Cac v:in d€ lien quail dEn cac thong tin hlnh anh da duQc r:it nhi€u nha khoa hQcquail tam nghien cUu VI t~m quail trQng cling nhu ynghla khoa hQc ciia no.. ViGc lOiu'u de tang tinh hif;
Trang 1£)~I HOC QU6C GIA TP HO CHI MINH
TRUONG D~I HOC KHOA HOC TV NHIEN
_uuu u* **_u uu
DU'dNG ANH DUC
THONG TIN HINH ANH
Chuyen nganh: Bao dam toaD h<;>c cho may tinh
va M th6ng tinh toaD
Ma s(f: 01.01.10
TOM TAT LU~N AN TIEN STTOAN HOC
Tp.Ho Chi Minh, 2002
Trang 2~,liD! 5f~
UJj
Cong trlnhduQc hoan thanh t~i~
Truong D;;tihQc Khoa hQc TV Nhien, D;;tihQc Qu6c Gia Tp H6 Chi Minh.
NguOi huang diin khoa hQc:
1 GS.TS Bili Doan Khanh D;;tihQc Paris VI, CQng boa Phap
2 GS.TSKH Hoang Van KiGm Truong D;;tihQc KHTN,
Co thi tlm hiiu lu~n an t~i:
Thu vi~n Qu6c gia Tp H6 Chi Minh,
Thu vi~n Truong D;;tihQc Khoa hQc TIf nhien, DHQG Tp HCM.
Trang 3Chlldng1 Mi'ldtlu
1.1 yeu CUllthrjc tt va Ii do thrjc hifll di tlli
Co 'the noi, ngay nay vi~c xay d\l'ng va quail Iy cac h~ th6ng thong tin hlnh anhmQt cach hi~u qua la mQt nhu du buc thie't Truoc he't, cac M thong nay d€uchua d\fng mQt h.tQngthong tin nit Ion Khai thac hi~u qua cac thong tin lo~i nay
se mang I~i nhii'ng IQi ich khong the ch6i ciii Trong y hQc, cac thong tin v€ connguoi, ban d6 gen, cac lo~i b~nh kern theo nhii'ng hlnh iinh C\l the, duQCt6 chuc
va lu'u trii' hQp Iy se giup nganh nay khai thac t6t nh:it cac k€t qua nghien CUllcua mlnh ph\lc v\l cho baa vf; suc khoe cua con nguoi Vif;c t~o ra kha Dang th\fchi~n ca m6 ao la mQt vi d\l Trong cac nganh cong nghi~p thie't ke' ch€ t~o may,thie't bi, ,cac mo hlnh thi€t ke' duQc t~o I~p lu'u trii' va xli Iy trong may tinh giupgiam chi phi ch€ t~o, thli nghif;m, Voi s\f giup do cua cac hf; th6ng thong tindja Iy (GIS), vi~c qUail Iy nha nuoc se hif;u qua hdn Kinh nghi~m cua cac nuocphat trieD the hi~n r6 di€u nay
Cac v:in d€ lien quail dEn cac thong tin hlnh anh da duQc r:it nhi€u nha khoa hQcquail tam nghien cUu VI t~m quail trQng cling nhu ynghla khoa hQc ciia no Tuyv~y, con r5t nhi~u v5n d~ m0 dn phiii nghiCn CUlllrong Iiinh vt.1'cnay ViGc lOiu'u de tang tinh hif;u qua cua cac h~ th6ng thong tin trong lu'u trii', xii' Iy va baam~t la r:it dang quail tam 90 la Iy do de th\fc hif;n d€ tai nay
1.2 M{lc lieu di tlLi
Voi cac nhu du th\l'c ti€n (j tren, d€ tai nay duQcxay d\l'ng dE gap mQtph~n vaovi~c Dang cao kha nail ung d\lng cua cac M th6ng thong tin hlnh anh Chungtoi se huang cac nghien' , mlph vao mQtso' bai loan t6i u'u C\lthe
Do cac hi; lh6ng thong tin hlnh anh rii't da d~ng, chung toi khong th~ khao sat h€tcac vii'n de lien quail Trong khuon kh6 cua lu~n an nay, chung toi t~p trung vaocac nghien cUu lien quail de'n cac thong tin hlnh anh d<j.ngvector, vif;c t<j.oI~p,lu'u trii'va xli Iy chung
