Luận án Phát triển một số phương pháp nhận dạng ảnh văn bản tiếng Việt

nhs6 h6a.Ban d~urie'nhanhla'ym~u(j dQphangiai cao,saud6 de'ndQphangiai tha'pbon.C\l th€ la truoclien,<lnhdu'QclammabfingbQIQclow-passvasaud6riEnhanhla'y 9 mill con.D~dongiangiasar~ngLlx=Lly=Ll.Ne'usadl;mgbQ19Ctftns6thipFIR (FiniteImpulseResponse)codQdai L.Ll, dinhly liy mill phatbi~ur~ngdn s6liy mill con(l/L1sub)phaiIt nhit b~nghailftntftns6nguongcilabQ19Clow-pass.Nghla la 1/Llsub>2/(L'Ll)ho~cL>2'(Llsub/Ll),trongdo Llsub/Llla h~s6liy mill con.Vi d~,ne'umu6nliy mill continhi~uvoih~s6la 3,bQ19Clow-passphaitlnhm5igia tq outputmill b~ngcachH1YtIlingblobit nhit 6 giatri inputmill. MQth~s6liy mill con b~ng2 di;ltdu<;lcb~ngcach liy trungblob 5 mill inputb~ngmQtbQ19C low-passki~uGauss.LOi;liky thu~tnay hi~ndangdU<;lcsa d~ngd~phanlOi;liky tv trongnhlingphilom~mnh~ndi;lngkytv (OCR)thuongmi;lichlnhxacnhit. i(x)t 1T 0 l l x i(k) t I~t0 ~ i/x)t It oL /---,' ~ il(k)b - I I I I ' , ,-~ ';. ~uuur---~ ...~ ztEimmr---b k. "unuu. . Hinh 2.2Anh huangcuavi~cILiUthongtinvi tri Bay giGchungtase chuy~nsangvin d~xacQinhdQphangiai.MQteacht6ng quat,dQphangiaiGangcaothlthongtindu<;lchmgiliGangnhi~u.Tuy omen,mQt dQphangiai quacaoclingco th~lamlQke'tciu n~ncilavanban.Honnlia,dQ phangi,Hcaoclingdoihoithie'tbi d~t i~nvaphucti;lPbon,duarakh6ilU<;lngdli li~ukh6ng16,khongdn thie't.Cu6i clIng, ch9nh!a dQphangiiii dU<;lcxac djnh b~nghai ye'ut6: nQi dungcila vanbanva m~cdichcila nhlingthaotaGtie'pthee. Th~tv~y,mQttai li~uvanbanin voimQtfontIondoihoi liy mill (j dQphangiiH 10 tha'pbond€ c6th€ dQcdu'Qcsovoi vanbantu'ongtv nhu'ngvoifontchii'nhabon. .. Ne'uthaotactie'prheala'ym~ula nhjphanh6a,tadn dQphangiai caoboneho cacmucxam. SimondenghjchQnL1sacehosaukhinhjphanh6a,ca'utrucdong manhnha'ttronganhvan banphairQngit nha't3pixel d€ tranhgay kh6 khantrong nhii'ngthao tac tie'prhea.C6 nhii'ngdQphan giai khac nhaudff du'QCde nghj sii' dl,mgchonhii'ngungdl,mgkhacnhau.Vi d1,l,Dengelsad1,lngmQtdQphtingiaira't tha'p(75dpi)trangbu'ocphando~nchoanhthu'tin.Trongkhinhii'ngh~th6ngOCR c6dQchinhxaccaol~isii'd1,lngdQphangiaitu300de'n400dpichonhii'ngvanban "thu'ang". 51,(dad~ngcuanhii'ngdQphangiaidu'QCsad1,mgbdicactaegiakhacnhaudenghj mQtungd1,lngphuct~p baag6mnhieutaeV1,lconmam6itrangso'd6c6th~thvc hi~nt6tbangeachsad1,lngdQmQtphangiai thichhQp.Nhu'v~yanhband~udn du'Qcla'ym~ud dQphangiaicao.DQphangiaitha'pboncuan6saud6c6th~d~t du'Qcbangcachsii'd1,lngky thu~tla'ym~uconmotabentren. N6i ng~ngQn,tie'ntrlnhIa'ymiiula bu'ocdn thi&tkhichuy€nd6imQtvanbanra d~ngso'boa.N6 c6th€ gayma'thongtin.Tuynhiensvma'tmatnayc6th€ du'Qc dieukhi€n banganti-aliasingvoinhii'ngthamso'du'Qcki€m soarbangdjnhIy la'y miiu.Ky thu~tu'ongtvclingc6thi dl(Qeapd1,lngkhichungtamu6nla'ym~ucon mQtanhso'h6a- la'ymiiud dQphangiaiband~ucaobon.Djnhly Ia'ym~ukhong doihai vanbanphaidu'Qcla'ymiiud mucdQphangiainacoDieunaycu6icling phl,1thuQcVaGung d1,lng. 2.2.2Lu'<jngh6a Mftu,sinhbditie'ntrinhIa'ym~u,nh~nnhii'ng iatrithvc,lient1,lcvanhu'v~ydn phaidu'QcIu'QngboathanhmQtso'hii'uh~ncacmuexamd~c6thi xii'Iy bangmay tinh.Ne'us6muexam,L bang2, 1u'<;Jngh6acan gQila nhjphanh6a.Nhj phanh6a la mQtthaotacph6bie'ntrongphantichanhvanbanvi haily do.Thu nha't,h~uhe't cacanhvanbantronggi6ngnhu'chic6haimall,denvatrang.Nhl(v~yY tu'dngnhi f L phanhoacovetlfnhien.Thuhai,nhiphanhoalamddngianra'tnhi~unhungthaa lactie'pthea,nhuphanda~nvanh~nd~ng.NhuV?y,trudelien chungIa sexem xettie'ntdnh1uQnghoat6ngquatmQteachng~ngQnvasaildo t?P trungVaGnhi phanboa. BinaryCode r(v) III lIO 101 100 011 010 001 000 r T r: t r ..j.. r~ + .. I r3 T ! r2 i Saturation- rI _. J "'- r.- [) ",-to.. I I I I i I Yo VI v? V1 V4 Vs v6 V7 Vg Sample Value Hinh 2.3.Hamd;j.ctrLlngcuatrinhILlQ'nghoa v~m~tv~t1y,1uQnghoaduQeth\1'ehi~nbAngmQtthie'tbi di~ntu:gQi1abQehuy€n d6ituclngt\1'-s6,g~ntrangnhungthie'tbi sO'hoahi~nd~i.Hlnh2.3minhhQamQt. ~ hamd~etrungeuamQtthie'tbi 1uQnghoadi€n hlnh.Thie'tbi d~ebi~tnayehuy€n d6im6igiatrim~uth\1'ethanhmQtrangtammueriengre,duQemahoabAng3bit sad\mgmahoanhiphan.Nhunggiatri Vjva rj gQi1.1caemuequye'tdinhvatai thie'tmQteachtudng(tng.TrangmQtsO'thie'tbi sO'boa,nguaisl'td\mgcoth€ ehQn s6muexam(bAngsO'muetaithie't),thuang1amQtlily thuaeua2.Trangnhungh~ th6ngkhae,consO'nayduQecO'dinh(j mQtgiatrikhalOn,256.Thie'tbi 1uQngboa tronghlnh3 d6ngnha'trangnhungmuequye'tdinheachd~unhau.Nhungthie'tbi lu<;Jnghoat6ngquatdu<;Jcxemxetbell dudikhongdn phai rheaquy1u~teh~tche nay. Thongthuang,nguoitath\1'ehi~n1u<;Jnghoatronghai bude.Bude thunha't,mQtcan sO'lOn,256eh£ngh~n,caemuexamdu<;Jesa dl;mgd€ hamd~etrungcuathie'.tbi lti<;Jngboahh nhumye'ntlohvdidQbaaboa.Trangoudetbu'hai,mQtcansonha 12 bon,tit2 de'n8, caemuexamdu<;1csa dl:lllgdlfavaoke'tquaeuabuoethunh!t. f)i~mchinnye'ueuacachtie'pc~nhaibuocnayla: buocthunh!trho tacachbi~u di~ns6eoth~dungehonhil'ng iai thu?tlinn vi nhuhistogramming,d~xacdinh mQthamd~ctru'ngt6iu'urhobuocthuhai. Tieuchuffnrho linn t6i u'uthuangdu<;1esadl:lllgnh!t la sais6 blnhphuongtrung blnh(MS£)giil'agiatrim~uvvamuetaithie'tr(v). E{e2}=E{[v-r(v)[}=f[v-r(v)[ p(v)dv (2.1) Trangdop(v)la hamm~tdQxaesu!teuabie'nng~unhienv,co th~la dQu'utien du<;1ebi 'trudceuanhil'ngvanbanho~eduQcx!p Xlb~nghistogrameuanhil'ngia trim~utrangdeh tie'pe~nhaibude.Vdi mQts6ehotrudeL caemuexam,MSEeo th~du<;1cbi~udi~nbdi : E{e2)=I to.(v-r)2 p(v)dvJ (2.2) dar(v)=rj lah~ngs6trongdo~nlvJ'vj+IJ. Vji p(v) ehotrudeva s6 caemuc tai thie'tL c6 dinh,cae muc quye'tdinh vj,j=l,...,L-l va eaemuetai thie'trj,j=O,...,L-l clfcti~uhoaMSE tuantheo nhil'ngquailh~gall: r I +r v;=;-2 ;; j=l,...,L-l (2.3) v., Jvp(v)dv r;=:;o' ;j=l,...,L-I (2.4) fp(v)dv Vj Tuynhien,kh6ngconhil'ngeaehgiaiquye'tdudid~ngkhepkinnaot6nt~itritkhi chapnh~nmQts6 phepx!p xl. M~tkhae,nhil'ngphuongphaps6 phaidu<;1es1l' dl,lng,d~nde'neachtrlnhbay d~ngbangeuaVjva r.irho nhi~uphanb6 tham86 ehuffn,nhuGauss,LaplacevaRayleight. 