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<strong>%XODQÕN</strong> 6 ]<strong>JHo</strong> <strong>LOH</strong> <strong>*|U</strong> <strong>QW</strong> <strong>6WDELOL</strong>]<strong>DV\RQX</strong><br />
Özetçe<br />
<strong>*|U</strong> <strong>QW</strong> VWDELOL]<strong>DV\RQX</strong> X\JXODPDODUÕQGD NXOODQÕP DPDFÕ\OD<br />
D\UÕN ]DPDQOÕ oDOÕúDQ EXODQÕN PD<strong>QW</strong>ÕN WHPHOOL bir süzgeç<br />
önerilmektedir. (OH DOÕQDQ ELU NHVWLULP VLVWHPLnin düzeltme<br />
fonksiyonu EXODQÕN PD<strong>QW</strong>ÕN WHPHOOL ELU VLVWHPOH JHUoHNOHQPLú<br />
NXOODQÕODQ NHVWLULP \DSÕVÕ EXODQÕN V ]<strong>JHo</strong> ROarak<br />
DGODQGÕUÕOPÕúWÕU )DUNOÕ WLSWHNL J U Otülü görüntü dizilerinin<br />
NRQXP YHNW|UOHUL EXODQÕN V ]<strong>JHo</strong>WHQ <strong>JHo</strong>LULOPLú YH HOGH HG<strong>LOH</strong>Q<br />
VRQXoODU VXQXOPXúWXU<br />
1. *LULú<br />
'LMLWDO NDPHUDODUGD |QHPOL ELU SUREOHP oHNLP VÕUDVÕQGD<br />
LVWHQPH\HQ NDPHUD KDUHNHWLQGHQ GROD\Õ J|U <strong>QW</strong> OHUGH PH\GDQD<br />
JHOHQ WLWUHúLPOHUGLU %X WLWUHúLPOHUL |QOHPHN DPDFÕ ile görüntü<br />
VWDELOL]<strong>DV\RQX</strong> NXOODQÕOPDNWDGÕU <strong>*|U</strong> <strong>QW</strong> VWDELOL]<strong>DV\RQX</strong><br />
DPDW|U ELU NDPHUDPDQ WDUDIÕQGDQ YH\D KDUHNHW KDOLQGHNL<br />
DUDoODUGDQ \DSÕODQ oHNLPOHUGH J|U <strong>QW</strong> O FHS WHOHIRQODUÕ YH<br />
robot-NDPHUD X\JXODPDODUÕ JLEL DODQODUGD NXOODQÕOPDNWDGÕU<br />
Kamera görüntülerinde, bütünsel hareket (imge<br />
çerçevesinin hareketi) ve yerel hareket (imge içerisindeki bir<br />
QHVQHQLQ KDUHNHWL ROPDN ]HUH LNL oHúLW KDUHNHW<br />
WDQÕPODQPDNWDGÕU <strong>*|U</strong> <strong>QW</strong> VWDELOL]<strong>DV\RQX</strong> LoLQ J|U <strong>QW</strong> Q Q<br />
E W QVHO KDUHNHWL HOH DOÕQDUDN NDPHUD NRQXPXQXQ J|VWHUGL÷L<br />
GH÷LúLPOHU LVWHQHQ YH LVWHQPH\HQ GH÷LúLPOHU RODUDN LNL WLSWH<br />
WDQÕPODQDELOLU % W QVHO KDUHNHWWHNL LVWHQHQ GH÷LúLPOHU<br />
NDPHUDQÕQ NDVÕWOÕ \HU GH÷LúLPLQGHQ ND\QDNODQDQ LVWHQPH\HQ<br />
GH÷LúLPOHU LVH WLWUHúLPOHUGHQ GROD\Õ ROXúDQ KDreket<br />
GH÷LúLPOHULGLU <strong>*|U</strong> <strong>QW</strong> VWDELOL]<strong>DV\RQX</strong>QGD DPDo J|U <strong>QW</strong><br />
GL]LVLQLQ E W QVHO KDUHNHWLQGHNL LVWHQPH\HQ GH÷LúLPOHUL<br />
