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26
Nghin cu so snh cc thut ton x l nh tnh su nh stereo ng dng trong
h thng camera th gic
Bch Ngc Minh*
Trung tm Pht trin i hc Quc gia H Ni, 144 Xun Thy, H Ni, Vit
Nam
Nhn ngy 16 thng 7 nm 2014 Chnh sa ngy 18 thng 8 nm 2014; Chp nhn
ng ngy 22 thng 9 nm 2014
Tm tt: C ba phng php c bn so snh s tng hp gia hai nh l SAD, SSD
v NCC.
Phng php NCC s dng s tng quan cho gia cc im nh nn cc php ton rt
phc tp.
Chng bao gm php ton bnh phng, tng, tch cc tng, khai cn nn vic
thc hin chc chn
rt tn thi gian. Cn hai phng php SAD v SSD c phc tp ca thut ton
khng khc
bit qu ln nn chng ta cn lm mt thc nghim kim chng cht lng bn su
v
tc thc hin. T chn ra mt phng php thch hp hn
So snh thi gian chy gia hai gii thut SAD v SSD cho thy vic la
chn cc thut ton
SAD l hp l hn, bi v cc thut ton SSD cn gn gp i thi gian chy.
Phng php SAD
c th gii quyt vn i vi vic tm su trong nh 3D. Mt im khng gian ly
nh
hai ng knh my ti hai v tr khc nhau. Chnh v th nn trc khi tm c su
ca im
nh, ta cn tm c cc im nh tng ng . Phng php SAD l phng php n gin
nht
tm c im nh .
Phng php SAD li c nhiu cch tnh ton, tnh theo phng php SAD truyn
thng,
phng php SAD iu chnh (da vo bin nh), phng php SAD phn on ( phn
vng nh).
y ta li la chn gia 2 phng php SAD iu chnh v SAD phn on gim 20%
so vi
SAD truyn thng.
Tip theo chng ta xem xt cc thut ton SAD phn vng lai c to ra bi s
kt hp ca
hai k thut: Belief Propagation v cc thut ton phn on Mean Shift.
Cch tip cn ny kt
hp nhng u im ca c hai phng php phn on. Cc thut ton Mean Shift
cho kt qu
nhanh chng v Belief Propagation thc hin phn on rt chnh xc.
T kha: Phn vng nh, Belief Propagation, Mean Shift, SAD , hnh nh
3D.
1. Gii thiu*
Mt xu hng pht trin mi l r bt s
dng camera th gic quan st nh mt
ngi. Mc d vic chit xut d liu t nh th
_______ * T.: 84-913550789 Email:[email protected].
Email:[email protected].
gic l kh khn hn l dng cm bin nhng
b li th cch thc ny cung cp cho r bt v
con ngi nhng d liu trc quan sinh ng v
y .
Khi x l tn hiu nh stereo th gic
thng c hai khu (Hnh 1).
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* Khu u tin l khu tin x l c nhim
v ly ra cc d liu c cha thng tin hu ch
cho vic pht trin cc ng dng th gic stereo
thi gian thc.
* Khu th hai cc ng dng th gic nh
ng dng ti to mi trng 3D, tm ng,
pht hin i tng
Hnh 1. Qu trnh x l d liu nh stereo th gic.
Trong khu tin x l, c mt c im
chnh l khi lng d liu thu thp bng
camera rt ln (ln hn nhiu ln so vi d liu
thu thp bng cm bin) cn c x l.
Mi cch gii quyt mi u phi c
pht trin trn mt nn tng sn c. phn tip,
cc k thut c bn ca x l nh 3D s c
a ra lm c s pht trin cho cc thut
ton v sau. Bc u tin, chng ta s tm hiu
v nh 3D v my quay 3D, nn tng c s u
tin ca h thng. Sau , cc k thut x l
trch ra ni dung ca nh s c bn n. Cc
thut ton c bn da vo m c cc
nghin cu hon thin hn.
1.1. nh 3D: L nh m bn thn n c cha ni dung v chiu su. Cc im nh
ngoi cc gi tr v mu sc, ta theo hai trc c bn cn c gi tr v chiu su.
to nn c tm nh 3D, ngi ta thc hin ng thi hai tm nh v cng mt ni dung
nhng khc hng.
Hnh 2. Mt cnh trong phim 3D.
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(Hnh 2) th hin mt tm nh 3D c
theo di bng mt knh chuyn dng. nh trn
c cu to t hai tm nh khc nhau c
trn bi 2 di mu khc nhau. Khi nhn nh trn
bng knh mt chuyn dng, mi mt ca ngi
xem s thy mt nh. S chnh lch v tr trong
2 tm nh nhn thy s to nn cm gic v
su cho ngi xem. Thc t, khi tch hai tm
nh ca mt nh 3D, chng ta s c th nhn
c nhng bc nh tng t nh trong ( Hnh 3).
nh 3D c nhiu ng dng hn l gii
tr. N c kh nng lu tr su im nh nn
cng c s dng cho cc ng dng yu cu
su im nh. Ni cch khc, t mt tm nh
3D, chng ta c th m t li khng gian hoc
ly nhng thng tin hu ch t su im nh
[1]. Cc i tng 3D cng c th c trch ra
t mt tm nh 3D.
a b
Hnh 3. nh 3D sau khi tch ra. a: nh nhn thy mt tri; b: nh nhn thy
mt phi
1.2. Stereo camera: L thit b thu nh 3D hoc thu phim 3D. V c bn,
stereo camera cng ging nhng my nh hoc my quay chuyn dng khc, nhng n
c hai ng knh mc song song (
Hinh 4)[2]. Hai ng knh ca mt stereo-camera c s dng ly hai hnh nh
trong mt nh 3D.
