Luận án tiến sỹ " Một số vấn đề tối ưu hóa và nâng cao hiệu quả trong xử lý thông tin hình ảnh " pdf

£)~I HOC QU6C GIA TP. HO CHI MINH
TRUONG D~I HOC KHOA HOC TV NHIEN
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DU'dNG ANH DUC

MOT SO VAN DE TOllJU HoA vA.
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NANG CAD HII;U QUA
TRONG xU' LY
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THONG TIN HINH ANH
Chuyen nganh: Bao dam toaD h<;>cho may tinh
c
va M th6ng tinh toaD

Ma s(f: 01.01.10

TOM TAT LU~N AN TIEN STTOAN HOC

Tp.Ho Chi Minh, 2002


~,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, CQngboa Phap

2. GS.TSKH Hoang Van KiGm Truong D;;tihQc KHTN,
DHQG Tp.HCM
Phh bj~n 1:
Phh bi9n 2:
Phh bi~n 3:

Lu~n an se duQc baa v<%
t;;tiHQi d6ng cham lu~n an tie'n S1cap
nha nuoc, Truong D;;tihQc Khoa HQc TV Nhien, DHQG Tp. HCM
vao h6i

giO

ngay

thang

nam 200

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.


Chlldng1

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 anh
mQt cach hi~u qua la mQt nhu du buc thie't. Truoc he't, cac M thong nay d€u
chua 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€ con
nguoi, 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 CUll
cua mlnh ph\lc v\l cho baa vf; suc khoe cua con nguoi. Vif;c t~o ra kha Dang th\fc
hi~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 giup
giam chi phi ch€ t~o, thli nghif;m, ... Voi s\f giup do cua cac hf; th6ng thong tin

dja Iy (GIS), vi~c qUail Iy nha nuoc se hif;u qua hdn. Kinh nghi~m cua cac nuoc
phat 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 hQc
quail tam nghien cUu VI t~m quail trQng cling nhu

y nghla

khoa hQc ciia no. Tuy

v~y, con r5t nhi~u v5n d~ m0 dn phiii nghiCn CUlllrong Iiinh vt.1'c
nay. ViGc lOi
u'u de tang tinh hif;u qua cua cac h~ th6ng thong tin trong lu'u trii', xii'Iy va baa
m~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 vao
vi~c Dang cao kha nail ung d\lng cua cac M th6ng thong tin hlnh anh. Chung
toi se huang cac nghien'
, .mlph vao mQtso' bai loan t6i u'uC\lthe.
Do cac hi; lh6ng thong tin hlnh anh rii'tda d~ng, chung toi khong th~ khao sat h€t
cac vii'n de lien quail. Trong khuon kh6 cua lu~n an nay, chung toi t~p trung vao
cac nghien cUu lien quail de'n cac thong tin hlnh anh dI~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€ C1J sail:
the

.

.
.

Nghien cau da sua't mQt mo hlnh lu'u trITcac thong tin hlnh anh d~ng
vector 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 va
Radon.
Nghien cUu kha Dang ung d1Jng ciia cac phep bie'n d6i Hough va
Radon trong bai loan xac djnh cac d6i tuqrg p.~!)gdu.Qng~
0,) H. \,(H .nr N Ii! EN!
i
',,~~C)
I
I ,.':
~, <- i'i;.
I.
I !i Ii"
,. :_:~
1
i"'
""'-'-""'~"". ' ""--1
j
,


Chtld45 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 anh
d<).ngvector. D6i tuQng ehinh ma chung toi quail tam la cae dcr li~u hlnh anh

ph\le V\l eho GIS va cae vii'nde lien quail.
2.1.

Thief kg dillifll

2.1.1.

Willged-edge topology
E

I

.

M~trai
t

c
G

.J

M~t phai

H

-

. Oinh

~

Cling

NgtiQcchi~ukim d6ng h6

mnlt 2.1 - Mil Itlnlt winged-edge

2.1.2.

topology

Cac cap topology trollg cd Sd d/7lifll
Mng 2.1. Mil hi tang quat cae dip topology

Cac cling chi giao

3

I Topology

nhau t<).inode. Cac

hmln
toan.

m~t kh6ng ch6ng hIp
Jen nhau, ta-t cii cae
m~t phil he-t loan b(>.

2

06 thi
phng
I(Planar
graph)

Node th\fe
th€, node

ke't va
Cling.

lien

Cae cling va node
khi dtiQc chie'u Jen
m~t ph~ng dc cling
chi giao nhau tai
node.

2

~


~

Node thl!C'
1)(\ (hi

tl~, node liGn

t6ng qUilt ket va
ClIng.

I

I

CltC clint! co th6 giao
nhau.

T~p h<;fpdc

Kh6ng Cae node
topo

node

tht,fc thE va cac clIng.

I

thl!C the,

Cac clIng chi co

clIng.

0

danh sach cae tQa d(\

0

ma khong c6 dinh
d~u va dinh cu6i

2.1.3.

Chi mllCklu)lIg giall (spatial illdex)
'\

Cell

Cell

1

3

"

0
Cell

15

Cell

14

Cell

13 Cell

12

Cell

11 Cell

10

Cell

'\

9

Cell

8

lfinh 2.2. M6 hlnh cay chi ml,lckh6ng 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


.
.
.

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 node
tren diy, hat nhanh trai phili Luongling VOldc cell thuQc ph~n bell trai hoi!.c
phili (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 cho
vi~c ti~n xii"Iy cac thong tin co ich lien quail d€n ca'u truc topo. Hon Qua, qua
phan rich ky thu~t loan, trang qua trlnh lam milnh, ta co the' k€t hQp vii,:c chinh
da'u dc diem co ti~m niing la node sau nay, dIng nhuciii thi~n dang k6 k€l quit
cua thu~t loan g6c.
2.2.1.2.

Vector hoa

ThuJjt toan 2.1:
Blidc 1: ChonmOtnode(dau mut hay glaDdiem) chlla xuII'P,.

Blidc2: Lan rheaGaG
diem bi~n,ghj nh~nI~i VaG
danh sach L cho den khi g~p nodeP2khac.
Blidc 3: Chondllong P'P2lam dlliJnggia dinh ban dau.
Blidc 4: Xacdinha vadiemxanhatM.
BlIlfc5: Neu a < Echon P'P2jam ket qua.
NgllQC chia P'P2lam hai phan P,Mva MP2. uII'P,Mva MP2nhll dii lam vol P,P2.
I~i
X
BlIlfc6: Ghi nh~nGaG
thOngtin 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 kh6ng
qua phlic t~p. Tuy nhien, trong truang hQp t6ng quat, thu~t loan nay kh6ng cho
k€t qua chinh xac.
ThuJjt toan 2.2:
BlIlfc1: ChonmOtnode(dau mut hay giaodiem) chllaxuII'P,.
Blilfc 2: Ghinh~n P, la nodedang xet. i = O. LIiUP, VaG
L[i++J.
Blilfc

3: Chon la diembi~nkeP, chlla xe!.
M
Neuchon dllQc thi danh ctauM dii xe!. P = M.
NgllQc I~i: chuyen sang BlIiJc8.