13 Bay giOchungta xernxet tru'onghQpngo~i1~nhu'ngquailtrQngvoi L =2. Do 1a tru'onghQpnhiphanboaanh.Khi doMSE trdthanh: E{e2}=f(v-ro)2p(v)dv+r (v-rl)2p(v)dv0 I (2.5) Gia sadingp(v) co th€ du'Qcu'oc1u'Qngtit histogramva Vo.V2tu'ongungvoi VmimVmax' Con 1~iba tharns6 dn du'Qctinh loan, do 1aTo,rI va VI' Tharns6 VI du'QcgQila ngu'ongnhiphanboa.Honntl'arivI) va rlVI) qic ti€u MSE, voi rnQtgia tq cho tru'ocilaVI,dongian1anhtl'ngiatritrungblnhtrongdo~ntu'ongung(2.4): ro(vl)= £vp(v)dv r p(v)dv r.(V ) - rvp(v)dvI 1 - rp(v)dvI (2.6) (2.7) Nhu'v~ydil d€ bie'nd6i VI titVode'nV2.MSE du'Qctinhb~ngeachthayrova rI b~ng rivI) va rlvI) tu'ongungvachQnVI* sacchoMSE la qic ti€u. Otsud~nghirnQtcachtu'ongttfnhu'nglieu chu~ndongianhonv~rn~tinhloan dtfatrenphantichbi~ts6.TrongGongthUGnay,MSE tu'ongdu'ongvoiphu'ongsai lOptrongO"~/(VI)'Ne'uO"~/(VI)du'Qcb6 sungVaGphu'ongsai lOpgitl'aO"l(VI),ta du'QcloanbQbie'nd6i 0"/ (dQCl~pVI)'Nhu'v~y,thayVIctfcti€u MSE,giaithu~t cilaOtsuq1'cd~iphu'ongsaigitl'alOp: VI* =argmax{po(v1)[,uo(v,)- ,urf + PI (Vl)[,ul (VI) - ,ur]2} Trangdo Po(VI)=m(vl) PI(VI)=I-m(vl) ,uo(VI)=,u(vl)/m(vl) ,ul(VI)= ,ur- ,u(VI) I-m(vl) ,ur = ,u(V2 = vma..,J Va 14 (2.8) (2.9) (2.10) (2.11) (2.12) (2.13) UJ(VI) =fp(v)dv" J.L(vJ = r: vp(v)dv Bi~uthuc(2.8)co th~dU<;5cdongianthanh: (2.14) (2.15) VI * =argmax { [J.LT.UJ(VJ - J.L(vI)f }UJ(vl)[l-UJ(v,)] (2.16) Khi v/ dadu<;5cxacdinh,caemuctai thie'trova r] co th~du<;5ctinhb~ngcachsa dl:lllgbi~uthuc(2.6)va(2.7),ho~cmQteachtuongQUang: 1'0 * =J.L( VI *) I UJ( VI *) r * - J.Lr- J.L(vJ*)I - 1-UJ(vl*) (2.17) (2.18) Th~tfa,cont6nt~imQts6lieuchuinlu<;5nghoakhac,ch~ngh~nentropy,clingdlfa trenhistogramcuacacmucxam.Histogramco th~du<;5ctinhtu loanbQanhvan banho~ctumQtHinc~ndiaphuonggioih~nxungquanhdi~manhdangxet.Cac histograml~nhungth6ngke khonggianb~cnha't.MQts6 th6ngke b~chai,sa d\lllgcaematr~nd6ngxU<lthi<%nclingda du<;5cnghiencUutrongva'nd~nhiphan boa. Noi chung,nghienCUllnhungke'tqua lu<;5nghoa la kho khan VI tinhkhong tuye'ntinhcuahamd~ctrungtrongtrlnhlu<;5ngboa.Ne'uL lOn,ch~ngh~n16, nhungke'tquacuanotraDendangchuy vacoth~gayranhungsail<%chmeamo khongth~cha'pnh~ntrongmQts6ungd\lllg.VI nhiphanhoara'tthudng ~ptrong Linhvlfcphanrichanhvanban,tase xemxetchi tie'tnhunganhhuangcuano trongmQttrudngh<;5pdi~nhlnh. Chncling vi d\l trongphftn2.1.Gia sa ding la'ymill i(x) d~tdU<;5cq~ai,(x), la phienbanlQclow-passcua i(x), xemhlnh2.4. il(k) la tinhi<%ula'ymill nhungchua dll<;5Cnhiphanhoa(ho~cla'ymill va lu<;5nghoavoi mQtgia tq ra'tIOnL). Gia thie't r~ngnguongnhi philo hoa VI du<;5ctinhbai giai thu~tOtsu va la'ygia tri V!I)=~. Phienbannhiphanhoacuai1(k) chIdinhbCiii}J)(k)vad6ngnha'tvoi i(k).Giatri nayd~tdu<;5cb~ngeachla'ymftutrlfctie'pi(x)makhongsad\lnglQcanti-aliasing. 15 Nhoding i(k) duQetrlnhbaykernv~m~t hill thongtinvi tri.Ham if2)(k) Ia phien bannhiphankhaed~tduQeb~ngeachgiastrr~nggiaithu~tOtsuclingea'pmOtgia tri nguongkhaeV~2)=X. D6tha'yr~ngtruonghQpt~nha't,buoenhiphancoth~ mangl~isais6v~vi tri la .:tL1I2.Nhuv~y,t6ngeOngsais6v~dOrOngcoth~eao b~ng,1.Ne'ui(x)bi~udi6nph~ngiaonhaueuamOtea'utruedo<;lnth~ngmanhvoi dOrOngthl;t'esl;t'eua2,1,truonghQpt~nha'tudnglingvoi sai s6 co lienquailla 50%! i(x). r- -~L~lJ. - - . ) '--~ ii' 1 ~ ~ ' (2)'I / ,-- - " . '=3/4/' I -~ I~I. ----- 0 nor--"- - v"'e on,,(k~--~=f-_ui- - . 'F:~ii-U ,.. . "",']. i i-LL. i~2\k~ i . r I() . x--.- k-. I 1- . k.- Hinh2.4.Meo!nOvitridonhiphanhoa. Toml~i,nhii'ngke'tqualuQnghoaco th~khongduQechuy trongh~uhe'tnhii'ng anhvan banne'uchungtastrdl;mgnhi~uhdn4 bitchom~u(L =16mucxam).Voi nhii'ngvanbanehliacacanhtl;t'nhien,nhuanhchVpcaethenh~nd~ng,L nenduQC chQnIOnhdn.Nhiphanboa,la truonghQpd~ebi~teualuQnghoavoiL =2,cofch trongnhi~ukhiaqnh. No giamluQngdii'li~uhilltrii'(xemph~nsail),vaddngian nhii'ngtbaolactie'pthea,nhuphando~nvanMn d~ng.Tuy nhien,nocoth~dua densl!mil matthongtinquailtrQngehonhii'ngea'utruedo~nth~ngnha-ea'utrue tlmtha'ytrongnhii'ngkyt~tincokichthuoeaha. 16 2.2.3Mah6aanh MQtanhvanbandU<;1cla'ym~uvalU<;1ngboacoth6chuamQtlU<;1ngduli~ukh6ng 15,di~unayco th6gaynennhungva'nd~v~m~tlu'utru,chuy6nd6i vaXl(ly. Phgnnayduaravi~cmahoaanhnhumQtgiaiphaprhova'nd~nay.Chungtachi quailHimtdinhunglu<;1cd5mahoakhongma'thongtin,traingu<;1cvdinhunglu<;1c d5ma'thongtin.Ma hoakhongma'thongtinnghlala anhbandgucoth6du<;1ctai t(,10mQteachhoanhaotuphienbanmaboa.Honnua,chinhunganhnhiphanse dU<;1cxtrly, dovai tron6i b~tcuachungtrangnnhvl,l'cphanrichanhvanban. Co hai di6mchinhcua ma hoa anh.Trudc he'tla mo hlnh lang gi~nggall.Ch~ng h(,1Q,nhungdi6manhk~cuamQtanhco khuynhhuangnh~nrunggia tri,tdng ho~cden.Tinhcha'tnaydoi khidu<;1cgQila "duthuakhonggian".MQteachd~c bi~tdongianmahi~uquakhacd6 l<;1idl,mgtinhduthuakhonggianla xemxet nhungduongch':lYk~nhaucuacaedi6manhdenva tr~ngthayVI xemxetchinh caedi6ma,.nh.Ke'tquanayflamtranglU<;1cd5mahoarun-length.Di6mthuhaila mahoaentropi.No khaithacd~cdi6mla mQtsoca'uhlnhkhonggiancoth6xua't hi~nthuongbonmQtso khac.Y tudngg5mstrdl,mgnhungtumahoang~nrho nhlingca'uhlnhthuongg~pvanhungtumadaibonrhonhungca'uhlnhhie'm,ke't quala duli~ulu'utrutrungblnhit bon.Trangphgntie'pthea,chungtasedungmQt vi dl,ldongiand6 minhhQamahoarun-length(2.3.1)va mQtlU<;1cd5 mahoa entropidu<;1cbie'tduditengQimahoaHuffman(2.3.2). 2.2.3.1.Ma h6arun-length Ma hoarun-lengthg5mbi6udi€n anh,rheatungdong,bangnhungvi trivachi~u dai cuanhungduongch':lYmaudenk~nhau.Nhuv~ymQtduongch(,1ydu'<jccm dtnhbangmQtc~pso.Sothunha'tchivi tricuadi6mcinhmatidend~uliendoivdi bientnii cliaann,trangkhisothlihaibi6udi€n socacdi6manhmaudenk~nhau tieprheadi6md~ulien.Moi dongduQcke'thucbangmQtso,chingh(,1nla0,bi6u di€n EOL (ketthucdong).Nhuv~ymQtdongtrongbi6uthibdimQtkyt1!EOL. 17 ,....- TronghinD2.5,dongthunha'tla tr6ngva nhuv~yduQcbi~udi~nbdi mQtEOL. Duongch~ydftutiencuadongthuhaiba:td§udcQthuhai,co7di~mannden,va. nhuv~yduQcbi~udi~nbAngmQtc~p(2,7).Tudngtv,duangch~ythuhaicuadong thuhaiduQcbi~udi~nbAng(13,2).Nhuv~ydongthuhaichicohaiduangch~y,va mQtEOL theesail c~p(13,2).Tie'ntrinhtie'pt1;1cde'nkhi chungta de'ndongcu6i rung. Cuoi rung,chungtaduQcke'tquanhusail(EOL duQcmahoa la 0): 16 f() Hinh 2.5.MQtVIdv v~anhnhiphan Nhuv~y,hinD2.5QuQcbi~udi~nbdimQtday50so'.Ne'usa d1;1ng4 bitd~bi~u di6nm6iso'till toanbQ ph~mvi [0,13],do~nmake'tquaseco4 x 50=200bit, daihoneachbi~udi6nchu§:nband§u:10x 16=160bitLTuynhien,coth~tha'v- J ding ph<;tmvi [0, 13]kh6ngduQcsii'dt,mgtO~illbQva trongthvct€ chi t~phQpbon s6 {O,2, 7, 13}la dn thie't.Nhuv~y chI dn hai bit d~ma hoat~p hQpnaybiing phepgan,vi d1;1, 18 0 (2, 7) (13, 2) 0 (2, 7) (13, 2) 0 (2, 7) (13, 2) 0 (2, 7) (7, 2) (13, 2) 0 (2, 2) (7, 2) (13, 2) 0 (2, 7) (13, 2) 0 (2, 2) (7, 2) (13, 2) 0 (2, 2) (7, 2) (13, 2) 0 0 10 ..... 