Quantification and Segmentation of Breast Cancer Diagnosis: Efficient Hardware Accelerator Approach

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1 Karlza Ota, Afad Aad Qatfato ad Segetato of Breast Caer Dagoss: Effet Hardware Aelerator Approa KHAIRULNIZAM OTHMAN Cetral of Dploa Stdes, Uversty T Hsse O 84600, Joor, MALASIA za@t.ed.y ttp://fee.t.ed.y/t-sr/ AFANDI AHMAD Ebedded Coptg Resear Clster Mroeletros ad Naoteology - Sasdd Resear Cetre (MNT-SRC Falty of Eletral ad Eletro Egeerg Uversty T Hsse O 84600, Joor, MALASIA afada@t.ed.y Abstrat: - Ts resear presets VLSI artetre for age segetato. Te artetre s based o te fzzy -eas algort wt spatal ostrat for redg te slassfato rate. I te artetre, te sal teratve operatos for pdatg te oogees ebersp atr ad lster etrod are erged to oe sgle pdatg proess to evade te large storage reqreet. I addto, a effet ppeled rt s sed for te pdatg proess for aeleratg te optatoal speed. Eperetal reslts sow tat te proposed rt s a effetve alteratve for real-te age segetato wt low area ost (te ad low slassfato rate. Key-Words: - fzzy -eas, age segetato, lsterg, FPGA, p Itrodto Breast aer s te ooest aer aog Malaysa woe all et grops []. A woa Malaysa as 0 ae of gettg a breast aer er lfete. Aordg to te Natoal Caer Regstry, te Age Stadardzed Rate (ASR of feale breast aer Malaysa s 47.4 per 00,000 poplatos 003 to 005 ad ts dropped to However, te ASR s ger ta tose oter Asa otres (Beg, 4.6, Hrosa 36.6, Cea 3.9 ad Seol 0.8 []. Tere are varatos te dee rates of breast aer aog te tree a et grops Malaysa. Aogst te Cese, te ASR s gest at 59.9 per 00,000 poplato, for te Idas, te ASR s 54. per 00,000 ad t s lowest te Malays at 34.9 per 00,000 poplato. Breast aer aoted for 3.3% of te total ber of te ew ases woe []. Tese dfferees ay be attrbted to te dfferees lfestyle, det ad reprodtve beavor aely tose tat relates to ldbearg ad breastfeedg prates. Stdes o breast aer ave bee approaed for ay years fro dfferet agles of portae; be t te ase of te dsease, te deteto of te dsease, te dagoss systes, etod of treatets before ad after srgery. Tese stdes ave bee dvded to two paradgs, oe w defes breast aer dsease as a loal ad regoal dsease; ad aoter as a systeat dsease. Te role of a srgeo aloe s adeqate for te breast aer tat s tally at a loal ad regoal dsease proess. However, we te breast aer s a systeat dsease te te volveet of systeat treatets s eeded besdes te srgery aloe to re t ad tere wll be a role for earler deteto of breast aer. Breast aer sreeg progras attept to detet ad eradate aer at te earlest possble stage to rease te rate of srvval aogst woe. Te early deteto of breast aer greatly proves te progoss. Oe of te earlest sgs of aer s te forato of lsters of ro-alfatos. E-ISSN: Isse 5, Vole, May 03