Blilfc 4: Chon P2 la diem ke P.

4


5: NA'u
P,la mOt ode
n tht

Bltcfe

L[I++] = P,. LIfUL vao file kA'tqua.
C~pnl1~tcae thOngtin topo dlnh - e~nhIIAnquan.
Quay'~I Bltae2.

6: Neu
d(M,P,P,)< dIP,P,P,)thl M = P;//C~p
nh~tM M luOn diemxado~n
la
P,P,nha:t.

Bltcfe

Bltde 7: NeukhoangeachdIM, 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.

Tim phiin giao cua hai da gitic biftky

2.2.2.

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 da
giac 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 16

nao 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.
Thu?t

So luQc v€ thu?t loan

loan cua chung toi dl!a tn~n

y

tudng 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]ng
sweep 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?t
loan.
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


Chtldll8

3

Phep biendili 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 vao
mQt phin cua phep bie'n d6i Radon lien quail Mn vit;c xac dint cac d6i tuQng
d<).ng
duong, d~c bit;t Ia duang th~ng.
Trong chuang nay, chung toi lin luQt trlnh bay cac d<).ngbi€u di€n khac nhau
cua phep bie'n d6i Radon.
3.1.

Phep bie'll dfli Radoll

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.
g(p,r)= [g(X,pxH)dx

(3.1 )

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:
g(p,r)= [[g(x,y)o(y-

px-r)dxdy

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
hi~u ling rang cu'a.

(3.2)

M khu

Ne'u lily m~u qua day, ta se nh~n du'Qccac thong tin du thita, con ne'u lily qua
thu'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<;1ng
khong t6t
NQi suy tuye'n tinh: kha nhanh, chill IU<;1ng
t6t

NQi suy rhea ham sin: rill cMm, chat lu<;1ng6t han nQi suy tuye'n tint khong
t
baa nhieu

6


3.2.

Phep bitll dtfi Radoll ehufill

3.2.1.1'IIep hie;, ddi Radoll (p, OJ
clla d,lullg tl"lllg
MOt trang nhang l<;1i
di~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:
g(x,y)

g(p,O)=[o(p

* -(pros

=o(p*-xcosO*-ysinO*)
0 - s sin O)cos 0 * -(psin

(3.3)

=:>
0 + scos O)sin 0 *)is

= [o(p*-pcos(O-O*)+ssin(O-O*))is
1

S111
=[-~ I' (0-0*

p*-pcos(O-O*)
S111-0* )
~o
. (0

(

.

}

(3.4)

+s s,neus111(0-0*)",,0

1
-lsin(O-O*~

va nEu e = e', nghia la since - e') = 0, ta se c6:

-

g(p,O)=

o
[-~ o(p*-p)is ={ f-~u<:(0\-'
JUS
~

nriu p* "" p
K
*
neu p
p

=

(3.5)

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 y
dng d day kh6ng bi giai h~n v6 huang cua duang th~ng v6n 1a viln d6 nay sinh
khi SlT
dvng 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.
3.3.

Phep bii/i, difi Hough (p, 'Z)

Y tudng chinh cua phep biEn d6i Hough la anh x~ m6i di6m trong anh ngu6n
vao mQt duang (hay mQt d6i tuQng) trang kh6ng gian tham s6, nguQc I~i, phep

biEn d6i Radon I~i biEn d6i mQt duang (hay mQt d6i tu'Qng)trong khOng gian anh
ngu6n vao mQt di6m trang kh6ng gian tham s6.
Phep bi6n d6i Hough c6 th6 du'Qcsuy ra tli phep biEn d6i Radon [II].
g(x,y)= [[g(x*,y*)o(x-x*)o(yg(x,y)= [[g(x*.y*)o(r-

y*)ix*dy* =>
y*+px*)ix*dy*

(3.1)

Ta c6 th6 xem phcp biEn d6i Hough lien tvc la mQt tru'ang hQp d~c bi~t cua
phep biEn d6i Radon. Tuy nhien, d d~ng roi r~c n6i chung hai phep biEn d6i
khac nhau. Cltn hm y r~ng phep biEn d6i Hough I~i thuang du'QC dvng d d~ng
sa
roi r~c.


TiYbi6u thuc (3.1) c6 th6 dua ra mQtthu~ttoan
xiiy dt!ng kh6ng gian tham 56 roi
r<)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')

(3.2)

°Hnngh O((MN),K)"" O((MN),M)
=

(3.3)

trang d6, chi 56 r duQc sit d\lng d6 th~ hic$ns61uQng diem anh ngu6n th~t stf dn
duQc bitn d6i, tuc la 56 di~m anh ngu6n c6 gia tIi khac o.
Ta c6 the giam chi phi tinh loan.
Thu~t toan 3.2: Phep bie-n d6i Hough d1f!jctiJi u'u bOa
Trang thu~t tmin teen, chi nhUng di~m anh c6 gia trj duong moi duQc bitn d6i.
3.3.1. Pluft hifll dlLdllgtlu'illg si'L
d{lIlgphep bitll diJiHOllgh
I-Dnh3.1 la anh 56 clItia 6 do<)nth:ing voi cac tham 56 tuong ling th~ hic$ntrang
Bang 3.1. Hlnh 3.2 la kh6ng gian tham 56 roi r<).c
tuong ling sit d\lng phuong
phap slant stacking roi r<).c
VOlcac tham 56 Ia'y mau duQc chQn theo Bang 3.2.
Cac ktt qua dUQC nh~n teen may tinh sit d\lng bQ vi xit Iy Intel PH 400 Mhz
ghi
Du'on thn
P

56

1

Bang

3

4

5

-0.10

0.25

-0.25

0.50

6
0.00

50
-41
29

T

xstart
xend

2

-0.33

70
-11
50

60
-50

9

40
-11
29

50
-50
9

20
-41
9

3.1 Cole tham s6 hidng ung vc1i cae du'iYng thi'lnll tronll IDnh 3.1 conll vc1i hoilDh di) diem d5u,
diem mdi cua m6i du'iYnll thi'lnll
.