D\UÕúWÕUPDN YH \DOQÕ] LVWHQHQ GH÷LúLPOHULQ J|]OHQGL÷L \HQL ELU<br />
görüntü dizisi elde etmektedir[1].<br />
Görüntü stabilizasyonu sistemi hareket kestirim sistemi<br />
YH KDUHNHW G ]HOWPH VLVWHPL ROPDN ]HUH LNL NÕVÕPGD HOH<br />
DOÕQDELOLU +DUHNHW NHVWLULP VLVWHPL <strong>LOH</strong> J|U <strong>QW</strong> GL]LVLQGHNL<br />
E W QVHO KDUHNHW GH÷LúLP YHNW|UOHUL KHU ELU oHUoHYH LoLQ ELU<br />
|QFHNL oHUoHYH\H ED÷OÕ RODUDN KHVDSODQPDNWDGÕU ø\L ELU<br />
görünW VWDELOL]<strong>DV\RQX</strong> VD÷OD\DELOPHN LoLQ WHPHOGH KDUHNHW<br />
NHVWLULP VLVWHPL VRQXFXQGDNL KDWDQÕQ PLQLPXP ROPDVÕ<br />
istenmektedir. Aksi durumda, hareket kestirim sistemi sonucu<br />
ROXúDFDN KDWD GR÷UXGDQ KDUHNHW G ]HOWPH VLVWHPLQL<br />
HWN<strong>LOH</strong>\HFHNWLU> @ %X oDOúPDGD KDUHNHW düzeltme sistemi için<br />
E W QVHO KDUHNHWWHNL \ NVHN IUHNHQVOÕ LVWHQPH\HQ GH÷LúLP<br />
E<strong>LOH</strong>úHQOHULQL EDVWÕUDFDN ELoLPGH ELU EXODQÕN V ]<strong>JHo</strong><br />
JHOLúWLULOPLúWLU<br />
2. <strong>%XODQÕN</strong> 6 ]<strong>JHo</strong><br />
<strong>%XODQÕN</strong> PD<strong>QW</strong>ÕN WHPHOOL VLVWHPOHU ILOWUHOHQPHVL ]RU YH<br />
PDWHPDWLNVHO PRGHOLQLQ ROXúWXUXOPDVÕ NDUPDúÕN RODQ J U OW O<br />
LúDUHWOHUGHNL J U OW Q Q EDVWÕUÕOPDVÕQGD JHOHQHNVHO VLVWHPOHUH<br />
J|UH GDKD L\L VRQXo YHUPHNWHGLU> @ %X oDOÕúPDGD EXODQÕN<br />
M. Kemal GÜLLÜ, Sarp ERTÜRK<br />
Elektronik YH +DEHUOHúPH 0 KHQGLVOL÷L %|O P<br />
Kocaeli Üniversitesi, ø]PLW<br />
kemalg@kou.edu.tr, sertur@kou.edu.tr<br />
PD<strong>QW</strong>ÕN WHPHOOL EDVLW ELU NHVWLULP VLVWHPL NXOODQÕODUDN EXODQÕN<br />
V ]<strong>JHo</strong> ROXúWXUXOPXúWXU<br />
2.1. <strong>%XODQÕN</strong> .HVWLULP<br />
Görüntü dizisinin istenen hareket vektörlerini elde etmek için<br />
NXOODQGÕ÷ÕPÕ] NHVWLULP \DSÕVÕ<br />
ˆ − ˆ +<br />
x k = xk<br />
−1<br />
+ Tvˆ<br />
k −1<br />
+ −<br />
−<br />
xˆ k = xˆ<br />
k + g(<br />
zk<br />
, xˆ<br />
k )<br />
(1)<br />
(2)<br />
denklemleriyle belirtilmektedir. Bu denklemlerde k zaman<br />
indisinde x LVWHQHQ GH÷HULQLQ |Q NHVWLULPL<br />
−<br />
xˆ k , x in son<br />
kestirimi<br />
+<br />
xˆ k , kestiricinin yineleme süresi T , gürültülü<br />
görüntü dizisi hareket vektörü z k , hareket GH÷LúLP KÕ]Õ<br />