2 Karlza Ota, Afad Aad Altog las ave te past bee reltat to se optatoal approaes dagost applatos, t s ow osdered tat te se of advaed g perforae etodologes wll be sefl adg las dagoss ad treatet plag. At preset, segetatos are aly oslted aally by edal spealsts. Altog ts tas appears sple, te realty s tat a dept owledge of aatoy ad pysology s reqred. Essetally, te epert observes a partlar age, deteres borders betwee regos ad lassfes ea rego. I addto to ts, to detfy saller age featres, otrast odfatos are ofte eeded. Altog, for a typal data, te etre epert aal segetato a tae several ors to opte, ts approa s peraps te ost relable ad arate etod of edal age segetato. Ts s de to te ese oplety of te a vsal syste, a syste well sted to ts tas. Ts rse a opportty for s to develop ardware for prospetvely evalated a opter-aded deteto (CAD deve sed wt data fro aograpy by assessg breast aers deteted; tor szes, stology, ad stage. Isgt aqred trog ts resear s epeted to be sefl for te developet ardware, w s detfed breast aer to be relevat to bo-ed egeerg proble solvg. Gve te assve voles of aograpy age data to be proessed, ad te osderable optatoal oplety of te algorts tat are volved, t s lear tat see a be pt to effet pratal se oly f effet ardware oproessg strateges are developed. Te appearae of fast reofgrable feld prograable gate arrays (FPGAs brgs abot a ew pat for te desg of s systes. FPGAs a perfor ateatal operatos o a etre vetor or atr at te sae te, ad te rret geerato of DSP-apable FPGAs yelds ltra-g perforae ad gly fleble sgal-proessg systes. FPGA-based pleetato also as te advatage of sort desg perod ad low ost of fabrato, w are stable for partal or oplete aelerato of varos algorts. Tese fators ae FPGAs a attratve platfor for pleetg te proposed segetato syste. However, te FPGAs preset lted resores to pleet ople ardware. Hee ltple FPGA board soltos or r-te otet swtg teqes provde te possblty of pleetg s ople syste by sg te ltpleg strateges. To esre syste tegrato ad tgt oplg betwee software proessg ad ardware aelerato sg FPGAs, t s essetal to develop stable ost applatos tat a be sed for te o-desg proess. Iage segetato plays a portat role opter vso ad age aalyss. Te segetato reslts a be sed to detfy regos of terest ad obets te see, w s very beefal to te sbseqet age aalyss or aotato. Te fzzy -eas algort (FCM [] s oe of te ost-sed teqes for age segetato. Te aray of FCM s de to te eployet of fzzess for te lsterg of ea age pel. Ts eables te fzzy lsterg etods to reta ore forato fro te orgal age ta te rsp or ard segetato. Altog te orgal testy-based FCM algort ftos well o segetg ost osefree ages, t fals to seget ages orrpted by ose, otlers ad oter edal agg. Te FCM wt spatal ostrat (FCM-S algorts [3] [5] ave bee proposed to solve ts proble by orporatg spatal forato to orgal FCM obetve fto. However, as opared wt te orgal FCM algort, te FCM-S algorts ave ger optatoal opletes for ebersp oeffets optato ad etrod pdatg. I addto, slar to te orgal FCM algort, te sze of oogees ebersp atr grows as te prodt of data set sze ad ber of lasses te FCM-S. As a reslt, te orrespodg eory reqreet ay prevet te algort fro beg appled to ages wt g deso. To aelerate te optatoal speed ad rede te eory reqreet of te orgal FCM, a ber of algorts [6] [9] ave bee proposed. Tese fast algorts a be eteded for te pleetato of FCM-S. However, ost of tese algorts are pleeted by software, ad oly oderate aelerato a be aeved. I [0] [], ardware pleetatos of FCM are proposed. Neverteless, te desg [9] s based o aalog rts. Te lsterg reslts terefore are dfflt to be dretly sed for dgtal applatos. Altog te artetre sow [] adopts dgtal rts, te artetre as for applatos wt oly two lasses. I addto, t ay be dfflt to eted te artetre for te ardware pleetato of FCM-S. Te artetre preseted [] operates wt oly a fed degree of fzzess for te orgal FCM. Te E-ISSN: Isse 5, Vole, May 03

