Analysis Of Clustering Algorithms for MR Image Segmentation Using IQI

Transcription

1 Avalable ole a Proeda Teholog 6 (0 ) d Ieraoal Coferee o Couao, Copug & Seur [ICCCS-0] Aalss Of Cluserg Algorhs for MR Iage Segeao Usg IQI S. Pael, K.S.Paa Depare of Copuer See ad Egeerg, Brla Isue of Teholog Mesra, Rah-8355(Ida) Absra Ths paper preses he aalss of luserg algorhs for edal MR (age resoae) ages usg IQI (age qual de). The luserg algorhs used are lassal C eas, fuzz C eas ad rough fuzz C eas. Wh he asssae of he lower ad upper approao of rough ses, he rough fuzz C eas luserg algorh proves he objeve fuo ad furher he dsrbuo of ebershp fuo for he radoal fuzz C eas luserg. These algorhs are pleeed o varous edal MR ages o dee dseases. The resuls of varous luserg algorhs are opared usg IQI de, ad has bee foud ha rough fuzz C eas (RFCM) luserg algorh fars beer as opared o lassal C eas ad fuzz C eas algorh respevel. 0 Publshed b Elsever Ld. 0 The Auhors. Publshed b Elsever Ld. Seleo ad/or peer-revew uder resposbl of he Depare of Copuer Seleo ad/or peer-revew uder resposbl of he Depare of Copuer See & Egeerg, aoal Isue See of Teholog & Egeerg, Rourela aoal Isue of Teholog Rourela Kewords: Segeao; Cluserg; Classal C eas; Fuzz C eas; Rough se; Rough fuzz C eas; IQI.. Iroduo Segeao refers o he proess of parog he age o ulple seges (soe o-overlappg eagful hoogeeous regos) []. The goal of segeao s o splf ad/or hage he represeao of age o soehg ha s ore eagful ad easer o aalse. There are a segeao ehods suh as hresholdg, luserg, opresso based ehod, hsogra based ehod, edge deeo, rego growg ehod, spl ad erge ehod, segeao hrough eural ewors e. Cluserg deals wh fdg a sruure a olleo of ulabeled daa. A loose defo of luserg ould A luser s The Auhors. Publshed b Elsever Ld. Seleo ad/or peer-revew uder resposbl of he Depare of Copuer See & Egeerg, aoal Isue of Teholog Rourela do:0.06/j.pro

2 388 S. Pael ad K.S.Paa / Proeda Teholog 6 ( 0 ) o oher lusers. ogg. Fuzz Se Fuzz se heor s he eeso of oveoal (rsp) se heor []. I hadles he oep of paral ruh (ruh values bewee (opleel rue) ad 0 (opleel false)). The dea of fuzz ses s sple ad aural [6]. For sae, we wa o defe a se of gra levels ha share he proper dar. I lassal se heor, we have o deere a hreshold, sa he gra level 00. All gra levels bewee 0 ad 00 are elee of hs se, he ohers do o belog o he se (Fg. (a)). Bu he daress s a aer of degree. So, a fuzz se a odel hs proper uh beer. To defe hs se, we eed wo hresholds, sa gra levels 50 ad 50. All gra levels ha are less ha 50 are he full eber of he se, all gra levels ha are greaer ha 50 are o he eber of he se. The gra levels bewee 50 ad 50, however, have a paral ebershp he se.. Rough Se (a) (b) Fg. Represeao of "dar gra-levels" wh (a) rsp se ad (b) fuzz se. durg he earl 980s ad furher developed over he las 5 ears [] provdes a approah o approao of ses ha leads o useful fors of graular opug. The bas dea s o dsover o wha ee a gve se of objes (e.g., pel wdows a age) approaes aoher of se of objes of eres. Objes are opared b osderg her desrpos []. Rough se heor offers a ovel approah o aage uera ha has bee used for he dsover of daa depedees, porae of feaures, paers saple daa, feaure spae desoal reduo, ad he lassfao of objes... Iforao Sse A daa se s represeed as a able, where eah row represes a ase, a eve, a pae, or spl a obje. Ever olu represes a arbue (a varable, a observao, a proper, e.) ha a be easured for eah obje, he arbue a be also suppled b a hua eper or user. Ths able s alled a forao sse [5]. More forall, s a par Y = (U, A); where U s a o-ep fe se of objes alled he uverse ad A s a o-ep fe se of arbues suh ha a : U V a a A The se V a s alled he value se of a. Eaple. A ver sple forao sse s show Table.

