a)imagel | TE, b) image 2 
Figure 8: Detected edges (image 1) projected on image 2 (right) 
  
  
a) image 2 : b) image 2 
Figure 9: Detected edges (left) and matched edges (right) 
To investigate the quality of the match, we have applied several 
different thresholds. Table 1 shows the number of matched 
edges between the two images with respect to the different 
thresholds used. 
Table 1: Thresholds and number of matched edges 
  
  
Case 1 2 3 4 5 6 7 
Buffer (pix) 10 10 10 5 5 3 3 
End-points 1 1 1 1 
Length (mm) - 0.8 0.8 08 08 0.8 0.5 
Angle (degree) 3 3 1 1 1 1 1 
  
Match. image 1 137 132 91 74 38 22 14 
Match. image 2 315 257 157 96 45 26 16 
  
  
Figure 10 portrays some of the matching results for both images 
according to the seven example cases presented in Table 1. As 
it can be seen from the table, the uniqueness between the 
matched edges varies significantly. In principle, the more 
restrictive constraints are applied, the more unique is the 
matching. In the last two cases, the correspondence is 
approximately one-to-one. The obtained results depend not only 
on the values of the thresholds but also on the order they are 
applied and the sequence of images that is used. For example, 
the threshold for the allowed difference in the length filters 
significant number of the matched edges (compare case 1 & 
case 2, and case 6 & case 7), but only if the detected edges of 
the first image are longer than the ones detected on the second 
image (as in our particular case). If the two images were 
exchanged, the buffer threshold and the endpoints considered 
(i.e. 2) would have the same effect. 
  
  
  
  
  
= e) case 77: buff-3, end-points-2, length-0.5, angle= 1 ve 
Figure 10: Matched edges on image 1 and image 2 
Finally, to compute the 3D line feature out of the matched 
edges, we have used all the candidates. As mentioned above, 
the two end points of the 3D line are the two most distant points 
on the 3D line of intersection (see Figure 4). Therefore all the 
3D lines are longer than the edges detected on the images (see 
Figure 11). We applied only one constraint at this step, i.e. 
maximum allowed 3D line feature length is restricted to 3 m. 
The constraint is selected with respect to the particular size of 
the line features that can be expected on the given facade. 
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