3 Karlza Ota, Afad Aad fleblty for seletg oter degrees of fzzess ay be desred to frter prove te FCM perforae. I addto, slar to [], te artetre preseted [] aot be dretly sed for te ardware pleetato of FCM-S. Te artetre relaes te restrto o te degree of fzzess. Te relaato reqres te eployet of -t root ad dvso operatos for ebersp oeffets ad etrod optato. A ppele pleetato for te FCM-S terefore ay be dfflt. To solve te proble, te proposed artetre, te -t root operators ad dvders are based o sple table loop, ltplato ad sft operatos. Effet ppele rts a te be adopted to eae te trogpt for fzzy lsterg. To rede large eory sze for storg ebersp atr, te proposed artetre obes te sal teratve pdatg proesses of ebersp atr ad lster etrod to a sgle pdatg proess. I te artetre, te pdatg proess s separated to tree steps: preoptato, ebersp oeffets pdatg, ad etrod pdatg. Te pre-optg step s sed to opte ad store forato oo to te pdatg of dfferet ebersp oeffets. Ts step s beefal for redg te optatoal oplety for te pdatg of ebersp oeffets. Te ebersp pdatg step optes ew ebersp oeffets based o a fed set of etrods ad te reslts of te preoptato step. All te ebersp oeffets assoated wt a data pot wll be opted parallel ts step. Te optato te of te FCM-S terefore wll be effetvely epedted. Te etrod pdatg step optes te etrod of lsters sg te rret reslts obtaed fro te ebersp pdatg step. Te wegted s of data pots ad te s of ebersp oeffets are pdated reetally ere for te etrod optato. Ts reetal pdatg see elates te reqreet for storg te etre ebersp oeffets. Te proposed artetre as bee pleeted o feld prograable gate array (FPGA deves [3] so tat t a operate oto wt a soft-ore CPU [4]. Usg te reofgrable ardware, we are te able to ostrt a syste o prograable p (SOPC syste for age segetato. Te proposed artetre atta lower lassfato error rate te presee of ose. I addto, opared wt ts software oterpart rg o te.53 GHz Itel Core Do, or syste as sgfatly lower optatoal te. All tese fats deostrate te effetveess of te proposed artetre. Cotrbtos to te Developet of -Meas Clsterg Models Itrodto We frst gve a bref revew of te FCM algort. Let X {,..., t } be a data set to be lstered by te FCM algort to lasses, were t s te ber of data pots te desg set. Ea lass,, s araterzed by ts etrod v. Te goal of FCM s to ze te followg ost fto: J t µ p v ( were, s te ebersp of lass, ad > dates te degree of fzzess. Te ost fto J s zed by a two-step terato te FCM. I te frst step, te etrods v,..., v, are fed, ad te optal ebersp atr {,,,...,,,..., t} s opted by, /( ( After te frst step, te ebersp atr s te fed, ad te ew etrod of ea lass s obtaed by t v t,, (3 A varat of FCM for age segetato s FCM- S, wose obetve fto s [] E-ISSN: Isse 5, Vole, May 03

4 Karlza Ota, Afad Aad J t v, v α ( + ard Γ t, Γ (4 v ard ( Γ Γ (8 were Γ s te set of egbors assoated wt, ad te Card(Γ s te ardalty of te set Γ. Te paraeter α deteres te degree of pealty. Te eessary odtos loally zg J are te gve by Note tat a be opted advae, ad te zato of J Eqato (4 s eqvalet to te zato of te followg ost fto., v v α + ard ( Γ α + ard ( Γ Γ v Γ v /( /( (5 t t, v + α, v J (9 Neessary odtos o, ad v for loally zg J a be derved are follows. v α t +, ( Γ ard ( Γ t ( + α, (6, v v + α v + α v /( /( (0 Te dsadvatages of Eqatos (5 ad (6 are te g optatoal opletes for optg, ad v. To aelerate te optato, observe fro (3 tat by sple aplato, v t, ( α ( + α t, ard( as ard( Γ Were Γ v Γ Γ v a be eqvaletly wrtte ( ard( Γ Γ + v (7 ( Te FCM ad FCM-S algort reqres large ber of floatg pot operatos. Moreover, fro Eqatos [5], [6], [7] ad [8], t follows tat te ebersp atr eeds to be stored for te optato of ost fto ad etrods. As te sze of te ebersp atr grows wt te prodt of t ad, te storage sze reqred for te FCM ay be pratally large we te data set sze ad/or te ber of lasses beoe g. Te pre-optato t s sed for redg te optatoal oplety of te ebersp oeffets allato. Observe tat, Eqato ( a be rewrtte as E-ISSN: Isse 5, Vole, May 03

