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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
Consequently, points will be eliminated from the point set if
their correspondening altitude is less than a fixed threshold.
However, in order to suit the needs for standard roof polygons
in this work, a modification was introduced to this criterion.
The computed altitude was divided by the base of the processed
triangle. This increases the probability of keeping corner points
and minimizes the discretization noise resulting from the
imperfection of region segmentation since the point elimination
procedure is applied in a recursive way. The recursive mode
comes from the fact that the elimination will start gradually
from zero to the fixed threshold value. This prevents damaging
the start point of elimination. If the elimination starts with high
threshold directly, the start part and the arc after it will be
damaged severely. Extracted polygons from the same example
shown in figure 6 and 7 where they are overlaid over the roof
segmentation results.
(b) Extracted roof polygons
(a) Ordered border points.
Figure 6: Complex roof polygons extraction.
As shown in figure 6(b), the extracted polygons are isolated and
not connected even though they belong to the same building.
First, vertices located within a close proximity to each other
were grouped together and this procedure starts with the
external vertices. Since the building footprint outer primitive
was defined precisely, those outer primitives were enforced in
the extracted polygons to define the building geometrical
borders. Another step was taken to enforce the alignment
between nodes which appear to be in a line. This was done by
computing the distance between each node and the closest line
and if this distance is less than the prefixed threshold, the node
will be shifted to that line. For interior nearby vertices, they
were grouped together at an average location of their position.
Figure 7: Connected roof polygons.
5. BUILDING WIREFRAMES
For each roof polygon, the plane-roof geometrical parameters
are estimated by applying a robust 3D regression method on the
irregular LIDAR data points inside each polygon. The
reweighted least squares adjustment is used to estimate those
parameters (inclinations in both directions x and y and height
intercept) through plane fitting. The fitting includes all points
inside each polygon collectively instead of the moving surfaces,
i.e. each and every point will contribute to the adjustment and
consequently in estimating the parameters. The point in
polygon technique was used to obtain all data points inside the
polygon in order to use them in the estimation. Due to the
existence of outliers in the data and miss-located LIDAR points
(being assigned to a roof segment to which it does not belong),
in addition to data uncertainty, the reweighted procedure during
the adjustment was used to diminish their influence on the
results since weights are assigned based on each observational
error in each of the adjustment iteration. The estimation of the
plane-roof geometrical parameters transfers their polygons from
: 2D space to 3D space.
After finalizing the 3D polygons of the roof segments, the 3D
coordinates of their vertices are computed based on the
geometrical parameters of each segment. As a final refinement
step, vertex heights within small close proximity will be
clustered in order to have typical closed building wireframes. A
thick plane will be dropped through each building and heights
in close proximity will be combined. Also to get the building
elevations, the terrain height was obtained for each building
from a LIDAR derived DTM. This enables the reconstruction of
building side polygons. The final result is the constructed
wireframe of buildings as shown in figure 8 and 9.
Figure 8: Reconstructed 3D view of the building processed in
figure 4.
Figure 9: Reconstructed 3D view of the building processed in
: figure 7.
aN
. DISCUSSION
The aim of this work is to design a simple and fast method to
reconstruct buildings in urban areas using LIDAR data only,
which can be useful in many applications. We restricted the
procedure to not require any other source of data other than the
LIDAR heights. This was done intentionally to avoid the
limitation of availability of other sources of information in
some areas. Sources such as ground plans, imagery and
multispectral data are not available for every desired site. The
presented algorithm of detailed building extraction is very
useful and effective in reconstructing large areas and it shows
satisfactory results when the data was not so dense (one spot
height per square meter only). More dense data might improve
the extraction procedure, especially the roof details. However,
