Luận văn Nhận diện cá nhân dựa trên chữ viết tay tiếng việt bằng phương pháp lọc gabor

Trang9 Chudng2 KE T CAU vA TRicR D~C TRUNG KE T CAU Trichd~ctntngla mQtchilenangquailtrQngcuamQth~th6ngnh~ndC;lngnoi chungvacuamQth~th6ngnh~ndi~ncanhandvatrenchITvie'tlaynoi rieng. Khaini~mke'tca'udu'Qcxua'thi~n(j hffuhe'tcacIOC;lianh.ddo,nolamQtda'u hi~uquailtrQngd~phantichcacanh. Chu'ongnaysetrinhbaycacthai ni~mlienquailde'nke'tca'u.Cacphu'ongphap trichcacd(ictrungkgtcduse du'Qcdu'ara clingvoi nhungdanhgia chom6i phu'ongphap.Tuy nhien,phu'ongphapma tr~ntu'ongtranhmilc xam(Gray LevelCo- occurrenceMatrice)vaphu'ongphapbi)irc Gaborsedu'Qctrinhbay chitie'tvi haiphu'ongphapnay du'QcsU'dt;mgra'tthanhcongtrongcacling dl,mg ? tu'ongtvnhu'lu~nvannay.D~cbi~tbi)irc Gaborsedu'Qclu~nvanIvachQnde thlfchi~nvi~ctrichd~ctru'ngke'tca'ucuacacanhtaili~uvie'tlaytie'ngVi~t. 2.1Ke'tci(u(Texture) [3] Trangnhi€u thu~tloanxU'ly anhva thi giacmaytinh,thu'ong ia thie'tcac cu'ongdQsangcuacacvungC1,1CbQtronganhla d€u nhu'nhau.Tuynhien,cac anhtrangthvcte'thu'ongthongth~hi~ncacvungC1,1CbQco caccu'ongdQsang d€unhu'nhau.Vi d1,1,anhcuamQtb€ m~tlambAngg6cocacvungcocu'ongdQ sangthongd€u. M~cduv~y,cacthayd6icaccu'ongdQsangIC;lihinhthanhcac m~ucotinhcha'tl~pIC;livatinhcha'tnaydu'QcgQilakgtcdutr{tcgiac[3]. Hi~nnay,ke'tca'ula mQtthai ni~mthongco dinhnghiaho~cra'tkhod~dinh nghIake'tca'u.Nhi€u taili~uv€ phantickkgtcdudu'QcbAtdffubAngcachthong Trang10 duaramQtdinhnghlachinhxacv€ k€t cffu.Clingnhu'v~y,mQts6adli<$ucod€ c~pd€n k€t cffuthu'ongboquadinhnghlav€ k€t cffuho~cchidu'aramQtdinh nghlathichhQpvoingfi'canhdangxet. Tuyv~y,sauday,lu~nvanseneura mQts6dinhnghlad~ngu'oidQcco th~ thamkhao. . Chungtaco th~xemk€t cffunhu'nhfi'ng i t~othanhmQtvungco th~thffy duQcb~ngmiitthu'ong.CffutrUccuavungnayla nhfi'ngd~cdi~mth~hi<$n cacmftul~pl~imacacthanht6t~othanhcacmftunaydu'Qcb6tritheomQt quylu~tnaodo[3]. . MQtvungtrongmQtanhco mQtk€t cffuc6 dinhn€u mQtt~pcacth6ngke Cl,lcbQho~ccactinhchfftCl,lCbQkhaccoth~nhinthffydu'Qcla c6dinh,thay d6ich~m,ho~cg~nnhu'cochuky [3]. . MQtk€t cffuanhdu'Qcmotabdi s61u'Qng,ki~ucuacacthanht6t~onenk€t cffuvasl1b6tricacthanht6naytheokhonggian[3]. . Khai ni<$mk€t cffuxuffthi<$nphl,lthuQcvao ba y€u t6: (i) mQtthutl1Cl,lCbQ naodo du<Jcl~pl~itrenmQtvung IOn(so sanhtheokich thu'occua thutl1), (ii) thut1!hinhthanhb~ngsl1b6tri khongngftunhiencuacacthanht6,va (iii)cacthanht6la cacthl1cth~gi6ngnhautheomQtcachtho[3]. . Ke'tcffula mQtthuQctinhbi~udi~nsl1b6tri theokhonggiancuacacpixel trongmQtvung[8]. . Ke'tcffuth~hi<$ndcactinhchfftnhu'tho,mill,vad€u [8]. . Ke'tcffula sl1l~pl~icacph~ntti'k€t cffucdbandu'<JcgQila texel(TEXture ELement).TexelchuamQts6pixelvoimQtsl1b6tritheochuky,g~nnhu'co chuky,ho~cngftunhien.K€t cffucuacacanhtl1nhienthu'ongla ngftunhien trongkhik€t cuacacanhnhant~othu'ongtheomQtquicachnhfftdinhho~c Trang11 c6chuky.K€t cc1ucoth~la tho,mill,trail,d€u, tuy€ntinh,cod~ngs6ng,co d~ngh~tV.v...