5 Karlza Ota, Afad Aad /(, p Were ( ppeled faso. I te proposed -t root rt, te goal s to opte, were (q + y + y yq p /( (3 Tat s, s a q-bts real ber s tat < <. We separate to two portos ad l as sow below Gve ad etrods v,..., v, ebersp oeffets,,...,, ave te sae P. Terefore, te oplety for optg ebersp oeffets a be reded by allatg P te pre-optato t. Wtot loss of geeralty, te degree of fzzess a be epressed as a / b (4 were bot a ad b are tegers. Bease sold be larger ta, t follows tat a > b > 0. Let r b, a b We te a rewrte Eqato (3 as (5 (q + y + y yq ( q+ ( q+ (q l yq+ + yq yq (7 (8 For te sae of splty, we frst osder te optato of. Observe tat / / l 3l ( + / / / ( + ( + / 8 l By retag te frst two ters of te Taylor seres, a be approated by l... p ( r / (6 / l ( ( l 3/ / Based o Eqato (6, we see tat te -t root operato s reqred for te pleetato of p. I te proposed artetre, a ovel -t root rt s adopted so tat P a be pleeted a Fro Eqatos (7 ad (8, we olde tat > q l. Terefore, te a error of te approato s less ta q. Followg te sae proedre, t a also be fod tat E-ISSN: Isse 5, Vole, May 03

6 Karlza Ota, Afad Aad 3 ( / ( + / / 3 + l / 3 / 3 / 3 l l ( 3 ( +... l 5/ 3 / 3 Tese reslts a be eteded for ay as follows: 3.0 Te Proposed Artetre Te goal of te proposed artetre s to pleet te FCM-S algort ardware. Te artetre s based o a ovel ppele rt to provde g trogpt for fzzy lsterg. It s also able to elate te reqreet for storg te large ebersp atr for te optato of ost fto ad etrods. ( ( / / ( l (9 Te -t root rt based o Eqato (9 s sow Fgre, w ossts of two tables, two ltplers, ad oe adder. Te tables store ( / ( l / ad for all te possble vales of l ad. Altog t s possble to ostrt a table dretly for, te ber of etres te table wold be q bease otas q bts. By otrast, bot ad l osst of oly q bts. Te ber of etres ea table sow Fgre s oly q. Coseqetly, te proposed rt s able to perfor fast ad arate optato wle atag low area ost. 3.. FCM-S Artetre Te goal of te ea optato t s to evalate te ea vale defed Eqato (8. Te a artetre of FCM-S s te fzzy lsterg t, w optes te ebersp oeffets ad etrods of FCM-S. Terefore, or dssso ts sbseto wll fos o te fzzy lsterg t of te FCM-S. Usg Eqatos (4 ad (5, we a rewrte te ebersp oeffets of FCM-S defed Eqato (0 as / / r ( + r, (( v + α p (3 Were p ( + α r / (4 Fg. : Te artetre of -t root t. Slar to te orgal FCM, t follows fro Eqato (4 tat te optato of P a also be separated to ters, were te -t ter volves te optato of ( + α r/. Fgre 9 sows te artetre for te optato of ea ( + α r/. Fro Fgre 9, we see tat te artetre a also be pleeted as a 4-stage ppele, slar to tat sow Fgre 3(b for optg ( r/. Terefore, te pre-optato t for FCM-S a be realzed as a 4 stage ppele. E-ISSN: Isse 5, Vole, May 03

7 Karlza Ota, Afad Aad Fg. : Te FCM-S artetre. Fg. 3: Te rt for evalatg ( + α r / Te oly dfferee s tat te frst stage of te ppele Fgre 3 as ger area ad optatoal opletes. Tere are two sqared dstae allato ts ad oe adder at te frst stage of te ppele Fgre 3. Fgres 4 6 dept te artetre for ebersp oeffets pdatg, etrods pdatg ad ost fto optato for FCM-S based o Eqatos (9, ( ad (3, respetvely. Slar to te orgal FCM algort, te proposed FCM-S artetre optes te etrods ad ost E-ISSN: Isse 5, Vole, May 03