100

100

90

90

eo

:
",50

'"

90
'"

~

80

------

70
80

" 50
J9

'"

'-'

90

'"

10

""",,

10

0
.50 -'"

.90 .",

-10

0

10

'"

90

'"

50

-1-0.8-08.0.4.0.20020.40.60.81

X

p

IDnh 3.1 Anh nllulln vtJi 6 do~n thAng

Hinh 3.2 Kh()ng IliaD tham sf, nli r~c (ke't qmi
cua phcp bW'n(l1i'1 adon cOnll nh... cua HoUllh)

U

8


Khong ian anh
Tham s<1
Gi» lri
M
101
N
101
t.x
1
1
t.v
Xmin
-50
Ymin
0

Khong gian tham 56
Tham s<1
Gi:1 tri
H
101
K
101
0.02
t.p

t.'t
1
-1
Dmin
0
'tmin

Bang 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'<;Icily m~u qua day d~c trong khi l<).i ho ke't
l
c
qua kha quail khi lily m~u thua bon.
3.4.

Phep

biendO'iHough (p, (J)

Phep bie'n d6i Hough co th~ du'<;Ic inh nghIa voi bQ tham sO'chuii'n (p, e). Tit
d

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(yg(p,O) = [[g(x*,y*)<5(p-x*cosO-

y*}:tx*dy* =>
y*sinO}:tx*dy*

(3.4)

TutuCing chinh cua phep bie'n d6i Hough (p, fJ)la mbi di~m anh trang anh ngu6n
se dU<;lcie'n d6i thanh mQtduang d<).ng trang kh6ng gian tham s6rai r<).c.
b
sin
3.4.1. Ch(Jn Ilia tham so'lily milu clIophep bie'n do'iHough (p, {lj
Cac viln d€ lien quail de'n vi~c chQn tham sO'dU<;lc
tdnh 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<).ihuang cho dc
t
ke't qua khac nhau trang tru'ang h<;lp d\lng bQ tham 56 (p, fJ).Di€u nay co the::
sl\'
du<;lc ra tit dch lily m~u kh6ng gian tham s6rai r<).c.
suy
3.4.2. So sanh giiia cae chie'n III(1c
tO111u
h6a
Sail day la b6n chie'n lU<;lc hiim t6i u'u hoa vi~c di d~t phep bie'n d6i Hough
n
(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 CUllnhhm lang 16c dQ

xl\'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


.

dU<;1c
lo~J.ibo b~ng each tang kich thudc cua khong gian tham s6 tuc la
tang s6htQng m1\t! R chlQc lily tren tn,lc p
ChiC-n 1l/<1e4: Tuelng tl,I'nhu chie'n lu<;1c nhung si\' d\lng them hai ma tr~n
3
tra CUusau:

xc(m,t)= xrel(m)*costheta(t) va ys(n,t) = yrel(n)*sintheta(t)-rhooff

Chtld45 4.

(3.5)

Xcic dink duang cong tren anh

4.1. Phep bitll deli Radoll t(illg quat (GRT)
GQi g(x, y) la tin hi<$t!ien t\lc tren cae bie'n s6lien t\lc x va y vii.gQi .; Iii.vector
l
tham s6 1]-chi~t!xac dinh bCii

; =(;"...,;,

,;ry)

(4-1)

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<;1c duang c6
cae
bi€u di€n d,!-ngtham s6 ~(x, y;;) = 0.
4.1.2. Phep

bienddi Radoll dlllg quat dtPlg rm r{lc

GQi j Iii.vector chi s6 tham s6 17
-chi€u dU<;1c nghTanhusat!:

dinh
j

=(j"...,j"...,jry)

(4-3)

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:

I; = I;
J

= ou),

;, = 0,(jJ

vdi

(4-4)

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<;1c duai d"ng:
vic't
;, = 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<;1cay mat! deli, tlic la:
l

10


(4-6)

X=Xm =Xmm +m~,m=O,I,...,M-I

(4-7)

Y=Y"=Y",;o+l1~y,I1=O,I,...,N-1

Thay bien thue (4.9), (4.11) va (4.12) vao phuong trlnh duong eong du<;lebie'n
d6i, ta co:
Y = Ymm + I1~Y = ~(xm;o+ m~;e(j))

(4-8)

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<;le
bie'n d6i co the dU<;leien di€n If.1i uoi df.lngsan
b
d

(lu'u y r~ng e6 stf thay d6i va tham 56)

;(m;j)= n = [~(Xmm
+m~e(j))-

(4-9)

Ymio
]

GQi g(m,l1) la phien bin roi rf.leh6a clia g(x,y), tue la g(m,I1)=g(xm'Y.) va gQi
g(j) l3.bie'n d6i Radon t6ng quat (GRT) roi rf.leeua g(m,n). Khi d6, g(j) dU<;le
djnh nghi'a nhu san:
MOot

(4-10)

g(j)= m=O
:Lg(m,;(m;j))

4.2. Allh X(l diilm ll1lh
Vic$ebie'n d6i cae diem anh mang gia trt 0 la khong din thiEt do cae diem anh
nay khong h€ lam anh huang Mn g(j). TiYdo, ta co th6 dua ra mQt ehie'n lu<;le
lfoe luc;1ng
eho phep bie'n d6i Radon ma khong tinh dEn cae diem anh b~ng 0
trang phep eQng eua bien thue (4.16). Nho d6, chi phi tinh loan d11<;1e
giam di
dang ke.
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$n:
Voi m6i gia tq j, thich h<;lp,htfe hic$n:
t
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 phai
lam troll trang khong gian anh eon IPM lam trOlltrong khong gian tham 56, nhu
trong so d6 Hlnh 4.1.

a

DQ phue tf.lPtinh loan tuong ang clia GRT vii IPM Iii:

,---'

"-'

-"

I~)H v'~.-nr-1'H1ifi~i
i
.:;..
- !
'T"!."

II

I

.,'

~i';

r--""'--

": ~;. ill'

1/HJ~
"

':-~-'I

(
~


°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<;1chuyEri d5i. Trong (4.19), ta giit dinh chi phi M ki€m tra cac gia tri khac
c
khong la khong dang k€.
!{h6ng gl,... anh g(m~')

"itm""1

Jih6ng glon th.", .61i(~J}

'~,'

.

x

x

~t

!!.h6nll"I." anh "(m,n)

Khlln" "10" tholll .6g(jl'Ji

~,
x
x

~t

H'mh 4.1. Ben Iren: Minh hQ3 GRT. Ben dum minh hQ3 II'M

L<;1i
diem chinh cua IPM 50 vdi GRT la khit nang bo qua cac diem anh co gia trj
b~ng khong cua IPM, lam cho IPM d~c bi~t thieh h<;1pdi cac anh nhi philo thua.
v
4.3.

