ibul 2004
nt of the
).
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370
gic data
structure
how they
topologic
5. The 3-
ng points
ibed by a
vo points
"can be
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
reconstructed with topological integrity. This table is a 3-D
surface generalization of the well-known dual independent map
encoding (DIME) structure in 2-D topology expression.
Table 1. Topological relationship of roof Figure 2i.
Polygon Edges Point - Point
a 7-3
] b 3-2
c 2-7
d 8-6
2 e 6-5
T 5-8
g 8-9
h 9-4
3 ; i s
f 5-8
] 7-9
h 9-4
2 k 4-2
c 2-7
g 8-9
] 9-1
s m 1-6
d 6-8
j 7-9
] 9-1
$ n 1-3
a 3-7
3. TEST AND RESULTS
In this study, the test data results from a pair of stereo images at
the scale of 1:4000. The location is Purdue University campus.
These distinct building points were measured manually under
stereo mode. During the measurement, operators need to
estimate the location of points in hidden areas, and all roof
corners must be completely denoted. In addition to these roof
points, operators also need to obtain one footprint of the
building on the ground to define the building base height. The
height information is a key issue before the 3-D reconstruction
process, because our approach needs to initially level the point
clouds and finally project the building outlines to the ground.
After the data collection, each building is one unit and is
reconstructed independently according to the procedures
described in last section. During the reconstructing process,
selecting tolerance parameters is necessary because the digitized
data may not be perfectly accurate. For the data measurement
error in most buildings, we apply a height tolerance 0.7 m,
beyond which data will be separated to different levels.
Moreover, in 2-D XY-plane, we apply a value of +5 degree for
deviation from perpendicularity, respectively in x and y
directions. Figure 3 shows four building images and their
building structures reconstructed by using our approach.
| rcx c
aa ANSTATT TT => P
n
Figure 3a)
557
Figure 3c)
Figure 3d)
Figure 3. Examples of reconstructed buildings.
In Figure 3a, the building is a simple polygon with one level.
Therefore, this level is partitioned into three rectangular bases,
which are then merged together to form the outline. Its outline is
directly projected into the ground to form the vertical walls.
Figure 3b shows a standard four-ridge points roof contains two
small rectangular rooftops. After rectangulation process, the
highest level has two rectangular bases contained by the
rectangular base just below it. Since our primitive models did
not include this situation, we make an assumption that these
belong to rooftops. In this case, we project these two polygons
directly to the level below them to form two small structures. A
more complicated case is shown in Figure 3c. Notice that the
building union in Figure 3c includes four structures. They are
one four-ridge roof model and three simple flat polygons. These
rectangular bases in this union can be distinguished and
reconstructed correctly and simultaneously by our approach.
Another complex building is shown in Figure 3d. In the
building image, this is a combination of two-ridge points roofs
and four-ridge points roof structure. Nevertheless, because we
suitably adopt auxiliary points during rectangulation and
remove the corresponding auxiliary lines after merging, all the
roof outlines are still illustrated well by merging different roof
models. Once the roof is reconstructed, the connectivity
between roofs and boundary outlines are correctly performed.
These examples indicate that our method for building outlines
with right angle corners presents quite satisfactory results.
Figure 4 shows the results obtained by applying our
methodology to the Purdue campus. Most campus buildings in
Figure 4a can be decomposed into several parts, and each part is
well reconstructed by our method. Notice that detail structures,
such as small rooftop structures, have also been reconstructed.
