das émane
==
Figure 8. Four screen shots in selected areas in the site of the
24,887 buildings created for the city of Aalborg.
5. CONCLUSIONS
The overall performance of the algorithms is surprisingly good,
considering the relatively low resolution of the laser scanning in
combination with distortions caused by a very unfortunate
interpolation of the raw data. In addition, the mutual
displacements of the two datasets (footprints and laser
scanning) are sometimes difficult to correlate, and undoubtedly
the cause of many problems. In our case, creating a building has
a success rate of 84 percent, although the qualities of these are
not always satisfactory.
In particular, the following algorithms are believed to be very
efficient and general for the purpose:
e Projected cluster area filter used for extraction of
planes from Hough space.
e Degenerate mesh filter where error detection is based
on mesh welding techniques.
These algorithms are innovative and not described in similar
articles like e.g. [Vosselman, 2001].
However, there are a number of obvious problems and
drawbacks of the methods described in this article.
5.1 Height jump lines
Currently, we have no method for detecting height jump lines,
as the sampling resolution is considered too low for this
purpose. Instead, by splitting the footprints into smaller units,
the influence of height jump lines is reduced, as the footprints
are often cut exactly at lines convergent to these. However, as
the resolution of laser scannings increase, solutions of height
jump lines are needed.
5.2 Aligning ridges and gables
In our methods we rely on using the Hough Transform for
detection of planes in 9. Planes are among the most simple
primitives in N°, but not necessarily the “atomic” unconstrained
primitives of building roofs.
In the case of roofs, some of the d.o.f. of a plane are often
constrained by another adjacent plane on the other side of the
ridge, just like the dependencies between the two sides of equal
length in an isosceles triangle. A Ridge Plane Pair is two planes
intersecting at the line of the ridge. Roof planes which have an
angle of more than 20 deg from horizontal often have such
accompanying planes. The line of intersection (the ridge) is in
e
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
most cases a strictly horizontal line, and the angle from
horizontal is often the same for both planes.
Figure 9. The Isosceles Triangle is
; : b
constrained in the same manner
as the Ridge Plane Pair. / f^,
a
Furthermore, planes are often strictly parallel to a line of the
footprint, meaning that the orientation of a roof plane is
achievable by rotating it from horizontal around an axis
convergent to one of the footprint lines.
Utilizing this knowledge on the dependencies of planes, major
achievements in precision is expectable. The Hough Transform
is a general method for detecting primitives in parameter space.
The more complex primitives, the more parameters to describe
these in parameter space, and thereby, more dimensions to
sample and traverse. However, being able to set up constraining
rules drastically reduces the number of samplings necessary in
each dimension of parameter space. Consequently, it is possible
to use the Hough Transform for detecting more complex
primitives, which should be done in future research.
6. ACKNOWLEDGEMENTS
The laser scanning and ortho photos were provided by COWI
A/S, Consultancy within Engineering, Environment and
Economics. Geometries of footprints and cadastres from the
technical feature map were provided by the Municipality of
Aalborg. The authors thank both providers for making these
data available.
7. APPENDIX — PRE PROCESSING OF SOURCE DATA
Proper pre processing of the source data is of vital importance
for the reconstruction algorithms.
7.1 Fixing geometries of footprints
It is desirable that the footprints as much as possible reflect the
actual 2D borders of the individual buildings.
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Figure 10. The background upper picture shows a snapshot of
raw footprints from the technical map. The lower
front picture shows the resulting shapes of these
footprints when cut by polygons of cadastres.
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