Hnh 4. H thng Stereo camera Bumblebee [3].
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(Hnh 5). th hin hot ng ca mt stereo
camera [3]. Cc chi tit s c thu vo 2 tm
nh thng qua 2 ng knh ca camera cng mt
lc. Lc ny, ta ca im nh thu c trn
hai tm s c mt lch nht nh, ta gi
lch l .
Hnh 5. Hot ng ca stereo camera.
Ta c:
= x1 x2 (1-1)
V khong cch t im A n camera s
c tnh:
Nh vy, t cc ta nh thu c ca
im A trn hai tm nh tri phi, ta s thu
c khong cch t camera ti im A.
Khong cch ny cn c gi l su im
nh k hiu bng z.
1.3.Tnh ton bn chnh lch: L mt trong nhng vn quan trng trong th
gic my tnh 3D. Mt s lng ln cc thut ton c xut gii quyt vn ny
[4],[5]. Mt trong nhng phng php tng i mi l Ci thin tnh ton Bn su t
hnh nh stereo theo phng php lai.
i vi cc cp hnh nh stereo c
chnh sa epipolar, mi im trong hnh nh
bn tri nm trn ng nm ngang ( ng
epipolar ) c th c im nh tng ng trong
hnh nh bn phi. Cch tip cn ny c s
dng lm gim khng gian tm kim chiu
su bn thut ton tnh ton. Chiu su ca
mt im nh l khong cch im khng gian
tng ng ti trung tm my nh. c tnh
bn su v pht hin cc i tng 3D,
cc im nh tng ng trong nhng nh tri v
nh phi cn c pht hin. Thut ton ny
bao gm cc giai on sau y (Hnh 6) :
1. Thu thp hnh nh,
2. Hnh hc Epipolar v ci thin hnh nh,
3. Phn on,
4. Thut ton ph hp stereo,
5. c lng bn su.
u tin, bin dng xuyn tm v tip tuyn
ca ng knh c loi b bng cch hiu chnh
my nh bi cc thng s bn trong v bn
ngoi my nh. lm c iu ny cn c s
hiu bit v cc thng s my nh vi mc ch
khc phc c hai hnh nh. Sau khi hiu chnh,
hnh nh c tch ra thnh cc khu vc bng
cch s dng cc thut ton phn chia lai c
xut. Cui cng, thut ton ph hp stereo
c p dng trn cc hnh nh phn on tri
v phi vi mc ch tm tt c cc tng
quan (im ph hp) v gn chiu su cho tng
phn on. u ra ca thut ton ph hp
stereo l cc bn su.
(1-2)
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Hnh 6. Thut ton SAD phn vng [6].
Trong phn tip theo, mc 2.1 trnh by v
tng quan v hiu chun my nh c bn. Hnh
nh ci tin da trn phn on c m t
trong mc 2.3. Phng php phn on Mean
Shift v Belief Propagation c trnh by
trong mc 6 v mc 7. Ti mc 8 trnh by v
thut ton SAD phn vng lai. Cui cng l kt
qu thc nghim v kt lun c trnh by
mc 9 v mc 10.
2. Ci thin hnh nh
2.1. Hiu chun my nh: p dng cc k thut khc nhau cho nh stereo vi
mt mc hp l chnh xc, iu quan trng l hiu chnh h thng camera. N l mt
qu trnh tm kim cc thng s bn trong v bn ngoi ca my nh. Cc phng php
hiu chun c in da trn cc mu hiu chun c bit chun b, cc i tng vi kch
thc v v tr c bit n trong mt h ta nht nh. Sau , cc tnh nng, chng hn
nh gc v ng, c chit xut t mt hnh nh ca m hnh chun. i tng vi cc tnh
nng c ngha thng
c chn hiu chnh c mt cch r rng cc v tr ca chng. Ngi ta thng dng
mt bn c n gin c th t c mc ch ny.
2.2. Chnh sa hinh nh: Chnh sa hnh nh (Hnh 7) l cn thit gim phc
tp tnh ton im nh tng ng trong hnh nh tri v bn phi. Mc ch ca vic ci
thin hnh nh l tm ng epipolar ca hai hnh nh theo lin kt chiu ngang.
iu ny c th c thc hin bng cch s dng cc bin i tuyn tnh xoay, dch v
nghing hnh nh. Cc thng s ni b camera v thng tin v nh hng v v tr my
nh c s dng trong cc php bin i.
Cc im 3D c phn chiu thnh cc
im trong hnh nh stereo tri v phi. Sau khi
ci thin theo (Hnh 8), cc ng epipolar ca
hai im phn chiu l song song theo chiu
ngang v lin kt dc theo mt phng hnh nh
mi. Cc im c nm trn cng mt ng
dy epipolar [7]. Do vn ph hp stereo
c gim xung tm kim mt chiu dc theo
cc ng ngang, thay v tm kim hai chiu
nh n c hin th trong (Hnh 8) [8],[9].