8 Karlza Ota, Afad Aad fto reetally. I te FCM-S, te reetal etrod for te -t lster p to data pot s defed as v (, ( + α ( + α, (5 J (, + α (6 As sow Fgres 5 ad 6, te goals of te etrods pdatg t ad te ost fto optato t are to opte v ( ad J(, respetvely. As t, te v ( ad J( Eqatos (5 ad (6 wll beoes v( Eqato ( ad J Eqato (9, respetvely. Fg. 4: Te rt for evalatg, for FCM-S. Fg. 5: Te rt for allatg v ( for FCM-S. E-ISSN: Isse 5, Vole, May 03

9 Karlza Ota, Afad Aad Fg. 6: Te rt for allatg ost fto J( for FCM-S. We a vew te ebersp oeffets, etrods ad ost fto for FCM-S as te eteso of tose for orgal FCM by replag wt + α. Terefore, te ebersp oeffets pdatg t, etrods pdatg t ad ost fto optato t for FCM-S also ave slar artetres to tose of ter oterparts orgal FCM. Te rts FCM- S reqre oly addtoal sqared dstae t ad adder for optg + α Te SOPC Syste Based o te Proposed Artetre Te proposed artetre s sed as a sto ser log a SOPC syste osstg of softore NIOS CPU, DMA otroller ad SDRAM, as depted Fgre 3. Te set of trag vetors s stored te SDRAM. Te trag vetors are te delvered to te proposed rt by te DMA otroller. Te softore NIOS CPU s rg a sple software for FCM. It does ot partpate te parttog ad etrod optato proesses. Te software oly atvates te DMA otroller for te delvery of trag vetors. Te CPU te reeves te overall dstorto of lsterg fro te proposed rt after te opleto of DMA operato. Te sae DMA operato for delverg te trag data to te proposed rt wll be repeated tl te ost fto J overges. Te CPU te ollets te etrod of ea lster fro te proposed rt as te lsterg reslts. Fg. 7: Te SOPC syste for FCM-based age segetato. 4.0 Eperetal Reslts Ts seto presets soe eral reslts of te proposed FCM-S artetre for age segetato. Te desg platfor of or syste s Altera Qarts II wt SOPC Blder ad NIOS II IDE. Te target FPGA deve for te ardware pleetato s Altera DE board [0]. For sae of brevty, te ages osdered ts seto are gray-level ages. Ea data pot represets a pel wt gray level vales te rage betwee 0 ad 55. For olor ages, ea pel beoes a vetor osstg of tree olor opoets: red, gree ad ble. I te proposed artetre, ea data pot a be a salar or a vetor. Terefore, te proposed artetre a be dretly appled to olor age segetato by pleetg as a 3-deso vetor. Te perforae of te age segetato s easred by segetato error rate, w s eqal to te ber of slassfed pels dvded by te total ber of pels. Seto ossts te optg of te peretage orrespodg to te approatos vetors ad te detals vetors. I te followg table are sow te opted vales of ea oeffets obtaed sg a fzzy ea for a alg ad a beg ase saple w tae fro MIAS Database. E-ISSN: Isse 5, Vole, May 03

