Full text: Close-range imaging, long-range vision

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| | 
| (a) ^ 
po EE Y seeds from 
+ seme e) 
geometric ES 
reconstruction | 
[ | seeds from 
In un ) semantics (d) 
| semantic 
semantic model 
Lie en 
Figure 1: Structure of geometric and semantic modelling 
system. From the input data (a), consisting of 3D line seg- 
ments, a set of seed segments (b) is chosen by virtue of 
some geometric properties. In the neighbourhood of these, 
preliminary geometric models consisting of planar faces in 
3D space are reconstructed (c). Firstly, the semantic la- 
belling performed in (e) allows to detect missing parts of 
the model and thus to determine additional seed segments 
(d) which in turn are used for geometric model instantia- 
tion. Secondly, the semantic labels are used to improve the 
overall model topology (f). 
fice to use triangular patches only. However, since quad- 
rangular patches are very common in building roofs, in- 
cluding them is advantageous for the practical application. 
The 3D line segments delineating the border of a patch will 
be referred to as patch segments. The term edge is delib- 
erately not used because of its widespread use in computer 
vision. Besides the collection of patches constituting the 
roof, the relations between the patches are of importance 
and will be integrated in the model as constraints. 
2.1 Patches 
A roof patch is a triangular or quadrangular face in 3D 
space. It can be accessed through two types of representa- 
tions, which are kept in parallel. On the one hand, a para- 
metric representation is provided, allowing direct inference 
of quantities such as angles or lengths. Three coordinate 
systems are involved in the parametrization: a world co- 
ordinate system O, a patch centered coordinate system 0! 
and a 2D coordinate system in the patch plane O". The re- 
lation between O and O' is illustrated in Figure 2. Figures 
3(a,b) show the parametrization of the triangular and quad- 
rangular patch models in the patch plane coordinate system 
O"'. The advantages of the chosen parametric representa- 
tion are that the quantities involved have an obvious mean- 
ing. Probability distributions have been obtained from a 
test dataset. Additionally, this representation allows to in- 
corporate symmetries between different patches of a roof 
In parallel to the parametric representation, a representa- 
tion based on the 3D world coordinates of the corner points 
Py,..., Pa of a patch is kept as well. Although this dual 
representation is redundant, its importance transpires when 
modelling the relations between the patches of a roof. Pos- 
sible relations are given by coincidence or equality con- 
straints and can hold either between coordinates or param- 
eters of different patches. Consequently, the dual repre- 
sentation allows to integrate diverse constraints such as 
geometric symmetry or topological connectivity simulta- 
neously and at the same level of complexity. 
Figure 2: Patch model; global and patch centered coor- 
dinate systems. T is the transformation from world co- 
ordinates to the local patch coordinate system including a 
translation t and a rotation around the z-axis by $1. $1 
is the angle between the x’, y'-plane and the x, y-plane. z 
and z' are parallel; the z^, y'-plane is horizontal. The slant 
of the patch plane is given by $», which corresponds to the 
rotation performed to get the 2D patch coordinate system 
O". (P,) denote the corner points of the patch ordered in 
mathematical positive sense. 
(a) (b) 
Figure 3: Patch models; patch plane coordinate system. 
Q'' is the origin of the 2D coordinate system in the patch 
plane. (p) denote the projections of the corner points into 
the patch plane. /;; denotes the line segments given by pi 
and p;. /;? and [3o are parallel to z". The inclination of the 
bordering segments is denoted by o and o» respectively. 
The full parametrization of a patch is given by specifying 
the height ^, and the width w in case of a quadrangular 
2.20 Constraints 
A roof is described by its constituting patches and the re- 
lations between them. These relations are modelled as 
constraints between parameters or coordinates of different 
patches in a roof similar to what has been done to describe 
dependencies within CAD-models (Seybold et al., 1997, 
Ault, 1999). Once a relation between patches has been es- 

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