Voi cac m\lc tieu tren, d€ tai nay se th\fc hif;n cac vii'nd€ C1Jthe sail:
. Nghien cau da sua't mQt mo hlnh lu'u trITcac thong tin hlnh anh d~ngvector voi cac ca'p dQ thong tin topology khac nhau
. Nghien CUuva'n d€ t~o I~p dir li~u d~ng vector tu dir li~u bitmap.Huong tie'p c~n chu y€u d day la dung cac phep bie'n d6i Hough vaRadon
. Nghien cUu kha Dang ung d1Jng ciia cac phep bie'n d6i Hough vaRadon trong bai loan xac djnh cac d6i tuqrg p.~!)gdu.Qng~
,
Trang 4Chtld45 2 T[JoIljp va bill tril dillifU anh vector
Trang khuon kh6 lu?n an nay, chUng toi sf!:chi ban d€n cae dcr li~u hlnh anhd<).ngvector D6i tuQng ehinh ma chung toi quail tam la cae dcr li~u hlnh anhph\le V\l eho GIS va cae vii'nde lien quail
mnlt 2.1 - Mil Itlnlt winged-edge topology
2.1.2 Cac cap topology trollg cd Sd d/7lifll
Mng 2.1 Mil hi tang quat cae dip topology
Cac cling chi giao nhau t<).i node.Cac
m~t kh6ng ch6ng hIp Jen nhau, ta-t cii cae m~t phil he-t loan b(>.
Trang 5Cac clIng chi co danh sach cae tQa d(\
ma khong c6 dinh d~u va dinh cu6i
Cell 15 Cell 14 Cell 13 Cell 12 Cell 11 Cell 10 Cell 9 Cell 8
lfinh 2.2 M6 hlnh cay chi ml,lc kh6ng gian
Cae bu8e thife hi~n:
. Chuan hoa tilt cii de d6i tu'Qngv~ tQa di,'>nguyen trong khoang [0,255]
. Djnh gia trj ciia kieh thu'oc bucket: la s61u'Qng t6i da cae d6i tWng n~m trang
1 cell (d~ nghj: bucket = 8)
3
Trang 6. Cell ban d~u Ja hlnh vuong 256x256 (0 255)
. N€u cell co s61uQng cac d6i tuQng vuQt qua bucket thl cell duQc ti€p t\lc chia
ra
. T6 chlic cac cell t~o duQc thanh cay nhj phan tlm ki€m VOlm6i a la mQt nodetren diy, hat nhanh trai phili Luongling VOldc cell thuQc ph~n bell trai hoi!.cphili (tren hoi!.cduoi) cua cell dang xet
2.2. Tfl-Odel /i{}u anh veCtor
2.2.1 Vector hod anh bitmap
Thu~t loan vector hoa ilnh g(')mcac buoc chinh sau:
Blidc 1: Lam manh dlliJng bi~n
Blidc 2: EJanh dau GaG glaD diem va GaG diem dau mut.
Blidc 3: Vector hoa
2.2.1.1 Lam manh dUang bien va danh dilu dc giao die'm
Trang cang trlnh cua minh, chung tai dii dtfa tren thu~n loan Zhang - Suen de'giiii quy€t bat loan cua mlnh Ly do chQn thu~t loan nay la no rilt thu~n ti~n chovi~c ti~n xii"Iy cac thong tin co ich lien quail d€n ca'u truc topo Hon Qua, quaphan rich ky thu~t loan, trang qua trlnh lam milnh, ta co the' k€t hQp vii,:c chinhda'u dc diem co ti~m niing la node sau nay, dIng nhuciii thi~n dang k6 k€l quitcua thu~t loan g6c
ThuJjt toan 2.1:
Blidc 1: ChonmOtnode(dau mut hay glaDdiem) chllaxuII'P,
Blidc2: Lan rheaGaGdiem bi~n,ghj nh~nI~i VaGdanh sach L cho den khi g~p nodeP2khac.
Blidc 3: Chondllong P'P2lam dlliJnggia dinh ban dau.
Blidc4: Xacdinha vadiemxanhatM
BlIlfc 5: Neu a < Echon P'P2jam ket qua.
NgllQCI~i chia P'P2lam hai phanP,Mva MP2.XuII'P,Mva MP2nhll dii lam vol P,P2.
BlIlfc 6: Ghi nh~nGaGthOngtin tapa d1nhc~nh.
