International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part BS. Istanbul 2004 
solution can be found, provided that these vectors are not 
collinear. D is the intersection of P and P'. The computed 
solution is: 
P. -— 
Rs Z 
Y 
,;— hormiN,AJN/) 
S 
  
  
  
  
  
  
  
  
Figure 3: Stereo line example. 
Figure 3 example displays the selected features (a) and the 
matched object on the computed solution (b). Then suc- 
cessive interactive actions are: 
- 1) translation along D (c), 
- 2) rotation around D (d). 
Both images may display a distinct part of the 3-D edge. 
This could be useful to limit the number of views when 
modelling large objects as no overlap is required. 
3.4 Shape of revolution configuration 
This solution estimates the axis A of a shape of revolution 
from the specification of its contours in two views. Let S, 
and S» (resp. S, and 5%) be the selected segments, and P; 
and P» (resp. Pj and P2) their interpretation planes with 
normal vectors V and Va (resp. Vi and V2). Axis À 1s the 
intersection of mediator planes P4; and P4,, where Par is 
given by point C and vector NU Be Ni 4 Na. 
      
  
  
If Ni and Ni are not collinear, the solution is: 
7, norm( Nm A N°) 
Rs : P; = £4 1 A 
Y zs norm CP SA s) 
where a L b is the othogonal projection of a on b. 
  
  
  
  
  
  
  
  
Figure 5: Shape of revolution example. 
Figure 5 example displays the selected features (a) and the 
matched object on the computed solution (b). Then suc- 
cessive interactive actions are: 
- 1) translation along .A (c), 
- 2) rotation around .A (d). 
It is interesting to note that this solution may handle any 
object that contains in particular a cylindrical or conical 
part. 
3.5 Coplanar features configuration 
This solution computes a 3-D plane 7T from the selection 
of a set of coplanar features in two images. It fixes two 
rotation and one translation parameters. Proposed sets are: 
e three points P; (resp. P/), à € [1,3]; each couple 
of interpretation lines £; and £; theorically intersects 
in point M;. The triplet (M,, My, M3) defines 77. 
Actually the interpretation lines do not intersect be- 
cause of numerical errors in calibration, numerization 
or manual selection tasks. Therefore each M; is com- 
puted as a rough but sufficient estimation as the mid- 
dle point between Z; and £j. The plane 7f can be 
computed if the three points are not aligned. 
e one line segment S and one point P (resp. S' and P/); 
the segments interpretation planes intersect in line D, 
and a point M is obtained by triangulation of P and 
P' (figure 6). If M does not belong to D, 7( is defined 
by D and M. 
  
  
     
    
     
     
   
   
   
    
    
     
      
    
   
    
    
   
    
    
    
   
    
    
   
     
   
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