Lily mau khong gian tham so'

Phep GRT yell du phai L1y miiu khong gian tham 56 day d~c, trong khi phep
IPM l~i lam ma trong khong gian tham 56 khi lily miiu khong gian tham 56 day
d~c; nhung l~i cho k€t qua t6t khi lily miiu tho. NMn xet nay la cel 5<'1ho thu~t
c
loan udc lu<;Jng
tham 56 duang cong du<;Jc iOi thi~u trang ph~n 5au.
g
4,4.

Um mil khong gian tham sf;'

Lam ma kh6ng gian tham 56 thong qua phep GRT co the dUQC
xem la m(Jt each
dung M philo do<).n
tham 56.
4,5.

Thufjt toan FCD (Fast Curve Detection)

Thu~t loan duQCd€ nghi cho phep udc lu'Qngtham 56 cua cac duang cong tren
anh 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 xac
dinh cac vung huu ieh trong khong gian tham 56. IPM thich hQp cho vi<,;cxac
dinh nhanh cac vung hG'uieh nha khii nang Himvi<';ct6t tren khong gian tham 56
12


I(y m~u th\ta va khii nang bo qua cac vung iinh c6 gia tri O.San day la
chinh cua thu~t toan:

y t\tong

1. Xfiy dl!ng khong gian tham s6 rCiir~c, nghia la chQn qi,min, va Liqj.
Ji
2. Xay dl!ng khong gian tham s6 rut gQncho IMP biing cach chQn:
J;=

!2V:'+ 11-

trong d6

';;nnn

rxlky hi~u

=

(4-12)
~nUn

+ V"i b.';"

b.';;

= (2V"i

s6 tr~n eila x (s6 nguyen

+ I) b.';i

nhiS nhilt IOn hdn x) va V,,/]a mQt

. s6 nguyen lien quail Mn qua tdnh tai ]ily m~u (xem bell du'<1i). d6 dung
Sau
]PM da u'<1c
lu'tJngil",j)'):
il'"m(/)=IPM{g(m,n)}

(4-13)

3. Dung mQt ham phfin ngtfong T M tlnh:
if, (/)=T(ifipm(J'))

(4-14)

Ham philn ngu'ung T lM;1ethiGt kG d6lo<).ibo tilt d cae t6 hy nghia. M(\t khil niing ch9n II/a cua T co thG Ia:
T (if/pm (J'))

=,u( ify.m
(J')- ~M)

(4-15)

Trang d6 M la s6 dong tren anh, Al chi mue d(\ co nghia, con pI,.) Iii ham b~c
thang Hamilton

4. Hi lily milu 06 nh~n dtfQcg,(j). Qua tdnh lai lily mITuco th6 du'Qcvic'l
nhtf san:

g,(j)=g,(/),

l=[;~:;~]

(4-16)

Qua trlnh nay se nhanh chong phu loan bQ khong gian tham s6 sac cho t<).i ac
c
vung c6 y nghia se mang gia trj 1 con ph1tn con ]<).i e mang gia trj O.

s
5. SITd\lng GRT M \tocltf<;lng g(j) trong nhung vung ma if,(j);e 0

g(j)=GRT{g(m,n)lg,(j);eO}
(4-17)
6. Nhtf trang btfoc 3, dung ham phan ngtfong voi mU'cdQ co nghia moi -12M
xac dinh cae dlnh. San khi phan ngtfong, tit cii cae gia tri khac 0 trong
khong gian tham s6 thE hi~n cac dtfCingGongttfdng U'ngtrong iinh g6c.
7. Cu6i cung, cac lham s6 off xac dinh dtf<;lc6 dtf<;lc han Io().ivao cae
s
p
dtfi'1ngGongkhac nhau.
4.6.

Xac djnh cae difi t"t/Ilg d{lng hinh trim

M6i mQt dtfCingIron dtf<;lc
xac djnh bdi 3 tham s6 la tQa dQ tam (xc,Yc)va ban
kinh r. Ne'u ap d\lng trl!c tie'p HT ho~c RT tren khong gian tham s6 nay ta phiii
deJim~t voi mQt phep bie'n d6i 3 chi~u. Cach tie'p c~n cua chung toi la chia qua
lrlnh xac oinh cac otfang troll lhanh 2 giai oo<).n:
1. TIm tilt d. tam cila cac otfCingtrOll.
2. TIm ban kinh cila cae dtfang Iron.
13


Be xac djnh tam ciia cac du'Clng
troll, trtI'octieD ta lu'u 9 la vol mQtdiem ba'tky P
ireD du'Clngiron, du'Clngvuong goc vol ti6p tuy6n cua du'Clngiron tq.i diEm P di
qua tam (xem Hlnh 4.2). Nhu' v~y,voi mQt 56 diem ireD du'Clngtron, cac du'Clng

vuong goc vol ti6p tuy6n di qua nhii'ng diem nay se d6ng qui tq.itam cua no.
Vol m6i diem ilnh, b~ng phu'ong phap b1nh phuong t6i thieu, ta co the xac djnh
duqc dltClngtiSp tuySn phil hqp nha't di qua diem nay d1,1'a cac diem ilnh n~m
vao
trong Hinc~n ciia diem nay.

IDnh 4.2. Cach xac dinh Him dLii'fngtron

Sail khi xac djnh duqc ta't cii.cac vj tri co the la tam cua mQt hay nhi~u duClng
iron ta phili xac djnh ban kinh cua cac vong iron tuong ling. Vol m6i tam ta xiiy
dlfng 1 histogram nhu' sail: vol m6i diem ilnh ta tinh khoilng dch d6n tam va lu'U
no vao histogram tuong ling. Gia trj clfc dq.i cua histogram se cho ta gia tri cua
ban kinh vong tron dn t1m.

-@B
ITmh4.3. Cae xac dinh tam qua cae dLiilngtrung tn/e

Sail kill xac djnh xong ta phili lam them mQt bu'oc Mu xii' 19 de tal khhg dinh
dc vong iron dii phat hi~n duqc b~ng each Mm sO'diem n~m ireD du'ClngtrOll.
Chia s6 diem nay cho ban kinh tuong ling ta nMn du'QcmQt gia trio NSu gia trj
nay nha hon mQt ngu'ong nao d6 vong troll se bj buy.
Rieng 0 buoc xac dinh tam duClngiron, ngoai thu~t loan dii tr1nh bay 0 ireD,
chung toi con di d~t mQt thu~t loan dlfa tren mQt tinh cha't khac cua dttClngtrOll.
(xem Hlnh 4.3)
BE tang t6c dQ tinh loan, ta c6 the si\' d1,1ngphcp biSn dai Hough ng5u nhi6n
(Randomized Hough Transform - RHT).