Blilfc 7: Neucon nodechlla xu iy thi quayI~i BlioC1
Nh~n xet:
Thu~t loan 2.1 se ho~t dQilgrilt t6t n€u cac duang tren anh can vector hoa kh6ngqua phlic t~p Tuy nhien, trong truang hQp t6ng quat, thu~t loan nay kh6ng chok€t qua chinh xac
ThuJjt toan 2.2:
BlIlfc 1: ChonmOtnode(dau mut hay giao diem)chllaxuII'P,
Blilfc 2: Ghinh~n P, la nodedang xet i = O LIiUP, VaGL[i++J.
Neuchon dllQc thi danh ctauM dii xe! P = M.
NgllQc I~i: chuyen sang BlIiJc8.
Blilfc 4: Chon P2 la diem ke P.
Trang 7Bltcfe 5: NA'uP,la mOtnodetht
L[I++] = P, LIfUL vao file kA'tqua.
C~pnl1~tcae thOngtin topo dlnh-e~nhIIAnquan.
Quay'~I Bltae2.
Bltde 7: Neukhoangeach dIM, P,P,) > € thl:
L[i++] = M; P, = M; M = P; P = P,.
Quay'~i Bltae 4.
Blide 8: Neueon nodeehltaXlIIy thl quayI~i Billie 1.
2.2.2 Tim phiin giao cua hai da gitic biftky
Trudc lien, ta hay th6ng nh5t m(Jtso' thu~t ngu [39], [41]:
. M(Jt loop bit3u di6n bien cua m(Jt da giac bao g6m m(Jt chu6i cac qnh dagiac djnh hudng khep kin M6i da giac co dung m(Jt loop
. M(Jt ring bit3u di€n mQt 16 trong da gik Co tht3 co nhi€u 16 ho~c khong co 16nao trang mQt da giac Cac ring co tht316ngnhau bao nhieu c5p tuy y
. M(Jtsweepline 1a duong th~ng song song vdi trl]c tung
. M(Jtscanline la duong th~ng song song vdi tfIJChoanh
2.2.2.1 So luQc v€ thu?t loan
Thu?t loan cua chung toi dl!a tn~n ytudng ban diiu cua thu?t loan
Weiler-Atherton Thu?t loan nay xac dinh phiin giao hai da giac khong tl! dt b5t ky bao
g6m 3 budc chinh [30]:
1 TIm cae giao di€m giua cae qnh eua 2 da giae MQt thu?t loan ling dl]ngsweep line dfi duQe chung toi xay dl!ng d€ thl!e hi~n eong vi~e nay
2 Sau khi dfi xac djnh duQe cae giao dit3m, m(Jt so' thong tin "!win chuyin" be)
sung se duQe them vao cae giao di€m d€ phl]e VI] eho bude eu6i eua thu?tloan
3 Trang phh eu6i, thu?t loan dl!a tren cae dli li~u cling c5p bCiihai bude trude
va xay dl!ng da giae giao b~ng caeh "bllftc" luan phien qua l<,iitren hai da
giae tll giao di€m nay de'n giao di€m khae
2.2.2.2 D(J phlic t<,ip thu~t loan
Chi phi thlfe hi~n trung blnh eua thu?t loan vao khoang O(k log2k)
5
Trang 8Chtldll8 3 Phep bien dili Radon & Hough trong xa.c dinh
doL tll(/Ilg tren dnll
Do d~c di€m cua chuyen nganh hyp cua mInh, chung toi se thi t~p trung vaomQt phin cua phep bie'n d6i Radon lien quail Mn vit;c xac dint cac d6i tuQngd<).ngduong, d~c bit;t Ia duang th~ng
Trong chuang nay, chung toi lin luQt trlnh bay cac d<).ngbi€u di€n khac nhaucua phep bie'n d6i Radon
3.1.1 Phepbie'1ldfj'iRadoll (p,r)
Djnh nghla:
Phcp bien d6i Radon g(p, r) cua mQt ham lien t\lc hai chi€u g(x, y) du'Qc xac dinh b~ng cach xe'p ch6ng (stacking) ho~c rich phan cac gia tri cua g dQc rhea
cac duang xco (slant) Vi tri cua du'ang th~ng duQc xac dint tit cac tham sO'
du'ung th~ng, he; sO'goc Jiva dQ dui T.
