The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3h. Beijing 2008 
polygon algorithm. This step is necessary for buildings contain 
ing more than one part. A rectangle parallel to the main orien 
tation (parallel to ridge line) is created. A rectangle is defined 
around the ridge line with equal distances of the edges to the ridge 
line. The limits of the rectangle are selected in this way that de 
tected building pixels (cf. Section 4) are all included. In figure 
10(a), the rectangle is displayed by red lines and the localized 
points are shown by green dots. The direction of the projection, 
which is equal to the orientation of selected ridge line (black line) 
is shown by the white arrow. 
5.3 Project 3D into 2D plane and fit 2D model 
The localized points are projected which is defined by a vertical 
plane. According to the type of the roof which has been deter 
mined by classification before, a 2D model is fitted to the pro 
jected points. For flat roofs just two vertical lines and a horizontal 
line connected to the top of them is fitted. For roofs with a ridge 
line, a model consisting of two vertical lines as well as two sloped 
lines which intersect at the ridge are fitted. Figure 10 illustrates 
the projected points with blue points and the 2D model fitted to 
the data set with black lines. 
(a) Localization of building part 
(b) Fit of 2D model to projected data 
Figure 10: Principle of projection based modeling 
5.4 From 2D to 3D space - LOD2 
The 2D model is converted to 3D by extruding it orthogonally to 
the projection plane. The 3D model comprises four walls plus one 
to four roof planes: a horizontal plane in case of a flat roof, two 
inclined planes in addition to two vertical triangular planes for a 
gabled roof and four inclined planes for a hipped roof. After re 
constructing 3D models for all building parts, they are combined 
to form the overall 3D model of the building. Figure 11 displays 
a building model produced by merging 8 building parts. The 8 
ridge lines leads to 8 parametric building models with hipped 
roofs. After combining the models an overall 3D model is pro 
vided. For nodes of the building parts which have to be merged 
because they represent e.g. the same corner of the building the 
average value is determined. Figure 11 shows that, there is a 3D 
segment which is not modeled and that is above the entrance of 
the Stuttgart new castle. A proper model for this area would be 
a dome which not taken into account in our approach. Further 
a flat roof model is created and added to the 3D building model 
as can be seen in figure 13. As shown in figure 14, edge refine 
ment is employed for not rectangular building parts . The model 
contains two parametric models, the gray points represents the 
points above the fitted model and the colored ones are the points 
below the model. As shown in figure 14(b) two nodes should 
be refined after combination. The distances between the original 
LIDAR data points to each edge line are calculated and the edge 
is extended (or shortened ) from both sides to the last point hav 
ing distance less than a certain threshold. Nodes generated from 
more than one vertex the average value is chosen. 2D information 
Figure 11: 3D Building Model 
about the building boundaries comprising protrusions and inden 
tations can be extracted from the result generated in LODI. The 
nodes of the protrusions and indentations are determined from the 
approximated polygon and the corresponding planes on the roof 
(either flat or inclined ones) are adapted. 
The figure 12 displays an approximation result for our building 
which is superimposed on original image as red color polygon. 
The reconstructed building model is overlaid on image in blue 
color. The figure shows that the 2D outline of the approxima 
tion result and 3D overall outline of the building model almost fit 
together. In this figure, one indentation part and two protrusion 
parts are available which should be included or excluded from 
the model. Indentation is a low height building model which is 
modeled using a cuboid. Two protrusions are excluded using in 
formation extracted from approximated outline. The inclination 
of the building roofs after including protrusions are adapted in a 
final step. 
Figure 12: Approximation of building outline (red polygon) and 
the reconstruction result (blue polygons) overlaid on original im 
age