T 
+00 
+00 
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ject was 2-3 
  
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In Figure 5 are shown the radial distortion curves of the three 
calculations. They are almost identical. In Figures 6 and 7 are 
shown the decentering distortion curves for x- and y- 
coordinates in a chosen direction. They are far from identical 
but on the other hand also the magnitude of the distortion is 
very small compared to the radial distortion. This gives more 
support for the suggestion that it might be enough to model just 
the radial distortion. 
S. CONCLUSIONS 
In this article a camera calibration method based on concentric 
camera rotation has been described. The simulations showed 
that if the captured image set is symmetric and if at least one of 
the images is totally overlapped by the others, there are good 
possibilities to succeed in solving the calibration parameters. 
Some care must be taken in rotating the camera but a small 
deviation from the concentricity does not spoil the results. The 
longer the distance from the camera to the object, the more 
deviation from the concentricity is allowed. 
The presented method does not use any 3-D control data. 
Because of the special imaging geometry there aren't any 
occlusions or lightning differences between the images. Based 
on the performed simulations and test with real data the single 
station camera calibration can be seen as an alternative to the 
more traditional calibration methods. 
  
  
  
  
35— 
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: mn / 
30r — [—— testfield | / 
|-- set1 | É 
| set2 | 7 
28] re 7 
o A 
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o / 
2 ; 
5 E 
S J 
S 15| / 
© / 
oc 
10} / 7 
5} 4 A 
| 
0 777 L 1 1 } 
0 100 200 300 400 500 600 700 
Radial distance: 
Figure 5. Radial distortion curves. 
REFERENCES 
Brown, D., 1971. Close-Range Camera Calibration. In: 
Photogrammetric Engineering, August, 1971, pp. 855-866. 
Fryer, J., 1996. Single Station Self-Calibration Techniques. In: 
International Archives of Photogrammetry and Remote Sensing, 
Vienna, Vol. XXXI, Part B5, pp. 178-181. 
Hartely, R., 1994. Self-Calibration from Multiple Views with a 
Rotating Camera. In: Lecture Notes in Computer Science, Jan- 
Olof Eklund (Ed.), Computer Vision —ECCV '94, Springer- 
Verlag Berlin Heidelbeg, pp. 471-478. 
Niini, I, 2000. Photogrammetric Block Adjustment Based on 
Singular Correlation. Acta Polytechnica Scandinavica, Civil 
Engineering and Building Construction Series, No. 120. 
Wester-Ebbinghaus, W., 1982. Single Station Self Calibration, 
Mathematical Formulation and First Experiences. In: 
International Archives of Photogrammetry, Commission V, 
Vol. 24, York, pp. 533-550. 
[- — testfield | 
set 1 
02 | se | 1 
Decentering distortion in x-direction: 
/ 
  
  
SE RT LM. SE 
o- 2300 “200 300 400 50 600 700 
Radial distance: 
Figure 6. Decentering distortion for x-coordinate. 
  
.—— testfield | / 
[== sail | A | 
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0.8- f 1 
0.6} d gl 
p 
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Decentering distortion in y-direction: 
  
  
  
0 100 200 300 400 500 600 700 
Radial distance: 
Figure 7. Decentering distortion for y-coordinate. 
—589—