International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B-YF. Istanbul 2004 
(i) All points include temporal points are converted into the 
absolute coordinate from relative coordinates by using the 
distance (D) between two points on object field. 
  
    
   
  
  
  
a jn ui 
[jm un m 
= n 9 
ul x a 
«o —— 
  
  
Figure 2a. Imaging of triple image. 
  
Distance measurement between two points 
Y 
Relative orientation 
Y 
Acquisition of 3 D coordinate for 
  
  
  
  
  
  
  
  
  
temporal control points 
Y 
Self-calibration of center camera 
Y 
Simultaneous adjustment 
y 
Calculation of absolute 3 D coordinate 
  
  
  
  
  
  
  
  
  
  
Figure 2b. Calibration procedures 
Following equation shows collinearity equations, 
Plein ene] 
; my (X - X)+ m(Y - Yo)+ m3(Z = Zu) 
my (X - Xo)- mylY = Yo) + m(Z - Zo) (1) 
6 -(y- M e?) 
T mai (X = Xo) + ma(Y Yo) ma3(Z - Zo) 
mylX - Xg)^ may (Y = Yo) + my(Z - Zo) 
  
where: (X, Y,Z) are 3D coordinate for temporal GCP, (X; ^p, Z0) 
are coordinate for exposure station, (x, y) are image coordinates 
of temporal GCPs, (x, y») are principal coordinate, r is 
distance from principal point to image point, k; is lens distortion 
parameter, and m; are rotation matrixes. 
Image coordinate are transformed by following equations. 
WzHa Xt-y 
(2) 
yzucba.sxTO, V 
Where, u and v are sensor (pixel) coordinates, up and vy are 
sensor coordinate for the principal point, x and y are image 
coordinate. 
Epipolar line from right image 
Epipolar line from left image 
  
  
    
  
» (Intersection of epfpolar lines) 
| 
| 
| 
pi (interesting point) 
  
  
  
Center image 
Figure 3. Correction of lens distortion 
However, it should be note that the lens distortion is not 
considered for the computed 3D coordinates of the temporal 
points, nevertheless lens distortion influences 3D coordinate of 
the temporal control points. 
In order to revise lens distortion, epipolar geometry is adopted 
in this paper. 
Epipolar line for a temporal control point on the left image is 
obtained on the center image, similarly epipolar line for the 
same point on the right image is obtained on the center image. 
The correction of lens distortion is performed using these 
epipolar lines since two epipolar lines should be intersect at the 
same point on the center image if there are no lens distortion. In 
this method, the lens distortion was corrected by calculating the 
orientation parameters to minimize the difference between 
intersection point (p?) and interesting point (p;) at the center 
image by following equations. 
H = le +Ay")}} —— > min (3) 
Where, Ax=x,(1 +kır 1 )-x(1+kırz)) 
Ay-yi(tkri)-yx0 kr) 
Figure 3 shows the concept of the correction for lens distortion 
using epipolar geometry. 
3. EXPERIMENTATION 
In order to evaluate the calibration method which is proposed in 
this paper, triplet images were taken using amateur digital 
camera CP-900Z(EPSON). Figure 4 shows appearance of the 
CP-900Z, and Table 1 shows the specifications. Table 2 shows 
imaging conditions and Figure .5(a)-(c) shows the triplet images. 
17 circular points are temporal control points and check points. 
3D coordinate for these points were measured by the total 
station MET2NV(SOKKIA MET2NV, distance accuracy — 
Imm, angle accuracy 3 2^" ), and image coordinate for the 
points are given as the center of area gravity by image 
processing. Table 3 shows the exterior orientation parameters