0 -> 2 -> 00 01 7 -> 10 13 -> 11 DI nhienphepgall phai du'<jesiip xe'pho~ctruy€n mQteachthichh<jp.Bay giOanh c6 th6du'<jcbi6udi~nchib~ng2 x 50=100bit. Ki6u phepgall nay trangth1;1'cIe' t':lathanhd':lngbandfiucuaphepmah6aentropi.(xemphfintie'prhea) Ton t':linhi€u phienbankhacnhaucuaphepmah6arun-length.Vi dl,l,thayVIma h6avi td cuadu'angch':lYbdikhmlngeachtuy~td6ieuan6d6ivoibientrai,chung taclinge6th6mah6an6bdikhaangeachtuy~td6id6ivoi du'angeh':lYtru'oecua clingda':lnthJng.Da tinhdongi.lnvakhongma-thongtint1;1'nhien,phepmah6a run-lengthclingc6th6du'<jesadl;mgffiQteachtr1;1'ctie'ptrangnhii'ngthaotaexa Iy .lnhnhu'IQcnhi~u.Vi dl,l,m6idu'angeh':lYng~nkhongc6Iane~ntrangdongtru'oe cling nhu'trangdongtie'prheae6th6du'<jela':li,khongquailtamde'neachbi6udi~n chufin. Ma h6arun-lengthla ffiQteachd6khaithacs1;1'd1;1'thilakhonggianeuacae.lnh.N6 khongxemxets1;1'du'thilagiii'acacdongk€ nhau.51;1'du'thilagiii'aeacdongnayc6 th6du'<jckhaithacb~ngeachsad~ngnhii'nglu'<jedomah6ac6th6d1;1'daantru'oc, nghIala sa dl,lngdii'li~ucuadongtru'oed6 d1;(daandongsailva mah6achi la nhii'ngkhaebi~t.Vi dl,l,dongthabatranghlnh5 tu'on"gt1;fdongthahaivanhu'v~y khongdn dlt<jCmah6a;chimQtilmab6sungdu'<je100trii'ha~etruy€n.MQtkhai thacdfiydu tinhdu'thilakhonggianla ma h6anhii'ngdi~mbieneuaanh.Tuy nhien,bQgiaimasaild6phainh~ndu'<jcroanbQanhtruoekhin6c6 th~giaima dongdfiutieDvanhu'v~ydn mQtvitngd~mIOnbon. 2.2.3.2.MaHuffman Ma Huffmankhaithactinhphanb6khongdongd€u eua'nhii'ngkhaDangtu'<jng IfltngtrangmQtthongdi~p.NghIala, caeky t1;(thu'angxua-thi~ndu'<jcbi~udi~n b~ngnhii'ngtil mangiintrangkhinhii'ngtil madaidlt<jesadl,lngchocacky t1;fit 19 xu.1thi~n.Ke'tquala dQdaitu trungblnhng~nhdn.Nhuv~ydi€m chinhye'ula ki€u tu mavdi dQdaic6th€ thayd6idt«;5c,dvatrennhungk..l}aHangtu<;5ngtru'ng. Trudclienchungtasexemxetphepmah6avasaild6la phepgiai IDa,di€u nay kh6ngddngiannhutru'ongh<;5pmah6arun-length. Vi~cxaydvngnhungtumag6mhaitie'ntrInh,rUtg9nvaphanchiaoXetvi d1,1t~p h<;5pcacs6 {G,2,7, 13}thudU<;5ctuphepmah6arun-length(xemhlllh2.6).C6th€ llh~nth.1ydingdn s6cilachungkh6ngb~ngnhau.Ta ses~pxe'pl,;lirheathlitlf giamd~nxacsu.1t(t~ns6tudngd6i)vagallcackyhi~u{Si;i =1, ...,4}chachung. Xet caccQtthlinha'tvahaitronghlnh2.6(a).Trangtie'ntrlnhrutg9n,take'th<;5p haiky hi~utftns6nh6nh.1thanhmQtkyhi~umdic6xacsu.1tla t6ngcilahaixac su.1t.Di€u naygiambdtmQtkyhi~u. (l~I~.'-: ::~J~=-:J~ ~-_; m_-r8;50-~~- ~!~--;:;{ 0.2°. I - ,---~i..L m- l_._~_~ -., 0.52I 1 (b) 0 Hinh 2.6Vi dl,lphepmah6ahuffman. (a)tie'ntrJnhrutg(;>n,(b)tie'ntrJnhphanchiao T~ph<;5pmdi cac ky hi~udU<;5cs~pxe'pl<;limQtl~nnuarheathli t1,1'giamcila cac xac su.1t.Di€u nay haant.1tlftn l~pthli nh.1tcila tie'ntrlnhrut g9n.Tie'pt1,1ctie'n trlnhde'nkhi chaconhaiky hi~u,hlnh2.6(a).Trangtie'ntrlnhphanchia,caeky hi~udt«;5et<;labaygiodu<;5cphanehiamQtcachd~quy.Luc nay,cactumadu<;5c xaydvngdftnb~ngeachthemcacbitGva 1VElacacke'tquaphanchia,xemhlnh 20 I i P(s-) --:'l: 2 I - --0.48 1 "'----0.48 1 .....,.0.52---- ------------- " I $2:0 01 <--0.20 01 -'. 0.0.32 0<1" . 0.482.------ $3: 7 000 '0.16 O(V o' '0.20 01 1 ! $ -t: 13 001 -<"0.16fool----------- 2.6(b).Cu6icling,tathudU<;1cmQtt~ph<;1pcaetITmacocacdQdaico thethayd6i {Sl : l'S2:01,s3:000,S4:0Ol}.£>Qdai trungblnhtfenky hi~ula: L =IJ.p(s;) i =1.0.48+2.0.20+3.0.16+3.0.16 =1.84bit/ (2.19) Nhodingmahoarun-lengthcilaanhtranghlnh2.5t~ofa 50ky hi~u.Nhuv~yma hoaHuffmanchocaeket quamahoarun-lengtht6ngcQngla 1.84.50=92bit. £>i€unaydu<;1csosanhvoi 160bitdoih6i choeachbi€u di8nchu§n.Lu'uy f~ng 100bit d~tdU<;1caph~ncu6iclingclingla mQt10~imahoaentropi.NhungsO'chua sad~lllgiua0va13kh6ngconhungtITIDa. Vi~cgiaimadu<;1ctht;t'chi~nquacaygiaiIDa.Di€u nayclingdU<;1cKaydt;t'ngtfong lien trlnh phanchiaoM6i phanchia du<;1canh x~thanhmQtki€m tfa d€ xac dinh xembit tiep rheala 0 hay I, hlnh2.6(b)va 2.7.M6i la cila cay bi€u di~nmQtky hi~u.Tientrlnhgiaimab~td~ua g6ccay,nuta.CacduangdidU<;1cxacdinhb~ng caclu6ngbit.Bit ky khinaod~tdenmQtnuthi, mQtkyhi~udU<;1cphatfa valien trlnhtfal~ig6c,b~tdfiugiaimamQtkyhi~umoi. ~ SlRoot ~ /. ~a ~ o~ 0 G Hinh2.7.Caygiaima Vi dlJ, haymahoahaidongdiu eilahlnh2.5thanhmQtlu6ngbitsaildomahoa chung.Ma hoarun-lengthduafachu6icaesO'sailday: 0,2,7, 13,2,O.V€ m~tk:Y hi~u,chungta du<;1c525j53545j52.B~ngeaehsa dlJngmaHuffman hlnh2.6(b),chu6i du'<;1cchuy€n thanhlu6ngbit: 011000001101.Tien trlnhgiai ma su dlJng cay giai 21 mavab~tdftud g6c.Khi bitdftutieDla0,chungtade'nnutb.Bit thuhai1a1.Nhu v~ychungtade'nkyhi~uS2,truyennoill, vatrdl<;lig6c.Bdi vi bitthubala 1- de'n ky hi~uSI>truyennodi vatrdl<;lig6c.Tie'ntrinhnayduQctie'pt1;1cde'nkhimQibit duQcdQc.Cu6i clIng,chungtaduQcchu6icacky hi~uS2S]S3S4S]SZtudngungvoi chu6icacs60,2,7,13,2,O. De'ngiil'ath~pDieD70,maHuffmanduQcxemnhucacht6tnh§t.Trangthlfcte', maHuffmanchi t6iu'ukhicacxacsua'tcuakyhi~ula caclily thuanguyendudng cua(112).H<;lnche'naygftndaydaduQCgiaiquye'tb~ngmQthQmamoi,cacmas6 hQc. Ma hoaanhcomQtItchsttlaudoivahi~nnay,nhieuluQcd6mahoathlfcte'duQc chu.1nhoabdiUy banTuva'nDi~ntha<;livaDi~nbaaQu6cte'(CCI1T)vaT6chuG Tieu chu.1nQu6cte'(ISO).DuoislfbaatrQcuahait6chuGnay,JBIG ciliaramQt chu.1nchacacanhnhtphanva JPEG ciliarachu.1nchacacanhmUGxam.Vi d1,1, phuongphapcuaJBIG sttd1,1ngcachxaydlfngdQphangiai khonggiantangdftn thayvi cachma-run-length,thea sanbdimQtbQmahoas6hQcthichnghithayvi bQma hoaHuffman tTnh,sttd1,1ngtrangvi d1,1truoc.ddQphangiai200dpi,JBIG thoduQcty l~Dengiil'a5 va62chacactaili~uthudngm<;likhacnhau.Nhlnchung, ty l~DentangrheadQphangiai. , K ~? 