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Figure 4: Forward intersection to obtain the 3D line feature 
  
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Computations of 3D line features: Last, the parameters of the 
3D line feature are computed by a forward intersection. The 
algorithm considers again ray intersections between the end- 
points of the matched edges. Since the rays may not intersect in 
3D space, a two-step procedure is applied. First, the 3D line of 
intersection is computed by intersecting the two interpretation 
planes, each defined by the projection centre and the edge in the 
image (van den Heuvel, 1998). Second, the rays passing 
through projection centres and the end-points of the edges are 
intersected with the 3D line of intersection. In the common 
case, the intersection results in four points (see Figure 4). The 
two points with the largest distance between them are selected 
as end-points of the constructed 3D line feature. 
  
Figure 5: Aerial image of TU Delft, The Netherlands 
3. EXPERIMENTS 
The algorithms are tested on images taken with a handheld 
camera Kodak DCS420 (black and white) with 1524x1012 
pixels of 9 um and a focal length of 20 mm. The images are 
used for both 3D reconstruction of the rough 3D model and 3D 
line extraction. More than 300 images are taken but actually 
less then 100 are considered appropriate for 3D reconstructing 
of the facades. For the 3D line feature extraction, we have 
concentrated on the building denoted with number 2 (see Figure 
5) because it exhibits a very regular pattern of vertical and 
horizontal line features that usually cause the greatest problems 
in line matching. Two of the images (called here image 1 and 
image 2) are used to illustrate the results. 
   
  
  
  
  
  
  
     
  
  
  
  
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Figure 6: Detected edges on image 1 within the facade of 
interest 
The edge detection algorithm is performed on both images with 
a) gradient threshold set to 1000, b) minimal length of the edge 
10 pixels and maximal width 3 pixels. These settings resulted in 
2363 and 2009 edges detected respectively on image 1 and 
image 2. The first constraint (i.e. the edges should be within the 
area delineated by the fagade) reduced the number of edges to 
631 and 217 (see Figure 6 and Figure 7). Furthermore, many 
“fake” edges (e.g. from cars, stairs) were eliminated. 
  
  
  
  
  
  
  
  
  
Figure 7: Detected edges on image 2 within the facade of 
interest 
The projection of the detected edges from image 1 onto image 2 
by intermediate projection onto the 3D fagade propagates all the 
edges to the second image (Figure 8). 
Figure 9 shows the difference between all the detected edges on 
image 2 and those that are matched with projected edges from 
image 1. It can be clearly seen that many fake edges from 
shadows, reflections or temporal conditions (e.g. open 
windows, the third window from right to left detected on image 
1) are eliminated from the set. However, the correspondence 
between matched edges (Figure 9b) is not unique, i.e. each 
projected edge from image 1 is matched with more than one 
edge of image 2. 
—235—