Hee Ju Park 
of epipolar line corresponding to P Let p, bea point of the left image corresponding to P.Letk , be a point on the 
epipolar line of the left camera image, À, a point on the epipolar line of the right camera. Then O,, O, P, k,, k : Le À 
on the same plane, which is called “coplanar condition”. Therefore the vectors oo, 0p,» 0k, and 0k, lie on the same B 
C 
plane. Let B be vector of baseline, f be the camera's focal length. Let R, and R, be the rotation matrices of the left 
camera and right camera. 
Let the terrestrial coordinates of O, , O,.be (X,,Y,,Z,), (X,,Y,,Z,). Let the photo coordinates of p,, ki. k, be Th 
fol 
(x Yn): (x, y). (x^, y). 0 
Bex 
a, a, a; by, b, bs 
R=|a, a, ant R= by Pa hy B 
as 05 03 by, ba 33 
The 
Then, 
Au 92 4a; X 
Op, X Yo 7 4) ma 05. Oy Xs Yor) (2) X 
0, 032 G3 So 
à, 0 4a; 
Ok -(X.Y.Z)-|a, 4» 4a5fx M) (3) Ab 
ay, 433 433 A 
b, b, b, B 
Ok, z(X.Y,Z)s|b, b, b4kx.y. (4) C 
b, bs, bs; 
Because the vectors B, 0, p. m k, satisfy the coplanar condition, Wh 
If v 
Be(O,P, xO,k,) 20 (5) coc 
Therefore, the 
Dx By B: m 
X n Y, Z, = BuY,Z~Z,Y)+BAZ, X~ X e) t Bz(X AY.— YıX)= 0 (6) 
X Y Z 
3 
ry 
From (2),(3),(6) The 
mat 
la (CZ pl - BzY,, ) + a, (BzY , -BZ p ) + ET (BxY T ByX pl )} x red 
+{a(BYZ „1 — BzY ,) c aj (BzX n-BZ,M* az (BAY ,, — ByX „1 )} y e? Ad 
ove 
+ {a 3(ByZ pl = B:Y ,; )) + a BzX pl T BxZ pl y+ a (BxY pl T ByX pl }f = 0 Cor 
j and 
(7) is the epipolar line equation on the left image which is corresponding to the point p(xpl,yp1) of the left image. This Cor 
can be represented as follows. con 
glol 
Ax+By+Cf = 0 (8) 
3.1 
Fir: 
  
698 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.