2.3 PHEP BIEN 001ANH Bie'nd6ianhla mQtthaataGxttly anhinputthanhanhoutput.Nhuv~yphepbie'n d6iduQcd?ctabdiquailh~input-output,matinhtlfnhienph1,1thuQcvaam1,1cdich cua thaatacoNhil'ngbie'nd6i hinh hQC(m1;1c3.1) co th~ph1,1cV1;1m1,1cdichdieD chinh nhil'ngslf sai l~chmeamo tuy rheaanh nh~nduQcva chu.1nhoachil'vie't l~ch.LQc(m1,1c3.2)If!thaataGcanbantrangxttlyanhvacoth~giupciiitie'nvi~c tachanhDen(ml,lc3.3).Phathi~nbiend6ituQng(m1,1c3.4)valammanh(m1,lc3.3) la hai (haaUlCthuongsttd1;1ngtrangphanrichanhvanban.Chung t<;lathanhgiaa di~ntudi~manhde'ncachbi~udi€n c§pcaabon. 22 - 3.1.Cacphepbi~nd5ihinhhQc A.nhvan banthudu'Qctu thie'tbi s6hoachill nhi~ulac dQnghlnhhQCkhacnhau,va co th€ du'Qcdi~uchinhb~ngnhii'ngbie'nd6i hlnhhQcthiGhhQP.Vi dt,l,mQtvanban khangd€ th~ngtrenmayquetse chora anhs6hoabi nghieng(hlnh2.8).Cacphep bie'nd6i hlnh hQccling co th€ du'QCsadt,lngd€ chu~nhoa chii'vie'ttay bi lc$ch. Trangnhii'ngbanve ky thu~t,cacky 11/va cacs6 co th€ du'Qcvie'ttheonhii'ng hu'angkhac nhauva nhu'v~yvic$cnh~nd~ngchungdoi h6i mQtmQtphepquay tru'ac. --'1 -~- lr<rat-. ~ :---..;1'J" , ~ "" C'...' ... .., 1r,,-..".' . . . " /eOW/e O nI , ' '.. ~t4. .~.. ' p. ' .. ' J' am. ", kien'rt'" anXl/? , fJrJic ' " y. ,,'ve «17a'." ,la ~., thamg;a ' Yltonn'J... J'. MINHVongt' .' I va~ II euI J.. thl/i, 1;~nme ~' 0 cUdc' '"Kue Va, Thon JYng,v/j IJaO ~onlatais,~h(J1.nayla PhlfCtCJp,va . :huYen 9thuang" '. ~~... (tn.faUyr P~alc611~'m9tIron" " lIay "., , "0/ de,.. .- , 117lak'" un,N", 9:tlsanc " ",U9"n.hr'h "vOlnl . a" ."18nii n 1Il/r}. . g \l:o o' , .,Uarn' ' oiV,Un r" ,na/./i" ... '" 9th. I , 'I nganh. flJh(fe'+/-."g <Jygi ~e""b ,(J1. " . . ta17g'/..[-~.. ' anntoar, ang ' 'lfeen.. ,VI ClO(j;' J/ lien . ' . C(jthe~ . CoquYen: CiP.Itakhi ' elmehot,..~qanhiJr) ~ithUiCh~sClCh \Ia",,;l?pthliho C a ha?han"e " u.'khk ofif)v."y '..'[l,nghi'a!",, len ..' "'anoilL' 'v Pat "1 h- q Ciy?-ro Q Ihyi naYd-oec!lIacYa' ~!i{h~'ch/'.m~laiSaon~Cokh';.'~eiaf ;~IU~19a~:~~fU?t~~:ne~ang:~h'!191trong~h~eCh~e~;~gth~~ .uq~tlen,H : ...yaChung~h~aviitra~h{1[Jho~cbatl/r}~dletJkie u,hOl I c~lQh.. h,alv~nban. lqCOqa..1,8f}l1tha,9l/ tochtJ.'~k()tJCi Thong~.' u Phap- AI ~Uaf7IroTi;"~dll1hrorao. 1)S!.'If!qUac t.911f7 dUn,, vOrAI.. IV("f:>,.,L." )01..1,1+1.-,'. ,0,."..., P '~ Hinh2.8.Motph~nanhvanbanbinghieng B€ d~tdu'QcmQtke'tquadi~uchinhdung,dn conhi~ubu'ac.Tru'ache't,chungta phai xac dinhki€u bi bie'nd~ngcila anhva tl;10mQtmahlnhtoanhQc.Trong tru'onghQpanh2.8,ki€u sai lc$chanhr5 rangla mQtphepquayva mQtmahlnh quaychinhxact5nt~itutoanhQcchu~n.Thuhai,chungtaphaixacdinhcacgia tri thams6cuaphepbie'nd6i,ch~ngh~ngocquay.Bi~unaypht,lthuQcvaoung dl,lllg.Tranghlnh2.8,gocquaycoth€ du'QcxacdjnhcnoloanbQvanbantrongkhi co tru'onghQpphaidu'Qcxacdinhct,lcbQchom6inhomkyt1!.Cu6icling,banthan sl;!di~uchinncoth€ d~tdu'QcquamOtquatrlnnhla'ym~ul~ianhs6hoabandffu. 23 2.3.1.1. Phuongphapcoban Nhungbie'nd6ihlnhhQcco th~du<;5ctrlnhbayIDQteacht6ngquat.D~ti(x,y)la anhbandauva {(x',y') 1ftanhbisail~ch.Haianhlienh~baicacphuongtrlnh: x'=J; (x,y) (3.20) y'=f2(X,y) (3.21) Anhbandaucoth~du<;5cbi~udi~ntheoanhsail~chnhusan. i(x,y)={(x',y')={(J;(x,y),f2(X,y)](3.22) Ki~usail~chanhdu<;5cIDOtabaitinht1!nhiencuafIC',,)vahC.,.).Cacphepbie'n d6iaffineCtuye'ntinh)g6IDtinhtie'n,dinhty1~,quay,vaxiencoth~du<;5cbi~udi~n b~ngmatr~n: ~){::: t){:)C3.2~ Bang1t6ngke'tnhii'ngtinhcha'tcuacacbie'nd6iaffine. Kiiu Tinhchat Tinhtie'n a;j=O;i, j =1,2. Thayd6i ty Iif: all =all =0 Quay a :g6cquay Xien ~:g6cxien Conhi€u hQbie'nd6ikhongtuye'ntinh,nhuphepchie'uvadathuG.Nhii'ngbie'nd6i naydu<;5csii'dl;lllgtrongvi~cIDOhlnhsail~chanhdoh~!h5ngcamerat~ofa.Trong lInh v~(cphantich van ban,tn;lcquailsatcua h~th5ngcameradu<;5csa:pxe'ptn,tc giaovoi ID~tvanban.Nhu v~y,cacphepchie'ukhongcanthie't.Trai l~i,cacphep bie'nd6idathUGra-tcoichkhiIDOhlnhcacsail~chanhdoh~th5ng5ngkinh.Hai lo~isai l~chanh thongthu'ongla barrel,do hlnhd~ngtroll cua 5ngkinhva pincushion- hlnh3.9.Cahaicoth~du<;5cxa'pXlbai: 24 all =cosa all =-sina all =sina a22=cosa all =1 all =tg all =0 all =1 . 3 r =Cm+Cd.r (3.24) Troncrd6r'=IX'2+y'2 r = 'X2+V20 'J ' V - Cmla dQphongd~iva Cdla h<$s6 sai l<$ch.H<$so cuoiclingamchobarrelva dudngchopincushion.H~so thli'hai la zerodo tinhdoi xli'ngcuah~th6ng6ng nnh.Bi~uthli'c(3.24)coth~dU<;1cvie'tl~iduoid~ngdathli'c: ( XI ) =Cm ( X ) +Cd ( X2 +<)X ) (3.25) y' Y (X2+y )y Nhlnchung,tacoth~sadl,mgcacphepbie'nd6idathli'cd~xa'pxi cacsail<$chanh hlnhhQckhacnhau. Biendi,lngBarrel Biendi,lngPincusion Hinh 3.9.cac biendi,lngquanghocdoongkinh 2.3.1.2. U<ic1u'<Jngthamso Do co nhi~ubie'nd6ihlnhhQcchocacli'ngdl,mgkhacnhau,chungtachixernxet haitruongh<;1ptrongphffnnay.Truongh<;1pthli'nha'tla xa'pxi gocl~chcuatrang vanbanvathli'hailaxa'pxih<$s6sail<$chanhcuah~th6ng6ngnnh. Giai thu~tudclu<;1nggocl<$chdu<;1cxernxettrongphffnsaild1,1'av oki~rntragia thie't.NghIala,chungtachie'uanhtheernQts6trl,lC,tinhcacbi~ud6theehudngva chQnhuangd~tc1,1'cd~itheelieuchuffnth~nghang.Xernhloh3.10.Trudclien, bi~u00chophepchie'ugoca du<;1ctinhboi: OJ H(y/;a) =2)<Xk'Y/) (3.26) k=-oe OJ = Ll(cosa..xk-sina.yJ,sina_'k+cosa.y/) (3.27) k=-oo 25 Vdi cae quy ude {(x~,y;)=On~u(x~,y;) n~m ngoai van ban, va /(x~,y;)={~ound(x~}round(Y~)]n~unguQel<,li.Sail do, vi~exac dinh tieuehu~n th£nghangA(a) dvatrensVbi~nd6i histogramgiuacaeduangth£nglien ti~p nhaurheahuangchidinhbdi anhusail: OJ A(a)=2)H(y,;a)-H(YI+I;a)]2 (3.28) 1=-«> ~y C, Hinh 3.10U8c llic;ng 6cnghieng Cu6i cling,goel~ehudelu<;1ngehobdi: a*=argmaxA(a)(3.29) Phuongphapnayco timquailtrQngthvet~VInocothSthaotaetrveti~ptrenanh muexammakhongdn phando<;inho~enhipMlnhoatrude. Bay giOchungtaxemxetvi~eudelu<;1ngcaeh~so'sail~ehanhdo6ngldnhrhea biSuthue(3.25).Phuongphapnayg6mnhi€u bude.TrudetienanhduQexaedinh, i(x,y) d~ttrongmQtludihinhvuongvaphienbanbi sail~eh{(x',y')eilano.Sail do,so'NcpcaediSmdi~ukhiSnduQe hQn,eh£ngh<;incaediSmgiaoeilaludi;Ncp phai IOnbonso'h~so'ehuabi~ttrangbiSuthue(3.25).Ti~pthea,caequailh~ ('\>Yj)B (x~,yJ,j=1 ,NcpduQethi~tl~p.Cu6icling,caeh~sf)ehuabi~tduQexae c1inhb~ngphuongphapblnhphuongevetiSu.Bi€u thuG(3.25)co thSduQevi~tl<;ii dudi d<;ingmatr~nnhusau: 26 z' =Z.C (3.30) Trangdo: Z'= ( X: ) ;Z= [ XI(x: +y2)X ) ;C =(cm )y YI(X-+y2)y \..Cd (3.31) Vdi m6ic~pdi~m{(Xj,yJB (x~,yJ,j=1,...,Ncp},chungta chnh~phuongtrlnh Z~=Zj .C +Rj' trongdoRj la vectorsais6cuaphepdo.Giai phapbinhphuongq(c .,? ,,\,Nrp RTR d h b? heu L'...Jj~l j j u<;1c 0 ch: A ( NCP ) -I ( NCP JC = ~Z~Zj ~Z~Z~(3.32) Trongdotchichuy~nvi cuamatr~n. Phuongphapdanhgianaybaatrumph~nsail~chanhtrenroanbQph~nanhdU<;1c mahlnhbdicungcach~s6. 