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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part BS. Istanbul 2004 
e two line segments 51 and S5 (resp. 51 and 55); The 
intersection of both interpretation planes P; and P: 
defines a line D; that should lie within 7. Because of 
numerical errors, D; and D» are not coplanar. Here 
again, a mean-squares estimation of 7l is computed 
from the selected segments. 
In the computed solution R 4, vector Z. is the normal vec- 
tor of 7L, P. — £40 70, and Y, = norm(CP, A Z,). 
  
Figure 6: Coplanar features geometry. 
The selected features may be some surface details that do 
not necessarily belong to the 3-D model. The operator is 
not required to explicitly indicate which set of features he 
will select. This can easily be guessed afterwards. In the 
same order of idea, the features are matched automatically. 
For the three-points set, all the possible combinations are 
tested. The distance between the interpretation lines of 
each couple is accumulated and the lightest combination 
is selected. For the two-segments set, an equivalent test is 
performed to select the combination that provides the near- 
est lines to coplanarity. 
  
  
  
  
  
Figure 7: Coplanar features example. 
Figure 7 example displays the selected features (a) and the 
matched object on the computed solution (b). Then suc- 
cessive interactive actions are: 
- 1) translation within 7T (ec), 
- 2) rotation around Z, (d). 
3.6 Parallel lines configuration 
This configuration relies on the selection of the projection 
in a single image of two lines assumed to be parallel in the 
207 
3-D space. It provides a direction which is used to facili- 
tate the registration task. Only two rotation parameters are 
fixed. 
  
Figure 8: Parallel lines geometry. 
The selected segments S4 and S» define two lines which 
intersect at point P,,. In projective geometry, this point 
Py, is known as a vanishing point where all lines with a 
common direction meet. This direction is given by vector 
GP... The computed solution is : 
2, norm(CPæ) 
Ra : P, = Pr 
— 
= norm(CP, AZ) 
I 
  
Figure 9: Parallel lines example. 
Figure 9 example displays the selected features (a) and the 
matched object on the computed solution (b). Then suc- 
cessive interactive actions are: 
- 1) parallel translation to the image plane 7 (c), 
- 2) rotation around Z, (d), 
- 3) translation along the interpretation line of P, (e).