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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
Figure 9: Split and merge of object parts
Figure 10: Merge of object parts and filling of a hole
Figure 11: Elimination of protrusions and filling of a notch
In Figure 12 it can be seen, that in some instances constraints
have to be added to the algorithm. E.g., the ground plane of a
building has to be fixed, so that the building is not hovering in
the air after the box-shaped entrance is eliminated. In case one
of the parallel facets is lying in the ground plane, it should be
fixed and the other facet has to be moved with whole distance
between the two facets.
Apart from fixing a ground plane, partial rescaling of the
building afler the generalization process might be considered,
so that the original volume is preserved. It is not trivial to find a
good solution, as the changes for each object occur in different
directions and sometimes also only for parts of the object. In
order to compute the directions and the parts of the object with
a need for a volume-reset more research is needed.
197
Figure 12: The ground-plane of a building should be kept fixed,
otherwise, after the generalization, the building can hover above
the ground.
3 SQUARING
3.1 Squaring of Roof-Structures
Up to this point orthogonal structures were assumed. Even the
slightest deviations due to measurement errors can heavily
influence the result, as facets might not be merged anymore.
City models with exact orthogonal geometry can be achieved,
e.g., by the reconstruction method of (Gülch et al. 1999), where
a building is generated from generic 3D primitives. Clearly non-
orthogonal structures such as roofs need to be kept. During
generalization, inclined roof structures are only eliminated for
small structures or for very coarse scales, i.e., if the object is
almost out of sight. In order to eliminate inclined roof-
structures, a roof-facet is forced to be horizontal or vertical by
rotating it either around its eave- (cf. Fig. 13) or its ridge-line.
This rotation process is called tapering in ACIS.
Figure 13. The roof-facet (yellow, bright) is rotated (tapered)
around the eave-line (red, dark) so that the roof-facet becomes
horizontal.
A roof often consists of more than one or two facets. For a
reasonable generalization, the inclined facets can not be seen
without their context. If only a part of a roof is eliminated, e.g.,
a smaller part of an L-shaped roof, the result will be not
satisfying. Roof-structures, that belong together, have to be
considered as a unit. For that reason, all roof-units of a building
have to be detected. In this paper roof-units are seen to be
defined by connected horizontal ridge-lines. Figure 14 shows a
building with two roof-units, marked by a red and a yellow
ridge-line. After connected ridges have been detected, for each
unit the average facet-area is computed. If the area is under a
certain threshold, the facets are tapered, i.e., the roof structure is
eliminated.