[8]. . Cac vungc6 k€t cc1ula cac m~utnli dai theokhonggiand1,1'atrens1,1'l~pl~i nhi€u hayit cuamQtthanhto'naod6 [8]. . K€t cc1ula mQtt~pcac tinh chc1tIan c~nCl;1CbQtheocac milc xamcuamQt vunganh[19]. . K€t cc1u lanhii'ng lmaconngu'oicamnh~n hu'la k€t cc1u [14]. . Theotudi~nWebster:k€t cc1ula d~cdi~mcc1utruccuacacsQidu'Qcd~tl~i vOinhau.Cc1utrucnayd~ctru'ngchomQtv~tli~u,mQtdO'itu'Qngtheocac kichthu'oc,hlnhdang,cachbO'tri,va s1,1'candO'igiii'achungvoi nhau[20]. Ifmh2.1saudayseth~hi~nmQtsO'lo~ianhk€t cc1ukhacnhau. ffinh2.1Caclo~ianhk€t cc1ukhacnhau. Trang12 Xacdinhcactinhcha'tc6th€ camnh~ndu'<;jccuake'tca'utrongmQtanhIa mQt bu'ocdffutienquailtrQngd€ di de'nmQtmohinhtoanchoke'tca'u.Cacthayd6i cu'ongdQsangtrongmQtanh,n6ichung,Ia cacd~ctru'ngke'tca'uthichh<;jpdu'Di illQtthayd6iv~tIy naod6theomQtb6icanhquailsat(ch~nghc;tnhu'soi,da trenbffibi€n, ho~cg<;jnu'Dc). Mo hinhchosv'thayd6i v~tIy nay Ia ra'tkh6. Vi v~y,ke'tea'uthu'ongdu'<;jcd~c tru'ngbdisv'thayd6ihaichi€u cuacu'ongdQsangth€ hi~ntronganh.£>i€unay clingchochungta tha'ydu'<;jc,khongc6mN dinhnghlake'tca'unaochungva chinhxacdu'<;jcdi~ndc;ttbflngngontucuathigiacmaytinh. Tuynhien,c6mQtsO'cactinhcha'trv'cgiaccuake'tca'udu'<;jcneusauday,nhin chung,Ia dung.£>6Ia: . Ke'tca'uIa mQttinhcha'tcuacaevung.Ke'tea'ueuamQtdi€m Ia khongxae dinh.Vi v~y,ke'tea'uIa mQtinheha'tngil'eanhvavi~exaedinhn6phailien quailde'ncaegiatrimuexamtrongmQtIane~nthuQekhonggiananh. . Kichthu'oeuaHine~nnayph\!thuQera'tIOnvaoki€u euake'tea'uho~ekleh thu'ocuacaethanhto'tc;tOnenke'tea'u. . Ke'tca'ulienquailde'nphanb6theokhonggianeuacaemuexam.Do v~y, cachistogramhai ehi€u ho~ecaematr~ntu'angtranhmuexamIa nhil'ng congC\!c6th€ du'<;jcsud\!ngd€ phantichke'tea'u. . Ke'tca'utrongmQtanhc6 th€ du'<;jcearnnh~ntheocaet1I~ho~edQphangiai khacnhau.Vi d\!,xet mQtke'tea'udu'<;jeth€ hi~ntrongmQtbuetu'onggc;teh. Khi dQphangiai tha'p,ke'tea'udu'<;jeearnnh~nnhu'ladu'<;jehinhthanhbdi cae viengc;tchriengIe trentu'ong,caechi tie'tbell trongeuaviengc;tehbi ma't. KhidQphangiaieaohall,chimQtsO'it caeviengc;tehdu'<;jenhintha'y,ke'tea'u du'<;jcearnnh~nseth€ hi~ncaechitie'tbell trongvien gc;teh. Trang13 . MQtvungduQccarnnh~nla c6ktt ca"ukhi s6cacd6ituQngthanht6 trong vungIOn.Ntu chic6rnQts6it cacd6ituQngthanht6xua"thi~nthld6la rnQt nh6rncacd6i tu'Qngchukhongphaila rnQtanhc6 ktt ca"u.N6i rnQtcach khac,ktt ca"u duQccarnnh~nkhi cacrn~u rnangynghIariengIe khongxua"t hi~n. . Ktt ca"ulienquaildtnh~th6ngtmgiaccuaconnguoi.Trong[7],cacnghien CUllv€ thigiaccuaconnguoidachungtodingvo naothigiacc6th~duQc mohlnhnhurnQt~pcackenhdQcl~p,rn6ikenhduQcxacdinhboi rnQtffn s6vahuangnha"tdinh.B6 clingla rnQtrongnhungly dod~sadvngbQlQc Gaborchovi~ctrichdi,ictrungktt ca"u. Ke'tca"uanhc6rnQts6cactinhcha"tc6th~carnnh~nduQcd6ngrnQtvaitroquail trQngtrongroota ktt ca"u.Nhungtinhcha"tsailcuaktt ca"ud6ngrnQtvai tro quailtrQngtrongroota ktt ca"u:d~udijn,m~tdC),tho,min,g6gh~,hili hoa, tuye'ntiob,cohuang,tdns6,phav.v... Trangcactinhcha"tneu0 tren,c6rnQts6tinhcha"tla khongdQcl~p.Vi dv,tinh cha'ttffns6khongdQcl~pvai tinhcha"trn~tdQva tinhcha"thuangchiapdvng chocaeke'tca'uc6huang. R5rang,carnnh~nktt ca"uc6 nhi€u lieu chutfnkhacnhau.B6 clingla ly do khongc6rnQtphuongphapbi~udi~nktt ca"urnQtcachdffydu chocacdlJ-ng khacnhaucuaktt ca"u. Ke'tca'uduQCsadvng0 caclOpbai loannhuphanlOpcacanh,tachcacanh thanhcaevung,xayd\ingcaccanhbachi€u titcacanhhaichi€u, va t6nghQp ke'tca'u. Nhu'daneu0 phffntruac,lu~nvanxerntai li~uvitt lay titngVi~tcuarnQtca nhan hu'rnQtanhktt