Phep bie'n d6i Radon tuye'n tint nay con du'QcgQi la slant stacking hay phep bie'n
d6i p- r: Su d\lng ham delta ta co, slant stacking co th€ du'Qcvie't nhu sau:
3.1.2 Cae thuQe ti1lh liell qlla1lvi(!eMy milll
Vdi mQt ant cho trudc, khong gian tham sO'phai auQc lily m~y au day Mkhuhi~u ling rang cu'a
Ne'u lily m~u qua day, ta se nh~n du'Qccac thong tin du thita, con ne'u lily quathu'a se co th€ lam milt mat mQt sO'thong tin quail trQng
3.1.3 So sa1lh cae plllld1lgphap 1lQiSllYkhae 1lhall
. NQi suy rhea lang gi€ng g~n nhilt: nhanh, chill IU<;1ngkhong t6t
. NQi suy tuye'n tinh: kha nhanh, chill IU<;1ngt6t
. NQi suy rhea ham sin: rill cMm, chat lu<;1ngt6t han nQi suy tuye'n tint khongbaa nhieu
Trang 93.2 Phep bitll dtfi Radoll ehufill
3.2.1.1'IIep hie;, ddi Radoll (p, OJclla d,lullg tl"lllg
MOt trang nhang l<;1idi~m chinh cua phcp bi6n d6i Radon chu5n la vic;c Om va
xacdinh duong thhg M6 hlnh mQt duong thhg vai tham s6 (p', 0') nao d6 vai
ham delta rho:
Tli kEt qua nay, ta c6 th6 thily du'Qc,qua phep biEn d6i mQtd!nh duQcthanh I~p
khi P= p* va 0 =0* (va cac giai h~n cling duQc tlm thily) HclnthE mIa, cM ydng d day kh6ng bi giai h~n v6 huang cua duang th~ng v6n 1a viln d6 nay sinhkhi SlTdvng slant stacking
3.2.2 Cae thul)e tillil liell quail den vife uty miiu
Ta c6 kEt lu~n tuclng W'nhu d6i vai phep biEn d6i Radon (p, r) Ngoai La,vi~c
khao sat cac giOi h~n lily m~u cling dii duQc d6 c~p chi tiEl trong lu~n van
Y tudng chinh cua phep biEn d6i Hough la anh x~ m6i di6m trong anh ngu6nvao mQt duang (hay mQt d6i tuQng) trang kh6ng gian tham s6, nguQc I~i, phepbiEn d6i Radon I~i biEn d6i mQt duang (hay mQt d6i tu'Qng)trong khOng gian anhngu6n vao mQt di6m trang kh6ng gian tham s6
Phep bi6n d6i Hough c6 th6 du'Qcsuy ra tli phep biEn d6i Radon [II]
Ta c6 th6 xem phcp biEn d6i Hough lien tvc la mQt tru'ang hQp d~c bi~t cuaphep biEn d6i Radon Tuy nhien, d d~ng roi r~c n6i chung hai phep biEn d6ikhac nhau Cltn hm y r~ng phep biEn d6i Hough I~i thuang du'QCsa dvng d d~ngroi r~c
Trang 10TiYbi6u thuc (3.1) c6 th6 dua ra mQtthu~ttoan xiiy dt!ng kh6ng gian tham 56 roir<)c Cac tham s61fly milu dii dt(Qc djnh nghTa trang hieu th((c (B.l 0).