NHVWLULP GH÷HUL vˆ GLU +DUHNHW GH÷LúLP KÕ]Õ NHVWLULP GH÷HUL<br />
( xˆ<br />
− xˆ<br />
)<br />
+ +<br />
k k<br />
vˆ<br />
−1<br />
−2<br />
k−1<br />
=<br />
(3)<br />
T<br />
IRQNVL\RQX <strong>LOH</strong> KHVDSODQPDNWDGÕU g() . ile gösterilen düzeltme<br />
IRQNVL\RQXGXU YH oR÷X ]DPDQ PDWHPDWLNVHO PRGHOLQLn<br />
oÕNDUWÕPÕ ]RUGXU %X oDOÕúPDGD g() . düzeltme fonksiyonu bir<br />
EXODQÕN VLVWHP NXOODQÕODUDN JHUoHNOHúWLULOPLúWLU<br />
2.2. Süzgeç Parametreleri<br />
BXODQÕN G ]HOWPH IRQNVL\RQX LoLQ NXOODQÕODQ EXODQÕN oÕNDUWÕP<br />
\DSÕVÕ ùHNLO GH YHULOPLúWLU YH J|U OG ÷ ]HUH JLULú- oÕNÕú’<br />
D VDKLSWLU *LULúOHU<br />
−<br />
I1 k = zk<br />
− xˆ<br />
k<br />
(4)<br />
I 2k = I1k<br />
− I1k<br />
−1<br />
(5)<br />
HúLWOLNOHUL\OH WDQÕPODQPDNWDGÕU Burada I1 ile belirtilen JLULú1,<br />
k. çerçevenin V ]<strong>JHo</strong>OHQPHPLú J|U <strong>QW</strong> GL]LVL vektörü ile x<br />
LVWHQHQ GH÷HULQLQ |Q NHVWLULPL<br />
−<br />
xˆ k DUDVÕQGDNL IDUN I 2 ile<br />
WDQÕPODQDQ JLULú I1 in k. ve ( k −1).<br />
GH÷HUOHUL DUDVÕQGDNL<br />
fDUN <strong>LOH</strong> KHVDSODQPDNWDGÕU<br />
JLULú<br />
JLULú<br />
ELOJL WDEDQÕ<br />
EXODQÕNODúWÕUÕFÕ GXUXODúWÕUÕFÕ oÕNÕú<br />
EXODQÕN oÕNDUWÕP<br />
motoru<br />
ùHNLO <strong>%XODQÕN</strong> G ]HOWPH VLVWHPL LoLQ NXOODQÕODQ JLULú- oÕNÕú<br />
EXODQÕN oÕNDUWÕP \DSÕVÕ
.XOODQÕODQ \HOLN IRQNVL\RQODUÕQÕQ \DSÕVÕ YH SDUDPHWUHOHUL<br />
EXODQÕN V ]JHFLQ oDOÕúPD YHULPOLOL÷LQL DUWWÕUDFDN úekilde<br />
EHOLUOHQPLúWLU +HU ELU JLULú YH oÕNÕú LoLQ DGHW *DXVV WLSL<br />
\HOLN IRQNVL\RQX NXOODQÕOPÕúWÕU Gaus tipi üyelik<br />
IRQNVL\RQODUÕQÕQ NXOODQÕOPDVÕQGDNL DPDo <strong>LOH</strong>ULNL oDOÕúPDODUGD<br />
EXODQÕN ILOWUH\L DGDSWLI KDOH JHWLUHELOPHN LoLQ üyelik<br />
IRQNVL\RQODUÕQÕn meUNH] QRNWDODUÕQÕn YH WDQÕP DUDOÕNODUÕQÕn<br />
ELUHU GH÷LúNHQOH GH÷LúWLUHELOLU ROPDVÕGÕU Gauss üyelik<br />
fonksiyonu, { c, σ}<br />
GH÷LúNHQOHriyle WDQÕPODQPDNWDGÕU EXUDGD<br />
c \HOLN IRQNVL\RQXQXQ PHUNH] QRNWDVÕQÕ σ JHQLúOL÷LQL<br />
belirtmektedir. Gauss üyelik fonksiyonu<br />
( x;<br />
c,<br />
σ )<br />
2<br />
1⎛<br />
x−c<br />
⎞<br />
− ⎜ ⎟<br />
2⎝<br />
σ ⎠<br />
y = gaussian = e<br />
(6)<br />
HúLWOL÷L\OH YHULOPHNWHGLU<br />
<strong>%XODQÕN</strong> VLVWHP WDVDUÕPÕQGD L\L ELU VLVWHP SHUIRUPDQVÕ<br />