10 Karlza Ota, Afad Aad Te orgal MIAS Database (dgtzed at 50 ro pel edge as bee reded to 00 ro pel edge ad lpped/padded so tat every age s pels. Ts s very sefl for edal resear prpose. MIAS Database also provdes arater of bagrod tsse, lass of aboralty, Severty of aboralty ad te oordate ad rads for t. I te odel, te resltg lsters to 7 are sow sperposed po te aogra data. As Fzzy-C Meas s a teratve algort, te eters of te lsters ew terato are sow sg dfferet olors te orgal age. Bold wte s te fal lsterg ad prevos teratos are sow gray spetr edted aogra. Altog reate dfferet oeffets sperposed lster eters, t does a deet ob of lsterg ts data. Besdes te lsterg reated dfferet folder ad saved as lster 0 to 6 (for lsterg 7 PNG forat fle. Te reslt for breast aer age wll be sow oe of te rsted age. Tese proveets te way we age ad dagose breast aer. Frterore, t elps te radology ad edal persoal ter daly rote to aalyss Breast aer aogra. Pratally speag, o dffltes ave ever bee eotered, ad eral overgee s sally aeved 0-5 teratos. Ts s depedg o te grey dstrbto ad te pel sze of te age. Weter loal a good lsterg s aoter atter, for t s easy to obta data sets po w p zes globally wt vsally appealg sbstrtre. To tgate ts dfflty, several types of lster valdty ftoal are sally allated o ea µ proded by FCM. Aog te ost poplar are te partto by allato of te etrod of te -t lster s aeved sg eqato (6. Reslt Fgre 8 sow te teratos over segetato reslt tat opted wt ot trag ad spervso. Fg. 8 Eperet aogras age wt dfferet pt Iteratos ad ed segetato. We evalated or algort o a seres of ages ldg te oes sow o te rgt sde Fgre 8. Ts oted by loadg dfferet breast aer dagoss for MIAS database. To see ow or algort fares t ters of effey we odted speed tests for all aogra MIAS Database by easrg ow log tey tae tl te fal lsterg (.e. tl te algorts ave overged. I order to arrve at fgres w are depedet of te ardware ofgred [9], we stadardze te so tat te fast algort s assged by settg lsterg 7 ad terato 5, prode g aray ad ger preso for te root age reated. E-ISSN: Isse 5, Vole, May 03

11 Karlza Ota, Afad Aad (a Orgal Maogra (b Segeted ( Clster 7(Target Fg. 9 (a s te orgal Maogra age ad 8 (b s te Segeted age. Te age s Clster to fve doat regos as sow o 9 ( -8 (. ( Clster (d Clster Reslt eperet for two dfferet Severty of aboralty breast aer sow grap Fgre 0 ad Fgre. Te reslt for Beg aboralty s 98.4% wle Malgat aboralty s 97.%. Eperet odted by opare te orgal dagoss rego w fro MIAS Database wt te age lster (te breast aer rego. Reslt Segetato 8 Segetat 7 6 Beg Malga Iterato (e Clster 3 (f Clster 4 Fg. 0 Reslt for Beg ad Malgat breast aer aogras age segeted wt dfferet pt Iteratos. Reslt Aray Beg Malga Iteratos (g Clster 5 ( Clster 6 E-ISSN: Isse 5, Vole, May 03