Thu~t toan 3.1 Phcp biC'n Mi Hough
DQ phuc t<).pciia thu~t loan:
°R'don=O(KHM)""O(M')
°Hnngh= O((MN),K)"" O((MN),M)
(3.2)(3.3)
trang d6, chi 56 r duQc sit d\lng d6 th~ hic$ns61uQng diem anh ngu6n th~t stf dn
duQc bitn d6i, tuc la 56 di~m anh ngu6n c6 gia tIi khac o
Ta c6 the giam chi phi tinh loan
Thu~t toan 3.2: Phep bie-n d6i Hough d1f!jctiJi u'u bOa
Trang thu~t tmin teen, chi nhUng di~m anh c6 gia trj duong moi duQc bitn d6i
3.3.1 Pluft hifll dlLdllgtlu'illg si'Ld{lIlgphep bitll diJiHOllgh
I-Dnh3.1 la anh 56 clItia 6 do<)nth:ing voi cac tham 56 tuong ling th~ hic$ntrangBang 3.1 Hlnh 3.2 la kh6ng gian tham 56 roi r<).ctuong ling sit d\lng phuongphap slant stacking roi r<).cVOlcac tham 56 Ia'y mau duQc chQn theo Bang 3.2.Cac ktt qua dUQCghi nh~n teen may tinh sit d\lng bQ vi xit Iy Intel PH 400 Mhz
Bang 3.1 Cole tham s6 hidng ung vc1i cae du'iYng thi'lnll tronll IDnh 3.1 conll vc1i hoilDh di) diem d5u,
cua phcp bW'n(l1i'1Uadon cOnll nh cua HoUllh)
Trang 11Bang 3.2 Gia tri tham s61a'y milD
3.3.2 Ch(Jn IIja tham sf;' lily milu clIo phep biendo'i Hough (p, 'l)
So voi phep bie'n d6i Radon, phep bie'n d6i Hough trClnen kh6ng chinh xac trang
tru'ang hQp kh6ng gian tham sO'du'<;Iclily m~u qua day d~c trong khi l<).icho ke'tqua kha quail khi lily m~u thua bon
Phep bie'n d6i Hough co th~ du'<;Icdinh nghIa voi bQ tham sO'chuii'n (p, e) Tit
bi6u thuc (2.16) co th~ suy ra dinh nghia cua phep bie'n d6i Hough nhu sail:
g(~,y)= [[g(x*,y*)<5(x-x*)J(y- y*}:tx*dy* =>
TutuCing chinh cua phep bie'n d6i Hough (p, fJ)la mbi di~m anh trang anh ngu6n
se dU<;lcbie'n d6i thanh mQtduang d<).ngsin trang kh6ng gian tham s6rai r<).c
3.4.1 Ch(Jn Ilia tham so'lily milu clIo phep bie'n do'iHough (p, {lj
Cac viln d€ lien quail de'n vi~c chQn tham sO'dU<;lctdnh bay trong [56]
C~n lu'u y la phep bie'n d6i Radon va phep bie'n d6i Hough co th~ cho ke't qua
gi6ng nhau trong truang h<;lpsl\'d\lng bQ tham sO'(p, 1) nhung l<).ithuang cho dc ke't qua khac nhau trang tru'ang h<;lpsl\' d\lng bQ tham 56 (p, fJ).Di€u nay co the::
du<;lcsuy ra tit dch lily m~u kh6ng gian tham s6rai r<).c
3.4.2 So sanh giiia cae chie'n III(1ctO111uh6a
Sail day la b6n chie'n lU<;lcnhiim t6i u'u hoa vi~c di d~t phep bie'n d6i Hough(p,fJ)
. Chie'11 lu'ge 1: Kh6ng sl\' d\lng bilt ky mQt phuong an t6i u'u hoa nao nhu
trang thu~t loan 3 L
. ChiC'I1lu'<;ie 2: Sl\' d\lng cac mang mQt chi6u d6 Ira CUll nhhm lang 16c dQxl\'ly
. ChiC'111u'qc3: Trang lhu~t loan 3.2 dn tie'n hanh vi~c kie::mIra xem gia
tl1 r co nhm trong kh6ng gian tham sO'hay kh6ng Thao lac nay co the::
9
Tham s<1 Gi» lri Tham s<1 Gi:1 tri
Trang 12dU<;1clo~J.ibo b~ng each tang kich thudc cua khong gian tham s6 tuc latang s6htQng m1\t! R chlQc lily tren tn,lc p
. ChiC-n 1l/<1e4: Tuelng tl,I'nhu chie'n lu<;1c3 nhung si\' d\lng them hai ma tr~ntra CUu sau:
xc(m,t)= xrel(m)*costheta(t) va ys(n,t) = yrel(n)*sintheta(t)-rhooff (3.5)
GQi g(x, y) la tin hi<$t!lien t\lc tren cae bie'n s6lien t\lc x va y vii.gQi ; Iii.vectortham s6 1]-chi~t!xac dinh bCii
vdi ; chie'm loan bQ khong gian tham s6
4.1.1 Phep hie,l ddi Radoll tdllg qluit d{lllg liell t!IC
Ph6p bic'n d6i Radon c6 th€ duQc dinh nghTa thco nhi6t! each khac nhau [11],[46] Trong d6, d,!-ngph6 bie'n nha't la
g(;)= [[g(x,y)o(~(x,y;;))dxdy (4-2)
Si\' d\lng dinh nghTa trang bi€u thuc (4.2), ta c6 th€ xac dinh dU<;1ccae duang c6
bi€u di€n d,!-ngtham s6 ~(x, y;;) = 0.
