Bundle adjustment is applied for camera calibration 
between the camera coordinate and telescope coordinate 
system. Unknown parameters are as follows: exterior 
orientation parameters 1 c, $, « (rotation parameters), X,, 
Y, Z(camera positions)) and interior orientation 
parameters ( f, x,, y, (principal points), a,, a, (scale 
factor), p, (lens distortion)}. 
  
Figure 6 . Target field A 
Image A (Figure 6) was taken from about 2.0m as an 
orientation image. The left-hand number superimposed in 
the upper left corner shows the zenith angle (V,=0°0' 
0",V=90°-Zenith angle). The number just to the right is the 
horizontal angle (H,=0 ° 0'1") and the distance 
(D=2.0128m). 
Table 2 shows the calibration results for the target field A, 
using 9 control points. The rectangular target in the image 
A corresponds to the above P, point and the black circles 
mean check points. RMSE for 42 check points are shown 
in table 3. With regard to automated targeting for check 
points, the following image processing procedure was 
developed. The basic steps of this image processing 
procedure are shown in figure 7. 
(^ 
( Original Image 
+ " Enhancement " 
- smoothing - 
Cleaned (Cleaned image ) 
" Segmentation " 
- optimal thresholding - 
(Binary Image —- Image 
+ =. * Extraction " 
V - region boundary - 
(Boundary Image ) 
  
   
   
   
     
  
  
  
  
        
       
" Recognition " 
- curvature of boundary - 
- area gravity of ellipse - 
- ellipse fitting with interpolation - 
  
  
mem ETES 
Le 
us 
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Figure 7. Flow oh _—— targeting 
  
Table 3. RMSE for check points 
  
  
  
     
    
  
(Target Field A B C 
  
  
+ o, 2g 
  
  
  
  
  
  
Figure 8. Multiexposure station 
Next, the target field B was taken by rotating the video 
theodolite 0° 0'17" clockwise and 27 ° 46'02" above the 
horizon, giving ^V,227'46'02" and AH,20'017". 
Finally, target field C was taken by rotating the video 
theodolite 25°05'20" clockwise and 27° 43'52" above the 
horizon, giving AV,=25°05'20" and A H,=27°43'52". 
Unknown parameters, w and ¢ for each sequential image 
should be estimated as the sum of changing vertical and 
horizontal values resulting in w , and ¢ , respectively. 
Here, w , and ¢ , are the calibration results of the 
orientation image. Consequently, wand ¢ are calculated 
as follows using the changing values in vertical (A V) , 
horizontal direction (AH) and w,, ¢,. 
w= wg+ AV; 
P ! (2) 
P=Po+ AH; 
where, A V, =(zenith angle-90°) and A H 5,50 in the 
clockwise case due to the relation between telescope 
coordinate(X,Y,Z) and the theodolite coordinate system 
(X*, Y*,Z*) in figure 5. 
However, each sequential image was taken at a different 
exposure station as indicated in figure 8, due to the 
discord between the center of the theodolite and the lens 
of the CCD camera. Each camera position has to be 
corrected to respond to the rotation of the video 
theodolite by the following equation, 
Table 2. Calibration results for the target field A 
Y, Za w Q K 
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996 
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