Tri Tri
Phi su
nh stereo ph hp
Bn su
Phn khc Hiu chnh nh
Phi
M hnh hiu chun
(Bn c)
Cc thng s hiu chun
Hnh nh vo
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Hnh 7. nh stereo trc khi chnh sa.
Hnh 8. nh stereo sau khi chnh sa.
2.3. Phn on hinh nh mu: Trong phn ny, hai phng php phn chia mu
sc c m t: Belief Propagation, Mean Shift. Mc tiu ca vic phn vng nh
l chia ton b hnh nh thnh mt tp hp cc phn on bao gm cc hnh nh. Cc
phn on cui cng phi p ng y bn iu kin sau [10]:
1.
2. Vi mi i v j, , tn ti
3. Vi th bt buc
4. Vi mi , tn ti
trong R i din cho ton b hnh nh, Ri (i
= 1, 2,..., n) l cc phn on khng rng,
khng chung nhau ca R, P(Ri) l thuc tnh
ging nhau ca tt c cc yu t trong Ri v 0
i din cho mt tp rng. Tng kt cng tc
phn on phi bao gm tt c cc im nh
trong hnh nh. y l iu kin tin quyt.
iu kin th hai th hin cc phn on khc
nhau khng chng cho nhau. iu kin th ba
th hin rng cc im nh trong cng phn
ng epipolar
ng epipolar
Trung tm chiu
Ca s tm kim im nh tng ng
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on phi c chung thuc tnh. Cc thuc tnh
phi khc nhau l iu kin cui cng.
C mt s thut ton c xut
gii quyt vn ny. Tuy nhin, tt c cc
thut ton ny u s dng hm chi ph kt hp
thit lp s tng ng gia hai im nh. C
ba phng php ph bin nht l phng php
da trn s khc bit cng tuyt i (AD),
phng php da trn s khc bit cng
bnh phng (SD) v phng php da trn s
tng quan cho chun (NCC).
2.4. Cc phng php th gic stereo chnh c th hin v mt ton hc nh
sau:
1- Phng php tng s khc bit tuyt i (SAD - Sum of Absolute
Differences):
(2-3)
Theo cng thc (2-3), vic tnh gi tr chnh
lch ca im (x,y) c thc hin bng php
tnh hiu trong ca s W. Do thut ton n
gin. Ca s W v phm vi chnh lch d cng
ln th s php tnh tng. Thng thng c th
thc tnh SAD vi ca s 3x3, hoc 5x5 hoc
7x7 hoc 11x11. Phm vi chnh lch d thng
chn di 120 vi cc gi tr tham kho nh 16,
50, 128. [11-13].
2- Phng php tng bnh phng khc bit (SSD Sum of Squared
Differences):
(2-4)
Phng php ny tnh tng ca cc bnh
phng ca cc hiu nn xut hin thm php
nhn trc khi tnh tng. Do phc tp
tng ln ng k [19].
3- Phng php da trn s tng quan cho chun (NCC)
(2-5)
Trong Il, Ir l nhng gi tr cng
trong hnh nh tri v phi, (x, y) l ta ca
im nh, d l gi tr sai lch c xem xt v
W l ca s phc hp. Vic la chn cc gi tr
sai lch thch hp cho mi im nh c thc
hin sau .
Phng php ny c phc tp cao nht
v xut hin cc php ton tiu tn nhiu ti
nguyn ca my tnh nh php bnh phng,
khai cn. Do vic ng dng ca thut ton
ny trong cc h thng thi gian thc l khng
kh thi.
(2-6)
tc l, cho mi im nh (x, y) v cho gi tr
khng i c s khc nhau d, chi ph ti thiu
c la chn. Phng trnh (2-6) c dng
cho phng php SAD. Tuy nhin, trong nhiu
trng hp la chn khc bit l mt qu trnh
lp i lp li, v chnh lch ca mi im
nh l ty thuc vo s chnh lch ca cc im
nh ln cn [14].
Cc thut ton phn vng lai l mt s kt
hp vi phng php SAD c p dng ph
hp vi hnh nh stereo tinh chnh cc bn
su cui cng . C hai, cc thut ton ph
hp vi m thanh stereo da trn phng php
m khng SAD phn on v cch tip cn lai
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xut da trn phng php phn khc hybrid
l hiu qu. tin.Tp hnh nh c tnh ton
trn 2,8 GHz b x l Intel Core i5 vi 4 GB b
nh DDR3 v kit pht trin FPGA DE2 m
phng.
Kt qu thc nghim SAD
phn gii Ca s Thi gian(s)
400x266 3x3 46
400x266 5x5 58.5
400x266 9x9 105
Kt qu thc nghim SSD
phn gii Ca s Thi gian(s)
400x266 3x3 106.5
400x266 5x5 335
400x266 9x9 891
Thi gian tnh ton cho cc thut ton SAD
l khong 105 giy v cho phng php phn
vng lai 29 giy, tng ng. Cc thut ton
ph hp vi hnh nh stereo da trn SAD lai
c v l thut ton hiu qu hn sn xut
bn chnh lch sch hn vi cc khu vc
ng nht. Mt khc, cc thut ton ph hp
vi hnh nh stereo da trn phng php SAD
sn xut mt bn chiu su r rng v hin
trng. Hn na, n to ra mt cht lng cao
hn v t li gy ra bi tc phn on hnh nh.