14

4.7. Xac djllh cae doLtll(lllg d{l1lg Ellipse
4.7.1. 1'111/(11
loall/(tlllIollgh
MQt ellipse hoan roan duQe xae dinh bCii5 tham s6 (tCladQ tam, 2 ban kinh va
g6e quay so VOltl1Jehoanh - Hlnh 4.4). Tuong tv nhu caeh xae dinh cae duang
troll dil trlnh bay d tren, vi~e xae dinh cae ellipse duQe ehia ra lam 2 giai do<).n.
Trude tien, ta phai xae dinh nhung tam ellipse gia djnh. Bieu nay dn den I
phep bien d6i Hough 2 chien. Sail d6 ta e6 th€ xae djnh 3 tham s6 eon I<).i ila
e
ellipse b~ng I phep bien d6i Hough thiGh nghi (Adaptive Hough Transform AHT) 3 ehi6n.
y

x

IDnh 4.4. Cae tham sri xae djnh mOt ellipse

Tam eua cae ellipse MQe xae djnh nha vao tinh chill hlnh hQc cua ellipse nhu
tdnh bay du8i day.
p

IDnh 4.5. Tinh ehl1t giup xae djnh tam ellipse

Xet 2 di€m A, B thuQe ellipse. Tiep tuyen v8i ellipse t<).i va B dt nhau t<).i .
A
P
M la trung di6m eila AB. B6i VOlmQt ellipse hoan hao, tam 0 eila n6 sc nitm
tren ria PM (xem Hlnh 4.5).
Yuen va cae d6ng sl/ [51] dil sa dl)ng phuong phap AHT thl/e hi~n mQtph6p HT
::Ichi6u 06 giam chi phi tinh roan trang qua tdnh xac djnh 3 tham s6 con I<).i ila
e

ellipse. Chung toi cling sa dl)ng ky thu~t nay, chi khac so VOlYuen v€ caeh tham
56 h6a ellipse.
Hlnh du8i day eho ta mQtvi dl) ket qua thl/e hi9n thu~t roan tren may tinh.
]5


\

,.,

i

;,

! /~':"::;'-\i(:'-~tr,\
,...,
,
/"\
. '\

\

\'

\,

/.

"""f- --,'

".,../\
,/'

;
i

"
"

/

,

\
Anh vUi mQt slJ ellipse

Cae ellipse xac djnh dri(jc

Irmh 4,6, MQtslJ k€t qua thtjc hi~n thu4t loan

.........

-

i"'.

a, Anh mil ung thri
' -' /
'--~/

)

.,,/'"

:

-- ~"

r-

~ )\

"".~

h, Anh

sau phfin ngriilng

'-"'.

cO

)

./
,.

c, Anh sau loc hi/!n

d, Cae ellipse Hm dri(jc

Irmh 4.7. K€t qua ung d\mg thu4t loan xae djnh mil ung thri

Nhtt dii philo tich CItrong cac chttcJngtruoc, phep bie'n d6i Hough va Radon c6
quail h~ m~t thie't voi nhau. TiJy da li~u dn xU'ly va nhu du thlfc te', ta c6 th€
de dang hit$u chlnh thu~t loan tren d€ dung phep bie'n d6i Radon thay cho
Hough, Cha't lu<;Ing chung se tang len nhu'ng biJ l'!-ithu~t loan sc ch~m hcJn.
n6i
4,7.2.

MQt thuljt to(m kluic xac dfnh ellipse

PhucJngphap de nghi g6m 2 giai do,!-n:dinh vi tam ellipse va xac dinh cac thong
56 con I,!-i.Trang giai dQan 1. tinh d6i xung hlnh hQc loan ct,IcduQc dung dau
lien cho vit$c dinh vi ta't ca cac tam c6 th€ (Xo,Yo) ua cac d6i tuQng d,!-ngellipse
c
trong anh, sau d6, ta't ca cae di€m bien du<;lc
philo lop vao mOt 56 nh6m dl1atheo
cae tam ghi dinh tren.

16


a~
NE

LU

L

u
NE
RD

(0)

Ibl

mnh 4.8. (a) Trinh bay sf! pMn IcJpcae di/fm bien eua mOt dol tu'!Jng
(b) SlcJp eua cae dit'm bien Ian eijn 4 eua di/fm P
VA,(-X"-Y2)

HA(x\,YJ

E
VA(x..Yt)
mnb 4.9. Ala dit'm bien eua do'! tu'ngang va dQe, va A' la dit'm d{)ixung eua A qua O.

Cac ellipse vOi cac tam khac nhau se n~m trong cac nh6m khac nhau. Trang giai
do\ln 2, can Cll tren ke't qua thu du<;Jc giai dQan 1, ta se xac drnh cac ling vien
d
cho 3 tham s6 con l').i t').o lien ellipse (a, b, 8) Ta c6 mQt vai drnh nghia va drnh
19 sau:
Djnh nghia 4.1: Cho ab la mQtd6i tu<;Jng, ia diem bien cila ab. V, D, L, R la
P
cac diem Ian c~n 4 eila P. Lop P du'Qcdrnh nghia theo de lu~t san (Hinh 4.8)
Lll4t 1: Ne'u cii L va V kh6ng la cac diem d6i tu<;Jng, thuQcv€ lop LV
P
Lll{jt 2: NEu cii R va V kh6ng la cac diem d6i tu<;Jng, thuQcve lOp RU

P
Lll!jt 3: Ne'u cii L va D kh6ng la cac di~m d6i tu'<;Jng, thuQc v€ lOpLD
P
Lll{jt 4: N6u cil R va 0 kh6ng Ii\.cae diem d6i lu'P
Lll!jt 5: Ne'u cac Iu~t 1,2,3,4 d€u kh6ng thoa, P thuQc ve lOpNE
Djnh nghia 4.2: Cho A(xa,Ya)la diem bien. Diem Ian c~n ngang HA(xl>Yo)cila A
(horiontal buddy point) du<;Jc
djnh nghia la di6m bien gan nhit d6i voi A ne'u
thoa
a) A E LU ho~c LD! n6u HAla bell phai A
b) A E RV ho~c RD, ne'u HAn~m bell trai A (Hlnh 4.9)
17


Djnh nghia 4.3: Cho A(x., y.) Ia <1i~mbien. Bi~m Hin c~n dQc VA(X.,YI) cua A
(vcrticnl buddy point) c:htl/c
djnh nghin Iii diem bien gdn nhfft d6i vl1iA n6u IIH'HI
a) A E LV ho~c RV ne'u VAphia duoi A
b) A E LD hoi).cRD ne'u VAn~m phia tren A (Hlnh 4.9)
Djnh Iy 4.1: Cho E Hi d6i tuQng d~ng ellipse voi tam 0(0,0), va cho A(x.,y.) la
di~m bien cua E; thl diem d6i Kung A' cua A qua 0 co tQa dQ (-x.. -y.) va cling

n~mtren bien cua E.

