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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
planar surface. The cluster algorithm is explained in detail in
[Hofmann 2003].
The single linkage is necessary, as the sizes of the clusters vary
with the roofs inclination and position to the origin and with the
laser scanner data accuracy in z. Here, the error model of the
laser scanner data was simplified by making the assumption that
within a small area planimetric errors are highly correlated as
they are mainly caused by the GPS/INS system on board.
Hence, for laser points of one flight strip within small objects,
only the accuracy in z must be taken into account. With
increasing inaccuracy of the laser scanner data and with
increasing point density, the clusters swell in size and the
borders of the clusters get fuzzier.
The single linkage connection also has the advantage that
parameter points of triangles of not planar but continuous
surfaces are collected in one cluster. In later analysis it will be
possible to create multiple regions (smaller planes) from one
cluster with the awareness that the planes should be connected.
This may be advantageous for roofs with multiple inclinations.
M anny mate:
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Figure 3-3. Association of parameter points to roof faces
3.2 Interpolate roof faces
At this stage of the analysis a number of clusters exists, that
contain parameter points of planar surfaces. As can be seen in
Figure 3-2, some parameter points originated from triangles
representing walls group to clusters as well. These clusters are
to be excluded from further analysis. The centre point of each
cluster is calculated. If its slope in parameter space exceeds
75 degree, the cluster is rejected as a wall object.
The remaining clusters are now fed into the roof face
interpolation process. The parameter points of each cluster are
sorted in descending order by their distance to the cluster
centre. The parameter point that is closest to the cluster centre
is identified in the TIN-Structure. Following a simple region
growing technique all neighbours of that triangle are evaluated
whether they occur within the cluster or not. If that is not the
case, but they still fit the clusters main properties the
appropriate neighbour is added to the region. Each parameter
point of a cluster is analysed only once. Figure 3-3 visualises
the association of parameter points of a cluster to the according
roof face. It can be seen that outliers of laser points resulting in
triangles that do not fit the characteristics of the roof face are
not included as potential roof points.
In the explained algorithm, multiple regions may be extracted
out of one cluster. Figure 3-4 demonstrates that on the right
roof face two regions have been extracted out of one cluster.
This may happen when there are problems with the scan line
registration. Complete rows of triangles have a different
orientation in object space than the actual roof face. The
advantage of the proposed method is obvious. A simple region-
growing algorithm might not associate the single bright grey
regions with each other without collecting too many triangles in
other situations. Interestingly, this building's model has been
reconstructed successfully (see Figure 4-1).
Figure 3-4. Multiple regions within one roof face,
view from top
Al regions extracted from one cluster are analysed on their
mergence with other regions of this cluster. They should be
merged in situations such as seen in Figure 3-4. If multiple
larger regions have been extracted out of one cluster, they might
belong to individual roof faces and should thus not be merged.
A region that has one single triangle is, if possible, merged with
a neighbouring region.
All laser scanner points that belong to triangles of a roof face
large enough to be detected are now gathered to groups. In
each group a plane is interpolated and a coarse bounding box is
determined. Equation 3.1 shows the chosen plane equation. a,
b and c correspond to the normal vector of the interpolated
plane and d is the offset parameter. X, Y and Z are the
directions of the object space coordinate system. The plane
parameters a, b and c are derived by applying a principal
component analysis to the point group. d can be calculated by
applying a planes point to equation 3.1.
aX+bY+cZ+d=0 (3.1)
The coarse bounding box of each region is necessary to aid the
intersection procedure. t is created using the lowest and
highest point and the points that are the resp. furthest on the left
and right side of the region. Using the constraint that the lower
edge (gutter) and upper edge (ridge) of a roof are very close to
being horizontal, horizontal lines are fit in the according points.
Perpendicular to them, lines are defined through the outer
points of the region.
3.3 Intersecting roof faces
At this stage of the building model reconstruction procedure a
number of plane objects exists, that still need to be associated
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