Abstract
Camera calibration is a preliminary step for many computer vision appli- cations. Recently, moving object detection and tracking methods have been successfully implemented in lots of surveillance systems. In addition, multi- modal camera cooperation provides more information to prevent the loss of moving objects. However they need much computational effect to obtain the information of moving objects from each camera. In this thesis, the archi- tecture of two-camera calibration is proposed to speed up the detection and tracking processes.
Basically, two cameras are installed in the proposed system. One can view the whole sense, and the other is a PTZ(Pan, Tilt, Zoom) camera which can capture the detailed information of moving objects. If two cameras are calibrated, the object information in the PTZ camera video sequence can be obtained from that in the fixed camera and the calibrated parameters.
Based on this strategy, the computation time of moving object extraction in the video sequence of the PTZ camera is reduced.
The calibration process consists of two modules. First, the corresponding points between two cameras are established using the block-based matching strategy. The calibrated parameters are obtained from those points using the epipolar plane constraints and the iteration techniques. Second, the self-calibration process was made for the PTZ camera. Similarly the corre- sponding points between the images of different rotation angles, and zooming
scales were constructed. The self-calibration parameters were also generated from these corresponding points by automatically rotating and zooming the PTZ camera. After calibrating these two cameras, when a moving object was detected in the fixed camera video sequence, the position of the moving object can be obtained by the parametric matrix and a linear transformation.
Besides, some experimental results were demonstrated to show the validity of proposed method.
Keyword:camera calibration, epipolar geometry, projection matrix
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™Í$Dóœè™Í$‚àìä³RD ²¾t[ýw²É[ ]zìä³D
²¾˚5Õ¶¡b óœè™Í$Ddè™Í$ÈYWÿ(fx, fy)dÖÊxW DyWíªW(dx, dy) dR×2-õ (u0,v0) Dskew$˚5Ñq¶¡b
â 2.10ªc, J˛øóœíq Õ¶¡b, ÿª)øóœíIä³M, ú˛È LøõPW7k, ç˛øPW = (XW, YW, ZW, 1), ÿª°|v˛ÈõÊdÞ,í
dõp = (u, v) ¥5, à‹câdÞ,íõp, ¸˛øóœíq Õ¶¡b, 6 ̶êr)øvõíöõÍ$è™P0 ÄMu3X4í.ªLä³, ‚àMDp(u, v)H p (2.10) 2íú_j˙¾ Z, É)ƒXW, YW, ZWís_(4j˙ ²Æ uz, c?)ƒ 3D ˛ÈõDóœ¡5õí¦(OP àÇ 2.6 Fý 6ª[ýÑ, F OP ¦(,íú˛Èõ (P1P2P3) îAdkdÞípõ, ºÌ¶)øvpõ íñøú˛Èè™ Jk°¦dÞ,põíú˛Èè™õ, ÿ.â°vN¬s ÁCÖÁJ,íóœAd, n?)øpõíñø¿ [78]
FJçBbw…7óœ¡b(, ÿªJ‚àóœAdí¡b, N¬.°P .°
iÝB.°ÿFi¦íd, YW˛¤u°íú@õ°)®dÈíú@õ² É[
Ç 2.6: AdkdÞª?í˛Èõ
Chapter 3
”(SDÔõªú
Ê,øı2Bb)ø, sX.°Öq (P Dì) ÝBsÁ.°Z¨ (q¶¡
b.°) íóœ, }.°íóœ¡b 7BbʪWÖóœía−v, ©vs"d Èíú@õu|½bíT, ÊøOí8”-, Bb1̶òQ)øóœíqÕ¶¡
b R°)dÈíú@õ, ˛·uÊrÍ„øí‘K-, cs_.°P0F†
Ùís"d 7àSÊs".°ií°øÒdvƒú@õ? ʤBbø‚à
”(S ( Epipolar Geometry) v|dÈ®ú@õíÉ[, J-ZÜsd È”(SíÌ„É[, 1‹J@àkú@õí°¦
3.1 ”(S (Epipolar Geometry)
çóœÑ„£ (uncalibration) í‘K-, ªN¬”(SíÌ„É[®ƒó œq Õ¶¡bí°¦ Oâk…d1ÌÛúdTú&½íÛb, c‚à”(Ô 4°¦ª?ú@íÔõP0, FJÿ.‡úqÕ¶¡b°¶TÜ
s"dÈí”(SÉ[ÑÇ 3.1 Fý, w2ABÑs".°iú°øÒ
†Ùíd, P Ñú&˛Èè™íÔõ, }IkdABíp1Dp2sõC1Ñó
P
Q
C1
C2
p1
p2
E1
E2
ep2
ep1
A
B
Ç 3.1: ”(S
œAímç2-, C2uóœBímç2- 7¦(C1C2DABí>õ}±ÑE1DE2, E1E2†˚ÑóœABíd”õ (epipole) ÊdB,íep1¹ÑdA2p1õí
”(, ²Æuz,p1ÊdB,íú@õ.rk”(ep1, °Ü, dBíp2ú@õ?