ca"u.Dov~y,bailoannh~ndi~ncanhand\iatrenchITvitt laytie'ngVi~tla rnQtbailoanthuQClOpbailoanphanlOpcacktt ca"u. Trang14 Conhi€u phuongphaptrichd~ctrungk€t ca'u.Sauday,lu~nvanse trlnhbay tomluQccaclOpphuongphaptrichd~ctrungk€t ca'u. 2.2Cacphtidngphaptrichd~ctrlingke'tca'u Cacphtidngphaptho'ngke: cacphuongphapnayla'ycacthongtinv€ k€t ca'u cuaanhb~ngcactinhcha'th6ngke cvcbQcuacacmilcxamcuapixel.Hai phuongphaptieubi€u cholOpcacphuongphapnayla:phuongphapmatr~n tuongtranhmilcxamva phuongphap hamtV'tuongquail.Chi ti€t v€ phuong phaphamtV'tuongquailduQctrlnhbaychiti€t trong[3]. CacphtidngphaphlnhhQc:cacphuongphapnaymatak€t ca'unhuladuQc hlnhthanhtITcacthanhto't",-onenk€t ca'u(texels)vachungduQcb6tritheomQt quylu~tnaodo.Hai phuongphaptieubi€u cholOpcacphuongphapnayla: phuongphaplatdaVoronoiva phuongphapca'utruc. Chi ti€t v€ haiphuong nayduQctrlnhbaytrong[3]. Cacphtidngphapd1}'atren mohlnh:cacphuongphapnaydV'atrenvi~cKay dl!ngmQtmahlnhchoanh.Ma hlnhnaykhangchid€ matak€t ca'umacond€ t6nghQpno.Haiphuongphaptieubi€u cholOpcacphuongphapnayla:phuong phapmahlnhvungng~unhienMarkovvaphuongphapmahlnhfractal.Chi ti€t v€ haiphuongnayduQctrlnhbaytrong[3]. Cacphtidngphapxii ly tin hi~uso'(congQilit cac phtidngphapIQc):cac phuongphapnaybi€u di~nanhtheomQtd",-ngmoisaochocactinhcha'tcuak€t ca'utrdnend~nhlntha'ybon.Cacphuongphaptieubi€u cholOpcacphuong phapnayla phuongphapIQctrongmi€n khanggiananh,IQctrongmi€n t~nsO' (biend6iFourier)vad~cbi~tlaphuongphapbqlQcGabor. Trang15 2.3Nh~nxetv~caelopphuongphaptriehd(ietrtingktt ea'u Cacd~ctIlingk€t ciu du'cbi h~nch€ trong cacungdl;1ngthlfct€ docacrangbuQcv~lo~ik€t ciu. Ch~ngh~nk€t ciu phai chinhqui(phaichuacacthanht6r6 rangva phaidu'<jcb6tri theornQtquylu~t nha'tdinh). Ohanianva Dubes [20]dffnghienCUllhi<$uquacua cac phu'dngphaptrichd~c tIlingk€t ciu. HnghienCUllcac d~ctru'ngk€t ciu voi tieu chi hi<$uqua la :" Cacd~ctru'ngnaochoty 1<$chinhxaccaotrongphanlOpcacanhk€t ciu 7". OhanianvaDubelsdffdung4 d~ctru'ngfractal,16d~ctru'ngrnatr~ntu'dngtranh milcxarn,4 d~ctru'ngvungng~unhienMarkovd€ sosanh.K€t quasosanhcho tha'ycacd~ctru'ngrnatr~ntu'dngtranhrnucxarnchod 1<$caonhit, ti€p d€n Ia cacd~ctru'ngfractal. Benqnh do,hai phu'dngphaptrichd~ctru'ngk€t ciu b~ngrnatr~ntu'dngtranh milcxarnvab~ngb(Jirc Gaborla haiphu'dngphapn6ib~cnhit,chok€t quat6t trongcacungdl;1ngtu'dngtlfnhu'tronglu~nvannay.Cacungdl;1ngdola:nh~n di<$ncanhandlfatrenchl1'vi€t tayti€ng Anh [9],nh~ndi<$ncanhandlfatrenchl1' viettayti€ng Trung [25],nh~ndi<$nca nhandlfa trenvan rna:t[23],nh~ndi<$n ngonngl1'va kich ban dlfa tren cac anh tai li<$u[9], nh~nd~ngFont dlfa tren phantichk€t ciu toanCl;1C[23],nh~nd~nggu'dngrn~tb~ngb(Jirc Gabor[13]. Dov~y,sauday,lu~nvanse trlnhbaychi ti€t v~haiphu'dngphaptrichd~c tIlingketca'ub~ngrnatr~ntu'dngtranhrnucxarnvab~ngb(Jirc Gabor. 