International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
   
  
The general idea was to model the axes of the fork tubes and 
then to calculate the wanted angle. Again, no homologous 
points were visible on the fork cylinders, hence fictitious 
observations in form of planes had to be introduced. In each 
image, unique points were digitised on the visible silhouettes of 
the cylinders. 
tp2* tpt! 
  
= tp? 
pr 
  
  
P1 
  
P2 
Figure 10: Modelling the fork cylinder axes 
In Figure 10 the SP represent some silhouette points that were 
digitised in the images. P1 and P2 are the perspective centres of 
two images. The planes that were defined through silhouette 
points and the perspective centres were called tangential planes 
(tp). For each tangential plane a perpendicular axis plane (ap) 
was defined, going through the corresponding silhouette points 
(SP). All these axis planes (ap) intersect in one line: the 
cylinder axis, on which two points were defined and fictitiously 
observed on all axis planes (ap) (see Figure 10). 
An additional restriction was set, stating that the axis of one 
part of the upper-fork (Figure 3: UF2) is equal to the axis of the 
lower fork (Figure 3: LF). 
This procedure of deriving the cylinder axis from observed 
silhouette points in the images was carried out for all three 
cylinder parts of the front fork. 
Finally, angle a (£1,2,3) could be calculated, since the axis 
exact orientation of the two parts of the upper fork (UF, UF2) 
were known. 
6. DISCUSSION 
This paper gives an insight on the advantage of employing 
fictitious observations in a hybrid adjustment. These 
observations seem to be the only solution when not enough tie- 
point- or control-information is available or when no 
homologous points can be found on certain features. Of course, 
the redundancy of the system increases much less with every 
observed non-homologous point than with a homologue one, 
but as shown in this example, many times there is no other 
solution available e.g. for the fork modelling! 
The effort of camera calibration was not negligible, since the 
distortion effects arising from the non-metric camera had to be 
modelled precisely to achieve the wanted accuracies in the final 
results (09570,0315 with and 0,=0,0384 without distortion 
modelling, with a o4,,4;,:70,03mm for an observed image 
coordinate). The standard deviations of image measurements 
when applying a distortion model ranged from +24um to 
+38um, compared to a range from +24um to +44um when not 
modelling the distortion effects. 
After the final adjustment, which was carried out with self- 
calibration, the accuracies of the interior orientation parameters 
were: +0.073mm and +0.173mm for the principal point 
coordinates. The principal point distance shrunk to 27.51 1mm 
(initial value 43mm) with a standard deviation of £0.112mm. 
This indicated that the pictures had been most probably taken 
by using a 28mm lens. 
The wanted angle o resulted: 213.6% £1.38. 
During the adjustment process data-snooping techniques were 
used to trace gross errors and to get a feedback regarding the 
measurement process. This was very important, since it is 
difficult to define exact a-priori accuracies for fictitious 
observations. Thus the a-priori accuracies of especially these 
observations were revised during the adjustment process using a 
Variance Component Analysis (VCA)! 
The whole adjustment system comprised 2212 observations 
(986 fictitious), 1677 unknowns and hence had a redundancy of 
535. Altogether 99 geometric features were introduced in form 
of planes, straight lines, cylinders and spheres. 
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