International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999 
by a dynamic split algorithm (Stilla et al., 1996). This 
vectorization step may profit from the MDL-principle (c.f. 
Weidner and Forstner, 1995) 
4.3. Sloped Roofs 
In order to test the hypothesis for case (iii), the gradient field of 
the elevation image (Fig. 7) is calculated. From the orientation 
of the gradients possessing a minimum value, a histogram is 
determined (Fig. 8). In this histogram, we search for peaks to 
determine major orientations and orientation intervals around 
them. 
These segments of homogeneous oriented gradients may still 
contain areas of different slopes. To separate such connected 
areas, the histogram of the slope is determined. If the 
distribution shows several significant peaks essentially differing 
in slope, then the segment is split into the corresponding areas. 
If the histogram does not show a few major orientations, local 
relations have to be considered. Several segmentation 
algorithms that are based on region growing are described and 
compared in Hoover et al. (1996). 
Out of the segments of homogenous orientation and slope, 
spatial planes are calculated by a least square fit. Recalculating 
the z-coordinate for the contour points by the plane equation, 
we ensure a planar 3D contour chain (Fig. 10). 
Fig. 7. 3D view of elevation data of a single building and the 
corresponding histogram. 
By thresholding the orientation image (Fig. 9 left) at the 
boundaries of the orientation intervals, segments of similar 
orientation are separated (Fig. 9 right). The areas resulting from 
the segmentation are then morphologically dilated and eroded 
to fill small unknown enclosed areas, remove small holes, and 
separate components, which are connected only by few pixels. 
Ji*. 
L_l 
Fig. 10. 3D contours of roof segments. 
A polygonal description is obtained by deleting points of the 3D 
contour chain. Special attention is required at the common 
edges of neighboring segments so that they form a single line. 
Since edges of neighboring segments do not intersect in exactly 
one point, a common vertex has to be calculated. 
Fig. 8. Histogram of gradient orientation. 
Fig. 11. Reconstructed sloped roof structure. 
5. UPDATE OF CITY MODELS 
For updating databases of 3D-city models, we propose a 
procedure in two phases. In a verification phase, the buildings 
that are already stored in the database are compared to the new 
elevation data by histogram characteristics. They are confirmed, 
modified or deleted. 
Fig. 9. Image of gradient orientation and segmented elevation 
image. 
In a classification phase, new buildings are searched in the 
elevation data of non-buildings. The discrimination of artificial 
objects from natural objects can be achieved taking into account