N c p dng cho cc hnh nh stereo chp
bi my nh lp th ca chng ti. B d liu
th nghim ca chng ti bao gm 25 cp hnh
nh stereo thc s trong mu xm quy m vi
kch thc 800x600 pixels. (Hnh 28)
Kt qu l, cn thit c nhiu ln lp li
tm ra cc thit lp tt nht ca s chnh lch.
Giai on ny to nn s khc bit gia thut
ton a phng vi thut ton ton cc. Qu
trnh tnh ton thng thm mt bc na
kt qu tt hn gi l khu lc (Hnh 9).
Hnh 9. S khi tng qut ca mt thut ton tng ng stereo.
3. Phng php SAD truyn thng:
Hnh 10. S khi tng qut ca phng php SAD truyn thng.
nh tri
Tnh
SAD
Chuyn i
nh xm
Chuyn i
nh xm
nh phi
T h thng camera stereo
Bn chnh lch
La chn
chnh lch
Tp hp chi ph ph
hp
Sng lc kt qu
Tnh ton chi
ph ph hp
Hnh nh
u vo
Bn
chnh lch
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Nh phn tch phn 2.4, phng php
SAD l phng php nhn din rt thun
tin. Song, bn cnh u im ca phng php
ny, n cn c mt s khuyt im v thi gian
p ng v xc sut li.
Cng thc (3-7) th hin tc ca thut
ton ny p dng vo vic tnh Bn chnh lch.
Trong cng thc ny, t l thi gian chy
chng trnh, S l s im cn tnh, W l kch
thc ca s tnh ton v L l khong cch yu
cu tnh ton. Vi cng thc trn, gi s c mi
1.5 triu php tnh hm chy trong 1 giy, tm
nh x l vi kch thc 640x480 pixel, kch
thc ca s l 5x5 pixel v khong cch thc
hin l 50 pixel.
Khi , thi gian php ton l 25.6 giy.
y l mt khong thi gian ln, hay ni cch
khc l tc tnh ton ca php ton l kh
chm.
a
b
c
d
e
f
Hnh 11. Cc kt qu tnh SAD thng thng. a) nh tri gc, b) nh phi gc,
c) Bn chnh lch mong mun, d) Bn chnh lch tnh bng phng php SAD vi ca
s 5x5, e) Bn chnh lch tnh bng phng php SAD vi ca s 7x7, f) Bn chnh
lch tnh bng phng php SAD vi ca s 11x11.
Mc d tc tnh ton rt chm, kt qu
tnh ton li khng chnh xc hon ton. Li
ca phng php SAD rt thng xuyn xy ra
do nhm ln trong qu trnh tnh ton. (Hnh
11) th hin mt s kt qu tnh bn sai lch
bng phng php SAD vi cc ca s 5x5,
7x7 v 11x11 thc hin trn nh Teddy [14].
Nhn xt, ng vi cc hnh trn, li cc b
xy ra nhiu nhng thut ton s dng ca s
so snh nh. Tuy nhin, hnh dng ca cc vt
th trong thut ton li c gi gn nht vi
hnh dng thc ca n. S dng ca s ln hn
s cho li cc b t hn, nhng hnh dng ca
cc vt th li b sai st ng k so vi thc t.
Hn th na, cc li ln vn khng th gim
thiu trong thut ton ny.
(3-7)
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Hnh12. Tc php ton SAD vi cc kch thc ca s khc nhau.
12) th hin thi gian ca thut ton o da
trn u vo l mt tm nh c kch thc
450x375. Nh vy, tc ca thut ton kh
b, khng thch hp cho mt h thng x l trn
robot, k c khi loi b tt c cc li.
Li ca phng php SAD l do u?
Phng php SAD da trn s so snh khc
bit gia cc ca s nh. Theo nh tng
thut ton th nh ca cc im hai tm nh l
ging nhau nht. Nh vy, kt qu tnh ton ca
thut ton ny thc s khng hiu qu cho h
thng dn ng chy trn robot. Nu thc s
trin khai mt h thng nh vy trn robot cu
h th s phi tn chi ph rt ln v kh nng
tnh ton m cha chc hiu qu. V vy,
phng php ny cn phi c ci thin c
c kt qu tt hn v ph hp hn cho h
thng thc.
4. Phng php SAD iu chnh:
Sau khi phn tch nhng nhc im ca
phng php xc nh bn chnh lch da
trn phng php SAD truyn thng, ti mun
xut mt phng php tt hn v cht lng
cng nh tc .
(Hnh 13) th hin cc bc ca phng
php mi nhm ly c bn chnh lch.
Nhng mc tip theo ca chng 3 s th hin
r tng bc ca phng php ny v ngha
ca chng.
4.1. Phng php SAD i vi ng bin
L phng php da trn phng php
SAD nhng ch p dng vi nhng im thuc
ng bin. Vi cch ny, ti k vng s c
c kt qu chnh xc hn vi tc tnh ton
cao hn.
Hnh 13. Phng php SAD iu chnh.
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Hnh 14. S khi tng qut ca phng php SAD iu chnh.