rkep2,,FJBb)ø:
”(Ì„ ( Epipolar Constraint): ÊdA,íLøõp1, FÊdB2ª?í ú@õîPk°ø‘ò(, (ep1)
7”(Sí°¶¨7, òQ‚à˛Ä (calibration) íóœ¡bR5, CòQ
‚àd2íýbú@õ, N¬ø<SÉ[V°), ¤j¶.Û9lTLS£
T, 7Bb6‚à(6íj¶Vqìú@õíª?¸ˇ, -í!…ä³ÿu”(
Sí½b@à
3.2 !…ä³ (Fundamental matrix)
ÊBbÜ!…ä³í@à‡, Bb.â7j!…ä³íS!ZD…™F[ý íÉ[ FJ…ü2Î7!…ä³í”(@àÕ, 6‡úóœIä³D!…ä
³íóÉ[d_zp Ê3.12Bb7j7”(Ì„, yº¯óœú@kd,í
Iä³, ÿªJ'püø−!…ä³Ê”(SFrÆí½biH
íl, cqBb˛øóœíIä³M1DM2(îÑ3X4íä³), ĤªøsÁó œíIj˙ŸA:
u1 = M1P4 = (M11m1)P4
u2 = M2P4 = (M21m1)P4 (3.1)
w2,P4Ñ˛Èè™õ P í5Ÿè™;u1,u2}ÑIkd,í5Ÿè™,
7øM1DM2í˝ií3X3¶}pÑM11DM21, ¬ií3X1¶}pTm1Dm2, FJM11DM21Ñ3X3ä³,m1£m2Ñø_ú&²¾ JøP4ZÑP í (Xw,Yw,Zw) è™[ý, ªZŸÑ:
u1 = M11P + m1
u2 = M21P + m2 (3.2)
ø,¾ P )
u2− M21(M11)−1u1 = m2− M21(M11)−1m1 (3.3)
ªø¥, BbI
m2 − M21(M11)−1m1 = m (3.4)
/e[m]XÑmí¥ú˚ä³, ?¹[m]Xm = 0, ¢t²¾Dr²¾íÕªà¥ú˚ä
³[ýÑtXr = [t]Xr ø[m]X° (3.4) siª):
[m]x[u2− M21(M11)−1u1] = 0 (3.5)
øsi áª):
[m]xM21(M11)−1u1= [m]Xu2 (3.6)
¢[m]Xu2 = mXu2,}D(u2)T£>, ?¹(u2)T(mXu2) = 0FJsi°(u2)T) ø:
(u2)T[m]XM21(M11)−1u1 = 0 (3.7)
Ĥ, â (3.7) ªc, ç˛øu1¸u2v, c_É[ÉDM1£M2ä³É 7
(3.7) 2Î7u2Du1¡bÕ, wìîÑ󜅙íI䳡b, ]ªøw‰bc¯Ñ ø_3X3íä³F
F = [m]XM21(M11)−1 (3.8)
BbÿzF ˚Ñ!…ä³
P
p1
p2
A
B
F
l’=Fp
1
C1
C2
Ç 3.2: !…ä³É[Ç
3.3 !…ä³D”(Ì„
Ê 3.2 2˛zp7!…ä³íSÉ[, QOÿ.âz!…ä³D”(Ì„
d_©!w (3.7) D (3.8) )ø:
p2TF p1 = 0 (3.9)
7p1Dp2Ñs".°i†Ùdí°øú@õ wD!…ä³íÉ[ªâÇ 3.2 ) ø 7Ä”(Ì„2, dA,íp1õ}ú@_dB2íl(¨,, ¢F p1Ñø_ú&
²¾, Ĥªø (3.9) 2íF p1eÑlíj²²¾, âkp2.ìÊl(¨q, FJp2í 5Ÿè™Dlíj²²¾q}kÉ ¯˛7!…ä³íÔ46Å—7”(Ì„í
Ü, ªeÑ:
lp1 = F p1 (3.10)
Bb?ølp1˚Ñp1Fú@í”( (epipolar line)
7F Ñø_3X3–Ñùíä³, FJBýÛbÿ ú@õn?ø!…ä³í¡b jÇ OøOÄkɲ¦ÿõ1.—J[ýc"díóœ¡b, C²¦íÔõ}
.Å–íª?|Û, FJ×Ö²¦yÖíú@õ°)|7“í!…ä³, 6˚Tÿ õƶ (eight points algorithm)
