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building model at least half of the roof faces are correctly
formed and parts of the other planes exists. An operator only
would have to edit a few corner points. If less information is
provided, the model is classified as incorrect. The
reconstructed building model is of no value. A visual
comparison of high-resolution aerial imagery and the analysed
point cloud provided the information about the shape of the real
building. Table 4-1 confronts the results for the two data sets
that have been available.
Most of the buildings that have been correctly reconstructed are
buildings with planar roof faces that do not have dormers. The
majority of buildings in the Swiss data sets have gable roofs
without dormers. Thus, they are easy to reconstruct. The result,
given in Table 4-1, confirms this.
Swiss data set Data set of Dresden
Correct 70% 46%
Partly correct 17% 30%
Incorrect 13% 24%
Table 4-1. Statistics to the correctness of reconstructed roofs
The lower success rate of the Dresden data is a result of the
constitutions of its roofs. The majority of buildings have hip
roofs, whereby most of them are equipped with dormers and
balconies, or smaller roofs are attached. Thus, numerous
buildings have not been processed in their entirety. Roof faces
that are too small (smaller than 10m?) could not be
reconstructed at all and yielded to incorrect results.
Figure 4-1. Example of building primitive reconstructed from
the 3D cluster analysis information
4.2 Geometric accuracy of the reconstructed roofs
Beside the correctness of the reconstructed building models
their geometrical accuracy is of most interest and will be
discussed in this section.
Cadastral data have only been available for the Swiss data set.
The outlines of 20 randomly selected reconstructed building
models were compared to it. Here, the length/width ratio and
the tilt angle of the main ridge directions have been analysed.
Table 4-2 supplies these results. Taken this fact into account
that cadastral data comprises the corner coordinates of walls and
the exact overhang is not known the results are as expected. If
one presumes a hangover of about 1m, which is typical for the
majority of alpine houses in Switzerland, the laser scanner data
would resemble the actual building quite well. The tilt can be
negotiated, as it would only be of importance in large-scale
applications.
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
Mean difference Standard deviation
Length/Width t 2m / *1.8m 0.7m
Tilt 0.8 degree 0.45 degree
Table 4-2. Mean differences as well as its standard deviation of
the length and width of reconstructed building models in
comparison to cadastral data.
High accuracy terrestrial measurements of the roof itself were
available for a small sample of five building models of the
Dresden data set. Statistically, this number is not meaningful,
but it gives a general idea of the accuracy that can be expected.
The correctly reconstructed buildings were evaluated by
comparing the end points of the eaves and the ridge with the
measured data. The achieved position accuracy of the ridge
points has to be analysed separately from the end points of the
eaves, as intersecting interpolated planes generated the ridge.
The ridge points achieved a RMS-error in position of 0.4m and
the corner coordinates of the roofs outline 0.9m. The worse
accuracy of the corner coordinates mainly is an issue of the
point density (1m). The accuracy in height, in terms of the caves
depends on the roofs inclination and position accuracy, is
considered with 0.1m very good. It was expected to be around
0.2m according to the laser scanner data error in z.
To verify the single interpolated roof planes, the standard
deviation of the perpendicular distances of the laser scanner
points of each plane was calculated.
30 arbitrarily chosen building models of the Swiss data set and
another 30 of the Dresden data set were analysed. The selection
comprises small buildings as well as large storehouses. The
mean perpendicular distance of the points that belong to one
roof face to the interpolated plane is 4,78cm. The standard
deviation of the distances off all points to their plane is 3.61cm.
There was no trend recognised that interpolated planes of larger
buildings fit better than those of smaller buildings. The main
statistical results that table 4-3 summarises are considered as
very good.
Linear distance [cm] Standard deviation [cm]
Minimum 2.01/0.5 14/12
Maximum 126/128 8.0/16.8
Mean 4.8 / 3.7 3.6/4.8
Table 4-3. Minimum, maximum and mean values of the
perpendicular distance of points to the interpolated plane and
standard deviation of the single distances for the Swiss/Dresden
buildings
5 CONCLUSIONS AND OUTLOOK
With the proposed method a tool has been developed, that
automatically generates building models from airborne laser
scanner data with an acceptable percentage of correct results.
The user only has to set parameters that define the mean point
density and the laser point accuracy in z. The algorithm works
quite fast. A machine operating with 700MHz and 512MB
RAM computes 100 buildings, such as seen in the figures of
this paper, in 3,2 minutes. The computation time increases, of
course, with the number of laser points per point cloud,
whereby most of it is the need of memory allocation.
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