3 S. Pael ad K.S.Paa / Proeda Teholog 6 ( 0 ) There are seve ases or objes (pels), ad oe arbue (Gra Value). Table. A eaple of a forao sse Pels X 0 X 50 X 3 00 X 4 00 X 5 00 X 6 55 X 7 00 Gra Value The reader wll easl oe ha pels 3 ad 4 as well as 5 ad 7 have eal he sae values of odos. The ases are (par wse) dserble usg he avalable arbues. I a applaos here s a ouoe of lassfao ha s ow. Ths poseror owledge s epressed b oe dsgushed arbue alled deso arbue; he proess s ow as supervsed learg. Iforao sses of hs d are alled deso sses [5]. A deso sse s a forao sse of he for Y ( U, A { d}), where d A s he deso arbue. A sall eaple deso able a be foud Table. The able has he sae seve ases as he prevous eaple, bu oe deso arbue (Cluser ) wh wo possble ouoes has bee added. The reader a aga oe ha ases 3 ad 4 as well as 5 ad 7 sll have eal he sae values of odos, bu he frs par has a dffere ouoe (dffere value of he deso arbue) whle he seod par has he sae ouoe. Table. A eaple Deso sse Pels Gra Value Cluser X 0 Yes X 50 o X 3 00 o X 4 00 Yes X 5 00 o X 6 55 Yes X 7 00 o.. Idserbl Idserbl eas possble o see or learl dsgush. Le Y = (U, A) be a forao sse, he wh a B A here s assoaed a equvalee relao ID Y (B): ID Y (B) = {(, ') U a Ba() a(' )} ID Y (B) s alled he B-dserbl relao [5]. If (, ') IDY ( B) equvalee lasses of he B dserbl relao are deoed [] B.

4 390 S. Pael ad K.S.Paa / Proeda Teholog 6 ( 0 ) The Idserbl relao for he above able s gve b ID({Gra value}) = },{ },{ }},{, },{, }}..3 Se Approao {{{ A equvalee relao dues a parog of he uverse (he se of ases our eaple). These paros a be used o buld ew subses of he uverse. Subses ha are os ofe of eres have he sae a rsp aer. For sae, he se of pels wh a posve ouoe ao be defed rspl usg he arbues avalable Tab.. desrpo of suh pels fro he able. I s here ha he oo of rough se eerges. Alhough we ao defe hose pels rspl, s possble o deleae he pels ha eral have a posve ouoe, he paes ha eral do o have a posve ouoe ad, fall, he pels ha belog o a boudar bewee he era ases. If hs boudar s o-ep, he se s rough. These oos are forall epressed as follows. B A ad X U Le Y = (U,A) be a forao sse ad le. We a approae X usg ol he forao oaed B b osrug he B-lower ad B-upper approaos of X, where, lower ( B( X )) { [ ] B X} ad upper( B( X )) { [ ] B X } The se; B B (X) = upper(b(x) / lower(b(x)) s alled he B-boudar rego of X, ad hus osss of hose objes ha we ao desvel lassf o X o he bass of owledge B. For our above eaple he lower ad upper approaos s gve b Le B = { Cluser() = Yes}, as gve b Tab.. We he oba he approao regos Lower approao, lower ( B ( X )) {, 6} Upper approao, upper ( B( X )) {, 3, 4, 6} Boudar rego, W ) { 3, } B B ( 4 Fg. Approag he se of pels usg he odoal arbue gra value. Equvalee lasses oaed he orrespodg regos are show.

