1510(pixel), and the principal point lies at the center of the image. 
In Fig. 3, there A is the angle between level projection of 
shooting aspect and direction of X; v is the angle between 
shooting aspect and vertical direction. Assume that the standard 
error of observation o0 is O.lpixel, and view the error of 
parameters calibrated as error criterion. 
y 
  
  
  
  
Figure 3. The sketch map of simulation 
1) In simulation, firstly only when the value ofangle V changes, 
we observe the extent of error of the principal point and the focal 
length influenced by V, Fig. 4 illustrates the error trend of the 
principal point and the focal length when V ranges from 
20? — 70? inthecaseof A = 45°, 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
© 1.86 
E 
5155 + 
  
WR 
a 
>} 
> 
2 
= 
en 
il 
p 
i 
C) 
| 
(2 
| 
C 
| 
w 
| 
Error 
«Ae dn. 
2) 
M 
Error 
c 
> 
= 
= 
0.63 
0.42 
0.21 
0.00 
  
20 25 30 35 40 45 50 55 60 65 70 
Angle(degree) 
Figure 4. The error curve of f and (x0, y0) obtained when the 
angle v changed 
The experiment above shows: when the angle V increases, the 
error of the focal length m, becomes little, namely the 
precision of f becomes high. But the three error curves trend 
stable when the angle v is in the range from 40° to 70°; the 
error of X, M,, becomes larger along with increasing the 
angle v, and the error of Vy, M, becomes contrariwise. 
Anyhow the errors of the focal length and the principal point are 
profoundly influenced by the shooting angle V . 
2) Only when the focal length f changes, we observe the extent of 
error of the principal point and the focal length influenced by f, 
Fig. 5 illustrates the error trend of the principal point and the 
focal length when f ranges from 1510 — 4010 in the case 
of À = v=45". 
  
3.10 
279 
248 
247 
1.24 à Be 
0.33 
D.62 
0.31 
  
1510 1760 2010 2260 2510 2760 3010 3260 3510 3760 401 
Focal length (pixel) 
Figure 5. The error curve of f and (x0, y0) obtained when the 
focus length changed 
3) Finally, only when the angle A changes, we observe the extent 
of error of the principal point and the focal length influenced by 
A, Fig. 6 illustrates the error trend of the principal point and the 
focal length when A ranges from 20° — 70° in the case 
ofv = 45°. 
  
  
— — 
hy om 
mom 
/o S 
-~ 
c 
Fa 
S 
S 
= 
S 
0.21 
0.00 
  
20 25 30 35 40 45 50 55 60 65 70 
Angle (degree) 
Figure 6. The error curve of f and (x0, y0) obtained when the 
angle A changed 
The experiment indicates: the angle A influences little on the 
errors of the focal length and X, , but influences much on the 
error of ys, from experiment (3) we can see when A439 
the higher precision can be obtained. However, in practice it is 
not easy to obtain the optimal shooting angle, thus the precision 
of calibrated parameter based on single-view calibration is 
unstable. Aiming at the shortage of this method of camera 
calibration, we propose the calibrating method based on multi 
orientations and multi views. 
4. MULTI-VIEW CALIBRATION WITH VANISHING 
POINTS 
In single-view calibration utilizing vanishing points, the exterior 
    
   
     
   
  
  
   
   
   
   
    
  
  
   
  
  
  
  
   
   
  
   
    
  
   
   
  
  
   
   
   
   
   
  
  
   
  
  
     
Internatic 
orientatiot 
calibratior 
parameter 
the accur: 
error anal 
and exteri 
and then c 
method ca 
Orientatio 
the other 
orientatioi 
of Fig. 1. 
Linking 
between 
points: 
Xv. 
Xoo 
Xr 
V 
The comp 
it just lin 
Therefore 
adjustmen 
ek. 
oo