2.3.1.3.La'ym~uI~ianh 56h6a Budccu6icungtrangdi~uchinhhlnhhcla xaydvngli;licuaanhkhangbi sail~ch 19tl(dngtll'phienbanbi sail~ch,quabi~uthac(3.20),(3.21)va(3.22).Nhii'ngbi~u thacnaydn dU<;1cdi~uchlnhchocacanhs6hoa i(k.f);x,I. /1y)va i (k'./1x',[. /1y'). Vdi mQtdi~mchotrudc(x=k.f);x,y=[./1y),di~m~',y,)tuongangdi;ltdU<;1cb~ng bi~u thac (3.20)va (3.21)nhln chungkhangn~mtren ludi xac dinh bdi {(k'./1x',z''/1y')/k',z'EN}.Nhuv~y,dn mQts6xa'pxi. Xa'pxi dongiannha'tlaphuongphapnguoitanggi~ng~nnha't.Nghiala, i'NN(x'. y') =1"[M roUn1 ~J6Y'roun{;,)] (3.33) Phuongphapt6thonla nQisuyluongtuy~n.Trudclien,chungtaxacdinhhlnhchii' nMt ABCD baaquanh(x',y')(hlnh3.11)saildotinhi(x',y') : " ( o,.,) _",(b1 ( ,, " ) 1SL x,Y -1 As'l ~) 1CD-1 AS, Jl (3.34) Trongdo: 27 i'AB=il(A)+(;,)U'(B)-i'(A)] (3.35) i'co=i'(C)+(;,)U'(D)-i'(C)] (3.36) NQiSHYlu'ongtuye'nnhinchungduGapungh~uhe'tungdt).ngtronglInhv\fcphilo richvanban.Tuynhien,ne'uanhdu'<;1cdi~uchinhco ty l~la'ymftutha'phdnannh bi sai l~ch,la'ymftul~isethaotic trenmOtphienban19Clow-passcuaanhbi sai l~chd6tranhrangcu'a. y ~x ~ ~ c b I Ay B a x Hinh 3.11.PhLiongphilpnQisuyILiangtinh 2.3.2.LQc Ph~nnaygidithi~uhaid~ng19Cs6hoatuye'ntinhvakhongtuye'ntinh.Mt).cdich la cungca'pcaecongct).cdbanchonhii'ngungdt).ng19Canhd6ivdi cacanhvan ban.L9Cg6mbie'nd6imOtannhinputi(k,l)thanhmOtanhoutputio(k,i)thu'ongIa mOthamnh~ncacgiatri inputtrongmOtvi tri quanhmOtHinc~nct).cbQ i(k,l). Tinh tuye'ntinhclingnhu'tinhkhongtuye'ntinhcuahamnayxacdinhcacbQ19C tuye'ntinh(khongtuye'ntinh).Ph~n3.2.1trinhbaycacbQ19Ctuye'ntinh.Sando hai ldpcacbQ19ckhongtuye'ntinhsedu'<;1Ctrinhbaytrongph~n3.2.2va3.2.3,xe'p lo~icac bQ19Cthut\l'va cacbQ19Chlnhthai. 2.3.2.1 LQctuye'ntinh Xet ldpcaebQ19CFiniteImpulseResponse(FIR),du'<;1cmotabdibi6uthucxo~n: 28 "" "" io(k,l)=i(k,l)*f(k,l) =L Li(k-k',l-l').f(k',l') (3.37) k'=-oo/'=-00 Trongdo f(k,l) la bQIQchuangungxung,condu<;1cgQila ID~tn~ho~cd~ngrnftu. Cahai i(k,l)va f(k,i) IaphffnrnarQngh~nche',nghlalachungnh?ngiatrizero bellngoaivunganhhuang.NhuV?y,t6ngtrongbi6uthuG(3.37)du<;1cgiOih~n trangIDQt?Ph<;1pconhuuh~ncacchis5.Vi d1,l,vairnQtID~tn~3x3,ph~rnvi cila t6ngcacchis5la k',t =-1,0,1.Cachuangungxungtie'prheathuangdU<;1csii'd1,lng trangphanrichanh: [ 1 2 1 ] It 2 4 2 1 2 1 +[~ [ -2 1 t 1 4 -2 1 [ -1 t -2 -1 {-:2 (3.38) (bQh}clowpassho4cliunmjn) 0 -1 ] 0 -2 (3.39) (bQ19Cxacdjnhbiend9C) 0 -1 -2 ] 1 (3.40) -2 (bQphathi~nbienLaplaceroi r(lc) 2 -1 ] 4 -2 (3.41) 2 -1 (bQ19Cxacdjnhthdngdang) -2 1 ] 5 - 2 (3.42) -2 1 (bQ 19Cmi'J rQng) NhungIan c~nIOnhon3x3clingc6th6du<;1Csii'd1,lng. Nhii'ngtinh chat cila IQc tuye'ntinhdU<;1cbie'tde'nva du<;1cIDa ta trongnhieutai li~u.N6i chung,cacbQIQctuye'ntinhthuangdu<;1csii'd1,lnglienke'tvai cacthaotaG khangtuye'ntlnhkhac.Vi d1,l,bQphathi~nbienLaplacephaitie'prheabairnQthli t1,lCphathi~nzero-crossingd~xacdinhcacdi6rnbien.£)6phathil$ndong,nhieu bQ IQc nh':lYearn vai IDQthuang C1,lth6 du<;1cap d1,lngva cac ke'tqua du<;1Cke'th<;1p vdi roantii'max-operatord6xacdinhhuang.lnhhuangC1,lCbQ.HonQua,c6th6can 29 sa dl,lllgde>phangiai dakh6nggiand6phathi~ncaedongco caede>fe>ngkhac nhau.Nhungvi dl,lminhhQavaitfOeuacacbe>lQctuy~ntinhtrongxa19anhvan ban:chungla nhungthanhphftncuacaegiai thu~tphliet~pnhunghi~mkhi sa dl,lngde>el~p.Ben qlllh do,nhi€u tar Vl,lphanrichco th6th1!ehi~nb~ngnhil'ng phu'ongphapthayth~dongianbon.Vi dl,l,phathi~ndongco th6du'<;1cth1!ehi~n b~ngnhiphanhoavalammanh(3.5),it nha'tchonhil'nganhvanbancoeha'tlu'<;1ng t6t. 2.3.2.2LQcs~pthuhi Caebe>lQes~pthlit1!kh6ngtuy~ntinhvacoth6d~tdu't Ianc~n3x3quanhdi6manhmachungtaquailtamirk,!).f)~tSk,/lat~phQpcaede> xamtrongIane~neua(k,!): Sk,l ={i(k',/')llk'-kl~1,11'-/1~* (3.43) va Rk,lla ehu6ico thli t1!euano: Rk.l={lj~r2~...~r9h E Sk,l} (3.44) Caeroantas~pthlit1!nhu'saildu'Qcbi~t: iik,l) =r] (anman) iik,l) =r9(giiinnil) (3.45) (3.46) (3.47) (3.48) iik,l) =r9- r] (phdthi~ndLlongviin) iik,l) =r5(trungtuyfn) Be>IQctrungtuy~nla be>lQes~pthlit1!ph6bi~nnha't,VInoco th6khanhi~uxung 11!ckh6nglammaanhinput.Nhlnchung,caebe>lQeco th6du'<;1capdl,mgehocae anhnhiphanvacaeanhde>xam(xem3.3.1).Chungtasetha'ytrongphftnti~prhea r~ngconhil'ngdi6mtu'ongt1!giii'acaebe>lQes~pthlit1!vacaebe>lQehlnhthai. 2.3.2.3.lQChinhthai LQehlnhthaid1!atrencaekhaini~m19thuy~tt~ph<;1pvarutracaed~ctru'ngeua d6i tu'tphftnta du'<;1eea'utruethiehhIJpva m9ttoantli'hlnh thai thiehh<;1p.No xemxetcaeanhnhu'caet~phQpva thaotaechungsa dl,mgcae thaotac logicnhu'he>iva giao.Toantii'hlnhthaitr1!equailnha'tla hit-or-miss. 30 Nghlala, chungtaquetanhinputvasosanht<;lim6ivi tricaediemanhIane~nvdi ph§ntaea'utrue.N6ue6mQtd6isanhbeanhac,giatridu<jexacdinhtrudeduc;1c gall ehoanhoutputt<;livi tri d6; trai l<;lianhoutpute6theduc;1ethi6t l~pclinggia tri nhu gia tri d6 euaanh inputho~eph§nbi! euagia tri duc;1edinhnghlatrude.Ch~ng h<;ln,phffntii'ea'utrue3x3tronghlnh3.12,trangd6"1" chiradiemanhthuQephffn ta ea'utrue,c6 theduc;1esad\:mgdedi~nvaocae16nhaeuaannhnhiphan.Cac roanta hit-or-missthfchhc;1pehocaetaevt,ldongiannhungkhongthfchhc;1Peho caetaevt,lphuet<;lp.Ti6pthea,chungtatdnhbayb6nthaotaecobanla nhungn~n tangquail trQngnha'tcuaquatdnhlQehlnhthai.. . . . . . . I ....... 1 1 1 . 1 1 1 1 1 . --1.1-- .11111. 1 1 I . 1 1 1 I 1 . . 1 1 1 1 1 . . . I . 11. . 1 1 1 1 I . ....... . . . . . . . Anhinput Philotli cautrue Anhoutput Hinh 3.12 Toan tlihit - mis B~tA la t~phc;1pbiendi€n anhnhiphan,nghlala, A={(x;,yJji(xi'yJ=I},vaB la phffntaea'utrue.