Based on this strategy, the computation time of moving object extraction in the video sequence of the PTZ camera is reduced

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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



f 0 p_x 0 0 f p_y 0 0 0 1 0

























X Y Z 1















= M P (2.4)

Y2.4ªøq¶¡b[ýÑ:

A =











f 0 p_x 0 f p_y 0 0 1











(2.5)

w 2.4D 2.5ªZŸA:

p = A[I_3X3|0]Pcam (2.6)

,HíNeI
=12qì
dÞíxWDyWsj²íªWuó°í, OøOóœ íxyWªW.øìÑó
(àbPóœíŸå), wxWDyWíªWÿª?.°
F J.â5?çxj²Dyj²íÿ·.
kf , 7ªøÿf }ÑfxDf_yJH[xWDyW í.°ÿ
Ĥóœíq¶¡bÿª[ýÑ:

A =











f_x 0 p_x 0 f_y p_y 0 0 1











(2.7)

Zccs

Y^ccs

X^ccs

Occs

(0,0,0)

Z wcs Yw cs

X wcs

O wcs WCS

CCS

R

t

Ç 2.5: óœÕ¶¡b

y6, q¶¡b2´¨7skewγ[ý
dÞxWDyWHidúkòií˛é

˙, ]q¶¡b¢ª[ýà-:

A =











f_x γ p_x 0 f_y p_y 0 0 1











(2.8)

.¬γ×ÖbªøwMIÑ0
 2.8Ñø_êcíóœq¶¡bä³

óœíÕ¶¡bDóœíÖqP0¸óœí¡5õ¿ìÉ
ws6É[ª}Ñ ìD s«, àÇ 2.5Fý: w2,RÑ WCS ìB CCS íìä³, 3 buøs.°í!…j²W (WCS D CCS) ìAø_íj²W
7t[ýÑø_P ²¾, ø WCS ,í¡5õ ƒ CCS í¡5õ
ª[ýÑ 2.9

P_cam =











X_cam Y_cam Z_cam











= R











X_W Y_W Z_W











+ t = [R|t]















X_W Y_W Z_W 1















(2.9)

(1)FJzìä³DP ²¾$˚ÑóœíÕ¶¡b

â 2.6D 2.9ªJRø, óœ
dÞ,íP0ª‚à˛È2íú&è™N

¬q¶¡bDÕ¶¡b)ø, à2.10Fý:

p = AP_cam = A[R|t]P_W = MP_W (2.10)

w2,AÑq¶¡b¨ü_AâRÑìä³ú_AâtuÑø²¾ú _Aâ
7MÑø_3X4íI
ä³, Ê7q¶¡bDÕ¶¡b
‰b
öõè

™Í$Dóœè™Í$‚àìä³RD ²¾t[ýw²É[
]zìä³D

 ²¾˚5Õ¶¡b
óœè™Í$D
dè™Í$ÈYWÿ(fx, f_y)dÖÊxW DyWíªW(dx, dy)
dR×2-õ (u0,v₀) Dskew$˚5Ñq¶¡b

â 2.10ªc, J˛øóœíq Õ¶¡b, ÿª)øóœíI
ä³M, ú˛È LøõP_W7k, ç˛øPW = (X_W, Y_W, Z_W, 1), ÿª°|v˛ÈõÊ
dÞ,í

dõp = (u, v)
¥5, à‹câ
dÞ,íõp, ¸˛øóœíq Õ¶¡b, 6 ̶êr)øvõíöõÍ$è™P0
ÄMu3X4í.ªLä³, ‚àMDp(u, v)H p (2.10) 2íú_j˙¾ Z, É)ƒXW, Y_W, Z_Wís_(4j˙
²Æ uz, c?)ƒ 3D ˛ÈõDóœ¡5õí¦(OP àÇ 2.6 Fý
6ª[ýÑ, F OP ¦(,íú˛Èõ (P₁P₂P₃) îAdk
dÞípõ, 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¦í
d, YW˛¤u°íú@õ°)®
dÈíú@õ² É[

Ç 2.6: Adk
dÞª?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°øÒ

dvƒú@õ? ʤBbø‚à

”(S ( Epipolar Geometry) v|
dÈ®ú@õíÉ[, J-ZÜs
d È”(SíÌ„É[, 1‹J@àkú@õí°¦

3.1 ”(S (Epipolar Geometry)

çóœÑ„
£ (uncalibration) í‘K-, ªN¬”(SíÌ„É[®ƒó œq Õ¶¡bí°¦
Oâk…d1ÌÛú
dTú&½íÛb, c‚à”(Ô 4°¦ª?ú@íÔõP0, FJÿ.‡úqÕ¶¡b°¶TÜ

s"
dÈí”(SÉ[ÑÇ 3.1 Fý, w2ABÑs".°iú°øÒ

†Ùí
d, P Ñú&˛Èè™íÔõ, }I
k
dABíp1Dp₂sõ
C₁Ñó

P

Q

C₁

C2

p₁

p2

E1

E₂

ep2

ep1

A

B

Ç 3.1: ”(S

œAímç2-, C2uóœBímç2-
7¦(C1C₂DABí>õ}±ÑE1DE₂, E₁E₂†˚ÑóœABí
d”õ (epipole)
Ê
dB,íep1¹Ñ
dA2p1õí