Gi s c mt cch no , ti c th gim
s im trong tp hp d liu cn tnh xung
cn 20% so vi ban u. Nh vy, tc ca
thut ton c th s tng ln n 5 ln hay thi
gian tnh ton s gim xung 5 ln. Tht vy,
theo phng trnh (3 -7) nu S gim i 5 ln v
cc gi tr khc vn gi nguyn, ta s c t gim
5 ln. Nh vy, ti s tm nhng im ng tin
cy nht tnh ton bn chnh lch nhm
gim li v tng tc .
Hnh.15. ng bin cng l ng bao i tng.
Nhng im c chn l nhng im
mang tnh phn bit cao, hay ni cch khc l
kh b nhm ln vi nhng im khc. Khi
chn ng bin lm tp hp d liu tnh
ton, bc u ta cng c th trnh c s
nhm ln gy ra bi cc im ln cn, li nhiu
nht trong nhng php ton trc.
ng bin cn gip to ra kt qu ni suy
chnh xc hn v sau . Nh vy, khi c c
ton b ng bao ca i tng v su ca
tt c cc im trn n, ta c th suy ra su
ca nhng im cn li.
Di nhng l do trn, ti chn ng bin
l nhng im s c tnh ton su trc
tip. (Hnh 16) l mt s so snh kt qu tnh
bn chnh lch da trn ng bin l 20%
bc nh, ng bin l 30% bc nh v ton b
bc nh. Vi kt qu th hin trong (Hnh
16), chng ta rt ra mt s nhn xt:
* Kt qu ca thut ton chnh xc hn i
vi nhng ng bin. S ng bin tnh ton
cng nh, chnh xc cng cao.
* Khi s im lm ng bin c tnh
ton nh n mt ngng no th kch thc
ca s tnh ton khng cn nh hng n kt
qu tnh ton na.
Vi nhn xt th 2, ta hin nhin c th
gim kch thc ca s ly SAD i m vn k
vng c c kt qu c chnh xc cao.
nh tri
Tnh
SAD
Chuyn i nh xm
Chuyn i
nh xm
nh phi
T h thng camera stereo
Pht hin bin
nh
Pht hin bin
nh
Bn chnh
lch
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Hnh 16. nh gi kt qu ca phng php SAD da trn ng bin.
4.2. Phng php trch chn ng bin mu
Phng php trch chn ng bin mu l
mt phng php ci tin hn so vi phng
php trch chn ng bin da trn nh xm.
S d phi trch chn ng bin mu v ng
bin nh xm khng th hin c ht cc
ng bao ca i tng. Cc nh xm khng
th th hin c ht cc tnh cht nh i vi
nh mu. (Hnh 17) th hin s khc bit gia
ng bin c ly t nh mu v ng bin
c ly t nh xm.
(Hnh 18) th hin l do ca s thiu ng
bin trong ng bin nh xm. Trong nh mu
hoc cc mng mu ca nh gc c nhng im
c s nhy bc ca mu sc hoc ng bin,
nhng trong nh xm khng c. Nh vy, thc
hin bt cc ng bin bng cc mng mu c
bn, ta s c cc ng bin kn hn v c
trng hn. Sau y s l cc bc xy dng
gii thut tm ng bin da trn cc mng
mu c bn:
* Bc 1: Ta coi 3 mng mu ging nh
nhng nh xm bnh thng khc, ta tm ng
bin bng ton t sobel.
* Bc 2: ng vi mi im ch c th c 1
gi tr nn ta s ly gi tr ng bin ca n
bng gi tr ln nht trong 3 gi tr tnh c
trn 3 mng mu.
Tnh ton SAD da trn 3 mng mu s
phi tn thi gian gp 3 ln so vi tnh ton
SAD da trn nh xm. Tht vy, nu coi mi
mu c bn tng ng vi mt nh xm, ta
s phi tnh SAD da trn 3 tm nh so v mt
tm. Nh vy, da theo cng thc (3-7), kch
thc ca s W s tng gp 3 khin thi gian
thc hin php ton t cng tng gp 3 ln, tc
php ton s gim i 3 ln.
Tuy nhin, da vo phng php ny, tc
php ton s khng b gim i 3 ln nh so
vi phng php SAD nh xm thng thng.
Tht vy, bi l mc d ng bin c ly
da trn 3 mng mu, mi im ch l ng
bin ca mt mng mu c bn. Nh vy, php
tnh SAD da vo im cng ch phi tnh
trn mt mng mu. V iu ny khin tc
thut ton lc ny khng b tng gp 3 ln.
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a
b
c
d
Hnh 17. ng bin 20% s im bng phng php Sobel mu v xm. a) nh xm b)
nh mu c) ng bin nh xm d) ng bin nh mu
a
b
c
d
e
Hnh 18. Cc mng mu ca hnh gc.
a)nh mu , b) nh xm , c) nh mu , d. nh mu xanh lc e. nh mu xanh
lam
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5. Phng php SAD phn vng
SAD phn vng l k thut s dng ni
suy mt bn su bao gm cc im
tnh c chun. S dng k thut ny trong
trng hp chng ta c th on c phm vi
ca nhng im cn tnh. Gi s mt im
c xc nh bn trong mt vt th m nhng
ng bin ca n c xc nh su.
Khi , tn ti mt xc sut cao rng nhng
im bn trong vt th s c su trong mt
phm vi nh xung quanh gi tr su ca cc
ng bin ca n. Khi , s gii hn su
tnh ton ca cc im ni suy c th lm mt
kh nng nhm ln gia im cho v cc
im bn ngoi.