(Ah duc;1exaedinhnhumQttinhti6neuaA baivectorb=(Xb'Yb)' nghlala, (A)b={(x"Y;)+(Xb'Yb~(Xi'Y;)EA}.B6n pheproanhlnhthaicobaneuaA ehobaiB duc;1edinhnghlanhusan: DilationAEBB=YeAh beB (3.49) Erosion A0B =I (ALb beB Closing A.B=(AEBB)0B OpeningAoB =(A0B)EBB (3.50) (3.51) (3.52) Chungta da tdnhbayt6mtiit cacpheproanhlnhthaitrencaeanhnbi phan. DilationmarQngvaerosionrutl<;lianhbandffu.Chungthuangduc;1esadt,lnglam millduangvi~n,lamdffycae16nhavakhanhi€u. 2.3.3Tachroi anhvan~n H§u h6tcaeanhvanbanla k6tquatitquatrlnhin a'nho~evi6ttrenmQtn~ndang nha't,eh~ngh<;lnnhutagia'ytr~ng.Tachrai anh- vanbanho~ecaebanverakhai 31 n~nlamQttrangnhungthaotaGdin bannha'ttrangxii'1:9anh,ph1,lcV1,lchoeacthao taGtie'pthea,nhuphando~nva gall nhan.Phffn2.3.3.1duara tie'll trlnhtachdl,l'a trennguongmUGxam,giathie'tn~nla d6ngnha'trangcahaimoitruongnhi~uva khongnhi~u.Trangphffn2.3.3.2chungtabo gia thie'td6ngnha'tva xettachroi anhtun~n. 2.3.3.1Ngu'ongdQxam Ne'uvanbancocha'tluQngt6tvacon~nd6ngnha't,quatrlnhtachcoth€ du'QCthl,l'c hic$nb~ngcachsii'd1,lngtrl,l'ctie'pphuongphapnhiphanhoamotatrongphffn2.2. Nhil'ngvanbanlo~inayne'uduQcquetd dQphangiaicaosechomQtke'tquatach hffunhuhofmbaa.Rtli thay,trangmQtso'truonghQpkhichungtaapd1,lngpht(ong phapnaychoanhcocacvungtdongphankhacnhau,ke'tquakhongnhumongdQi. Cac dongtuongphantha'pbi boma't.B~ngcachdi~uchinnnguong,co th€ khoi plwccacdongnay.Tuynhien,lUGnayl~ixua'thic$ncacdi€m anhnhi~utrenn~n. Phuongphal?di~uchinhduQcd~nghig6mch(;mmQtnguongvoi mQtty l~ph~n tramchotruoc,ch~ngh~n10%,cacdi€m annco dQxamtha'phonnguongnay (phuongphapp-tile).Trongphffnsail,chungtatrlnhbayhaicachtie'pc?nd€ giai quye'tva'nd~nay.D€ dongian,chungtasechiminhhQacacphuongphapnguong roanCI,lC,tuydingtrangmQtso'truonghQp,caephuongphapngu'OngC1,lCbQthleh hQpbon. Cachtie'pc?ndffubaag6mlQcanntruockhinhiphanboa,sii'd1,lngbQlQclammill tuye'ntinh,clIngca'pbdibi~uthUG(3.38).Co th~tha'yr~ngnhi~ugiambot,nhu'ng cacca'utrucdongdayd~cla chomQtso'pixeldinhvaonhau.Clingco th~sii'd1,lng cacbQlQcl'J16ngtuye'ntinh,nhutrungtuye'nch~ngh~n.Tuynhienke'tquakhac bic$tla ra'tit. Cachtie'pc?n tnuhai thii'lo~ibenhi~usailkhinhiphanboa.MQtbQlQctrung ruye'nduQcapdl,lngchoanhnb!phantra thanhhQlQcchinhcoth€ la'pd~ycac16 32 rnho,lamkhitcackhehonhovalo~ibonhi6uxung.Cachnayd6ikhiphavoke't cffuho?clamdinhcacchCi'l~i. 2.3.3.2N~nk~tc~u Nhi~uchudngtrinhso~nthaovanbanhi~nd~iclingcffpkhanangt~oran~nke't cffu.Ch~ngh~n,mQtvanbanduQcthie'tke'n6i b~td~16icu6ns1,1'chu9cuadQc gia VaGmQtsO'vungnaGdo.Kh6ngmay,no t~ora nhi~uvffnd~d6i vdiOCR. Trongph~nsau,chungtam6tamQtky thu~tddngianvahi~uquadlfatrenqua trinhlQChlnhthaid~giaiquye'tva'nd~tachanhkhoin~n. Trudclien,anhduQcnhiphanhoa,sii'dl,mgphudngphap cuaph~n2.2.Tie'prhea mQtpheploanerosionduQc.ap dl,mg,sa dl,mgph~nta ca'utruc3x3.Cu6icung, pheploandilationduQcthlfchi~ntrenanhduQcanmOllboiclingph~ntii'ca'utruc. NghTala, anhnhiphandffduQcnO.Co th~nh~ntha'ydingne'ukichthudccuacac ph~ntii'ke'tca'unhohdnkichthudcuacacph~ntaca'utrucvacuavanban,ky thu~tnaythlf.chi~nt6t.Ne'ukh6ng,sedn xa19pht1ct~phdn. 2.3.4.Bi~udi~nvaphathi~nbien Sau1u1.itachkhoin~n,cacd6i tuQngduQckhoanhvung,danhgia va cu6icung phanlo~i.MQtd6ituQngduQcchidinhhoanroanboibiencuano,biencoth~duQc phathi~nboigiaithu~tsau. 1. Quet anh den khi gq.pdiem anh den. GQi no la pixel 1. 2. L~p Neu "diem anh hien thdi lei den" Thi "do ngu<;1c" Nguqc li?-i "sang phai" Ben khi "gq.p pixel 1" Giciithu~tdotlmbien 33 I I ------------- > Hinh3.13 Dotimbienclangian Hinh3.14 Do timbienvdinhi~udOitll<;1ngphacti;lp (011) 3 (010) 2 (001) I 000) 4 0 (000) 7 (Ill) 5 (101) 6 OW) Hinh3.15 Mii chu6iFreeman 34 ~4 ffinh3.13minhhQavi~cpMt hi~nd6ituQnglienke'tdongian.Chungtahillyding pixelgi6ngnhau,ch~ngh<;\npixel1,dllQCphathi~nnhieul~n.Tuy nhien,co the khii'chungmQtcachd~dang.Noi chung,anhcothechuanhieud6itllQng,g6mcac 16h6ng,made'nluQcchungcothechuanhi~ud6ituQngnhobon.Ch~ngh<;\n,vi~c dorimphaiduQcl~p d~quyd€ phat hi~nmQibienbellngoaivabelltrongcuamQi d6i tUQng.ffinh3.14trinhbayquatrinhdorimanhchuacacd6i tuQngl6ngnhau. LttuY dingdo rimmQibientrongva ngoait~onenmQtphando<;\nanhinputvdi nhieuvung(xemphfin4). MQt bien dllQCchi dinhbdi cactQadQ(x,y)- trencacdi€m anhcuano,gQila cac diembien.MQteachbi€u di~ncodQnghonlamahoaFreeman.ChicactQadQ (x,y)- cuadi€m biendfiutienduQcIttugiil'.Cacdi€m bientie'prheaduQcmahoa lienquailde'ndiembientrudc.ffinh3.15trinhbay8machu6i,m6imaduQcbi€u di~nb~ng3bit.Vi dl;l,cacdiembienhinh3.14duQcmahoanhusalt: 077 175 4 443 3 1 Ho~c: 000 III III 001 III 101 100 100 100 all all 001 CacdiembienthudllQCcod<;\ngmQtdllongcongdong.Noi cachkhac,chu6itQa dQ(x,y)tuanrheamQtchuky.Di~unayco nghiala bienco th€ dllQcbi€u di~n b~l1gnhil'ngchu6iFourier,vdicach~sO'd~ctadllongcongdong.Honfilla,nhil'ng h~sO'naycothedu'Qcke'thQpvaocacbQmotaFourierduaracactinhchatkhong d6irheaphepquayvaphepthayd6ivi trL 2.3.5.Lammanhvabi@udi~neautrue Hfiuhe'tnhfrngd6itllQngtronganhvanband~ucocaeeautruedong.Trongnhil'ng lingdl:lngct,).th€, mQtthaythe'thichQpd€ bi€u di~nd6ituQngbdibiencuanola bi€u di~ndong.No co tfimquailtrQngth1!cte'vinocoth€ dongiannhi~uthaotac tieptheetrangphanrichCalltruc.Cachbi€u di~ndongco thed<;\tdllQcb~ngtie'n trinhlammanh. 35 Hinh3.16Quy LfacIanc~ndi!!lammanh Y tlidngchinhcuaquatrlnhlammanhla x6anhi€u l~ncacdi€m biend~giamb€ fQngdongconmQtpixel.Di€u nayphaidu<;JcthlfChi~nkhongcin tachraid6i tu'<;Jng(tachd6itu<;Jngthanhhaiph~n)clingnhukhongdn x6acaedi€m cu6idong. N6i cachkhac,chungtac6th~nh?ntha'ylammanhla x6acacdi€m bienc6di€u ki~n.Giiii thu?tsongsongdongian,khongnh~yearnvdinhi~uduangvi€n, nhu sau. Sa dt:mgquyudcl?nc?nhlnh3.16,d~tNT(P1)la s6cacbi6nd6i0 (tr~ng)thanh1 (den)trongchu6ic6thITtlf ,vaNZ(P1)la s6cacIanc?nkhac0 cuaPI- Di~manhPI du<;Jcx6a(d~tbAng0) n6u: 2=:;NZ(~)=:;6 (2.53) va: NT(~)=1 (2.54) va: Pz.P4.Ps=0 hor;icNT(P2):j;1 {2.55) va: Pz.P4. P6 =0 hor;icNT(P4):j;1 (2.56) Tien trinhdLtr;cli;ipdenkhikh6ngconthayd6inaatrangdnh. MQt s6 IOncac giai thu?tlammanh,khacnhaubdi nhil'ngdi€u ki~nx6a,da du<;Jc d€ nght-TrangmQtGongtrlnhnghiencUug~nday,20giaithu?tkhacnhaudadu<;Jc tht!chi~ntrongd6xemxetcaclieuchugnnhu'khaDangxayd!,1'ngl~i,t6cGQtinh roan,tinhn!ongtlf Goivdi Calltruelien quail,chatlU<;1ngcila ca'utruc,tinhk6tnoi saukhi lamminh,vavand€ songsong. 