\DNDOD\DELOPHN LoLQ |QFHOLNOH VLVWHPLQ L\L WDQÕQPDVÕ \HOLN<br />
IRQNVL\RQODUÕ YH NXUDO WDEDQÕQÕQ GLNNDWOL bir biçimde<br />
belirlenmesi gerekmektedir. %HOLUOHQHQ JLULú-oÕNÕú \HOLN<br />
IRQNVL\RQODUÕ YH NXUDO WDEDQÕ VÕUDVÕ\OD ùHNLO<br />
verilmektedir.<br />
YH 7DEOR GH<br />
(a)<br />
(b)<br />
(c)<br />
ùHNLO D JLULú E JLULú<br />
(d)<br />
F oÕNÕú \HOLN IRQNVL\RQODUÕ<br />
WDQÕP DUDOÕNODUÕ YH G JLULú-oÕNÕú \ ]H\ GD÷ÕOÕPÕ<br />
Tablo 1: <strong>%XODQÕN</strong> VLVWHP LoLQ NXUDO WDEDQÕ<br />
*LULú<br />
NB N Z P PB<br />
NB NB N N Z Z<br />
N N N Z Z P<br />
Z N Z Z Z P<br />
P N Z Z P P<br />
PB Z Z P P PB<br />
*NB=Negative Big, N=Negative, Z=Zero, P=Positive,<br />
PB=Positive Big<br />
3. 2UWDODPD $OPD øúOHPL<br />
Hareket vektörlerinin biriktirilmesiyle elde edilen<br />
J U OW O NRQXP GH÷HUOHUL V ]JHFH JLrilmeden önce<br />
EDVLW ELU RUWDODPD DOPD LúOHPL \DSÕOPDNWDGÕU %X |Q<br />
LúOHPLQ \DSÕOPDVÕQÕQ QHGHQL KDP J|U <strong>QW</strong> GL]LVL KDUHNHW<br />
YHNW|UOHULQLQ DQL GH÷LúHQ E \ N WLWUHúLPOHUH VDKLS<br />
RODELOPHVLGLU %X WLWUHúLPOHUL GR÷UXGDQ GLNNDWH DOPDN<br />
LoLQ EXODQÕN V ]JHFLQ \HOLN IRQNVL\RQODUÕQÕQ WDQÕP<br />
DUDOÕNODUÕQÕQ JHQLú WXWXOPDVÕ JHUHNPHNWH YH EXQXQ<br />
QHWLFHVLQGH VWDELOL]DV\RQ YHULPL G úPHNWHGLU Ham<br />
görüntü dizisi hareket vektörü ak ile gösterilip, |Q LúOHP<br />
uygulaQGÕ÷ÕQGD ROXúDQ J|U <strong>QW</strong> GL]LVL KDUHNHW YHNW|U<br />
zk ile J|VWHULOVLQ %X |Q LúOHP <strong>LOH</strong> ak nÕQ VRQ GH÷HULQLQ<br />
RUWDODPDVÕ<br />
z k−<br />
1 = ( ak<br />
+ ak<br />
−1<br />
+ ak<br />
2 + ak<br />
−−<br />
3)<br />
/ 4<br />
(6)<br />
úHNOLQGH DOÕQPDNWDGÕU %X LúOHP VDGHFH ELU oHUoHYH V UHVL<br />
gecikmeye neden olmakta, IDNDW DQL GH÷LúHQ E \ N WLWUHúLPOHU<br />
N o N WLWUHúLPOHU KDOLQH LQGLUJHQPHNWHGLU %|\OHOLNOH EXODQÕN<br />
V ]JHFLQ \HOLN IRQNVL\RQODUÕQÕQ WDQÕP DUDOÕNODUÕ<br />
GDUDOWÕODELOPHNWH YH GDKD L\L VWDELOL]DV\RQ VRQXoODUÕ HOGH<br />
edilmektedir.<br />
4. Deneysel Sonuçlar<br />
Deneysel sonuçlarda ilk olarak, yolda yürüyen bir kameraman<br />
WDUDIÕQGDQ \DSÕODQ oHNLPGHQ HOGH HGLOPLú araba görüntü dizisi<br />
YHULOPHNWHGLU ùHNLO GH araba görüntü dizisi için örnek bir<br />
çerçeve görüntüsü görülmektedir.