Hnh 19. SAD phn on.
(Hnh 19) , gi thit su ca nhng
im thuc ng bin bao gm E1 v E2
tnh c v tnh chun. Khi , gi tr v
su ca A ch c th dao ng xung quanh cc
gi tr su ca E1 v E2 dn n kh nng
tnh ton su ca A c nng cao ln, mt
khc li khng b nhm ln vi mt im cng
c cu trc mu tng t l im B.
Hnh 20. S khi tng qut ca phng php SAD phn vng.
nh tri
Tnh
SAD
Chuyn i nh xm
Chuyn i nh xm
nh phi
T h thng camera stereo
Phn on
Phn on
Bn chnh
lch
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Gi thit bin php ny khng c s
dng, khi nh i chiu c th xut hin
mt im ging vi im cn tnh nm ln
cn khong cch vi im B. Khi ny, thut
ton SAD c th a n s nhm ln gi tr
su ca A. im A c th c tnh nhm v
nh hng trc tip n cc im nm bn cnh n.
Tm li, phng php SAD phn on dng
tt trong trng hp ni suy da theo gi tr tnh
ng. S dng bin php ny gip gim li v tng
tc . Tnh ton bn chnh lch l mt trong
nhng vn quan trng trong th gic my tnh
3D. Mt trong nhng phng php tng i mi
l Ci thin tnh ton Bn su t hnh nh
stereo theo phng php lai.
C nhiu phng php tnh Bn chnh
lch, y ta nghin cu hai phng php ci
thin tc tnh ton ( SAD iu chnh v SAD
phn vng).
6. Belief Propagation
Belief Propagation l cc thut ton
c pht trin ch yu l vi mc ch tm
xc sut cn bin trong mng Bayes. Ngoi ra,
cc thut ton cng c th x l cc m hnh
ha khc nh m hnh Markov Random Field
(MRF), y l mi quan tm nht nh trong
vic ti u ha cc hm nng lng ton cc
c tm thy trong my tnh th gic. M hnh
MRF l m hnh th v hng, trong cc
nt i din cho cc bin ngu nhin. Xc sut
chung P(x1,..., xn) ca m hnh MRF pair-wise
c th c vit phn tch nh sau:
(6-6)
y xn i din cho cc nt ca th, Z
l hng s chun ha v cc sn phm trn ij l
hn cc nc lng ging gn nht trn mng
vung. Tim nng i(xiyi), biu din cho xc
sut cho mt trng thi nht nh xi Xi trong
nt i da trn quan st v tim nng ij (xi,xj)
biu th s ph thuc iu kin gia cc nt ln
cn. Bin quan st yi him khi c vit ra mt
cch r rng [15].
Thut ton Belief Propagation (BP) th hin
trong (Hnh 21) cc thng ip c chuyn i
trong mt m hnh ha thng qua mt lot
cc bn tin c gi i gia cc nt ln cn
xung quanh trong mt li hnh nh lin k 4.
Bn tin c cp nht trong cc ln lp. Trong
mi bc lp, mi im nh ca th lin k
tnh ton thng ip ca mnh, da trn kt qu
ca bc lp trc, v gi tin nhn mi ca n
ti tt c cc im nh lin k 4 (hng xm)
theo hnh thc song song [15].
Hnh 21. M hnh c bn cho phn vng nh.
M hnh c bn cho phn vng nh, nh th
hin trong (Hnh ), l mt th vi hai loi
nt: nt n (vng trn) v cc nt quan st (hnh
vung). l hm chuyn trng thi gia mt
cp nt trng thi n khc nhau v l hm o
lng gia cc nt trng thi n v nt d liu
quan st c. Trong BP, mi nt s gi mt
thng ip ti cc nt lng ging trong biu
din phn b xc sut [15].
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7. Phng php Mean Shift:
Thut ton Mean Shift [16] c xut
bi Fukunaga v Hostetler. Cc thut ton da
trn mt c lng ht nhn [17]. Thut ton
ny l thut ton lp phi tham s. Cho mt tp
hp cc im d liu d-chiu c i din bi
cc gi tr xi, i = 1, 2,..., n trong d-chiu khng
gian Rd. S lng ca im xi thuc khu vc d-
chiu xung quanh x vi cnh di h c cho
bi:
(7-7)
trong h xc nh bn knh ca ht nhn
v K (x) l ht nhn hoc hm ca s. Nh vy,
c tnh mt ht nhn c cho bi:
(7-8)
Trong l ht
nhn i xng xuyn tm, l h s ht
nhn v c chun ha lin tc.Sau ,
phng trnh (7-10) c th c vit li :
(7-9)
c tnh ny c th c xem nh l
gradient ca xp x mt :
(7-10)
Mt ht nhn mi c nh ngha l
, trong
l hm ht nhn mi v l
hng s c chun ha. Sau khi thay th trong
phng trnh (7-12):
(7-13)
S dng phng trnh (7-13) thay i trung
bnh c xc nh:
(7-14)
Cc thut ton Mean Shift da trn vic tnh
ton lp i lp li vector dch trung bnh v thay
i c ngha v lin tc hin thc ha v tr
ht nhn bng phng trnh [15],[16]. xk +1 =
xk + m (XK). (7-15)
8. Thut ton SAD phn vng lai:
Trong phn vng nh, phng php lai kt
hp hai hoc nhiu hn cc thut ton phn
vng nh khc nhau [18]. y chng ta xem
xt cc thut ton lai c to ra bi s kt hp
ca hai k thut: Belief Propagation v cc
thut ton phn on Mean Shift nhanh chng
v rt chnh xc.