”(, ²Æuz,p1Ê
dB,íú@õ.rk”(ep1,
°Ü,
dBíp2ú@õ?

rkep2,,FJBb)ø:

”(Ì„ ( Epipolar Constraint): Ê
dA,íLøõp1, FÊ
dB2ª?í ú@õîPk°ø‘ò(, (ep₁)

7”(Sí°¶¨7, òQ‚à˛
Ä (calibration) íóœ¡bR5, CòQ

‚à
d2íýbú@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‡úóœI
ä³D!…ä

³íóÉ[d_zp
Ê3.12Bb7j7”(Ì„, yº¯óœú@k
d,í

I
ä³, ÿªJ'püø−!…ä³Ê”(SFrÆí½biH

íl, cqBb˛øóœíI
ä³M1DM₂(îÑ3X4íä³), ĤªøsÁó œíI
j˙ŸA:

u₁ = M₁P₄ = (M₁₁m₁)P₄

u₂ = M₂P₄ = (M₂₁m₁)P₄ (3.1)

w2,P₄Ñ˛Èè™õ P í5Ÿè™;u1,u₂}ÑI
k
d,í5Ÿè™,

7øM₁DM₂í˝ií3X3¶}pÑM₁₁DM₂₁, ¬ií3X1¶}pTm₁Dm₂, FJM₁₁DM₂₁Ñ3X3ä³,m₁£m₂Ñø_ú&²¾
JøP₄ZÑP í (X_w,Y_w,Z_w) 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) = 0
FJsi°(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:

p₂^TF p₁ = 0 (3.9)

7p₁Dp₂Ñs".°i†Ù
dí°øú@õ
wD!…ä³íÉ[ªâÇ 3.2 ) ø
7Ä”(Ì„2,
dA,íp1õ}ú@_
dB2íl
(¨,, ¢F p1Ñø_ú&

²¾, Ĥªø (3.9) 2íF p1eÑl
íj²²¾, âkp₂.ìÊl
(¨q, FJp2í 5Ÿè™Dl
íj²²¾q}
kÉ
¯˛7!…ä³íÔ46Å—7”(Ì„í

Ü, ªeÑ:

l
_p1 = F p₁ (3.10)

Bb?øl
_p1˚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) óœÖqP0Ïæ
ú.°Ô4í

á
dú@õ«n

(1) sÞ$:

ílA`ø_.ëóÈísÞ$àÇ3.3 Fý, Ç 3.3 2ÑsÞ$íŸáÇ, 7 (a)(b) q
d}Ñóœ[0k
£Þ$íø˝ø¬¦dõðÇ, BbªøvÇe Ñs_.°Þí
d, 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), 7
d¬ií

!‹Ñ®Ôõ%¬!…ä³(F°)í”(, Ç3.5(b) ®”(,}™ýABCDEÑ [ý®ÔõFóú@í”(

(a) sÞ$˝V
d (b) sÞ$¬V
d 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,

‚à
d,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: W
dí”(!‹Ç

dZ‡úÖ.°íóœP0ªW¿t Ǿ

(3) sÁóœÖqP0Ïæ:

J-Z‡ú.°ÖqP0íÏæ, }Ñ: óW¦d óœ}0kñ™Óíó æsV óœîPkñ™Óí°V
ú.°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

¦í
d, 6°š_àk”(Ì„íÜ
¿tú: óœîPkñ™Óí°V

óœ0kÒ
í°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†Ù
d (b) óœ0˝i/Tò[×I0í
d

(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, Î7Þí
dÕ6ª@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©, 7øOÊ
dTÜ (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–), 7l
Ñpõ%¬!…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 õ
dè™;(u2, v₂)Ñqõí
dè™; 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.°†Ùií
dª?

}Ôõ\wFÓñaÏí8$|Û, àÇ 3.18 F[ý
Ç 3.18(a)(b) Ñs".

°iD.°P †Ù°øÒ
í
d, Ç 3.18(a) 2íõú@B
d 3.18(b) E Ñø‘”(!‹, ÄÑ (a) 2íÔõÊ (b) 2ßÞ
£$aÏ7ú@íÔõ, Ö

”(E?¦¬ú@õí–
, ºÌ¶Ê
d3.18(b) 2ú@ƒó°íÔõ
FJJc

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|×íóÉ[b‘KÕ, 1Ó‹|×íóÉ[bCM.â×kø_ƧM (threshold) nøvõeÑó°íú@õ, à (3.12) Fý

C_MAX > threshlod (3.12)

J-Ñ}чúÔõú@!‹FTíÔõªúõð, ílBbøõð}Ñ (1)

‚à.ëóÈí
£$ (2) ú@Ò
ø˝ø¬íóœÖqP0D (3) °VÖqíó œ
ú¿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"°øÒ
í
d!‹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 ÑÒ
íóæsiv, 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˝

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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 4^jψ¹(x