36 P3 P2 P9 P4 PI Ps Ps P6 P7 Noi chung,caedongmanht<,toboi giai thu~tlammanheh1i'ahai ki~upixelden, di~mthongthudngvadi~md~ebi~t.M(>tdi~mthudngco2pixeldenIane?ll.M(>t di~md~ebi~tco 0, 1,3 ho~e4pixeldenIan e~n.Nhii'ngs6naycon dU<;1egQi1ath1i' W'euapixel den.Nhu v~y,m(>tpixel co th1i'tv 0 la mQtdi~meachly, th1i'tV 1 la di~mke"thue,th1i'tv2la di~mn~mtrendong,th1i'tv3la di~mchii'T, vamQtpixel coth1i'tv41amQtdi~mgiao,hlnh3.17a. MQteachthichh<;1pd~motadiu trueeuaanhlammanhIabi~udi€n d6thi.Cae nut dU<;1ek "th<;1pvdi caedi~md~ebi~tva caedudngeongvdi caedongmanhgiii'a caenutne"uco, xemhlnh3.17b.Chinhxaebon,mQtnutdU<;1echI dinhboi ki~ueua no (caehly, diEmcu6i,chii'T, ho~cgiao)vavi tri (cactQadQx,y).MQtclinggiii'a hai nutco thEdu<;1cbi~udi€n boimaehu6iho~cboi mQts6xa'pxl, nhucacll,lc giaeho~cacb-spline. . Di€m cuoi Di€m col~p Di€m thU'C1ng Hinh3.17 a.Minhhoacaeki~udi~m b. Bi~udi~nea'utruedla a M(>tgiaithu~tdongiand~tlmxa'pXldagiaeeuamQtdudngcongnhusau.Xa'pXl dudngcongb~ngdo<,tnh~ngn6icaedi~meu6iA vaB. Ne"ukhoangeachtitdiEm xa nhit trendudngeongC de"ndo<,tnAB lOll honnguongdinhnghlatrudc,n6i A vdi C va C voi B. L~pl<;lithuwe ehonhii'ngdo<,tnmdi AC vaBC de"nkhi nguong dinhnghlatru'dedU<;1cthoa. 37 A ? 2.4.PHAN E>OANANH Phando~nla tie'ntrlnhehiaanhthanhnhi€u vung,m6ivungchuamQtd6itUyng ho~cmQtnh6mcacd6itU<;1ngclingki~u.Ch~ngh~n,mQtd6i tu<;1nge6th~la mQt ky tl!trenmQttrangvanbanho~emQtdo~nth~ngtrongmQtbanve Icythu~tho~c mQtnh6mcaed6i tu<;1nge6th~bi~udi~nmQtt11ho~ehaido~nth~ngtie'pxuevoi nhau.Trangphanrichanhvanban,4 giaithu~tphando~nthuangdU<;1csii'd\mgla gallnhiinthanhph~nlienthong,phanrichcay-X-Y, lamoboerheaduangch~y,va bie'nd6iHough.ChungsedU<;1Cmotachitie't rongcacph~nsau. 2.4.1.Cannhanthanhphanlienthong Ky thu~tnaygallrhom6ithanhph~nlienthongcuaanhnhiphanmQtnhanrieng bi~t.Nhanthuangla caeso'tl!nhienb~td~ut11mQtde'nt6ngso'caethanhph~n lien thongtronganhinput.Giai thu~tquetanht11traisangphaiva t11trenxu5ng duoi.Trangdongthunha'tchuacaepixelden,mQtnhanduynha'tdu<;1egallrhom6i duangeh~ylien t1,lcuacacpixelden.Voi m6ipixeldeneuacaedongtie'pthea, cacpixelIanc~ntrendongtruocvapixelbelltraidu<;1cxemxet(hlnh3.l8(a)).Ne'u ba'tky pixeLIan c~nnaGdu<;1cgall nh11n,nhiintudngtl!du<;1egall rhopixeldenhi~n thai; ngu<;1cl~i, nhiin tie'prheaehuasii'd1,lngdU<;1eehQn.Thu t1,lCnay tie'ptl,lcclIo de'ndongcu6iclh anh. Luc ke'tthuctie'ntdnhnay,mQthanhphftnlienthongc6th~chuacacpixelc6cac nhiinkhacnhauVIkhichungtaxemxetIanc~ncuapixelden,ch~ngh~npixel"?" tranghlnh3.l8(c),pixeld5ivoi Iane~ntrcHvanhungIane~ntrongdongtru'oce6 th~dU<;1cgallnhiinmQtcachriengbi~t.(Trongvi d1,lnay,chungtasii'd1,lngnhiin euaIanc~ntrai).MQttlnhhu5ngnhuv~yphaidU<;1exacdinhvagill I~i.Sauti~n tdnhquet<lnh,vi~cgallnhandu<;1clIGanta'tb~ngcachth5ngnha'tmallthu~ncae nhiinva gall l(;licaenhiinchuasii'd1,lng.f)~minhhQarho thut1,lC,xemhlnh3.18. 38 . p p p . . L ? a. Uin c~ncua"?";P=dongtnlac;L=lanc~ntrai ** *** 11 222 ** *** 11 222 **** **** 11112222 ******** 111?**** * * * * * * * * *** * *** * *** ** *** ** * * * * * * * * * * * * * * * * * * b. Anh band~u c. Tien trinhdanhnhan ...11...222 11...111.... ...11..222 11...111.... ..1111.2222 1111.1111.... . . . 1 I 1 1 1 I 1 1 . . . . . . . I 1 I 1 1 1 1 1 . . . . . . . . . 1 1 I 1 . . . . . . . . . . . I 1 I 1 . . . . . . . . 1 I 1 . . ) . . .. . . . . . 1 1 I . . 2 . . . ..111..)). 111..22.. .44..111. .)) ))..111..22.. ..44 ))....... d. Saukhiquetd~ydli e.Ketquadanhnhansaurung Hinh3.18E>anhnhancaethanhph~nlienthong 2.4.2.Phantichcay-X-Y. Phanrichdiy-X-Y la giaithu~tphando~nph6bi€n trangphanrichanhvanban.Y tudngcdbancuagiai thu~tla khaithacdnhco ca'utrUcdQcho~cngangcuah~u h€t cacanhvanban.MQttrangvanbanthuangg6mcacdongvanbanngangkhac nhau.Nh~nxetnayd~nd€n ytUdngchi€u ngangcacpixeldentrencactn,lcdQc, phando(lntrangthanhcacdaitr~ngvacaedaivanban.MQtdaitr~ngtuongling vdi ffiQtt~phQpcaedonglien tl,lcit bonn pixeL,vamQtdaivanbanlingvdi t~p hQpcaedonglientl,leeoit nha'tnpixeln€u nguongduQed~tb~ngn. Saudo,m6i 39 dai van ban e6 th€ duQeehi€u dQetrentl1;1en§.mngangthuduQecac vi trl cila cac ky tl!trongdelinay.Thil tl,1Csaltc6 th€ duQCsadl,1ngd€ rutracaeky t1,1': 1. Tfnhroanphepchieungangd{fiwJi roanbi?trang. 2. Phiin tickphepchieudi rut ra cacdong. 3. V6'imJi dong,tinhphepchieudQc. 4. Phiin tickmJi phepchieudt;ltdu(/ctrongb£c6'c3 di rut ra cackYtfC. Tuy nhien, t5ngquathdn,c6 th€ dn thlfehi~nnhi~uhdnhai phep ehi€u d€ d(;lt d€n cac ky t1,1'.Hlnh 3.19trlnhbay mQteffuhlnh khonggian (caeky t1,1'duQcbi€u di~nmQteachtuQngtrungbdi cachQp)trongd6mQts6ky tlf chid(;ltduQcsaltphep ehi€u thti'ba (ngang).C6 th€ nh~nthayf§.ngnhungvan banphti'ct(;lpbone6 th€ doi hoinhi~uphepehi€u hdnd€ rutfa caeky tlfriengbi~t.Nhuv~y,d€ baadam co th€ ho(;ltdQngduQe,giaithu~t5ngquatsechi€u vanbandQcvangangd€n khi hai phepchi€u lien Wcd(;ltk€t quatudngt1,1'. Saukhi thtfchi~n phepchieuthu2 .+. chieu dung :~ - - ~::8]J:0: ::0::::::::' ~:o~:~:~:0: ~:D~:~O:~:~:~:O:~:~O:~:~:~:~:~:~:~:~:~:~::: Saukhithl,fchi~n phepchieudiiu tien(chieungang) Hinh 3.19Vi dl,JcuamQtvanbandoihoi baphepchi€u. Cffutrueduli~ut1,1'nhiend€ lu'uk€t quaeilagiaithu~tla mQtcaye6caenutbi€u di~ncaevunghlnhehunh~t.M6i nute6th€ c6nhi€u nutcon,m6inutconbi€u di~nmQtvungconciia vungchaoCaenuteu6i(nutla) la nhungnutkhongth€ phanchiathemdu'Qcfilla.Chungbi€u di~ncacvlingkhongth€ phanehiavaduQe 40 I gQila cacth1,1'cth€ figureDto'.Hlnh3.20trlnhbaymOtvi dl,lcilavanbantrongdo cacky t1,1'dU<;1cbi€u di~nbdicachOp,vabi€u di~ndiy cilano. Anh vanban Hinh 3.20 Anh vanbanvad;;tngbi~udi~ntheocaycuan6 MOtvin d~vai giaithu~tphanrichcay-X-Yphatsinhtrangs1,1'hi~ndi~ncilamOt sO'd.;lllgd6hQaCl,lth€. Khi do,dn thie'tkhoanhvimgchungvaapd1,lngphantich thanhphftn,lienthong. Trangphftnmotabell tren,phanrichcay-X-Y beanloandU<;1cxemxetnhumOt giaithu~thaicip theenghiakhongcotrithuGcilavanband€ th1,1'chi~nphando~n. MOtsO'lacgiasii'd1,lngtri thUGd€ huangdftnphanrich.S~l'ke'th<;1pthongtincip caova thip rhoke'tquat6tnhu'ngdoi.hoir~ngphftntrlnhbaycilavanbancomOt ciu trucdu<;1CdinhnghianaGdo.QuailtrQngbon,saisO'trongduli~udonhi~uco th€ dftnde'nthit b~iv~phando~nvakhongth€ suachuadt1'<;1c.VOJeachtie'pc~n trongdo tie'ntrinhcip caovacip thip du<Jctachrai, vin d~duli~unhi~udu<Jc beande'ngiai do~ngall nhansando.Vu di~m13.lu<Jngdii'li~uphaigiai quye'tsan do nhohonnhi~ucachbi€u di~nbandftu. 