5 S. Pael ad K.S.Paa / Proeda Teholog 6 ( 0 ) C Meas algorh C eas algorh s he bas luserg algorh. Ths algorh aes a pu daa (age) ad he uber of lusers o be osrued [0]. Ths algorh aes ol wo pass hrough he daa se. Seps of hs algorh s gve below Beg wh lusers, eah ossg of he frs saples. For eah of he reag saples fd he erod eares. Pu he saple he luser defed eares o. Afer a saple s assged, reopue he erod of he luser. Go hrough he daa for d e. For eah saple, fd he erod eares. Pu he saple he luser defed wh hs eares erod. 3. Fuzz C Meas algorh Fuzz -eas (FCM) s a ehod of luserg whh allows oe pee of daa o belog o wo or ore lusers. The advaage of FCM s ha assgs eah paer o eah luser wh soe degree of ebershp (.e. fuzz luserg). Ths s ore suable for real applaos where here are soe overlaps bewee he lusers he daa se [7]. Le X = {, } a se of gve daa. A fuzz pseudoparo or fuzz - paro of X s a fal of fuzz subses of X, deoed b P = {,,... } whh sasfes 0 for all for all ad, where s a posve eger Gve a pseudoparo P = {,,... }, he luser eers {v,v } assoaed wh he paro are alulaed b he forula v () for all, where > s a real uber ha govers he fluee of ebershp grades. The perforae de of a fuzz pseudoparo P, J (P), s he defed ers of he luser eers b he forula J P v () where. s soe er produ-dued or spae R p ad v represes he dsae bewee ad v. Therefore he goal of FCM s o fd a pseudoparo P ha zes he perforae de J (P) [3]. Seps of FCM

6 39 S. Pael ad K.S.Paa / Proeda Teholog 6 ( 0 ) Le = 0. Sele a al pseudoparo P(0). () Calulae he luser eers v () b he equao () for P () ad he hose value of. Updae P (+) b he followg proedure: For eah X, f v 0 for all, he defe = j v v j (3) If v 0 for soe C, he defe I for I b a o egave real ubers sasfg I =, ad defe = 0 for -I. Copare P ( ) ad P ( + ). If (P ( + ) P ( ) Here, s ool fed o ad s ow as he fuzzess paraeer. Ths hoe allows eas opuao of he ebershp values. Whe eds o he fuzz C- lassal C Meas. Whe eds o f, all luser eers ed owards he erod of he daase X. 4. Rough Fuzz C Meas algorh Based o he lower ad upper approaos of rough se, he rough fuzz -eas luserg algorh aes he dsrbuo of ebershp fuo beoe ore reasoable[4]. Le X={,,..., } be a se of objes o be lassfed, he h lass be deoed b w, s erod be v, ad he uber of lass be. The objeve fuo of RFCM algorh s gve b J (U,V) = j dj j, j upper( R( w )) We a also ge he ebershp forula for RFCM algorh as follows (4) j l, j upper( R( w )) d ( d j lj ) (5) Cerod forula s uhaged ha s

7 S. Pael ad K.S.Paa / Proeda Teholog 6 ( 0 ) v j j j j j Le = ( j ) represe he fuzz luser w assoaed wh he erod v. Afer opug j for lusers ad objes, he values of j for eah obje j are sored ad he dfferee of wo hghes ebershps of j s opared wh j ad j be he hghes ad seod hghes ebershps of j. (6) If ( j j he j lower(r(w )) as well as j upper(r(w )), oherwse j upper (R(w )) ad j upper(r(w )). Af ebershps j of he objes are odfed. The values of j are se o for he objes lower approaos, whle hose boudar regos are rea uhaged. The ew erods of he lusers are alulaed as per he above equao. The a seps of he RFCM algorh proeed as follows: Assg al erods v hresholds Se erao ouer =. j b equao (5) for lusers ad objes. If ( j j j lower(r(w )) as well as j upper(r(w )), Oherwse j upper(r(w )) ad j upper(r(w )). Furherore, j s o par of a lower boud. Oherwse, j lower(r(w )). I addo, b properes of rough ses, j upper(r(w )). j osderg lower ad boudar regos for lusers ad objes. Copue ew erod equao (6) Repea seps o 7, b reeg, ul j( j ( ) >. 5. Epereal resuls I hs seo epereal resuls o real edal MR ages are desrbed deals. Eah age s segeed b he above hree algorhs ad he resuls are opared. 5. Ipleeao All he ages are olleed fro Advaed Medare ad Researh Isue, Sal Lae, Kolaa, Ida [].The ages used are bra MR ages, breas MR ages, ad ee MR ages respevel. The segeed ages are show he fgures below. The frs se of ages used s bra MR age whh shows he spos of bra uour. Ths s a fuzz ad a lle blurred pe of age. The feed areas are show b he red arrows. Here we a see ha RFCM gves beer resuls as he blurred rego (daed wh red arrows) s well segeed wh respe o he oher wo. The uber of lusers used here s 5. The orre hoe of uber of lusers s ofe abguous, wh erpreaos depedg o he shape ad sale of he