ùHNLO Deneylerde NXOODQÕODQ araba görüntü dizisinden örnek<br />
bir çerçeve görüntüsü<br />
ùHNLO 4’ de araba J|U <strong>QW</strong> GL]LVL LoLQ \DWD\ YH G úH\<br />
GR÷UXOWXODUGD |Q LúOHP oÕNÕúÕQÕQ HWNLVL YH EXODQÕN V ]<strong>JHo</strong><br />
oÕNÕúÕQGD HOGH HG<strong>LOH</strong>Q G ]J Q NRQXP vektörü GH÷HUOHUL<br />
görülmektedir. gQ LúOHP oÕNÕúÕQGD DQL WLWUHúLPOHULQ JHQOLNOHUL<br />
G ú U OPHNWH ve etkiOHUL D]DOWÕOPDNWD E|\OHFH EXODQÕN ILOWUHQLQ<br />
\HOLN IRQNVL\RQODUÕQÕQ WDQÕP DUDOÕNODUÕ GDUDOWÕODELOPHNWHGLU.<br />
(a)<br />
(b)<br />
ùHNLO Araba dizisi için; D G úH\ NRQXP E \DWD\ NRQXP<br />
|Q LúOHP YH EXODQÕN V ]<strong>JHo</strong> oÕNÕú GH÷HUOHUL<br />
'L÷HU ELU |UQHN J|U <strong>QW</strong> GL]LVL, yolda giden bir motosiklet<br />
]HULQH PR<strong>QW</strong>H HGLOPLú ELU NDPHUD WDUDIÕQGDQ \DSÕODQ çekimden<br />
elde edilen motosiklet görüntü dizisidir. ùHNLO ’ de araba<br />
görüntü dizisi için örnek bir çerçeve görüntüsü verilmektedir.<br />
ùHNLO Motosiklet görüntü dizisinden örnek bir çerçeve<br />
görüntüsü<br />
Motosiklet J|U <strong>QW</strong> GL]LVL LoLQ \DWD\ YH G úH\ GR÷UXOWXODUGD |Q<br />
LúOHP oÕNÕúÕQÕQ HWNLVL YH EXODQÕN V ]<strong>JHo</strong> oÕNÕúÕQGD HOGH HG<strong>LOH</strong>Q<br />
düzgün konum vektörü GH÷HUOHUL ùHNLO GD J|U OPHNWHGLU<br />
(a)<br />
(b)<br />
ùHNLO Motosiklet dizisi için; D G úH\ NRQXP E \DWD\<br />
NRQXP |Q LúOHP YH EXODQÕN V ]<strong>JHo</strong> oÕNÕú GH÷HUOHUL<br />
5. Sonuçlar<br />
Araba dizisi için, öQ LúOHPGHQ <strong>JHo</strong>LULOPLú \DWD\ YH G úH\<br />
konum YHNW|U GL]<strong>LOH</strong>UL EXODQÕN V ]JHFH JLULOGL÷LQGH HOGH<br />
HG<strong>LOH</strong>Q oÕNÕú konum YHNW|U GL]<strong>LOH</strong>UL ùHNLO 4’ de görülmektedir.<br />
ùHNLO 4-D GD GL]LQLQ KDP G úH\ KDUHNHW NRQXPODUÕQD<br />
EDNÕOGÕ÷ÕQGD DQL YH E \ N WLWUHúLPOHU J|]OHQPHNWHGLU ùHNLO 4b’<br />
deki ham yatay konum vektörleri LVH \DYDú GH÷LúLPOL ELU<br />
NDUDNWHULVWL÷H VDKLSWLU 0RWRU GL]LVL HOH DOÕQGÕ÷ÕQGD \DWD\GD YH
G úH\GH E \ N WLWUHúLPOHU YDUGÕU IDNDW G úH\ NRQXPGDNL<br />
