4.4. Estimated Precision from Relative Orientations 
To determine the impact of these effects, relative orientations have been 
performed using all targets (240 - 256 per image). The coordinates of these 
targets were corrected in advance and no additional parameters were used. To 
stabilize the configuration, all points were added as vertical control point 
with height zero. The standard deviation of these control points was fixed to 
10 mm, so that they did not have any influence on the precision. The sixteen 
relative orientations of the images with the same kappa rotations had an 
average sigma naught of 0.48 pm (table 5.). This precision corresponds to 
0.018 pixel. About 35% of the observations was redundant. 
  
  
  
  
  
# image pairs 16 
# observations 1152 - 1232 , average 1199 
redundancy 334 - 452 , average 420 
Go [um] 0.39 - 0.56 , average 0.48 
Oo [pixel] 0.015 - 0.021, average 0.018 
Table 5 Performed relative orientations 
8. Conclusions 
1. The main scope of this project was to estimate the accuracy of target 
location using a digital camera. The results are very clear: Under well con- 
trolled conditions the empirical precision of target location can reach 1/30 
pixel for targets with a diameter of appr. 10 pixels. Smaller targets of 
appr. 6 pixels diameter can be located with a standard deviation of appr. 
1/20 pixel. The analysis also showed that there are still local systematic 
effects. Compensating for these could further reduce the standard deviations 
to appr. 1/50 pixel. Thus the geometric precision of the used CCD-camera of 
Hamamatsu is very high. 
Due to the extremely high redundancy these results are quite reliable. 
They were achieved by applying a rigorous least squares matching (LSM) algo- 
rithm. However, no radiometric calibration of the camera was performed; only 
the local variations of brightness and contrast were taken into acount in the 
LSM algorithm. 
2. In the course of this study we obtained further results, which are 
worth mentioning: 
- We also determined the centres of the targets solely based on the centres 
of gravity in the binary image (cf. sect. 3.2) The estimated standard 
deviations turned out to be worse about a factor 1.5 compared to the LSM 
approach. Thus the LSM algorithm proved to be really effective. For certain 
applications, however, the analysis of binary images may be sufficient and 
under controlled conditions may lead to accuracies of 0.1 pixels. 
- The empirical results coincide with the internal standard deviation of the 
LSM algorithm within a factor 1.5 to 2 in both directions. For the small 
targets the internal estimates were too pessimistic, for the large targets 
they were realistic or a bit too optimistic. The main reason for these dis- 
crepancies seems to be the different sharpness of the targets in the image 
and in the used model. If one would introduce a sharpness parameter in to 
the LSM algorithm, as proposed by Thurgood and Mikhail (1982), the internal 
estimates could be expected to be too optimistic in all cases, because they 
only reflect the matching precision and not that of the camera geometry. 
- The ratio between the standard deviations for the small and the large tar- 
gets is very close to the theoretical expectation ((3/2 vs. 4/2). 
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