J-чú!…ä³D”(Ì„-FTí®.°í”(¿t, ‚à®d,²¦í ú@õ°)|7“!…ä³, âú@õ.%¬”(íÌ„Ç,!…ä³í<2 }
‚à:(1) sÞ$(2) ú@õ}Ó–D (3) óœÖqP0Ïæú.°Ô4í
ádú@õ«n
(1) sÞ$:
ílA`ø_.ëóÈísÞ$àÇ3.3 Fý, Ç 3.3 2ÑsÞ$íŸáÇ, 7 (a)(b) qd}Ñóœ[0k£Þ$íø˝ø¬¦dõðÇ, BbªøvÇe Ñs_.°Þíd, J-Ñ«n²¦ú@õíÞu´à!‹, Zøõð}
Ñ: c²¦íw2øÞ$,íú@õC°v²¦sÞ$,íú@õí¿t
¿tø: c²¦øÞ$ú@õ¿t
çBbc²¦ø"Þ$,íÔõÑú@õv, àÇ 3.4 2F™ýíõ, 7N¬
ÝÖú@õF°)í|7“!…ä³, %âú@õD!…ä³íSÉ[ª)øÔ
õí”(u´%¬ú@õ, !‹àÇ3.5Fý
Ç 3.5(a) 2, õ}[ýF²¦¿tíÔõ (ABCDE), 7d¬ií
!‹Ñ®Ôõ%¬!…ä³(F°)í”(, Ç3.5(b) ®”(,}™ýABCDEÑ [ý®ÔõFóú@í”(
(a) sÞ$˝Vd (b) sÞ$¬Vd Ç 3.3: óœ}0ksÞ$í˝¬sV
Ç 3.4: c²¦øÒsÞ$íú@õ
A
B
C
D
E
A B
C
D
E
(a) ²¦íÔõ (b) ®ÔõßÞí”(
Ç 3.5: øÞú@õí!…ä³D”(É[
Ç 3.6: sÞ$²¦íú@õ
¿tù: °v²¦sÞ$,íú@õ
ç°v²¦sÞ$íú@õ°¦|7“ä³, WàÇ 3.6 F™ýíHú@õ, 7 Ç 3.7 †ÑÔõD”(íú@É[
%âÇ 3.4 D 3.5 í¿t, c²¦øÞ$,íú@õ, û_w!‹1̶ŗóœ ÊÇøÞ$í”(Ì„ 7Ç 3.6 DÇ 3.7 í¿t2, çÊ®Þ$,²¦ú@õv, F íú@õ˛·?^írk”(Ë¡ FJâ,HsÞ$í¿tªø, F²¦í
(a) ²¦íÔõ (b) ÔõßÞí”(
Ç 3.7: sÞú@õD”(íÉ[
ú@õıªJÖß, |ßÖƒªJ¨Ö®_ÓKíÔ}0–, Ñ„p,H í!, J-Bb./‡úú@õí}0–T«n
(2) ú@õí}0–.°:
Î7²¦Þí½b4Õ, QOBbÑ7yüì!…ä³2ú@õ²¦í}0,
‚àd,ú@õí²¦}0./«n!‹ }Ñ: ü–}0íú@õ²¦D ˜ í²¦ú@õs¿t
¿tø: ü–íú@õ}0
çBbc²¦ü–}0íú@õv, WàÇ 3.8(a) 2ɲ¦.ëÞ$,}0í Ô¸ˇ, Ç3.8(b) Ñõð¿t²¦íÔõ, ªJ)ƒÇ3.8(c)(d) íú@õD”
(ú@!‹Ç âÇ 3.8(c)(d) 2ªø, ÖÞ$,íú@õªJÅ—”(Ì„, OÊ .ëÞ$ÕíwìÔõ1³êrrk”(,, àÔDDEõíÔõDßÞí
”(Fý, ]Ê-øõð2, BbtOzú@õí}0–Ø×_c"d–¿t
(a) ú@õ²¦¸ˇ (b) ²¦íú@õ
A D E C
B
A
E D C
B
(c) ²¦íÔõ (d) ÔõßÞí”(
Ç 3.8: ü–ú@õD”(É[Ç
(a) ú@õ²¦¸ˇ (b) ²¦íú@õ
(c) ²¦íÔõ (d) ®ÔõßÞí”(
Ç 3.9: ׸ˇú@õíÔõD”(É[
¿tù: ˜í²¦ú@õ
çBbá“‚à ˜íú@õ}0²¦, Ç 3.9(a) ÑF²¦í¸ˇ, Î7.ë Þ$,íú@õÕ, ´¨wF–ÓKíÔõ, Ç3.9(b) ÑF²¦íú@õ, 7 Ç 3.9(c)(d) Ñ®ÔõD”(íÉ[Ç âÇ3.8DÇ3.9s_õð!‹ªø, F²
¦íú@õ}0¸ˇªJ²ì!…ä³D”(íß;, ç}0×ÌGv”(?