u tin, chng ti p dng cch lc hnh
nh bng thut ton Mean Shift. Bc ny rt
hu ch cho vic loi b ting n, lm mn v
phn vng nh. i vi mi im nh ca mt
hnh nh, tp hp cc pixel ln cn c xc
nh. Cho Xi l u vo v Yi hnh nh lc,
trong i = 1, 2,..., n. Cc thut ton lc bao
gm cc bc sau y [19],[20],[21]:
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* Khi to , , .
* Tnh ton thng qua Shift bnh ch , ni
hi t im nh.
* Lu tr cc thnh phn ca mc xm ca
cc gi tr tnh ton ti ,
ni l thnh phn khng gian v , l
thnh phn phm vi.
Th hai, hnh nh c chia thnh cc on
s dng thut ton phm Mean Shift. Trong
bc th ba, thc hin sp x ng bao ca
cc phn on. Th t, cc phn on nh c
sp nhp vi nhau thnh nhng on tip gip
tng t nh hu ht cc phng php Belief
Propagation. Cui cng, chng ta tch hp thut
ton phn on lai xut vi thut ton ph
hp stereo SAD. Phng php ny SAD lai c
th cung cp kt qu bn su chnh xc
cao.
Hnh 22. Thut ton SAD lai.
Tnh ton lch: Trong mc ny, chng ta
din t qu trnh ca s so snh chnh lch ni
nh c a vo l nhng mnh (on) ln
u tin v sau nhng im c cng iu
kin bn tri v bn phi nh c tm thy.
y l mt tng c gii thch cho
vng 3D duy nht im P trn (hnh 23).
a ra khong cch ca vt c quan st bi 2
my quay cng nhn theo mt hng hng
nhng khong cch khc nhau c bit (nh
ngha) l ng c bn. Sau , vt th xut
hin v tr tng t trong c hai nh 3chiu.
Khong cch gia vt bn tri v bn phi
nh c bit (nh ngha) l khong chnh
lch d bi (8-16). XL v XR l ta x ca c
lng ta 3D cn trn nh phng bn tri v
bn phi l IL v IR .
(8-16)
(8-17)
Khi bn tri v bn phi ca nh phng
quay c c cng v tr phng, ta y ca 2
nh l bng nhau (yL = yR) v c chnh lch
ta ngang (trc x) l (xL - xR).[22]
iu ny c ngha l chnh lch c
tnh ton, cng c th thay i c khi
thay i thng s ca my quay: chiu di tiu
c f v khong cch ca ng c s B = 2l.
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Hnh 23. Mt h thng stereo n gin .
9. Nhn xt v nh gi:
9.1. Phng php SAD truyn thng
Hnh 24. Mt s kt qu Bn chnh lch SAD truyn thng. a .Bn chnh lch vi
ca s 5x5;
b. Bn chnh lch vi ca s 7x7; c. Bn chnh lch vi ca s 11x11;
Hnh 25. th thi gian, ph v chnh xc.
a) b) c)
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9.2. Phng php SAD c iu chnh:
Hnh 26. Mt s kt qu thc hin tm SAD trn ng bin.
Hnh 27. th thi gian, ph v chnh xc.
Thi gian thc hin tnh bn chnh lch
theo phng php SAD iu chnh gim rt
nhiu so vi phng php SAD thng thng.
c.Phng php SAD phn vng:
Trong cuc th nghim tip theo, cc
phng php lai xut c th nghim trn
bn hnh nh stereo thc t c thc hin bi
h thng camera stereo. Thut ton ny c p
dng c tnh s chnh lch ca cc khi
9x9 t hnh nh bn tri tham chiu bng cch
tm kim cc khi ng c vin tng ng ca
hnh nh bn phi. Bn chnh lch cui cng
ca bn hnh nh lp th th nghim, c th l
sch, vt, khi lp phng v ta c th hin
trong (Hnh 28). C th, cc (Hnh 28-b) cho
thy cc bn khc bit c to ra bi thut
ton SAD m khng phn on v hnh. (Hnh
28-c) kt qu theo thut ton phn chia lai. Bn
chnh lch sn xut bi my nh ni
Bumblebee c hin th trong (Hnh 28-d).
a) b) c)
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Hnh 28. Kt qu thc nghim trn bn nh th nghim mu xm.
a) Hnh nh tham kho, b) Bn chnh lch sau khi s dng thut ton SAD m
khng phn on c) Kt qu ca thut ton SAD lai, d) H thng camera
Bumblebee.
Cht lng ca cc bn khc bit c
biu din nh l t l phn trm ca cc im
nh vi cc li sai lch ny (pixel c s ph
hp xu) [6]:
(9-18)
trong X * Y i din cho kch thc ca
hnh nh, dC l bn chnh lch tnh ca hnh
nh th nghim v dT l bn chnh lch s
tht. S tht chnh lch bn mt t l
nghch o ca khong cch tht mt t.
