第４回　 カメラキャリブレーション

mutty@ics.kagoshima-u.ac.jp

mutty@ics.kagoshima-u.ac.jp

-CV mutty@ics.kagoshima-u.ac.jp(affine projection): x = a11X + a12Y + a13Z + a14 = a21X + a22Y + a23Z + a24

- - : - CCD- RGB

mutty@ics.kagoshima-u.ac.jp

- cos4 - mutty@ics.kagoshima-u.ac.jp

- - 6 (t)(R)

- 5 mutty@ics.kagoshima-u.ac.jp

CV mutty@ics.kagoshima-u.ac.jp

(world coordinate system)D: (rigid transformation)RRt= RtR= I

(camera calibration):

mutty@ics.kagoshima-u.ac.jp

Tsai(1986) -1(xw,yw,zw)(x,y,z)(x,y,z) (Xu,Yu):(Xu,Yu) (Xd,Yd) : (Xd,Yd) (Xf,Yf)

mutty@ics.kagoshima-u.ac.jp

Tsai-2{(Xf,Yf) (xw,yw,zw)} 5+6= - - - - -:1.0 -

mutty@ics.kagoshima-u.ac.jp

Tsai-3A/DCCDCCD(Cx,Cy)(Xdi,Ydi) T-1r1 T-1r2 T-1Tx T-1r4 T-1r5T2TRfTxf, T,k1,k2

mutty@ics.kagoshima-u.ac.jpfdx,dy

Z.Zhang

"A flexible new technique for camera calibration". IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(11):1330-1334, 2000. http://opencv.jp/sample/camera_calibration.html

mutty@ics.kagoshima-u.ac.jpAa,b)A(a,b) f=(-aa-bb)-1/2

Aa,b) mA(a, b, f)Aa,b) mA (a, b, f)

( mA , mA ) = 0

f=(-aa-bb)-1/2

mutty@ics.kagoshima-u.ac.jpP(x,y) m(x, y, f) l:Ax+By+C=0 n(A, B, C/f)N

2CV mutty@ics.kagoshima-u.ac.jp

mutty@ics.kagoshima-u.ac.jpWeng(1992): (u,v) (u ,)5 u=k1u(u2+v2) + 3p1 u2 +p1v2 +2p2uv + s1(u2+v2) =k1(u2+v2) + 2p1uv +p2u2 +3p2v2 + s2(u2+v2)

-3

- E, F mutty@ics.kagoshima-u.ac.jp

PnP Haralick(1991):6DeMenthon(1992):Horn(1990), Faugeras(1990): 25

mutty@ics.kagoshima-u.ac.jp

uncalibrated/weakly calibrated stereo - Roberts and Faugeras(1993): weakly calibrated :F Self-calibration -Basu(1993): active calibration mutty@ics.kagoshima-u.ac.jp

essential matrix)CV mutty@ics.kagoshima-u.ac.jpxtRx~+tepipolar planexttRx~+t=0ab=-baab=ab(ab) ab+= abaxt tRx~+tt=0

essential matrix)CV mutty@ics.kagoshima-u.ac.jpxtRx~+tepipolar planexttRx~+t=0xt tRx~+tt=02ee~

Ffundamental matrix)CV mutty@ics.kagoshima-u.ac.jp m=Ax, m~ =A~x~ xt Ex~ =0

A-1 m t E A~-1 m~ =0

m t A- E A~-1 m~ =0 FF - - f |f|=1 Zf=0 min|Zf|2=min|fZZf|2 fZZ

epipole mm te~ e~e e~e,

{(X,Y)&(X,Y) , (xw,yw,zw)} Yakimovsky 34 11rank3 mutty@ics.kagoshima-u.ac.jp(1985):

40cm330(X,Y,Z)1(1)2(2)

(Homography) Hbama = Hba mb

CGVRImage-based rendering, Augumented reality - Potmesil(1981): - Cook(1984): - (1996):

mutty@ics.kagoshima-u.ac.jp

mutty@ics.kagoshima-u.ac.jp

mutty@ics.kagoshima-u.ac.jpf:d :w: :