12 Karlza Ota, Afad Aad Fg. Aray reslt for Beg ad Malgat breast aer. 5.0 Coldg Rears Te proposed FCM-S artetre as bee fod to be effetve for edal age segetato. To lower te segetato error rate, te proposed artetre, te spatal forato s sed drg te FCM trag proess. Te artetre a also be desged for dfferet vales of degree of fzzess to frter prove te segetato reslts. I addto, te artetre eploys g trogpt ppele to eae te optato speed. Te -t root rts ad verse operato rts te artetre are desged by sple loop tables ad ltplers for lowerg te ardware resore ospto. Early eperetal reslts reveal tat te proposed artetre s able to aeve segetato error rate dow to 5% for osy ages. Codt for ftre aalyss wt te real Dgtal Maogra Mae ad ts resear predt sefl for Breast Caer Progoss. I addto, te SOPC artetre attas speedp p to 50 over ts software oterpart. Te proposed artetre terefore s a effetve alteratve for applatos reqrg real te age segetato ad aalyss. Referees: [] L SR, Hala. Caer Idee Peslar Malaysa Te Trd Report of te Natoal Caer Regstry Malaysa. Kala Lpr: Natoal Caer Regstry, Malaysa 008. [] Bezde, Jaes C. Fzzy sets approate reasog ad forato systes. Klwer Aade, 999, ISBN: [3] Aed MN, aay SM, Moaed N, Farag AA, Morarty T. A odfed fzzy C-eas algort for bas feld estato ad segetato of MRI data. IEEE Tras. Med. Iagg. 00;: [4] Ca, Welg, Soga Ce, ad Daoqag Zag. "Fast ad robst fzzy -eas lsterg algorts orporatg loal forato for age segetato." Patter Reogto 40.3 (007: [5] Ke-S Cag, Hog-Log Tzeg, Saro Ce, Jay W, Tzog-Jer. "Fzzy -eas lsterg wt spatal forato for age segetato." opterzed edal agg ad graps 30. (006: 9-5. [6] Cao R, Dave J, Bezde J. Effet pleetato of te fzzy -eas lsterg algort. IEEE Tras. Patter Aal. Ma. Itell. 986;8: [7] Ceg, Ta Wa, Dtry B. Goldgof, ad Lawree O. Hall. "Fast fzzy lsterg." Fzzy sets ad systes 93. (998: [8] Esr, S.; Jgwe Ke; Hall, L.O.; Goldgof, D.B.;, "Fast arate fzzy lsterg trog data redto," Fzzy Systes, IEEE Trasatos o, vol., o., pp. 6-70, 003 [9] Kole, Jo F., ad T Hteso. "Redg te te oplety of te fzzy -eas algort." Fzzy Systes, IEEE Trasatos o 0. (00: [0] Hwag, We-Jy, Ze-Ceg Fa, ad Tsg- Mao Se. "Uspervsed Iage Segetato Crt Based o Fzzy C-Meas Clsterg." CENICS 0, Te Fft Iteratoal Coferee o Advaes Crts, Eletros ad Mro-eletros. 0. [] Jesús Lázaro, Jagoba Aras, José L. Martí, Carlos Cadrado, Arado Astarloa. "Ipleetato of a odfed Fzzy C-Meas lsterg algort for real-te applatos." Mroproessors ad Mrosystes 9.8 (005: [] L H, ag CT, Hwag WJ. Effet vls artetre for fzzy -eas lsterg reofgrable ardware. Proeedgs of Te 4t Iteratoal Coferee o Froter of Copter See ad Teology; Saga, Ca. 7 9 Deeber 009; pp [3] Ha S, Deo A. Reofgrable Coptg: Te Teory ad Prate of FPGA- Based Coptg. Morga Kafa; Sa Frasso, CA, USA: 008. [4] NIOS II Proessor Referee Hadboo. Altera Corporato; Sa Jose, CA, USA: 0. Avalable ole: ttp:// (aessed o 0 Deeber 0 E-ISSN: Isse 5, Vole, May 03

13 Karlza Ota, Afad Aad [5] L SR, Hala. Caer Idee Peslar Malaysa Te Trd Report of te Natoal Caer Regstry Malaysa. Kala Lpr: Natoal Caer Regstry, Malaysa 008. [6] Bezde, Jaes C. Fzzy sets approate reasog ad forato systes. Klwer Aade, 999, ISBN: [7] Aed MN, aay SM, Moaed N, Farag AA, Morarty T. A odfed fzzy C-eas algort for bas feld estato ad segetato of MRI data. IEEE Tras. Med. Iagg. 00;: [8] Hwag, We-Jy, Ze-Ceg Fa, ad Tsg- Mao Se. "Uspervsed Iage Segetato Crt Based o Fzzy C-Meas Clsterg." CENICS 0, Te Fft Iteratoal Coferee o Advaes Crts, Eletros ad Mro-eletros. 0. [9] Jesús Lázaro, Jagoba Aras, José L. Martí, Carlos Cadrado, Arado Astarloa. "Ipleetato of a odfed Fzzy C-Meas lsterg algort for real-te applatos." Mroproessors ad Mrosystes 9.8 (005: [0] Strat II Deve Hadboo; Altera Corporato: Sa Jose, CA, USA, 0. Avalable ole: ttp:// (aessed o 0 Deeber 0. E-ISSN: Isse 5, Vole, May 03