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Boersma, Saskia M. 
  
  
  
  
Figure 4: Testfield 
Figure 5: Configuration of 8 images 
33 Bundle adjustment 
The parameters of the interior orientation of the three cameras and the exterior orientation for each camera were 
determined with a least squares bundle adjustment. A set of 5 additional parameters was used to compensate systematic 
errors (figure 6). Non-significant and non-determinable parameters were excluded from the estimation process in an 
automatic way (Kruck, 1998). The average standard deviation of the 3D co-ordinates is 0.1 mm in X and Y, and 0.2 mm 
in Z. A root mean square of image co-ordinate residuals of 5 % of a pixel was achieved, corresponding to 37 microns in 
object space. 
  
  
  
Parameter 5 Parameter 6 Parameter 17 Parameter 25 Parameter 26 
5 y 6 Y W y 25 y 26 y 
      
  
  
Figure 6: Additional parameters 
We noticed radial and non-radial distortions. Softplotter, the software package we use for the DSM generation, only 
provides the possibility to correct the image for radial lens distortions. We developed a program to correct the images 
for the additional parameters. Besides, this program creates fiducials in the corners of the image. This simplifies the 
interior orientation in Softplotter. 
Table 1 lists the estimated camera calibration parameters and their standard deviations for one of the three cameras. 
Similar results were obtained for the other cameras. Four calibrations were carried out with an average time interval of 
one month between the different epochs. The average value for each parameter is calculated out of four epochs. The 
difference of each epoch with the average is listed. The numbers in the table show that this difference is not larger than 
about three times the average standard deviation of the corresponding parameter. This demonstrates the stability of the 
system. 
  
  
  
  
  
  
  
  
  
Camera 1 Average value Average , epoch] , epoch 2 , epoch 3 , epoch 4 
Focal length (um) 6034.3 2.1 1.5 -1.9 -6.3 6.7 
Principal point X (um) -11.7 0.8 -2.2 0.5 -0.6 2.4 
Principal point Y (um) 69.6 0.9 1.6 19 -1.6 -1.7 
Parameter 5 6.2 0.1 0.1 -0.3 -0.1 0.2 
Parameter 6 1.6 0.1 0.1 -0.2 -0.3 0.3 
Parameter 17 8.4 0.0 -0.1 0.2 0.0 -0.1 
Parameter 25 111.5 0.5 -0.4 -0.5 0.4 0.4 
Parameter 26 -122 0.9 -0.8 2.2 -1.5 0.3 
  
  
  
  
  
  
  
  
  
Table 1: Results of camera calibration for camera 1 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 87