Å—”(Ì„, 6nªJH[óœ˛¤5Èíó²É[
w,Hs .°íõðø−, –á#ìíú@õÖ ˜n?H[óœ¡b 5Èí²É[ Oóœ˛¤5ÈíÖqP0u´6}à”(Ì„íA? Ĥ…
Ç 3.10: óœW¦dý<Ç
Ç 3.11: Wdí”(!‹Ç
dZ‡úÖ.°íóœP0ªW¿t Ǿ
(3) sÁóœÖqP0Ïæ:
J-Z‡ú.°ÖqP0íÏæ, }Ñ: óW¦d óœ}0kñ™Óíó æsV óœîPkñ™Óí°Vú.°P0í¿t
¿tø: óW¦d¿t
sÁóœóW¦d, ?¹sÁóœP ,í.°OE°øÒ†Ù Ç 3.10ÑsÁóœíÖqý<Ç, Ç3.11Ñ®óœÈú@õí”(É[Ç
Ç 3.12: óœóæ˝¬sVÖqý<Ç
Ç 3.13: ø˝ø¬díú@õD”(É[Ç
¿tù: óœ0kñ™ÓíóæsV
óœ}0k™ËÓíø˝ø¬, w=1ÖqàÇ 3.12 Fý, 7Ç 3.13 Ñ ˜²
¦ú@õ(íÔõD”(É[ 7Ç3.13ÑsXìDP ÖqÏæíóœFR
¦íd, 6°š_àk”(Ì„íÜ ¿tú: óœîPkñ™Óí°V
óœ0kÒí°øV, OÄÖqP0‡(íÏæ, FJ}¨AóœíAdÄi
.°7‰“rÖ Ç3.14ÑóÉídœÖq=1Ç, Ç3.15Ñú@õD”(íÉ[
Ç âÇ 3.15 ªø, ˝¬sióœAdpéíiÏæ, _UrÖú@õ}\wF
„øíÓKaÏ, O®ÔõßÞí”(î?¦¬®Aíú@õ– FJâ,Hú
¿tªø, !…ä³D”(Ì„.}ÄÑóœÖqíi P07êÞ._àíÕ
Ç 3.14: óœ°VÖqí=1ý<Ç
Ç 3.15: óœ°VÖqíú@õD”(É[Ç
(a)óœ0k¬i†Ùd (b) óœ0˝i/Tò[×I0íd
(c) ²¦Ôõ (d) ßÞí”(!‹
Ç 3.16: [×I0.°íú@õD”(É[Ç
”
J,íÖq×·àó°í[×I0, OçsXóœ[0óÏÝ×v, }ßÞóœ [×I0.°íAd8”êÞ QOBby¿tO[×I0íÏ, çsÁóœ|Û 7[×I0í.°vàÇ3.16(a)(b) Fý, Ç3.16(b) í[×I0péªÇ3.16(a) ò, OÊÇ 3.16(c)(d) íú@õDFßÞí”(ú@!‹E?Å—”(íÌ„‘K
FJ,HÖ.°P0 .°iD.°[×0í¿t)ø, !…ä³D”(Ì„
ª@àkL<íóœÖq2, Î7ÞídÕ6ª@àkwF.°ÞíÓK,
çBbªJ‚àÔõFßÞí”(vƒú@õª?|Ûí¸ˇ(, Ôõíªú6 ÿuQO.âní½õ
p
q1
A
B
correlation
l’=Fp
q2
q3
8X8
8X8
Ç 3.17: Ôõªú
3.4 Ôõªú
Ê,øı2, ªJpüí)øú@õ.rk|7“(!…ä³í”(, ¢Ä
dÑ°øvÈF†Ùí°øÒ, ÖAd}Ħdíi.°, 7û_AdíÓñ$
ÕFÏæ, Oúkø_ú@õíÔ4«n-, ª‚à–)íóÉ[b (Correlation) TѪúª?|ÛÔõíj¶
s"dÖÑs".°iF†ÙíåÞ, O°øvÈFAdíó¼MDG‰“
·øìí‰æÉ[ª©, 7øOÊdTÜ (Image Processing) ,ÿª‚à–
)íj, N¬óÉ[b‡s_–)u´ó°ó¼MíG‰“C À3>,í Ïæ, 7óÉ[bàkÔõªúíjªàÇ3.17Fý Ç3.172, dA,ípõ ÑF²¦íÔõ, Ç2øpõí–)¸ˇqìÑ8X8í–), 7lÑpõ%¬!…ä
³F Fú@í”(, Ê©/4í”(l,íq1q2q3®õ#ìó°8X8×üí–), ‚
à (3.11) l®–)ÈíóÉ[bMC, 1Ê”(,vø_|×CMíqõeÑú
@õ
C = 1 M
(i,j)∈Q
(I1(u1− i, v1− j) − I1)(I2(u2− i, v2− j) − I2) (3.11)
k (3.11) 2,(u1, v1)Ñ p õdè™;(u2, v2)Ñqõídè™; QÑJpõCqõ
Ç 3.18: Ôõ.|ÛÊ”(,
Ñ2-íø_–)¸ˇ (à3X35X58X8¸ˇ),MÑ–)¸ˇqídÖõ_b, I1DI2ÑpõDqõ–)qíó¼ÌM C†ÑóÉ[bM, óÉ[bM×H[pDqõ
Q¡
O1ÝFíÔõøì}|ÛÊÇø"d,, ÄÑ.°†Ùiídª?