2^j y

2^j) (3.13) ψ₂j2(x, y) = 1

4^jψ²(x 2^j

y

2^j) (3.14) 7
dÊxj²Dyj²,íòä?¾¸¼bÉ[ªyªø¥[ýÑ 3.15D 3.16,

W₂j1 = S(x, y)∗ ψ₂^j1(x, y) (3.15)

W₂j2 = S(x, y)∗ ψ2^j2(x, y) (3.16)

Í7øxysj²,í?¾½hlv
d,®P0í?¾#, à 3.17:

W₂jS(x, y) =

|W₂^j1S(x, y)|²+|W₂^j2S(x, y)|² (3.17)

Ç 3.22(c)(d) Ñüš²TÜ(í?¾Ç, øüš²(í (c) Ç
d²¦?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˝i
d²¦íÔõ

Ç 3.24: óÉ[bªúíú@õÉ[Ç

¥ù: Ôõªú

%âüš² (wavelet) ²¦|?¾œòíÔõP0, }‚à®Ôõí|

×óÉ[bM3.11MøÊÇø"
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!‹àÇ 3.24 Fý, w2Ç2H

íõ™ý7ªú˜ÏíÔõ, Ñ?

yªø¥í¾ÎØÖíú@õ, J-í Iteration Method ÿyÑø½bíÙ²¥

¥ú: ú@õí¥ºÙ²(Iteration Method)

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õíß;

M =

(i)∈np_1iF p_2i

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@

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°¦dií
d,?êÞÔªú˜Ïí8”, FJJ-í¿tÑ„õ®Üíª W4, ·JG²¦Ôõíj#ìáú@õP0

Chapter 4

óœÞI
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ÖÁóœ2
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4.1 ÞI
Ü

Ê 2.2íóœ¡b2Ü7óœÊ
dè™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&˛ÈõI
BóœADóœBíI
ä³, 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

ÞI
²ä³

4.2 |üjj

N¬ (4.6) ªøs"ÞÈíI
²É[cDp₁Dp₂íú@õè™É, Ä

¤Bbªø (4.6) Ÿ)yÌÑ:











x_p y_p 1











=











m₀ m₁ m₂ m₃ m₄ m₅ m₆ m₇ m₈













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



x_q x_q 1











(4.7)

ªø¥, ªøm8G“ (normalize) Ñ1, ¢ªZŸÑ:

w





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x_p y_p 1

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



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=











m₀/m₈ m₁/m₈ m₂/m₈ m₃/m₈ m₄/m₈ m₅/m₈ m₆/m₈ m₇/m₈ 1











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

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x_q x_q 1











w











x_p y_p 1











=



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





m
₀ m
₁ m
₂ m
₃ m
₄ m
₅ m
₆ m
₇ 1





















x_q x_q 1











(4.8)

ø (4.8) Ǫ)ú_:j˙:

















m
₀x_q+ m
₁y_q+ m
₂ = wx_p m
₃x_q+ m
₄y_q+ m
₅ = wy_p m
₆x_q+ m
₇y_q+ 1 = w

(4.9)

ø w H,ùª):







m
₀x_q+ m
₁y_q+ m
₂− m
₆x_px_q− m
₇x_py_q = x_p m
₃x_q+ m
₄y_q+ m
₅− m
₆y_px_q− m
₇y_py_q = y_p

(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°|I
ä³M12í®¡b

J-Ñä³|üjjí@à: cqBb#ì7n íú@õ, Hp (4.10) 2 })ƒJ-íÉ[:



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

x_1q y_1q 1 0 0 0 −x_1px_1q −y_1px_1q 0 0 0 x_1q y_1q 1 −x_1qy_1p −y_1py_1q x_2q y_2q 1 0 0 0 −x2px_2q −y2px_2q 0 0 0 x_2q y_2q 1 −x2qy_2p −y2py_2q

. . . . . . . .

. . . . . . . .

x_nq y_nq 1 0 0 0 −x_npx_nq −y_npx_nq 0 0 0 x_nq y_nq 1 −x_nqy_np −y_npy_nq





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2nX8

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m
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x_1p y_1p x_2p y_2p . . x_np y_np







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(4.11)

?ªZŸA:

A.M = b (4.12)

y‚à|üjj°) M

M = (A^TA)⁻¹A^Tb (4.13)

7M Ñø_8X1íä³, ?¹ÑÞI
²ä³qí®¡bM, çk°)I

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d2, N¬Ç4.1(a)(b) líI
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±¡Ûbúóœd[× òüíŠ?, FJBb.ây¿øµí 5¾[×íõð!

‹, J-ÿu‡ú[×I0¿tíø<
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dà Ç 4.3(a)(b) s"
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dú@õ Ç 4.1: N¬I
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Ç 4.4: óœìD[×I0.°íú@É[Ç

Chapter 5

õ ð!‹

YWJ,Öıíóœ
Ä (Camera Calibration) Ü, …díõð‚àóœ í”(S!¯7sÁP0Di·.°íóœAdSÉ[, 1ªø¥N¬”(D

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5.1 õ ð =1-Z

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