.

Djnh Iy 4.2: Cho E la d6i tuQng d~ng ellipse voi tam 0, A la diem bien cua E,
va A' Ia diem d6i Kung ctia A qua O.Cho HA va VAI~n luQt la cac diem Ian c~n
ngang va dQc cua A, HA,va VA'I~n IUQtla cac di€m Ian c~n ngang va dQc cua

A' (Hlnh 4.9). Thl
IAVAI=I:w:l

1AH:1=IA'HA.I,

Djnh Iy 4.3: Cho E la d6i tuQng d~ng ellipse voi tam 0(0,0) va goc dinh huang
8""'0, cho A(x.,y.) la di€m bien cua E voi x.;tO va y."",O,va cho HA(x"y.),
VA(X.,YI)a hai diem lail c~n ctia A. Thl 3 tham s6 hlnh hQc (a, b, 8) cua E co the
l
du<;1C dinh b~ng tQa dQ cua A, HAva VA,
xac
Djnh Iy 4.4: Cho E la d6i tu<;1ng
d~ng ellipse vai tam 0(0,0), cho A(x., Y.) la
di€m bien cua E VOlxa;tOva Ya""'O, cho HA(x" Yo)va VA(Xa, l) la hai di€m Ian
va
Y
c~n cua A. Thl, d6i tuQng d~ng ellipse la kh6ng co huang ne'u va chi ne'u HA la
diem d6i Kung cua VAqua O. Co nghla la, 8=0 ne'u va chi ne'u XI=-X.va YI=-Y..
Djnh Iy 4.5: Cho E la d6i tuQng d~ng ellipse vai tam 0(0,0) va 8=0, va cho
A(x.,y.) la diem bien cua E. Ne'u Ix.I < [y.l, thlli\y di€m bien khac A*=(XioX.);
nguQc I~i, lily A*=(Y"Yl)' Thl, hai tham s6 hlnh hQc (a, b) cua E co the dUQC
tinh
b~ng tQa dQ ctia A va A*.
4.7,2.1.

Giai do~n I - Binh vi cac tam cua ellipse
Thu4t tmin 4.1 TIm dip lIoi xdng;

Khait~o mang trang G, mill cell g6m counterc va link I;
Quet(scan)anh F

Wi mlli diem bi~n A(x.,y.), kiem Ira lOpcua n6
N€uAeNE ho~ckhOngc6 hai diem Ian can HAva VAcuaA
KhOnglam gl ciI;
Nglf\Jc
I~I
U'y 2 diem Ian can HA,VAcuaA, va d~t w = IAR AI,h = IA VAl
G[h, w].c t- G[h,wl.c + 1;
A(xa,ya) dlf\Jc
tMm vao danh sach nO'I €t dlf\JcnO'ik€t biJi G[h,wl.l;
k
KlemIra mlli cell(h,w) lrang G
N€uG[h, w].c ~ 2
Ba'1 hal th\lCthe nao lrang danhsach nO'ik€1dlf\JcnO'I €1bai G[h, w].link dlf\Jcxem
kY
k
nhlf c~p d61xung;

18


Tu Binh 194.1 va Binh 194.2, ta bie't r~ng ne'u td
E voi tam 0 trong anh F, thong qua thu t1,1C
tren, m6i di6m bien A cua Eva die-m
d6i xung A' cua noqua 0 phai dI1<;1c xet nhu mQt c~p c16ixung va du<;1c~t
xem
d
vao trang cling mQtdanh sach n6i ke't.
, Thu~t tmin 4.2: TIm Him Ellipse & PMn lo,!i diem

Khoi

t?O hai mang tr~ng I va I', m6i cell g6m counter c va link I;

Voi m6i c~p

d6i xling

EJ~t (xo, Yo) = [(x"
Neu hai di~m

A(x"

y,) va A'(x",

y,) + (x",

Ian c~n

y,,)

y,.J]I2;

HA va VA khOng

d6i xling

qua

(xo, Yo)

Iit/h

ellipse

bi quay

BOg6m A, HA'VAdiJQC
them VaG
danh sach n6iketdiJQC ket bi'fi l[xo,Yol,l;
n6i
I[xo,yo],C'f-I[xo,Yo],c+ 1;
NgiJQc
I?i
nm'di~m bien A* khacd\la theo GaG sau:
luat
a, neu Ixa - xoi< Iya - Yolthl
A* f- (XI, Yo+ xa - xo)
b, neuIxa - xol <:Iya - Yoith1 A* f- (xo+ ya - Yo,y,)
80 g6mA va A* diJQchemvaodanh sach n6i ket diJQc ket bi'fi l'[xo,yo],I;
t
n6i
I'[xo, Yo],cf- I'[xo,Yo),c+ 1;
Ap dung thuat loan peakdetectingvoi I[x, y].c va i'[x, y),c;
Xemx!H m6i peak(xo, o)diJQc
Y
trlch d€ chon lingviencho tam ellipse;

4.7.2.2.

Giai do~n 2 - Xac djnh 3 tham so' a, b, o

Trong giai dQan 2, din cu tren ke't qua cua giai dQan 1 va cac Binh 19 4.3 dEn
Binh Iy 4.5, 3 tham so' (a,b,O) cho m6i c16ituQng d;,tngellipse se c1uQc tha'y.
tlm
4.7.2.3.

Ke't qua thtfc nghil%m

Be so sanh, ta cling ap dl,lI1gphucJng pIlar TsujifMatsumoto[60] d6i voi llinh
4.10(a). Tren may PIll 733MHz, 256MB RAM, ke't qua c1uQC
trlnh bay trang
bang bell du'oi. Til' bang nay, ta tha'y r~ng phu'cJngphap tren la nhanh hcJnva dn
it khong gian hill tIii'hcJn.

~

Phtfdng pha

237 mili giily

Ph/p d~ nghi
Tsuji/Matsumoto

472 mili giily

Wu/Wang

1085 mili giily

Yin/Chen

879 mili giil
Bang 4.1. So sanh cae phu'(fng phap

19


,

"Q ~,~
(.,

(bl

a. Anh ban (Ulu
b. Anh

~
I
'

~

"
3'~

. '---

)'~

,

nllU(Jng

".4

-.
.(

phlln

~. ~".",-,
,-)
"

~ -.......
~2

~au

,-

)'--z..)

,-.

(e)
e. Sau khl xae dinh Cae tiim

d. Cae ellipse 11m du'<;1e

Irmh 4.10. Vi dl.lap dl.lng thu4t toan de dinh ellipse

4.8.

van d€ phep bien dili Radoll vfli {lllh Ifill

Khi anh ngu6n co kich thu'oe lOn, phep bien d6i Radon ding nhu' phep bien d6i
Hough se gi!-pmQt sO'kho khan [12]:
1. ThC1i ian xii'ly ra't lilu. Kieh thu'oe b/}nho doi hai qua Ion.
g
2. D/}ehinh xae se giam kill de du'C1ng iim xa gO'etQa d/}.
n
4.9.