}Ôõ\wFÓñaÏí8$|Û, àÇ 3.18 F[ý Ç 3.18(a)(b) Ñs".
°iD.°P †Ù°øÒíd, Ç 3.18(a) 2íõú@Bd 3.18(b) E Ñø‘”(!‹, ÄÑ (a) 2íÔõÊ (b) 2ßÞ£$aÏ7ú@íÔõ, Ö
”(E?¦¬ú@õí–, ºÌ¶Êd3.18(b) 2ú@ƒó°íÔõ FJJc
²¦ø|×óÉ[bMíú@õ1.ê¾, ĤÑ7ü\Í$^?í ì4, Î7²¦
|×íóÉ[b‘KÕ, 1Ó‹|×íóÉ[bCM.â×kø_ƧM (threshold) nøvõeÑó°íú@õ, à (3.12) Fý
CMAX > threshlod (3.12)
J-Ñ}чúÔõú@!‹FTíÔõªúõð, ílBbøõð}Ñ (1)
‚à.ëóÈí£$ (2) ú@Òø˝ø¬íóœÖqP0D (3) °VÖqíó œú¿t
(a)óœ A ¦dÇ (b) óœ B ¦dÇ
(c) ²¦Ôõ (d) ”(,ªú!‹
Ç 3.19: óœÖq‰“üí.ë£$ªú!‹
(1) .ëóÈí£:
‚à.ëóÈ£$}&!‹ß;, íl−„óœ}N¬sXÖqióÏ.
×/P ó¡íóœ, †Ùs"°øÒíd!‹Ç, àÇ 3.19(a)(b) Fý Ç 3.19(c)(d)ÑÔõD!…ä³FßÞ|í”(D®õÈíªú!‹, %âÇ3.19(d) ª)øw®ªúíÔõîªJú@ƒ®dÈó°íú@õ
(2) óæsVíÖqP0:
çBbyªø¥L<íR¦d, 1/øóœíÖqP06péíÏæÝÖ, w Öqà°Ç3.12F0, 7Ç3.20Ñõð¿t(í!‹É[Ç âÇ3.20)ø, çÖq ÑÒíóæsiv, w”(?rkú@õ,ÿªJN¬ (3.11) D (3.12) °)
Ç 3.20: ø˝ø¬¦díªú!‹
Ç 3.21: °i×iÏæíÔõªú!‹
ÔõÊ®dÈíú@õ
(3) óœ°VÖq:
Oà‹øóœÖq0k°iv, ¤vóœE?Å—”(íÌ„D!…ä³í@à, ON¬Ç3.21í!‹)øw!‹1.àã‚F‚&í7 ÄÑ°VÖq}¨A¦di
,Ïæ, çióÏrÖv}û_ÔõßÞrÖí‰, 7 (3.11) D (3.12) î N¬–)íj«óÉ[bCM, J‰“Ø×v6}à–)qídÖ!Z, FJ@
àóÉ[bíÔõªúʤ, 1._àk¤õð,
3.5 ú @õíA²¦û˝
ÄJ,í®¿t!‹î¦²kú@õ²¦í ˜DÖ›, Ñ=UÍ$írA
“^?, ‚àdTÜ (Image Preocss) íxXA²¦ú@õªeÑ…dÇø½ bí«n J-Z‡úA²¦ú@õíj, Yå}A: (1) Ôõ킦(2) ®Ô
õíªú(3) ú@õí¥ºÙ² (Iteration Method) ú_¥Møû˝
¥ø: Ôõ‚¦
Êdú@õªú‡Ôõí²¦uíb5², …d²¦íÔõb²k ˜D qkªú ‡iíÔ4 чúÔõí ˜4, lø®d‚àüš² (wavelet) d‡TÜ[14][15][16], 7üšª[ýÑ 3.13 D 3.13, w2ψ1(x, y)ψ2(x, y)Ñ
