Claus Brenner 
  
  
  
  
  
  
  
  
  
  
  
  
  
NC c 
N C E 
a C C c 
as a5 
c pa C e bm c L:nc 
C 
p n 
a c n c 
ca P 
D n c p c hn 
  
Figure 9: Region labeling. Left: Set of possible region labels: compatible (c), previous (p), next (n), left (L), right (r), 
inverse of previous (a), inverse of next (b). Right: Examples for possible label sequences. 
3.3 Putting it together 
After accepting planar regions as being part of the roof, one has to actually intersect all regions to obtain a single, 
connected roof surface. This can be accomplished using a modification of the approach from the previous section. This 
time, instead of generating a plane for each edge of the ground plan polygon, one plane for each accepted region is 
generated. Moreover, it is possible to use region adjacency information from the segmentation in order to guide the search 
process. In figure 10(b), line segments are shown which are computed based on the region plane equations and the region 
adjacency graph. We cannot use this adjacency information as "hard" constraints for the search, since it is not stable 
enough. But we can introduce it as a means to reach the correct solution more quickly. Figure 10(c) shows the final roof 
structure. Note again the upper part, where some of the roof planes are much larger than the segmented regions they are 
based on. Note also that new roof plane adjacencies not present in the segmentation were generated. 
  
Figure 10: (a) Regions selected by the rule-based approach. (b) Region adjacencies and intersection lines. (c) Final roof 
structure. 
4 RESULTS 
Figure 11 shows more results of our approach. In figure 11(a) the situation for a simple saddleback roof is depicted. This 
roof is handled correctly, albeit a parametric modelling approach or the method described in (Haala and Brenner, 1997) 
would presumably yield the same result. The situation is different in figure 11(b), where the lower part of the building is 
actually L-shaped. This results in an additional roof surface for which there is no hint in the ground plan. Also the short 
horizontal ground plan edge on the left side does not lead to a roof surface. Figure 11(c) shows a similar example, where 
the simple ground plan suggests a saddleback or hip-roof type building whereas it is L-shaped and has two surfaces which 
emanate from a ground plan vertex rather than a ground plan edge. Finally, in figure 11(d), the ground plan suggests a 
fairly complex building (cf. Fig. 7), although from the segmentation, we can see that only two roof surfaces are present. 
The roof structure is recovered correctly by the algorithm. 
5 CONCLUSION AND OUTLOOK 
We have presented a new approach for the reconstruction of buildings which relies on ground plans and DSM's from 
laser scanning. We have shown that this approach is able to reconstruct buildings of fairly complex structure. The entire 
  
90 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.