2.4Triehcaed(ietrtingke'tea'ub~ngmatr~ntHongtranhmITexam Giiisa{I(x,y),0:::;x :::;N-I, 0 :::;y :::;N-I }Ia rnQtanhcokichthu'ocNxN voi G milcxam. Matr~ntu'dngtranhrnucxarncokichthu'ocGxG,Pdtheovecrddoid=(dx,dy) dliQcdinhnghlanhu'sau: Trang16 Phftntli'(i,j)euamatr~nPdla s6lftnd6ngxua'thi~neuae~pcaemilexami vaj theoveetddoid. MQteachhinhthile,taco: Pd(i,j)=I {eel,S),(t,v»:I(r,s)=i,I(t,v)=j}I ddo,(r,s),(t,v)E NxN,(t,v)=(r+dx,s+dy),va 1.llaban56euamQt~phQp. Vi du:XetmQtanhcokiehthu'oe4x4coehila3milexam: l(x,y) = 1 1 0 0 1 1 0 0 0022 0022 Matr~ntu'dngtranhmilexam3x3euaanhnayvoiveetddoid =(1,0)du'Qexae dinhnhu'sau: [ 4 0 2 ] ~=2 2 0 002 SaudayIacaevi dl;lehocaeveetddoikhae. Void=(0,1),taco: 4 2 ° Pd=IO 2 0 002 VOi d =(1,1),ta co: 3 1 1 ~= 1 1 0 1 0 1 Trang17 . Matr~ntuongtranhmuexamdinhnghIanhutrenlakhongd6ixung.Nhung mQtmatr~ntuongtranhmuexamd6ixungcoth~du'<Jexaedinhtheoeong iliuesail: p=Pd +Pod. . Ma tr~ntuongtranhmuexamehobi€t caetinheha"tv€ phanb6 theokhong gianeuacaemuexamtrongmQtanhk€t ea"u.Vi d\l,n€u hffuh€t caephffnt-« khaekhongeuamatr~nt~ptrungd caeduongeheothlk€t ea"uco tinhtho theoveetodoid.Haraliektrong[3]diiduaracaed~etrltngk€t ea"udu<Jetinh titmatr~ntuongtranhmuexamnhusail: G-l G-l Nanglu<Jng:It =LL Pd2(i, j) i=Oj=O G-l G-l Entropy:12 =- LLPd(i, j )logPd(i,j) i=Oj=O G-l G-l (fJQtItdngphiin: h =II i- j JPAi,j) i=O j=O G-l G-l Pd (i,j) Imhd~u: 14 =~~l+ABS(i- j) Trang18 G-l G-l L L (i - JLx )(j- JLy )Pd(i,j) i=Oj=O Tudngquail:15 = (J"x(J"y ? d do,~xva ~yla caetrungbinh,crxvacryla caedQl~ehehuilneuaPdCx)va G~ ~1 P.(y)ttidngling.VOi:Pd(y) =LPAi, y) vapAx) =LpAx,j) i=O j=O Theo[3],phudngphaptrichcaed~etrungk€t ea'ubAngmatr~ntudngtranhmue xamd~nd€n mQts6khokhannhusau: . KhongcomQtieuehuilnnaod~ehQnveetddoid. . Khi G lOn,caematr~ntudngtranhmuexamcoldehthtioeGxG.Dov~y,vi~e tinhcaematr~nttidngtranhmuexamehocaeveetddoikhaenhaula khong khathi. . Voi mQtveetddoi d ehotrtioe,mQts6caed~etrtingdti<;1etinhtu matr~n ttidngtranhmuexam.Di€u doehotha'y,eftnphaicomQtphtidngphapehQn mQtphftncaed~etrtingnayd~motaehok€t ea'u. M~cdtiv~y,trongtrtiongh<;1pcaeanhtaili~uvi€t tarsaukhidti<;1cnhiphan,chi c6haimuexam.Vi v~y, matr~nttidngtranhmucxam,khia'y chico ldehthtioe 2x2.Do do,phtidngphaptriehd~ctrtingbAngmatr~nttidngtranhmuexam thuongdtiQcsii'dl;mgtrongcaeungdl;mgco xii'ly trenanhnhiphan.Trong[9] dilsudl;mgmatr~nttidngtranhvoinhi€u vectddoikhacnhauvadildc;ttk€t qua khacaotrongungdl;1ngnh~ndi~neanhandlfatrentaili~uvi€t tar ti€ng Anh. Tuynhien,mQtdi~my€u d6ivoiphtidngphapmatr~nttidngtranhmuexamla chitrichcacd~ctrtingk€t ca'utheomQtdQphangiaiduynha't.Di~my€u nayco theduQCcai ti€n bAngeachsii'dl;1ngcaebi~udi€n k€t ea'udaphangiai.M~t Trang19 khac,cacnghienCUllv€ h~th6ngthigiaccuaconnguaidah6trQchocachtie'p c~ndaphangiai.CacnhanghienCUlldachungtodng,vonaothigiaccuacon nguaico th€ duQcmohinhnhumQtt~pcackenhdQcl~p.M6i kenhse duQc di€u chlnhtheomQtfinsO'(phangiai)khonggianvamQthuangriengbi~t.Theo [19],xii'l:9bandfiutrongnaonguaith1!chi~nmQtki€u phantichtfinsO'khong gianvatie'pthea,vo naothigiacsephanchia cacte'baad€ dip ungtheocac tfinsO'vacachuangkhacnhau.MQtsO'cach~th6ngtrichd~ctrlingke'tca'utheo tfinsO'khOnggianva huangda duQcduafa. :E>~cbi~tbQlQcGaborla mQt phuongphaptrichd~ctIling ke'tca'uduQcsii'dl;lngtrongcac h~th6ngnhuv~y. Trangcach~th6ngnh~ndi~nca nhant1!dQngd1!alIen sinhtrAchQcnoi chung vanh~ndi~ncanhand1!alIen chITvie'tlaynoi rieng,bQlQcGabordachoke't quara'tt6tso vai mQtsO'cacphuongphapkhac(k€ ca phuongphapmatr~n tuongtranhmucxam)[1],[13],[9],[20],[9],[14],[23],[24],[25]. Do v~y,lu~nvan se sii'dl;lngbQlQcGabord€ trichd~ctrlingke'tca'utrongcac I anhtai li~uvie'tlay tie'ngVi~t. I Sauday,bQlQcGaborseduQctrinhbaymQtcachchitie'ttus1!hinhthanh,phil tri€n,va ungdl;lngcuanotrongcacbailoanphantichke'tca'utOivi~cthie'tke' ffiQtbQlQcGaborhQp1:9chovi~cnh~ndi~ncanhant1!dQngd1!alIen chITvie't laytie'ngVi~t. 2.5Trichcacdi,ictrttngke'tdiu biingbi)IQcGabor 2.5.1Ly thuye'tGabor DennisGaborchoding1:9thuye'ttruy€n thongd1!atrenhaiphuongphaptach bi~tsanday: Phuongphapthlinha't:motatinhi~unhu'mQthamcuathaigian. Phuongphapthuhai:motatinhi~unhumQthamcuatfinsO'.PhantichFourier la ffiQtd~;lllgcuamotanay. Trang20 Ly thuy€'tGaborduaramN phuongphilpmoid€ motatinhi~utheocahaimien thaigianvatftns6. Gaborxethaiphuongphilpbi€u di~ntinhi~uneud tren.Bi€u di~ntrongmien thaigiansexacdinhbiendQcuamQtinhi~ut~im6ithaidi€m tucthai.Trong khido,bi€u di~ntrongmientftns6 sa dl:mgmQtchu6ivo h~ncaehamtuftn hoandu<;1cxacdinhb~ngtftns6,biendQva phacuachung.Hai phuongphilp bi€u di~nnayla ly tu'dng.Bdi vi bi€u di~ntrongmientftns6chor~ngmQttin I hi~utrongmienthaigianladaivoh~nkhitftns6cuamQtinhi~uhUllh~ntrong mienthaigiankhongth€ xacdinhchinhxacdu<;1c.TuonghI, mQttinhi~utuc thaitrongmienthaigian(ch~ngh~nhamxungdonvi) co mQtph6tftns6chua ta"tcacaetftns6khacnhaudu<;1cphanb6delltrongmientftns6.£Heuki~nnay lakhongthoamanchocaetinhi~utrongthtfct€'.Vi dt;lmQtinhi~ula mN song amnh~cbaag6mmQts6n6tnh~cvoimQtftns6d~cbi~tnhu'ngchungdu<;1cth€ hi~nemtrongmQtkhoangthaigianhuuh~n. R5rang,caebi€u di~nnhuv~ykhongthichh<;1pchophantichcaetinhi~uco chieudaihuuh~ntrongmienthaigiannhuth€ hi~ntronghinh2.2. 4.5 4 f(t)- 4 3.5 3.5 3 3 2.5 2.5 2 :2 1.5 1.5 0 1 a10 20 3[] 4[] 50 a) 100 200 300 b) lfmh2.2:Vi dt;lhaitinhi~uvoicaed~cdi€m thaigian- tftns6khacnhau. i'---- Trang21 Tronga),ra rangtinhic%ula tu~nhoanva bie'nd6iFourierseduQeapd1,mgd€ chocaet~ns6euano. Trongb) PhantichFourierla khongchinhxaeVI tin hic%uth€ hic%ncaet~ns6 khacnhautrongcaekhoangthaigianng~nkhacnhau.Do v~ytinhic%unayc~n phaicomQtbi€u di~nthaigian- t~ns6d€ phantichmQtcachehinhxae. Tie'pthea,Gaborxet caedapling t~ns6 (ph6Fourier)euacaeduangeong Gaussianvoi cacchi€u rQngkhacnhau.CaeduangeongGaussiannayco cac dQlc%chehuffn(cr)tllc%nghichvoi nhauthongquacactr1,lethaigianva t~ns6 tUdnglingnhuth€ hic%ntronghlnh2.3.Theocaevi d1,lnay,Chungtad~dang nh~ntha"ygiuathaigianva t~ns6cuamQttinhic%ucomQtst,tlienhc%m~thie't. TheoGabor,docrunhla xua"tphatdi€m d€ hlnhthanh19thuye'teuaong.Gabor d3:tlmtha"ym6iquailhc%nayva hlnhthliehoanob~ngcaehc%thliequailtr<;mg dU<;1cd~nra co thli tt,trongph~nsan. . -at2 ~UJUUaD~ c ~ ~ ~- t ~ I Biga d6i Fourier I ~ /Lf - AT j a 00 't -,. i a=5 --1: 8..=0 .5 8.=0.1 ~ f a=O ~ ....f Hlnh2.3Ph6FouriereuacaeduangeongGaussianvoicaeehi€u rQngkhac Mall. Trang22 DQ l<%chchuftncua m6i du'angcongGaussiantheotrt;lCthai gian la ti 1<%nghich voi dQl<%chuftncuaph6pbi€n d6icuano theotrt;lCtgns6. Ap dt;lngnguyen19bfftdinhcuaHeisenberg,Gabordu'ara m6iquailh<%bfftdinh trongmi~nthaigianvami~ntgns6nhu'sau: f1tf1j >!2 (2.1) ? ddo: ilt lakhmingbfftdinht~imQtvi tricuatinhi<%utrongmi~nthaigian. M lakhoangbfftdinhcuatgns6tinhi<%utrongmi~ntgns6. d(2.1),Gaborchungtor~ng: 1. Khangth~xacdinhmQtcachchinhxacmQtkhoangcuatinhi<%utrongmi~n thaigianclingnhu'tgns6 