dS(x, y)ôxWDyWj²íòäM, j[ýÑüší¼b,
ψ2j1(x, y) = 1 4jψ1(x
2j y
2j) (3.13) ψ2j2(x, y) = 1
4jψ2(x 2j
y
2j) (3.14) 7dÊxj²Dyj²,íòä?¾¸¼bÉ[ªyªø¥[ýÑ 3.15D 3.16,
W2j1 = S(x, y)∗ ψ2j1(x, y) (3.15)
W2j2 = S(x, y)∗ ψ2j2(x, y) (3.16)
Í7øxysj²,í?¾½hlvd,®P0í?¾#, à 3.17:
W2jS(x, y) =
|W2j1S(x, y)|2+|W2j2S(x, y)|2 (3.17)
Ç 3.22(c)(d) Ñüš²TÜ(í?¾Ç, øüš²(í (c) Çd²¦?¾œ
(a)óœ A ¦dÇ (b) óœ B ¦dÇ
(c) d A üš!‹Ç (d) d B üš!‹Ç Ç 3.22: üš²!‹Ç
Ç 3.23: Ç 3.22˝id²¦íÔõ
Ç 3.24: óÉ[bªúíú@õÉ[Ç
¥ù: Ôõªú
%âüš² (wavelet) ²¦|?¾œòíÔõP0, }‚à®Ôõí|
×óÉ[bM3.11MøÊÇø"d,dªú, ÊY岦óÉ[bMœòíÖ ú@õ !‹àÇ 3.24 Fý, w2Ç2Híõ™ý7ªú˜ÏíÔõ, Ñ?
yªø¥í¾ÎØÖíú@õ, J-í Iteration Method ÿyÑø½bíÙ²¥
¥ú: ú@õí¥ºÙ²(Iteration Method)
N¬ (1)(2) F²|Víb ú@õ1.}êrÄ, }Äd*óNCú@
õ\wFÓñaÏ8”êÞªú˜Ïíú@õ, 7ɲ¦|×íóÉ[bM1.\
„u|ßíªúj, FJBb‚àú@õD!…ä³íÌÏÏM 3.18‡iú@
õíß;
M =
(i)∈np1iF p2i
n (3.18)
Jªúí!‹Éýbú@õ˜Ï, ˜Ïíú@õ}ÄR×|7!…ä³í”(, ª N¬võÏÏM×kÌÏÏMíÔ4, ^푲ªú˜Ïíú@õ, ÊYWw|
Ç 3.25: ªú˜Ïú@õD”(É[Ç
Ç 3.26: ¥ºÙ²(íú@õ
Ç 3.25)øáí!…ä³Ö}Ä<r˜Ïíú@ßÞ<RÏí8$, OJ²¦í˜
Ï_býv, wú@õDßÞí”(!‹Eª¡54, FJBbªø˜Ïíú@
õ‡ú”(Ë¡í–ydøŸªú, थºí‚à©Ÿ½hy£íú@õøò½
©˜Ïíú@õ, òƒhíÌÏÏM'üC‡i˜Ïíú@_bˇÍÓÖv, [ý
²¦íú@õ˛·}0Ê!…ä³í”(¸ˇ,, 6ª[ý!…ä³˛Å—vÇF
²¦í®ú@õ ¤j¶Î7Tòú@õíüÕ, ª±Q½©¸ˇ, 6fn*ó NCæHó°–íß× wÇ 3.26ѽµ‡iêíú@õ!‹, w2^£7¶}R
×”(íú@õ, 6±Q7ú@õ.ÊÇød7ªú˜Ïí8$ ¤jÖªø
¶M˜Ïíú@õ^£, çõðÇ*óNCrÖÔóNv, }ßÞrÖ˜Ïíú
@õ, 7û_”(!‹.?Å—BbÛ°í”(Ì„, /|×óÉ[bªújÊ.
