ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002
component analysis is applied to the resulting image in order to
create additional candidates for planar patches. Figure 6d shows
the final segment label image created for one of the building
regions from Figure 5e. The r.m.s. errors of planar adjustment
varies between X5 cm and +15 cm for the segments
corresponding to the "homogeneous" points. The segments
having a r.m.s. error larger than +10 cm possibly still
correspond to more than one roof plane. In the planar regions
created by the analysis of the originally inconsistent points, the
r.m.s. errors vary between 425 cm and +5 m. Some of these
regions correspond to trees, and other regions still correspond
to more than one roof plane. In the future, a further analysis will
split these regions into smaller ones corresponding to even
smaller planes in object space. This can be accomplished, e.g.,
by a height segmentation of the DSM in these regions. Table 1
shows the distribution of the r.m.s. errors of the planar fit.
r.m.s. error [m] Regions Pixels [96]
0.00 - 0.05 241 30.6
0.05 - 0.10 333 44.4
0.10 - 0.15 96 9.3
0.15 - 0.20 133 8.8
0.20 - 0.50 26 0.9
0.50 - 1.00 10 0.2
1.00 - 2.00 14 0.5
2.00 - 3.00 42 2.6
3.00 — 4.00 36 1.8
>= 4.00 15 0.9
Table 1. Distribution of the r.m.s. errors of the planar fit.
Regions: number of planar regions in the respective range of
r.m.s. errors. Pixels: percentage of pixels in these regions
compared to the number of all pixels in all planar regions.
68% of the pixels in the building candidate regions are
classified as belonging to a planar region.
5.2 Grouping planar segments to create polyhedral models
To derive the neighborhood relations of the planar segments, a
Voronoi diagram based on a distance transformation of the
segment label image has to be created (Ameri, 2000): each pixel
inside the region of interest not yet assigned to a planar segment
is assigned to the nearest segment. The distances of pixels from
the nearest segment are computed by using a 3-4 chamfer mask.
Figure 7 shows a Voronoi diagram of the segment label image
from Figure 6d. From the Voronoi diagram, the neighborhood
relations of the planar segments are derived, and the borders of
the Voronoi regions can be extracted as the first estimates for
the border polygons of the planar segments (Figure 8).
Figure 7. A Voronoi diagram of the label image in Figure 6d.
After deriving the neighborhood relations, neighboring planar
segments have to be grouped. There are three possibilities for
the relations of two neighboring planes (Baillard et al., 1999).
First, they might be co-planar, which is found out by a
statistical test applied to the plane parameters. In this case, they
have to be merged. Second, two neighboring planes might
intersect consistently, which is the case if the intersection line is
close to the initial boundary. In this case, the intersection line
has to be computed, and both region boundaries have to be
updated to contain the intersection line. Third, if the planes do
not intersect in a consistent way, there is a step edge, and a
vertical wall has to be inserted at the border of these segments.
After grouping neighboring planes, the bounding polygons of
all enhanced planar regions have to be completed. (Moons et
al., 1998) give a method for doing so and for regularizing the
shape of these polygons at building corners. Finally, the planar
polygons have to be combined to form a polyhedral model, and
vertical walls as well as a floor have to be added to the model.
dm
Le
Figure 8. The roof polygons of the b
back-projected to an aerial image.
The tools for grouping planes and for computing intersections
and the positions of step edges have not yet been implemented.
Figure 9 shows a VRML visualization of a 3D model created
from intersecting vertical prisms bounded by the borders of the
Voronoi regions with the respective 3D roof planes. The
structure of the roofs is correctly resembled, but the intersection
lines of neighboring roof planes are not yet computed correctly.
However, the visualization shows the high potential of the
method for generating roof planes from LIDAR data.
Figure 9. VRML visualization of a model created from the
boundary polygons of the Voronoi diagram in Figure 5e.
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