Khd lldllg SOllg SOllghoa phep

bien Radoll
dili

GQig(m,n) la anh nhi philo co kich thu'oe N x N. GQi K = la sO'lu'<;Ingi€m bien
d
teen anh. Trong

tru'C1ng h<;lp xa'u nha't, K

= O(N2) = sO'lu'<;Ing

di€m

teen anh.

GQi L

sO'lu'<;Ing u'C1ng tren anh. Thu'C1ng L ra't nha so VOlK. Ta se chia tf\le P
d
co
thi
thanh M do~n, nghla la, bien d6i Radon se d11<;1e h<;lp M phep ehieu. Do
t~p
tu
goe a thayd6itu 0 Mn rr/4, tf\le Tse thay d6i tu -N Mn N. Do do, truoe lien, ta
se xii'ly de goe tu 0 den rr/4 sau do se xii'ly de goe can I~i biing deh ap d\lng
de bien d6i affine teen ph~n can I~i (xem chi tiet 0 ph~n sau). Gia sii' ta ehia
tf\le T thanh T do~n, T =2N + I.
Thu~t toan 4.1 Thu~t toaD hie-n d6i Radon daub cho cae du'O'ngth~ng co h~
s6 goc trong do~n [0, 1].

20


Chi phi cua thu~t toannay se xa'p xi O(MK). Gia sii' thai gian tinh loan la yMK
gia'y trong do rmQt h~ng s6. Ta se dn O(N2)don vi bQ nha d€ htu iinh va GeL)
M htu cac dttang thhg. Ta se gQi cong vi~c nay la TI' Vai cac goc athuQc phfin
can If!.i,ta se hi~u chinh Thu~t loan 4.1 M phu h<;Jp hu sail:
n
VOigocatrong

khming 1TI2

de'n 1TI4
(cong vi~c T2):

Dung gU, i).

.yOi gocatrong

khoang 31T12 e'n 1TI2
d
(cong vi~c TJ):

Dung gU, N-i).

VOi gocatrong

khoang 31T12 e'n 1t(cong vi~c T4):
d

Dung g(N-iJ).

Nhu v~y t6ng thQi gian xii'Iy lOan iinh la 4yMK giay.
4.9.1. TllllQttoall sollg .Wllg h6a dl7lifll t11ll511ILY
L (Data-Parallel RT)
Gia sii'ta co P processors. Trong thu~t loan nay, chung toi philo chia dl1li~u theo
nguyen tilc t6i u'u hoa d€ darn baa can biing s6 lu<;Jng di€m bien trong cac
cac
phftn giao cho P processors xii'Iy.
DRTO: chia anh lam P cQt, m6i cQt kich thuac NIP, m6i cQt giao cho 1 procesor.
DRT1: chia iinh thanh P cQt saDcho m6i cQt chua xilp xi KIP di€m bien. M6i cQt
giao cho 1 processor.

GQi ilia chi phi (tinh b~ng gifiy) khai t~o vi~c gii'i mQt thOng di~p giua cac
proccssor, v lit nghich dao cua bang thong cua nwng (giiiy/word) tren multicomputer co bQ nha phan b6. T6ng chi phi se la 4yMKiP + 4Mlog(P)( 11+ Iff).
Chi phi lu'utru se t6n khoiing GeL)cho cac dttang thhg va o(tI/P) M lu'uanh.
4.9.2. TllllQt toall kit Ilf/p SOllgSOllghOa dillifll va xii Ii (DTRT)
Trong DRT, vai P processor, chung ta dung cii.P processor d€ thl1c hi~n lfin lu<;Jt
Tl , T2, TJ n5i de'n T4. Tuy nhien, do cac cong vi~c nay hoan loan dQCI~p nhau,
ta co thc5dung P/4 processor M xii' Iy m6i cong vi~c mQt cach d6ng thai. T6ng
thai gian thl1chic$nloan bQ cong vic$cse la 4yMKiP + Mlog(P/4)(1l + Iff). Chi phi
bQ nha cua DTRT se vao khoang O(N2/(P/4» = O(4N2/P).
4.9.3. TllllQt tOall SOllg SOllg hOaxii Ii (feh qte(ATRT)
Gia sii' ta co P

= 4Q

processor.

Ta co th€ dung Q processor

cho m6i cong vi~c TI

, T2, TJ va T4' Ta co th€ ma rQng vic$csong song hoa xii' Iy. Ta co th€ chia cong
vic$cTj thanh Q cong vic$c,gQi la Tjl,Ti2,'" TjQ.Xet cong vic$cTl' Cong vic$cnay
baa g6m vic$ctinh tilt cii.M phep chie'u cua cac goc atrong khoiing ttt 0 Mn 1t/4.
Ta co th€ yell du T1j chi tinh M/Q phep chie'u Mi voi cac goc a trong khoang
ttt (j-1)1TI(4Q) Mn j1Tl(4Q). Thai gian thl1c hic$n se vao khoang f(M/Q)K=
4yM/(4Q) = 4yMKiP giay va day la thu~t loan nhanh nhilt cho de'n thai di€m
nay. Tuy nhien, day khong phai la mQt phuong an tie't kic$m bQ nha VI m6i
processor doi hoi O(N2) don vi bQ nha d€ lu'u anh. Nhu v~y, ne'u du bQ nha thl
thu~t loan nay la lai giai t6t nhilt,.

21


4.9.4. Tllu4t toan song SOllg116axu Ii tlcll ctjc vUihI)nMt tllfCMATRT)
aid stt Lac6 P =4Q proccssor, mi'li proccssor c6 hi) nhd kkh Lilltdca won!. D~l
R la s6 nguyen nho nhilt hdn hon hay b~ng N2/G . Khi d6, LachI co the ap d\lng
thu~t loan DRT tren R (hay nhi~u bon) processor tIll bi) nhd mdi duo Gia sii' Q Ia
mi)t h<;lps6 nghla la Q