°¦diíd,?êÞÔªú˜Ïí8”, FJJ-í¿tÑ„õ®Üíª W4, ·JG²¦Ôõíj#ìáú@õP0
Chapter 4
óœÞI²ä³
ÖÁóœ2dÈíÔõú@É[, ªN¬,HFT£í”(Ì„DÔõª ú©) OçJcuÀÓ󜅙íìCÿ‰“Z‰v, ÖEª_à,Hí½©
ªúj, OwªeÑdÞíZ‰, ?ªày “/ÄíóœÞIä³V
°)s"díè™É[ J-YåÑóœÞIÜTÜ, 1ªø¥‚àÖ ú@õN¬|üjj°)|7íIä³
4.1 ÞIÜ
Ê 2.2íóœ¡b2Ü7óœÊdè™Í$Döõè™Í$}Å— (2.10) íÉ[, 7sXÖqÉ ìiCÿ.°íóœªø (2.10) “Ñ:
p1 = M1P (4.1)
p2 = M2P (4.2)
w2,p1Dp2}ÑóœADóœBíè™õ,M1DM2uø_3X4íä³, M1£M2}
Ñöõè™Í$íú&˛ÈõIBóœADóœBíIä³, P õÑöõè™Í
$2í5Ÿè™õ
¢ÄM1DM2uø_ 3X4 íÝ£j$ä³, .ªòQ,M1DM2í¥ä³, F Jlø (4.2) si°(M2)TU¬iíä³AÑø£j$ä³, à-Fý:
(M2)Tp2 = (M2)TM2P (4.3)
पø (4.3) ísi°((M2)TM2)−1, पø(4.4) H (4.1) q:
((M2)TM2)−1(M2)Tp2 = P (4.4)
p1 = M1((M2)TM2)−1(M2)TP2 (4.5)
Ê (4.5) 2, ªøp1Dp2ÈcDM1£M2É, ªøw “Ñ:
p1 = M12P2 (4.6)
7 (4.6) 2íM12Ñø_3X3íj$ä³, FJ?ª˚M12ÑsÞp1Dp2Èí
ÞI²ä³
4.2 |üjj
N¬ (4.6) ªøs"ÞÈíI²É[cDp1Dp2íú@õè™É, Ä
¤Bbªø (4.6) Ÿ)yÌÑ:
xp yp 1
=
m0 m1 m2 m3 m4 m5 m6 m7 m8
xq xq 1
(4.7)
ªø¥, ªøm8G“ (normalize) Ñ1, ¢ªZŸÑ:
w
xp yp 1
=
m0/m8 m1/m8 m2/m8 m3/m8 m4/m8 m5/m8 m6/m8 m7/m8 1
xq xq 1
w
xp yp 1
=
m0 m1 m2 m3 m4 m5 m6 m7 1
xq xq 1
(4.8)
ø (4.8) Ǫ)ú_:j˙:
m0xq+ m1yq+ m2 = wxp m3xq+ m4yq+ m5 = wyp m6xq+ m7yq+ 1 = w
(4.9)
ø w H,ùª):
m0xq+ m1yq+ m2− m6xpxq− m7xpyq = xp m3xq+ m4yq+ m5− m6ypxq− m7ypyq = yp
(4.10)
(4.10) 2s_j˙ÿ_„øb, FJÛbû ú@õn?ßÞÿ_j˙, 6nªJj)ÿ_‰bM Ñ7±Q.Äüõíß×, 1U)°|íjy ì, Ä¤Ê õT,Bb‚àyÖ íú@õ, N¬|üjj°|Iä³M12í®¡b
J-Ñä³|üjjí@à: cqBb#ì7n íú@õ, Hp (4.10) 2 })ƒJ-íÉ[:
x1q y1q 1 0 0 0 −x1px1q −y1px1q 0 0 0 x1q y1q 1 −x1qy1p −y1py1q x2q y2q 1 0 0 0 −x2px2q −y2px2q 0 0 0 x2q y2q 1 −x2qy2p −y2py2q
. . . . . . . .
. . . . . . . .
