International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
Figure 14: Connected horizontal ridges determine two roof- 
units (dark red and bright yellow). Dependent on the size of the 
structure (average facet-area) roof-units are eliminated. 
Figure 15 shows results for the squaring of roofs. It can be seen, 
that additionally triangular facets are eliminated first, so that, 
e.g., a hip-roof becomes a more simple saddleback-roof. Like 
for the generalization of orthogonal building structures, a 
scaling should be added. In this case, it can be restricted to the 
z-coordinate. The decision if the original ridge-height, eave- 
height, or, e.g, an average of both should be taken for the 
result, depends on the goals of the user. 
Figure 15: Examples for roof-squaring 
3.2 Squaring of wall-structures 
The squaring of walls is not realized by now. The basic idea is 
that in most cases strong deviations from the right angle have to 
he preserved in order to obtain the characteristic shape of a 
building (cf. Fig.16, top). Two cases exist, where a wall- 
squaring would be reasonable before applying our 
generalization process. On one hand, a squaring should be 
done, if there are only small deviations from a right angle. This 
happens, when the building was not reconstructed from ideal 
3D primitives. On the other hand, a structure with strong 
deviations, which is small enough to be eliminated in case of 
orthogonality (cf. Fig.16, bottom), should be squared, so that 
the facets can be merged after a parallel movement. 
  
Figure 16. Strong inclinations have to be preserved for large 
structures (top), whereas small parts need to be squared 
(bottom) 
The squaring of walls is highly non-trivial. While for the 
detection of inclined roof-facets reference directions are 
available (a roof facet is neither vertical nor horizontal), for 
vertical walls the reference directions are the main directions of 
the building. These can be seen in nearly all cases as 2D vectors 
in the x-y-plane. Yet, even for 2D generalization of ground 
plans the derivation of the main orientation is not solved 
satisfactory. An overview of common approaches and the 
. problems linked with them is given by (Duchéne et al. 2003). In 
all of them, a maximum of two main directions is obtained. For 
simplification of building data often more than two main 
directions would be reasonable (cf. Fig. 17). 
      
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Figure 17: Buildings with more than two main directions. 
4 CONCLUSIONS AND OUTLOOK 
An approach for generalization of 3D building models is 
introduced, which is inspired by scale-space theory from image 
analysis. Whereas first ideas comprised a combination of 
mathematical morphology and curvature space, similar to 
reaction-diffusion-space, our new approach allows to simplify 
all orthogonal building structures in only one process. It works 
by moving parallel facets towards cach other until the facets 
meet and merge. Because of this it is suitable only for 
orthogonal building structures. 
For the therefore necessary squaring of non-orthogonal 
structures the treatment of roofs and walls has to be done 
differently. A procedure for the squaring of roof-units is 
introduced and the main problem concerning the wall squaring 
is discussed. The latter is not realized by now. A future goal is 
the wall-squaring, particularly the determination of the main 
directions of a building. The procedure has to also find the 
correspondence between the main directions and building parts. 
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