8 394 S. Pael ad K.S.Paa / Proeda Teholog 6 ( 0 ) dsrbuo of pos a age ad he desred luserg resoluo of he user. I addo, reasg uber of lusers whou peal wll alwas redue he aou of error he resulg luserg, o he eree ase of zero error f eah pel s osdered s ow luser. The seod ages used for luserg s breas MR age. The red arrow shows he area of he breas whh s feed b breas aer. Fg. 4(b,,d) shows he resuls of all he luserg algorhs ad applao of RFCM gves ore proe resuls(see Fg.4(d)), Slarl, RFCM fars beer ase of ee MR ages (see Fg. 5(d)). The oparave aalss of hese algorhs are also doe usg IQI dsussed subseque seo 5.. (a) (b) () (d) Fg. 3 Coparso of segeao resuls o a Bra MR age (a) Orgal Iage (b) K Meas segeed () FCM segeed (d) RFCM segeed (a) (b) () (d) Fg. 4 Coparso of segeao resuls o a Breas MR age (a) Orgal Iage (b) K Meas segeed () FCM segeed (d) RFCM segeed 5. Iage Qual Ide (a) (b) () (d) Fg. 5 Coparso of segeao resuls o a Kee MR age (a) Orgal Iage (b) K Meas segeed ()FCM segeed (d) RFCM segeed I s based o easuree of sruural dsoro ad s a good approao of pereved age dsoro.

9 S. Pael ad K.S.Paa / Proeda Teholog 6 ( 0 ) A uversal easure ha odels a dsoro as a obao of hree dffere faors: loss of orrelao, easuree approah does o deped o he ages beg esed, he vewg odos or he dvdual observers [9]. If X= {, } ad Y= {, } are he orgal ad es age sgals, he he ew qual de s defed as where Q 4, (7),,,. As saed earler, Q s a produ of hree opoes: The da rage of Q s [-,]. Q ( ) ( ). (8) The IQI values obaed for he above luserg algorhs are show he Table 3 below. Greaer he value of IQI beer s he qual of age ad hus beer s he luserg algorh(see. Table 3). Table 3. IQI value for dffere luserg algorhs Cluserg algorh IQI value (for Bra MR age ) IQI value (for breas MR age) IQI value (for ee MR age ) C Meas Fuzz C Meas Rough Fuzz C Meas

10 396 S. Pael ad K.S.Paa / Proeda Teholog 6 ( 0 ) Coluso The aalss of luserg algorhs for edal MR (age resoae) ages usg IQI (age qual de) s doe. The luserg algorhs used are lassal C eas, fuzz C eas ad rough fuzz C eas. Wh he asssae of he lower ad upper approao of rough ses, he rough fuzz C eas luserg algorh proves he objeve fuo ad furher he dsrbuo of ebershp fuo for he radoal fuzz C eas luserg. These algorhs are pleeed o varous edal MR ages o dee dseases. The resuls of varous luserg algorhs are opared usg IQI de, ad has bee foud ha rough fuzz C eas (RFCM) luserg algorh fars beer as opared o lassal C eas ad fuzz C eas algorh respevel. 7. Referees Defao Ad Applaos of a Fuzz Iage Proessg Shee Isue of Teholog, Meo Ave. Teologo 909, Chhuahua, Chh., Meo [] M.I. Chao, "Fuzz Barzao ad Segeao of Te Iages for OPCR," Ieraoal Coferee Sgal Proessg Applao ad Teholog, Boso Massahuses U.S.A., pp , 996. [3] Sopor Chura- Fuzz C Mea : A sasal feaure lassfao of e ad age segeao ehod. Rough-Fuzz Cluserg Algorh for Segeao of Bra MR Iages [5] Rough Se : A uoral [6] hp://pa.uwaerloo.a/zhoosh/fp.h Fuzz Models for Iage Proessg ad Applaos -90. [8] Aboul Ella Hassae, Ajh Abrah Rough Ses ad ear Ses Medal Iagg: A Revew Iforao Teholog Boede, Vol. 3,o. 6, oveber 009 A Uversal Iage Qual Ide [0] Pawa Kuar,Dee Coparave Aalss of FCM ad HCM Algorh o Irs Daa Se Ieraoal Joural of Copuer Applaos ( ) Volue 5 o., Augus 00 [] Advaed Medare ad Researh Isue, Sal Lae, Kolaa, Ida [ ] Aboul Ella Hassae, Ajh AbrahaJaes, F. Peers, ad Gerald Shaefer, A Overvew of Rough-Hbrd Approahes Iage Proessg