xnq ynq 1 0 0 0 −xnpxnq −ynpxnq 0 0 0 xnq ynq 1 −xnqynp −ynpynq
2nX8
m0 m1 m2 m3 m4 m5 m6 m7
=
x1p y1p x2p y2p . . xnp ynp
(4.11)
?ªZŸA:
A.M = b (4.12)
y‚à|üjj°) M
M = (ATA)−1ATb (4.13)
7M Ñø_8X1íä³, ?¹ÑÞI²ä³qí®¡bM, çk°)I
(í®Ôè™v, cÛbHƒ (4.8) É[2, ¹ª°)ÊìÞC[×ÿ
(ídè™P0
J-}‡ú (1) 󜅙íì(2) óœíI0[×D (3) óœÊì£[×
I0‰yíúõð¿t, 6N¬,H<r.°í󜉓V„õÞIä³íª W4
(1) ìÞIä³:
çóœ¦dP0ì, Od…™Ëìií.°, ?¹óœ…™?D−„
wììi ¤vBbøõð}A-¿t, „pIä³íZ4: ‚ à£$áIä³ ²¦×¸ˇíú@õáIä³
¿tø: ‚à.ëóÈí£$
Ç 4.1(a)(b)Ñ‚à£$í.ëóȲ¦dÈíú@õ, Ç4.1(a)(b) TX íú@õ°¦ìIä³@àkÇ4.1(c)(d) 2 Ç4.1(c)(d) ‹[7ø_ôôÓ Kkd2, N¬Ç4.1(a)(b) líIä³ú@Ç4.1(c)(d) 2®Ôõíú@
õP0àÇ 4.1(e)(f) Fý
¿tù: ˜²¦ú@õ¿t
à¿tøíõðªø, à‹ÇᲦíú@õÉÌk¶}–qv, wú@õí
^‹1.}Ä J-ÿtOø£$¦¾, 1ªø¥²¦y ˜íú@õ, 7J -íÇ4.2†Ñ¿tí!‹Ç
(2) óœ[×I0í.°:
OÛ-BbUàíóœ.ycc‹›kì[×I0íóœ, ª?}ÄÑ×í
±¡Ûbúóœd[× òüíŠ?, FJBb.ây¿øµí 5¾[×íõð!
‹, J-ÿu‡ú[×I0¿tíø<dD!‹
íl, çóœl‚àáqìíI0¦d, yR¦ø"[×I0y׆Ùídà Ç 4.3(a)(b) s"dFý, 7Ç4.3(c)(d) †Ñs"dN¬ÞIä³í!‹
(a) óœád (b) óœìd
(c) ÓK[0áP0 (d) ÓKìP0
(e) ÔyÓK,²¦Ôõ (f) ìdú@õ Ç 4.1: N¬Iä³í®Ôú@õ
Ç 4.2: óœìdí¿t!‹Ç
õðÇN¬Ç4.3)øÞIä³@àk[×I0.°ídYÍA, FJBb ªJtOøóœìD[×ø–¿t
(3) óœìD[×I0.°:
ÄÛDóœÎ7ªA™ìÕ´ª−„w[×I0íZ‰, FJóœìD[×
I0í!¯@à6nuBb%(tõðíy½b@à w¿tD!‹àÇ4.4Fý â Ç 4.4 ªø, çóœÎ7ÀÓíì P Õ, y‹,[×I0íZ‰6Eª_àÞ Iä³Vú@ÔõÈí²É[ FJ5(íõð!‹ZªYWIä³íÄü ú@É[, @àkóœìD[×I0.°íŠ?,
(a) á[×I0d (b) [×I0yZ(d
(c) ád²¦íÔõ (d) [×(íú@õ Ç 4.3: s".°[×I0íIÉ[Ç
Ç 4.4: óœìD[×I0.°íú@É[Ç
Chapter 5
õ ð!‹
YWJ,ÖıíóœÄ (Camera Calibration) Ü, …díõð‚àóœ í”(S!¯7sÁP0Di·.°íóœAdSÉ[, 1ªø¥N¬”(D
|×óÉ[bM (correlation value) °)s"d,|ó¡íú@õ ç)øsÁó œÈú@õíP0v, ª−„Ë˝¬¹Ù (Pan) ,-bé (Tilt) D[× (Zoom) Š?í Sony EVI-D30óœ, N¬ RS-232øóœ0|Q¡d2-íi, 1 yªø¥ªOóœ[×I0 (Zoom In) íŠ?, ª‡ú>EíÔõCñ™
Ó®ƒúÔìú@õ–í[×^? J-Z}A,Híõð¼˙Mø}A: õð
=1-Z óœ”(SDÔõªú£óœìD[×®üÌH
5.1 õ ð =1-Z
Ê…ıíõð2, 3bu!¯óœí”(SD󜅙íìD[×Ô4
FJBbqì74?.ró°sÁóœ: øÁÑìrÙœ3bÑaec_Ò
íd, 7ÇøÁóœuø«Ë® (Pan) Dò (Tilt) ì£[× (Zoom In) Š?íóœ, 3b‡ú×Ò2í¶}ÒTÔì–aeDÔŸí^? wõð
Rotation Zoom In B A
Ç 5.1: õðóœÖq=1<Ç
íÖq=1àÇ 5.1 Fý: w2óœAÑìaec_ÒíóœBuø«Ë?ì
(Rotation) D[× (Zoom In) Š?íóœ, óœB‡úóœAFaeíc_Ò
2í¶}–TÔì–ae, Ç 5.2(a)(b) }ÑóœADóœBÊóœá“v F†Ùíd
(a)óœ A †Ùd (b) óœ B †Ùd Ç 5.2: óœ AB á“P0£[×I0F†Ùíd