trongmi~ntgns6cuatinhi<%udo. 2. Tichcuakhoangbfftdinhtrongmi~nthaigianvakhoangbfftdinhtrongmi~n tgns6phai IOnhonmQth~ngs6naodo. I NghIala n€u mQttinhi<%ud '<jcdinhnghIatrenmQtkhoangthaigiantucthai duynhfft(ilt=O)thlnosekhangdu'<jcxacdinhmQtcachdgydutrongmi~ntgn 86(M=oo).Ngu'<jcl~i,mQttinhi<%ud '<jcxacdinhmQtcachchinhxactrongmi~n tgns6(M=O)nophaicochi~udaivah~n(ilt=oo).Gifi'ahaithaiqtcnay,mQtin hi<%ula bfftdinhvoi mQtmucdQnaodo theoca haimi~nthoigianva tgns6. Nhu'ngtichcuahaikhoangbfftdinhnayt6ithi~uphaib~ngY2. Gaborchira dingco t6nt~imQtd~ngtinhi<%uco th~bi€n d6i (2.1)trdthanh d!ngthuc(nghIala iltilf=Y2). Tinhi<%unayla s1;1'di~uch€ tichcuamQtdaDdQngdi~uboatheomQtgns6bfft IcyvoimQtKungco d~ngla mQthamxac sufft. Hamnay(saunaydu'<jcgQilahamGabor)du'<jcxacdinhnhu'sau: Trang23 g(t)=e-a2(t-tO)2.(cos[2Il f(t - to)+fjJ]+isin[2Il f(t - to)+fjJ]) (2.2) ? ado: . ala hflngs6Gaussiand~di€u che"caehamdaDd(>ngdi€u hoa.a ti l~nghich vdichi€u r(>ngcuahamGaussian. . toxacdinhHimcuahamGaussian. . f la tgns6cuadaDd(>ngdi€u hoa. . ngdi€u hoa (co lien h~vdi tamcuahamdi€u che" Gaussian). Hinh2.4th~hi~nm6ilienh~v€ thaigianvatgns6cuahamGabor. g(t) t 6.t G(fj f M Hinh2.4BaplingKungtrongmienthaigian(phachan)vadaplingtgns6cuano trongmientgns6. Trang24 Khi phantkh Fourier,G(f) du'<jckhaitri€n thanhmQtchu6iFouriervaget)chinh lacach~s6trongkhaitri€n FouriercuaG(f). V€ nguyent~c,cacs6h~s6nayla voh~n.VI v~yd€ tinhdaplingt~ns6titdap lingxungtaphaidungmQthamcii'as5d€ c~tC1;ltdaplingxungtlicbodicacdap lingxag6ckhichungtronenkhanhosovdi cacdaplingg~ng6c.Ngu'aitacon gQiphantkh Fouriercii'as5(haybi€n d5iFourierthaigianngiin)trongtru'ang h<jphamcii'as5la hamGaussianla phepbi€n d5iGaborvanhu'v~ychi€u rQng cuahamGaussianchinhla chi€urQngcuacii'as5. Vdi sl!th€ hi~nnhu'tren,chothffyhamGaborcoth€ C1;lCbQhoamQtcacht6iu'u (dotkh .MM dungb~ngY2)mQtinhi~utheocahaimi€n thaigianvat~ns6. Tuynhienvi~cC1;lCbQhoanaykhongphaila tuy9maphaimantheonguyen19 bfftdinh.Tlic la tkh ~tMphailuonluonb~ngmQth~ngs6(¥2).Theo[7],khidff chQndu'<jcdQrQngcii'as5trongmi€n thaigian,hamGaborsechodQphangiai t~ns6t6tnhfftnhu'th€ hi~ntronghinh2.5. ...~ ::;Q tn ~ ((CtI E-t ----...- ~ T (ThiYi gian) Hinh2.5C1;lCbQhoamQtinhi~utrongcahaimi€n thaigianvat~ns6. Trang25 2.5.2Thie'tke'b()IQcGabord~trichcacd~ctrtingke'tca'u Trongtruangh<Jptinhi<$ula anh,mienthaigiannhudffnoi0 trensedu<JcgQila mienkhonggian(spatialdomain)vamient~ns6noi0 trensedu<JcgQila mien khonggiant~ns6(spatialfrequencydomain). Trongmienkhonggian,mQtanhdu<JcxemnhumQtt~ph<Jpcacpixel.Trong mienkhonggiant~ns6,mQtanh du<JcxemnhumQtt6ngvo hC;lncachamtu~n hoan.Daugman[6],trongcacth1lcnghi<$mlien quande"ncacdii'ki<$nsinhly hQC va tam ly hQccua h<$th6ngthi giac con nguaiva dffchungto ding co mQts1l lienh<$m~tthie"tgiii'adaplingt~ns6cuachungva daplinghuangcuachung. OngdffchQnramQthamcokhanangdi€u chinht~ns6vahuangmQtcachdQc l~p.HamongchQnchinhla hamGaborhaichi€u du<Jcxacdinhb~ngcacpha chanva Ie cuano. Hlnh2.6th€ hi<$nla mQtphachancuab(J lQcGaborhai chi€u.Trong[6],b~ngmohlnhcaccoche"thigiaccffpthffp,cachamnaydu<Jc nhanxo~nvaianhnh~pvavi the",cachamnaycondu<JcgQila b(JlQcGabor. Hlnh2.6MQtlQcGaborhaichi€u (phachan). Trang[25],mQtb(JlQcGaborhaichi€u