(2) 
(3) 
Hee Ju Park 
  
T 
an Qi: as 0 —D- By an Az Az | (X 
A= x (9) 
B aA: A2 A3 Bz 0 —Bx |A: a» a» Yr 
C 
Au A: ds —By Bx 0 an a» Q5 f 
The epipolar line equation for the right image which is corresponding to the point p, on left image is obtained as 
follows: 
—— — — 
— 
Because the vectors B , O, p, and O,K, satisfy the coplanar condition, 
— 
— 
Be(O,P, xO,k,) 20 (10) 
Therefore, 
Bx By Bz 
X set i Zn z BxY,.Z -Z,Y)r By Zu X X tBuX AY Y X0 (11) 
xX’ y^ 7' 
So we can get the following epipolar line equation for the right image which corresponds s to p, of the left image. 
Ax B'y'4Cf 20 (12) 
JA i bu bs bs I 0 —Bz By Q1 Ar A| (X, 
B Da b» bs | Bz 0 —DBxlàà a» Aa y» 
C bs b: bs; —By Bx 0 dv (Us: 3s f 
(13) 
When we use pixel coordinates, we have to know the transformation between pixel coordinates and photo coordinates. 
If we have a pixel coordinate (u,, Ju ) of the left image, we can get (Xp ; Yor) by transformation between pixel 
coordinates and photo coordinates. The epipolar line equation (8) always passes two points (0,- st , MES 0) . and also 
B AC 
the epipolar line equation (12) always passes two points (0,-—7)- UE We can get the pixel coordinates of these 
points by transformation between photo coordinates and pixel coordinates. Then we can get the epipolar line equation 
represented in pixel coordinates. 
3 PROPOSED MATCHING METHOD 
The basic proceeding of the proposed method is composed of two separate steps: in the first stage we apply point 
matching, and in the next stage we perform line matching. The positions of matched points are used as a constraint to 
reduce the number of possible line matches. 
Additionally we can get the approximate differences for each colour channel between corresponding regions in 
overlapping images for the matched point set. This serves as another supporting constraint for line matching. 
Concerning point matching the similarity between corresponding areas near the point is used as local consistency check, 
and the positional relation between possible neighbouring matched points is used as global consistency check. 
Concerning line matching the similarity in shape, the angle of the lines, the flanking regions' colour serve as local 
consistency check, and the relation between possible corresponding lines and neighbouring matched points serve as 
global consistency check. A scheme of the basic flow of the proposed matching method is shown in Figure 1. 
31 Point Matching 
First we generate points for matching by the Foerstner Interest Operator [Foerstner et al, 1987] for each image. As 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 699