4.1.2 Phepbienddi Radoll dlllg quat dtPlg rm r{lc
GQi j Iii.vector chi s6 tham s6 17-chi€u dU<;1cdinh nghTanhusat!:
Slf tUelngung giua vector chi m\lcj vii.phien ban Ia'y m~t! cua vector tham s6, ky
hi<$u Iii I;J' duQc th€ hi<$n dudi d,!-ng:
vdi O,(j,) Iii.ham Ia'y m~u tham s6.
Ne'u chQn phuong phap Ia'y m~u d~u, ham 0, c6 th€ dU<;1cvic't duai d"ng:
;, = 0, (j, ) = ;""",,+ j,!),,;, , j,=O, ,J,-! (4-5)voi ;,,",'" la chij.ndudi va 6.;, la khoang each lily mat! Clla r;,
Gia si\'khong gian tham s6 va khong gian anh det! du<;1clay mat! deli, tlic la:
Trang 13(4-6)(4-7)Thay bien thue (4.9), (4.11) va (4.12) vao phuong trlnh duong eong du<;lebie'nd6i, ta co:
Sii'd\lllg phuong phap xllp xi lang gi~ng g~n nhllt viio bien thue (4.13), chi 56 roi
rf.le ~(m;j)eua duong eong du<;lebie'n d6i co the dU<;lebien di€n If.1iduoi df.lngsan(lu'uyr~ng e6 stf thay d6i va tham 56)
Phuong pIlar Anh Xf.ldiem anh (Image Point Mapping - IPM).
Thu~t toan IPM baa g6m cae buoe san:
1 Khai tf.lOg(j)=0 voi mQi gia trtj
2 Voi m6i diem anh g(m,n);c 0, thtfe hic$n:
Voi m6i gia tq j, thich h<;lp,thtfe hic$n:
j=(j"Q(m,l1;j,))
g(j):= g(j)+ g(m,n)
MQt trang nhfi'ng diem khae bic$tco ban gifi'a GRT va IPM Iii GRT yell diu phailam troll trang khong gian anh eon IPM lam trOlltrong khong gian tham 56, nhutrong so d6aHlnh 4.1
DQ phue tf.lPtinh loan tuong ang clia GRT vii IPM Iii:
Trang 14°ORT =O(MIT JI,., ) a/PM=O( (M N),ftJI/.1 ) (4-11)
trang d6 (MN), chI ra ding chI mOt 56 gidi h~n cac diEm anh (cac gia tri khac 0)
la du<;1cchuyEri d5i Trong (4.19), ta giit dinh chi phi M ki€m tra cac gia tri khackhong la khong dang k€
!{h6ng gl, anh g(m~') Jih6ng glon th.", 61i(~J}
"itm""1 '~,' x
~t x
!!.h6nll"I." anh "(m,n) Khlln" "10" tholll 6g(jl'Ji
~,x
H'mh 4.1 Ben Iren: Minh hQ3 GRT Ben dum minh hQ3 II'M
L<;1idiem chinh cua IPM 50 vdi GRT la khit nang bo qua cac diem anh co gia trjb~ng khong cua IPM, lam cho IPM d~c bi~t thieh h<;1pvdi cac anh nhi philo thua
Phep GRT yell du phai L1y miiu khong gian tham 56 day d~c, trong khi phepIPM l~i lam ma trong khong gian tham 56 khi lily miiu khong gian tham 56 dayd~c; nhung l~i cho k€t qua t6t khi lily miiu tho NMn xet nay la cel 5<'1cho thu~tloan udc lu<;Jngtham 56 duang cong du<;JcgiOi thi~u trang ph~n 5au
Lam ma kh6ng gian tham 56 thong qua phep GRT co the dUQCxem la m(Jt eachdung M philo do<).ntham 56
Thu~t loan duQCd€ nghi cho phep udc lu'Qng tham 56 cua cac duang cong trenanh nhi philn chhg h~n nhu duang th~ng hay hyperbol,
Thu~t loan FCD dting IPM nhu' la bu'dc ti~n xli' 19 cho GRT nhhm m\lc dich xacdinh cac vung huu ieh trong khong gian tham 56 IPM thich hQp cho vi<,;cxacdinh nhanh cac vung hG'uieh nha khii nang Himvi<';ct6t tren khong gian tham 56