=RS

vdi S la mOt s6 nguyen. Khi d6, Iai giai 19 tudng sc

Iii t:).oS cong vi~c tren m6i nh6m trang 4 nh6m processor va thl1chi~n vi~c song
song h6a duli~u cffp R trang m6i cong vi~c trang S cong vi~c nay. T6ng chi phi
tinh loan cua thu~t loan trong tru'ang h<;lpnay b~ng "){M/S)K/R = '}MK/(RS) =
4'}MK/(4RS) = 4'}MK/P.Chi phi truy~n thong b~ng (M/S)log(R)(1L vr). Nhu
+
v~y, t6ng thai gian thl1chi~n th~t loan se Ia 4'}MK/P +(M/S)log(R)(1L+ vr).
Cu6i cung, ta c6 the thily, vdi tu cach la tru'ang h<;lp
rieng cua phcp biC"nd6i
Radon, phep biC"nd6i Hough hoan loan co the du<;lcsong song hoa nhu cae
phuong an da: d~ ra Mi vdi phep bie-nd6i Radon.
4.10. Nlillg cao IIifU qua bang logic mil
Trang phuong pIlar Hough, khong h~ co sl! khac bi~t nao d6i vdi cae diem anh d
g~n hay xa d6i tu<;lngduang th~ng dang du<;lexct trang qua trlnh t1ch lfiy viio
khong gian tham s6. Trong tru'ang h<;lpanh ngu6n bi nhieu hay cae duang th~ng
trang anh ngu6n cae bien di) dao dOng kha Ian tIll m6i QUangth~ng trang anh
ngu6n khong du<;le x:).ehinh xae vao 1 diem trang khong gian tham s6. Trang
anh

phuong pIlar ung dl1ng logic ma vao vi~e xac djnh cae duang th~ng, gia trj ham
thiinh VieDma IL du<;lc
sii'dl,lllgtrong vi~e c~p nh~t mang t1chlily:

( )-

O,

ne'u d(p, Po) > 8

I1-pPo - {1.0/(d(p, Po)/8), ne'u ngu'qcl
vdi d(p, Po)Iii khoang deh giua p vii Po vii alii nguong ehQn tru'oe.

4.11. Vector 1I6aban d6 dung Radon va Hough
ThuiH loan du<;le
thl1ehi~n theo cae bude ehinh sau:
1.
2.
3.
4.

Xae djnh tilt ca cae giao diem tren ban d6
Tie-n hanh cilia vung ban d6 thiinh cae manh con
Vector h6a tilt ca de manh ban d6
Ghep n6i cae manh da:vector h6a.

Diem milu eh6t eua thu~t tmin Iii d eh6 ta phai xae djnh cae do:).n thhg chu
khong phiii cae duang th~ng.
Qua trlnh xae djnh de do:).nth~ng du<;le

thl1ehi~n theo trlnh t1fsau:
1. Xae djnh 1 peak e6 gia trj tuong ung IOnnhilt trong khong gian tham 56 (gQi
Iii peak "d~m" nhilt)
2. Xii'I9 peak viYatlm du<;le pIlat hi~n cae do:).nth~ng tuong ung trang khong
de
gian anh
22


3. Lo<).i o cac do<).n
b
thhg vua tlm duQckhoi kh6ng gian anh va cac duong d<).ng
sin tuong ling voi cac di€m thuQc cac do<).n
th~ng nay trang khOng gian tham
56. Peak tuong ling cling duQc 10<).i
boo
4. Quay l<).i uoc 1 neu con peak chua xli'1,9.
b
4.11.1.

Xac djnh peak "dijm" nMI

Tren kh6ng gian tham so, ta xac dinh vi tri (Po, 00) co gia tri gRadon(Po, 00) clfc
d<).iNeu gia tri gRadon(Po, 00)nho hon nguong To thich hQp duQc chQn trl1octhl
(
chilm dlit vil$c xac djnh cac do<).n
thhg). Vung Ian c~n [Po-dp, Po+dp]x [eo-de,
~}+dO]cua diSm (Po, 00)trong kh6ng gian tham s61a vung co th€ chlia peak ncn
ta lien hanh xac dinh trQng tam cila vung nay voi trQng 56 t<).i 6i vi tri (p, fJ)la
m

gRadon(p, fJ). Vi tri cila trQngtam se duQcchQnla vi tri ciia peak tuongling
4.11.2.

Xac djnh tal cd do(fn tiding co tham sr/ (Pb 0/) trong khO1lggia1l
dnh

X€t mQt do<).n
th~ng xac djnh bc'litham 56 (p/, 0/), tQa dQ 2 dfiu do<).nthhg la
(X,,'ar" Yslarl) va

.

.
4.11.3.

(Xend, Yend).

np hQp giao di€m cila cac duong hlnh sin tuong ling voi cac di€m thuQc
do<).n
th~ng nay voi duong th~ng 0= 0 (trang kh6ng gian tham 56) Ia do<).n
th~ng co cac di€m dfiu Ia (p = X,'arl,0= 0) va (p = Xend, = 0).
0
T~p hQp giao diem cila cac duong hlnh sin tuong ling voi cac diem thuQc
do<).n
thhg nay voi duong th~ng 0= nl2 (trong kh6ng gian tham 56) la
do<).n
th~ng co cac diem dfiu la(p= YSlar" n/2) va (P= Yend,0= nl2).
0=
Cijp nhijt khOng gia1ldnh vel khOng gia1l tham sff

Voi m6i do<).n
th~ng vua xac dinh duQc, 10<).i tilt ca cac di6m thuQc do<).n
bo
th~ng
d6 ra khoi kh6ng gian anh (dn dlfa vao dO day cila do:)n thang d6 lo<).i o het
b
nhung diem thuQCoo<).n
th~ng, o~c bil$t trang trl1ong hop oo<).n
th~ng c6 dQ day
[un). Tuc1ngling vdi vii;c Jo<.li () cac diem nay, kh6ng gian tham s6 cling dn
b
duQc c~p nh~t l<).i. au khi thlfc hil$n xong giai oo<).n
S
nay, ta quay l:)i buoc 2.a M
tiep t\lc xli'1,9cac peak con l<).irong kh6ng gian tham so.
t

Ket lu4n
Vdi ml.)c lieu d~t fa, lu~n an dii dat duQc mot 56 ket qua Cl.)th€ sau:

.

Giai quyet bai loan vector boa ban d6 theo hai huang tier e~n. Huang tier c~n ilia
nhilt dung cae thu~t loan xu Iy anh truy€n th6ng thong qua de bude ti~n xu Iy, lam
manh duong bien, ... u€ Jin JuQt vector boa loan anh. Phuong phap nay co u'u di€m
Ja co t6c do xu Jy eao. Dong gap ehinh eila lac gia trang phu(Jng phap nay Ja c1iiciij
lien va t~n dl.)ng t6t mot s6 thu~t loan lien xu Jy anh d€ nang cao chill JuQng va t6e
do xU'Iy. Nho k0t hQp vdi each t6 chUc lliu trITdcr Ji~u hQp Iy, anh vector nh~n duQc
co kern theo cae thong tin topology b6 trQ rilt hieu qua cho qua trlnh HI dong xac
23