2.4.3.Lamnhoedu'ongch~y(run-lengthsmear) Gi6ngnhuphanrichcay-X-Y,giaithu~tlamnhoetheeQuangch~u-RLSdoihoi s1,1'Qi~ucblnhdQl~chtruac.TruaelienRLSphathi~nmQiQuangch~y{fAng(cacsO' 0 lient\Ic)Clladongvasandoehuy€nd5inhungQuangch~ycoehi~udaing~nhon 41 nguongdinhnghlatrudc,T thanhnhii'ngQuangch~yden.Cac Quangch~yden khongd6i.Ch~ngh~nvdiT=3,RLSchuy6nd6idong 000 1 1 0 1 0 1 1 1 0 0 1 0 0 0 1 1 100 thanh: 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 Ho~tdQngcilagiaithu~tRLSnhusau:trudctienapdt:mgrheatUngdongvasaudo rheatungcQt,thuduQchaianhriengbi~t.A.nhcu6iclingduQcktt hQpbdiphep roanlogicAND giii'ahaianhvuaduQcsinhtrudcdo. Ktt quacila giai thu~tRLS co th6duQCsa d\mgd6 gall nhanthanhph~nlien thong,thuduQcmQtt~phQpcacvung.Nhii'ngvungconch thudcra'tIOnrheacac tQadQx,y- thuangtuonglingvdicacd6ituQngd5hQatrongkhih~uhtt cacdong vanbant~oracacvungduQckeodairheachi~ungang., 2.4.4.Bie'nd6i Hough Khongnhunhii'ngphuongphapphando~ndaxemxettrudcday,trangdocacd6i tuQngriengbi~tphaiduQctachrai,bitn d6iHoughlamvi~ct6tk6cakhicacd6i tuQngbi dinhvdinhau.Xetbie'nd6iHoughdungd6phathi~nduangth~ng. y b b=xla+Yl x a 1 I , Xl X2 X3 .a Hinh 3.21 Ph<ithi~ndl1<'1ngth~ngb~nggiaithu~tHough Chungta hayxemxetphuongtrlnhcila mQtdo~nth~ngy =ax+b,cacthams6 (a,b)daduQcxacdinh,xemhinh3.21.Ntu di6m(Xl>YI)thuQcv~do~nth~ng,thlr5 rangdingba'tky ci,ip(a,b)thoaYI=ax!+bclingIamQtlerigiai.Noi cachkhac,vdi 42 rnQtdi€rn (Xf,YJ) chotn.toc,du'ongcongb=-xja+YJtrangkhonggiantharns6 (a,b) rno ta rnQiWi giai c6 th€. Bi€u tu'ongt1,tcling dungchocac di€m (XbY2),(X3,Y3),... N~u n di€rn (Xf,Yj),(Xz,Y2),..., (xmYn)niirn tren cling rnQtdo~nth~ngtrongkhong gian anh,cac du'ongcongtu'ongungcua chungphaica:tnhauclingrnQtdi€rn (a*,b*)trongkhonggiantharns6.D1,tatrentinhchfftnay,giai thu~tHoughdu'<;jc rnotanhu'sau: 1. Lw;mghoakh6nggianthamso(a,b)thimhcactebaa. 2. T(;lO6 tichlilyAcc(a,b)vakhiJit(lOcacthanhphdncilanobangkh6ng. 3. Vai m6ipixelden(x,y)trongkh6nggiandnh,mri tebaac£laAcc(a,b)thoa b = -XCI+y dLC(!Ctang len mQt. 4. Phathi?ncactri qtcd(lidiaplutO"ngtrongkh6nggianthamso'(a,b).M6i tri ung vaimQt{)ph(!pcacdilmcungdLCimgthangtrongkhonggiandnh. TrongthlfCt~,giatrta khongxacdtnhchocacdu'ongth~ngdung.MQtd~ngdu'ong th~ngtharns6 thichh<;jphonla r =x.cose+y.sinB,trangd6 ria khoangcachtit tamcuakhonggian(x,y)d~ndu'ongth~ngva e la g6ccuaphaptuy~nd~ndu'ong th~ng.Bi€u nayd~nd~nrnQtdu'ongconghlnhsintrangkhonggiantharns6(B,r) chorn6idi€rn (x,y).Gi,Uthu~tHoughkhongd6i.Nhi€u khiaqnh thlfchi~nv€ 1:9 thuy~tkhaccuabi~nd6iHough,baag6rnlu'<;jngh6atharns6vaphathi~ncaccrt clfcd~idtaphu'ongdadu'<;jcnghienCUll. Bi~nd6iHoughc6 th€ du'Qcapdt,mgchobfftky du'ongcongtharns6nao,ch~ng h~ndu'ongtroll,ellipse,vaciinhii'ngdu'ongcongkhongtharns6.N6 torarfftrn~nh d6i voi anhnhi~uva d~cbi~tgiupichtrongvi~cphannchcacbanve Icythu~t, trongdohftu h~tcacdu'ongcongla nhii'ngdo~nth~ngvacaecungtrOll.Honnii'a, cacchu6ivanbantrongcacbanveIcythu~tco th€ du'<;jcphathi~nquabi~nd6i Houghbiingcachxemm6iehu6inhu'mQtdo~nth~ngeocaephftntli'lacaek:Ytlf. 43 2.5clal THI~UTRICH CHQN D~CTRVNC MQttrongnhlingml;ledieheuaphantiehannvanbanla phanlo~icaeIcytt,tvacac ky hi~uthanhcaelOp.TriehehQnd~etrungla mOtbuoctrQgiup,lamehovi~c phanlOpd€ dang.TriehehQnd~etrungla mOtd6i tuQngnghieneUutrongnh~n d~ngm~uva co th~duQechia thanhhaieachtie'pe~n,th6ngke vaca'utrUc.Ml;le dieheuaphftnnayla trinhbaymOts6phuongphaptrieDehQnd~etrungdongian vahi~uquadaduQesli'dl;lngrOngdi tronglInnvt,tephantiehannvanban. 2.5.1.Cacd~ctrlinghinhhQc Caed~etrunghinhhQedongiancoth~ra'tcoannhudngtrongnhi€u lingdl;lng. Ching h~n,caekiehthuoet~eohuangx-vay-euathanhphftnlienthongcoth~du dephanbi~tcaeky tlftucaephftnd6hQa.Duoidayla mOtdanhsaehkhongdfty ducaed~etrunghinhhQe. 1. Caekiehthuoetheophuongx,y,vatyl~euachung. 2. Chuvi 3. Di~ntieh 4. Caekhoangeachelfed~ivaelfeti~utubiende'ntamkh6i 5. S6cae16 6. S6Euler=(S6thanhphftnlienthong)- (S6l6) 7. E>O5nd!nh=(ChuVi)2/(41t.Di~ntieh) 8. Caeda'uhi~u(phepehie'ungangvadQCcuacaepixelden) TronglInnvt,tephantiehanhvanban,nhlingd~etntngnaythuongduQcsli'dl;lngd~ phanlOptruoecaed6ituQngthanhky tt!vaanhd6hQa.Saudo,caethanhphftn tronglo~ikY tt,tdu<jegli'iehotrlnhOCRtrongkhicaethanhphftnd6hQaduQephan tichbdi trinhnh~nd~ngd6hQa.Ngoaiml;lediehphanloptrUoe,mOts6d~etntng teenclingcothi gapphftndangk~vaophanlopcaeky tt,teu6icling. 44 2.5.2.Caemoment Cacd6itu<;1ngclingcoth€ du<;1cmotabaimoment.ChungdU<;1cdinhnghlanhusail: Mp,q =J li(x,y),xPyqdxdY(5.57) Trongdop vaq la cacca'psO'nguyenkhongamcuamoment,i(x,y)la anhmt1'c xam cua d6i tu<;1ng,va D Ia phftnma rQngkhonggian cua d6i tu<;1ng.Lu'uyrang ne'ula anhnhiphanvaigiatri 1chocacpixeldenva0chocacpixeltr~ng,thiMo.o la di~ntichcuad6i tu<;1ngtrongkhiMl,ova Mo.lla cactQadQx,ycuatamkh6i IU<;1ng.Co th€ tha'yding t~ph<;1pvo hC;lncac moment{Mp,q;p,q =0, 1,2, ...}xac dinhi(x,y)mQtcachduynha't.Tuynhien,vaicacgiatrip vaq lOn,cacmomentlId nennh~yearnd6ivai nhi€u nentrongthl{cte'chicacgiatrip va q nhodU<;1csa' dl:lllg. Cac momentdinhnghlabai bi€u tht1'c(5.57)dQcl~pvi tri va nhuv~ykhongth€ dU<;1csa dl,lllgmQteachtrl{ctie'pd€ sosanhhinhdC;lng(ngoC;litrll di~ntich).MQt dinhnghlakhac,caemomenttam,nhusail: M;,q=JJDi(x,y).(x-xy(y-jiYdxdY (5.58) Trong do: MIo -- Mo,l (5.59)x=~, y- MMo.o 0,0 T~p h<;1pcaemomentamea'phai (p+q=2),M;.o,M~.2,M~1d-inhnghlaellipseqUail tinhcuad6i tU<;1ngva thudU<;1cquacacvectoreigen,huangBchinhcui:1d6i tu<;1ng: 1 [ 2.M~1 ] O=-arctan M e -Me,2 2.0 0,- (5.60) £)i:!.cbi~t,coth€ nh~ntha'yrangcaet6h<;1pmomenttamsaildQcl~pvaihuangcua d6i tU'<;1ng. rfJl=M~.o+M~.2 (5.61) rfJ2=(M~.o-1}1~,2)2+4(M1~1)2(5.62) 45 Do tinhcha'tkhongd6itheophepquay,caet6h<;fpcuamomentra'thii'uichd6ivdi OCR. 2.6. KET LU~N Trongchuangnay chungta dffxemxet caephuongphapxii'19anhkhacnhau thuangsii'dt,mgtrongnnhvrj.cphilotichanhvanban.CaephuongphapdU<;1cnh6m thanh4 lol;li:thunh~nanh,bie'nd6i anh,philodol;lnanhva trichchQnd~ctrung. Cacht6 chucnaydrj.avaocaebudcxii'19cuanhi€u h~th6ngphilotichanhvan ban hi~ndangdU<;1csa dt,mg.f)i~mchinhtrongchuangnay la trlnhbay cae9tudng eoban,va dongian- nhungky thu~tn€n tangnha'trangphilotichanhvanban. 46