Phng trnh (9-19) cho thy lm th no
tnh ton bn chnh lch s tht mt t t
bn
(9-19)
vi DT l s tht bn su mt t, h l
chiu cao t mt phng t, DT * h l khong
cch tht mt t, B l c s gia cc my nh,
IRES c phn gii hnh nh v f l tiu c.
a) b) c) d)
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Bng 1. So snh kt qu ca cc gii thut tnh bn chnh lch
nh kim tra
SAD
thng
thng
SAD
phn
vng lai
H thng camera
Bumblelee
Quyn sch
9,64% 4,12% 3,59%
Ci vt 8,48% 4,72% 3,83%
Rubic 9,26% 4,37% 3,51%
Ta nh 9,91% 4,21% 3,65%
Cc bn chnh lch thu c t vic
xut lai phn on da trn thut ton SAD
phn vng lai c so snh vi cc phng
php khc (s dng h thng camera
Bumblebee v phng php SAD m khng
phn on). Trong ( bng 1), s khc bit gia
t l phn trm im nh li chnh lch c
trnh by. Nh c th thy trong (hnh 28), cc
thut ton SAD phn vng lai to ra kt qu
chnh xc hn so vi thut ton SAD m khng
phn on. Ngoi ra, hiu sut ca phng
php l gn t n hiu sut ca h thng
camera Bumblebee.
Cui cng, cc thut ton phn on lai
tn dng c li th nhanh chng ca thut
ton Mean Shift v chnh xc t thut ton
Belief Propagation. Li th ln ca mt thut
ton SAD lai l bt k phn on u c pht
hin c nhn dng t ng. Thut ton ny
t c mt hiu sut phn on gn thi
gian thc v kt qu chnh xc cao.
10. Kt lun:
Bi vit nghin cu so snh cho vic khi
phc bn su da trn cc thut ton phn
vng lai c xut s dng qu trnh lc.
Cc thut ton c th nghim trn thc t
vi cnh phc tp v tnh trng nh sng km
da trn h thng camera stereo cng nghip t
Bumblebee, t kt qu th nghim ta c th tm
mt bn chnh lch, m dch chuyn chnh
lch gia hai hnh nh v cui cng l c s
dng c tnh gi tr chiu su. Da trn cc
thut ton tng bnh phng khc bit (SSD)
v tng s khc bit tuyt i (SAD) c th tm
thy bn su trc tip. Ty thuc vo cc
k thut ph hp da trn cc thut ton SAD
v SSD mt nguyn tc gia thi gian chy v
cht lng cn phi c la chn. Cui cng,
thut ton SAD ph hp hnh nh stereo c
la chn thc hin cc th nghim tip theo,
bi v cc thut ton SSD i hi gn nh tng
gp i thi gian. Kt qu th nghim c
trnh by trong (Hnh 28) cho thy thut ton
SAD phn vng lai cho kt qu tt hn hn
thut ton SAD m khng cn s dng pjaan
vng v SAD iu chnh nhng hi km hn so
vi my nh ni ca h thng Bumblebee. Cc
thut ton SAD phn vng lai c xut
cng cho thy hiu sut cao hn. Trong tng
lai, ti d nh thc hin nghin cu v cng
kim tra cc thut ton phc tp hn.
Ti liu tham kho:
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for stereo vision. In IWCIA, 2005, vol.
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[13] Craig Watman, Fast Sum of Absolute Differences Visual
Landmark Detector, Robotic Systems Laboratory Department of
Systems
Engineering, RSISE, Australian National
University, Canberra, ACT 0200 Australia, Email:
[email protected]
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applicasions.Laboratory of
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48
Comparative Study of Image Processing Algorithms Calculate
Depth Stereo Image Camera Applications in the Visual System
Bch Ngc Minh
Centre Development Vietnam National University, Hanoi, 144 Xun
Thy, Hanoi, Vietnam
Abstract: There are three basic methods to compare the
similarity between two images, which is
SAD, SSD and NCC. NCC method is using cross- correlation between
the pixels so the calculations
are complex . These include the arithmetic average, total,
multiplication total, square root should this
method definitely perform very time consuming. Both SAD method
and SSD method doesnt much
difference the complexity of the algorithm so we need to do an
experiment to verify the quality of the
depth maps and the speed of execution. From the results that we
choose a more appropriate method
Comparison of running time between SAD and SSD algorithms show
that the choice of the SAD
algorithm is more reasonable, because the SSD algorithm needs
nearly twice the time to run. SAD
method can solve the problem of finding depth in 3D images. A
point in space to acquire images of
two lenses in two different locations. Therefore so before
finding the depth of the pixel, we need to
find the corresponding pixels. SAD method is the easiest method
to find the pixel .
SAD method has many calculate ways, calculate by traditional
methods SAD, adjustment SAD
method (based on the image border) , segmentation SAD method
(image segmentation). In Here we
choose between two methods of adjustment SAD method and segment
SAD method decreased 20 %
compared with traditional SAD.
Then we consider the hybrid algorithm SAD partition is created
by the combination to two
techniques: Belief Propagation and the Mean Shift segmentation
algorithm. This approach combines
the advantages of both methods segment. Mean Shift algorithm is
fast results and Belief Propagation
perform very accurate segmentation.
Keywords: Image segmentation, Belief Propagation, Mean Shift,
SAD, 3D image.