du<JchoboimQtc~pheva hocacpha chanvaIe tuonglingnhusau: Trang26 x2+i1 -- he(x,y;f,O)= 2 e 20-2 .cos[2I1f(xcosO+ysinO)] 2I1D" x2+i ho(X,y;j, (})= 2~0"2 e- 2'" .sin[2I1/(xcoS{} +ysin(})](2.3) 110,hela caedaplingxungtrongmi~nkhonggian.Caedaplingtffns6eua110,he trongmi~nkhonggiantffns61a: He(u,V)= [HI (u,v)+H2(u,V)]2 HJu,v) =[HI(u,v)-H2(u,v)] 2} (2.4) ? ado: j =H va I H2(u, v)= e-2IT20-2[(U+fCOSBf+(v+fSinBf] HI (u, v) = e-2IT20-2[(u-fcosB)2+(v-fsinBY] f latffns6trongmi~nkhonggiantffns6. elahu'angeuadaodQngdi~uboa. (j laehi~urQngeuadu'ongeongGaussian. Voi f=-JU2+v2va B=arctg(;). I1mh2.71affiQtdaplingxungeuaphaehan trangmi~nkhonggianvadap lingtffns6tu'dnglingeuanotrongmi~nkhong giantffns6. Trang27 In' u 1", OJ'J -= 'ca I;n '0. . ~ OJ'J -= ~ .~ () :00 .fI \1\ Hang CQt a) b) I1mh2.7 a)Bapungt~ns6cuaphachantrongmi€n khonggiant~ns6. b)Bapungxungcuaphachantrongmi€n khonggian. Tit (2.3)va (2.4),tanh~ntha'yb(JlQcGaborhaichi€u th1!chi~nvi~cC1;lCbQh6a anhtheocahaimi€n khonggianvami€n khonggiant~ns6.Trongmi€n khong gian,mQtdapungxungcuab(JlQcGaborla mQthamdi€u boadu'QcC1;lCbQb~ng mQtcii'as6Gaussian.Trongmi€n khonggiant~ns6,chungtac6th€ xemb(JlQc Gaborla mQthamGaussiandu'Qcdi€u che'bdimQthamdi€u boac6mQt~ns6 nha'tdinh.VI bie'nd6iFouriercuamQthamGaussianla Gaussianenbi€u di~n hamGabortrongmi€n khonggiant~ns6 chi la hai hamGaussiandu'Qcdich chuy€nvaikhoangdichchuy€ndu'Qcxacdinhbdit~ns6cuahamdi€u boa.V€ m~tloanhQC,ra rangb(JlQcGaborthoamannguyenly ba'tdinhkhike'thQpca haimi€n khonggianva khonggiant~ns6.Daugman[3],dacmracacquailh~ ba'tdinhnayla ~~u ~n/4va~y~v~n/4vai~, ~yla cacdQrQngtheocactr1;lc x,ytrongmi€n khonggianva ~u,~v la cacbangthongtheocactr1;lcu, v trong mi€n khonggiant~ns6. Nhu'v~y, khi ap d1;lngbQlQcGabord€ trichcacd(ictntngkgtcdun6ichungva ke'tca'ucuacactai li~uvie'tlaytie'ngVi~tn6irieng,chungtac~nphaixacdinh haithams6quailtrQngd6la t~ns6f vahu'ang8.Tuynhien,dayla mQtva'nd€ Trang28 md.VI hic%nnay,chuaco mQtbaacao nfwchothffyvai m6iungdt;mgC\lthe, trongdo,co sii'd\lngbqlQcGabordetrichcacd~ctru'ngke'tcffunhunenchQnf vaenhuthe'nao7(baonhieutffns6f 7 baanhieuhuange 7,dingnhucacgia hi nayIabaanhieu7).VI v~y,lu~nvannaychiapd\lngnhungthams6f vae duQcchQnbdimQts6tacgiadi tru'aclamvai tie'ngAnhva tie'ngTrungvatrai quacacthii'nghic%mC\lthekhith\fchic%nnh~ndic%ncanhant\fdQngd\fatrenchii' vie'tartie'ngVic%tdechQnracacthams6f vaechobQlQcGabor. M6i mQtc~p(phachanvaphaIe)cuabQlQcGaborduQcdi€u chinhtheotffns6 vamQthuangc6djnh.Do v~y,cffnphaico cacxemxetquantrQngtrongvic%c chQntffns6vahuangdexacdjnhcackenhchobQlQcGabor.Vic%ctrichcacd(ic tntngktt cifulien quande'nca haitinhchfftcuake'tcffutrongcacanhtai lic%u vi€t tartie'ngVic%tIahuangvatffns6. Sauday,chungtasephantichmQts6vffnd€ lienquande'nvic%cchQntffns6va huangchobQlQcGabor. ChQnt§n sf) Vic%cchQntffns6chobQlQcGaborph\lthuQcvaokichthuaccuaanhnh~pva djnhly Iffymftutrongxii'ly tinhic%us6.Gia sii'anhnh~pco kichthuacNxN,d day,N thuongco gia trj la lily thuacua2 (doco th\fchic%nbie'nd6i Fourier nhanh)khi do,tffns6f phaithoaman:f::;;N/2.Tuynhien,quath\fcnghic%mvai N=256,nhuv~ymi€n giatrjcuaf la: 2,4,8, 16,32,64,128thlf=128la khong d~tduQcke'tquat6ttrongtrichcacd(ictntngktt cifu[6].Do v~y,f chicongiai h~ntrongkhoang:2,4,8, 16,32,64. Khith\fchic%ncaid~tcholu~nvannay,vaif=2vaf=64,chothffyke'tquakhong tat.Nencu6icunglu~nvanchQncacgiatrichof la:4,8,16,32. Trang29 Ch(;mhu'ong Clingtrong[14],[25],cacvungtie'pnh~ntrenvonaophantichanhnh~ptheo8 huangla 0°,45°,90°, 135°, 180°,225°,270°,315°.Tuynhiencachuangnay coSl,l'd6ixungtungc~p(theokhoangcachla 180O)nhuth€ hil$ntronghlnh2.8. Dov~y,chungtachQncacthams6cho8la:0°,45°,90°,135°. 