opesated ae, (h) seeted ae, () a soothe as opted b the proposed flter F. 4. shows the teredar ad fal reslt of a seetato proess, perfored o a heavl INUotaated MR ae. The hooeet orreto seeds after two staes. F. 4() shows the behavor of the proposed flter tehqe: whte pxels date plaes 968

5 17th IFAC World Coress (IFAC'08) Seol, Korea, l 6-11, 008 whh reqred avera a ve optatoal le, whle bla oes sfes those plaes where avera was eessar. Table 1. Mslassfato rates ( %) wth varos soothe flters, ase of heavl INU-otaated MR aes Strtr eleet Avera wdow sze 11 Avera wdow sze 19 oe 3 tes Oe 3 tes Avera sqare ross ross ross Table 1. shows the slassfato peretaes of the proposed INU opesato ad MR ae seetato ethod, deped o the sze of the avera wdow expressed pxels, the strtr eleet of the orpholoal rtero of the proposed flter, ad the ber of soothe teratos perfored eah le of the odfed FCM alorth. The experetal data reveal that the proposed flter tehqe proves the seetato qalt assred b the avera flter. The best seetato was obtaed s a 3 3 sqare shaped strtr eleet sed b the orpholoal rtero, obed wth avera s a wdow sze of pxels. Us several repettve staes dr INU opesato a rede the test dfferee betwee tsse lasses, whh leads to slassfatos. That s wh the estato s lted to two steps, perfor several staes s ot reoedable. 4. CONCLUSIONS A ovel sooth flter has bee proposed to assst bas or a feld estato ebedded to the ovetoal FCM alorth shee. The proposed ethod proved to seet aratel ad effetl MR aes the presee of test o-fort. Althoh the proposed ethod seets -D MR bra sles, t ves a relevat otrbto to the arate voletr seetato of the bra, bease the seeted aes ad the obtaed fzz ebershps a serve as exellet pt data to a level set ethod that ostrts 3-D ortal srfaes. Frther wors a at develop a otext sestve pre-flter for the elato of INU artefats, too, so that the seetato a be perfored s a hstora-based q FCM alorth. ACKNOWLEDGEMENTS Ths researh was spported part b the Hara Natoal Researh Fds (OTKA) der Grat No. T069055, the Hara Natoal Offe for Researh ad Teholo (NKTH), the Sapeta Isttte for Researh Proras (KPI), ad the Cotas Fodato. REFERENCES Ahed, M.N., S.M. Yaa, N. Mohaed ad A.A. Fara (00). A odfed fzz -eas alorth for bas feld estato ad seetato of MRI data. IEEE Tras. Med. Ia., 1, Axel, L.,. Costa, ad. Lsterd (1987). Ihooeet orreto srfae-ol MR a. Aer.. Roeteol., 148, Bezde,.C. ad S.K. Pal (1991). Fzz odels for patter reoto. IEEE Press, Psatawa, N. Bra, B.H., A. Mada ad R.A. Robb (1998). Optzed hooorph sharp as for MR rasale hooeet orreto. IEEE Tras. Med. Ia., 17, Ca, W., S. Che, ad D.Q. Zha (007). Fast ad robst fzz -eas alorths orporat loal forato for ae seetato. Patt. Reo. 40, ohsto, B., M.S. Ats, B. Maewh, ad M. Aderso (1996). Seetato of ltple sleross lesos test orreted ltspetral MRI. IEEE Tras. Med. Ia., 15, Leept, K.V., F. Maes, D. Vaderele ad P. Setes (1999). Atoated odel-based bas feld orreto of MR aes of the bra. IEEE Tras. Med. Ia., 18, L, X., L.H. L, H.B. L ad Z.G. La (005). Partal vole seetato of bra aet resoae aes based o ax a posteror probablt. Med. Phs., 3, Lew, A.W.C. ad Y. Ho (003). A adaptve spatal fzz lster alorth for 3-D MR ae seetato. IEEE Tras. Med. Ia.,, Pha, D.L. ad.l. Pre (1999a). Adaptve fzz seetato of aet resoae aes. IEEE Tras. Med. Ia., 18, Pha, D.L. ad.l. Pre (1999b). A adaptve fzz C- eas alorth for ae seetato the presee of test hooeet. Patt. Reo. Lett., 0, Sal, M.Y. ad L. Y (005). A tellet odfed fzz C-eas based alorth for bas feld estato ad seetato of bra MRI. Patt. Reo. Lett., 6, Szlá, L. (006). Medal Iae Proess Methods for the Developet of a Vrtal Edosope. Peroda Polteha Ser. El. E., 50, Szlá, L., S.M. Szlá ad Z. Beó (007). Effet Featre Extrato for Fast Seetato of MR Bra Iaes. Let. Notes Cop. S., 45,

6 17th IFAC World Coress (IFAC'08) Seol, Korea, l 6-11, 008 Vov, U., F. Perš, ad B. Lar (007). A revew of ethods for orreto of test hooeet MRI. IEEE Tras. Med. Ia., 6, Wells, W. M., W. E. L. Grso, R. Ks, ad F. A. olesz (1996). Adaptve seetato of MRI data. IEEE Tras. Med. Ia., 15, Worth, A. (000) Iteret Bra Seetato Repostor. Zha, Y., M. Brad, ad S. Sth (001). Seetato of bra MR aes throh a hdde Marov rado feld odel ad the expetato-axzato alorth. IEEE Tras. Med. Ia., 0, Zhao, Q.,. So, ad Y. W (007). Iproved fzz - eas seetato alorth for aes wth test hooeet. Adv. Soft Copt, 41,

An alternative estimator for estimating the finite population mean in presence of measurement errors with the view to financial modelling

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