WLWUHúLPOHULQ JHQOLNOHUL \DWD\ NRQXPD RUDQOD GDKD ID]ODGÕU<br />
gUQHN GL]<strong>LOH</strong>UGHQ GH J|U OHFH÷L ]HUH KÕ]OÕ YH \DYDú<br />
GH÷LúLPOL WLWUHúLPOHULQ EXOXQGX÷X NRQXP vektörü dizileri<br />
ILOWUHOHQGL÷LQGH YDURODQ DQL WLWUHúLPOHU EDVWÕUÕOPÕú YH<br />
NDPHUDQÕQ X]XQ V UHOL KDUHNHWL NRUXQPXúWXU<br />
%X VRQXoODU GR÷UXOWXVXQGD JHUoHNOHúWLU<strong>LOH</strong>Q EXODQÕN<br />
V ]JHFLQ LúOHP \ N G ú N ROGX÷XQGDQ JHUoHN ]DPDQOÕ<br />
X\JXODPDODUGD NXOODQÕODE<strong>LOH</strong>FH÷L YH HWNLQ ELU VWDELOL]DV\RQ<br />
JHUoHNOHúWLUGL÷L J|U OPHNWHGLU> @ 6DELW \HOLN IRQNVL\RQODUÕ<br />
QHGHQL\OH IDUNOÕ J|U <strong>QW</strong> GL]<strong>LOH</strong>UL LQFHOHQGL÷LQGH V ]JHFH JLU<strong>LOH</strong>Q<br />
J|U <strong>QW</strong> GL]LVLQLQ NDUDNWHULVWL÷LQH J|UH ED]HQ VWDELOL]DV\RQ<br />
YHULPLQLQ G úHELOGL÷L J|]OHQPLúWLU øOHULNL oDOÕúPDODUGD \HOLN<br />
IRQNVL\RQODUÕQD DGDSWLIOLN ND]DQGÕUÕlarak hareket<br />
NDUDNWHULVWL÷LQGHQ ED÷ÕPVÕ] HWNLQ ELU VWDELOL]DV\RQ VLVWHPLQLQ<br />
JHOLúWLULOPHVL DPDoODQPDNWDGÕU<br />
6. 7HúHNN U<br />
%X oDOÕúPD 7 UNL\H %LOLPVHO YH 7HNQLN $UDúWÕUPD .XUXPX<br />
7h%ø7$. WDUDIÕQGDQ ((($* -006 nXPDUDOÕ DUDúWÕUPD<br />
SURMHVL NDSVDPÕQGD GHVWHNOHQPLúWLU<br />
7. Kaynakça<br />
[1] E. Yaman, F. Tekin, S. Ertürk, “Kalman Filtresi ile<br />
Görüntü Stabilizasyonu”, EEBM 9. Ulusal Kongresi,<br />
Kocaeli, sf 557-560,2001.<br />
[2] S. Erturk, T. J. Dennis, “Image Sequence Stabilization<br />
Based on DFT Filtering, IEE Proc. On Image Vision and<br />
Signal Processing”, Vol 147, No 2, pp 95-102, 2000.<br />
[3] M.K. Güllü, E. Yaman, S. Ertürk, “Image Sequence<br />
Stabilisation using Fuzzy Adaptive Kalman Filtering”,<br />
Electronics Letters, Vol. 39, No. 5, (2003) 429-431.<br />
[4] D. Simon, “Fuzzy Estimation of DC Motor Winding<br />
Currents”, in: North American Fuzzy Information<br />
Processing Society Conference, New York, NY, 1999,<br />
pp. 859-863.<br />
[5] gUQHN <strong>6WDELOL</strong>]DV\RQ 6RQXoODUÕ<br />
http://mf.kou.edu.tr/elohab/ipl/research.htm
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