45" 18(1'0'" 223" 90" 270" 135" 31~ Hlnh2.8Cachuanglad6ixungvainhautungc~p. Nhuv~y,vaim6i(t,8),chungtaxacdinhdu<;1cmQtkenhcuabQlQcGabornhu tronghlnh2.9(cota"tca 16kenhtheo4t~ns6va4huang). Kenh 1: f=4,8=0°, Kenh 11: f=16,8=90°, Kenh 2: f=4,8=45°, Kenh 12: f=16,8=135°, Kenh 3: f=4,8=90°, Kenh 13: f=32,8=0°, Kenh 4: f=4,8=135°, Kenh 14: f=32,8=45°, Kenh 5: f=8,8=0°, Kenh 15: f=32,8=90°, Kenh 6: f=8,8=45°, Kenh 16: f=32,8=135°. Kenh 7: f=8,8=90°, Kenh 8: f=8,8=135°, Kenh 9: f=16,8=0°, Kenh 10: f=16,8=45°, Trang30 (b) (c) Hinh2.9 (a)BQlQcGabor16kenh. (b)LQcvdi t~ns6caotrongmi~nkhonggian. (c)LQcvdit~ns6ilia'p trongmi~nkhonggian. Tht;ichi~nIQcGabortrenmQtanhnh~plex,y) Voim6ikenhcuabQlQc(ungvdim6ic~p(f,e» 1. TinhHe(u,v)vaHo(u,v)(b~ngphepbitn d6iFouriernhanh) 2. Tinh cacanhdu'<JclQccualex,y) theoHeva Ho(b~ngphepbitn Fourier nhanhngu'<Jc),chungtadu'<Jchaianhqe(x,y)vaqo(X,y). 3. Anh cualex,y) trongmi~nkhonggianla: qij(x,y)=~q;(x,y)+q~(x,y) 4. Trich2d~ctru'ngtuqij(x,y) la trungblnh(Meanij)vadQl<%chuffn(Stdij). Nhu'v~yvdi 16kenh,chungtasehlnhthanhdu'<JcmQtvectdd~ctru'ngcuaanh I nh~plex,y) vdi 32thanhph~n.Vdim6ikenh,theot~ns6,chochungtadu'<JcffiQt d~ctru'ngcuaanhtai li<%uvitt tar nh~pla dQphangiai cuaktt ca'uchii'vitt tar Trang31 (ffi~tdQphanb6cuacackyhI)vatheohu'ong,chochungtadu'QcffiQtd~ctru'ng v€ hu'ongcuaketcffuchitvietlay(phanb6v€ hu'ongcuanetvietlay). Trongchu'dngnay,lu~nvandfftrinhbayffiQts6khaini~ffilienquaildenketcffu vatrichd~ctru'ngke'tca'ucuacacanhn6ichungvacacanhtiii li~uvie'ttarn6i rieng.Ben c(;lnhdo, lu~nvanclingdfftrlnhbayffiQtcachchi tiel haiphu'dng phaptrichd~ctru'ngketcffuIa phu'dngphapffiatr~ntu'dngtranhffilicXaffiva phu'dngphaplcvOibQlQcGabor.Tuy nhien,theocacling d\lngdffneutren,bQ lQcGabor la phu'dngphap!richd~ctrUngket cffucho ket qua t6tnhfft.Vi v~y, lu~nvandffsad\lngbQlQcGaborde trichd~ctru'ngketcffutrongcacanhtai li~uvietlaytiengVi~t. Nhu'v~y,saukhisad\lngbQlQcGaborvoi 16kenh,chungtadff!richdu'Qcd~c tru'ngcuaanhtai li~uviet lay tiengVi~tcuaffiQtca nhanla ffiQtvectd d~c tru'ngg6ffi32thanhphftn. Phftntiep theocuaquytrlnhnh~ndi~nca nhandl1atrenchitviet lay tiengVi~t la phanlop (canhan)chovectdd~ctru'ngnay.V€ nguyentiic,bfftIcyffiQtbQ phanlopnaoclingcotheapd\lngdu'QCvoivectdd~ctru'ngnay.Tuynhien,bai tminphanlOpcacchitvietlaynoichungva chitvietlay tiengVi~tnoiriengla bailoanphannhi€u lOp(corfftnhi€u canhan).S61u'Qngcaclopnhu'v~yla vo h(;ln enchungtakhongthenaoquailsathetdu'QCvi nhu'dffnoi (jphftndftus6 Iu'QngcaclOpgftnb~ngdaTIs6cuaffiQtkhuvl1c,ffiQtqu6cgia,vv...Dov~y,lu~n vansechuyenbai loanphannhi€u lOpthanhbai loanphanhailop (Cungho~c Khac).Chu'dngtieptheocualu~nvansetrlnhbayro v€ bai loanphanhailOp nay(Dichotomizer)clingvoi nhitngdanhgiav€ no sovoi bai loanphannhi€u lop(Polychotomizer).