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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
laser scanner point cloud are tested for valid intersections in
order to complete the roof. The reconstructed roofs are then
assessed for their correctness and accuracy.
2 DATA SET AND PRECONDITIONS
At the start, some preliminary information is provided about the
data. The proposed method has been applied to two different
data sets. The first data set has an average point spacing of
1.5m This point spacing means that smaller features of houses,
such as dorms, cannot be mapped. The standard deviation of
point coordinates within one stripe is in x and y about 30 cm
and in z 20 cm. The data was taken in Switzerland in an alpine
region and contains mainly gable roofs. The second data set is
rasterised data with a point spacing of Im. This data set covers
several streets of Dresden, Germany, where buildings have
rather complex roof structures.
For the study, 100 point clouds each containing only one
building including some surrounding ground points, have been
extracted from each of the laser scanner datasets.
[Hofmann 2002] gives an example for the process of extracting
such laser point clouds automatically. The extracted point
clouds contain buildings with common roof types such as pent,
gable and hip roofs. Some of the buildings also have
combinations of them.
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Figure 2-1. A building’s point cloud with TIN-structure
3 BUILDING MODEL RECONSTRUCTION
The basic idea of the developed method is that all triangles of a
TIN in the laser scanner points of a planar surface (in this case a
roof face) should have the same position parameters in object
space. Collecting all triangles with similar parameters should
therefore gather all laser points of one roof face; a building
modelling procedure can be applied to planes interpolated into
the laser points of each roof face. The following section will
describe the method of grouping laser points of roof faces and
the building model reconstruction procedure. The following
paragraph explains the basic parameters of the approach.
In many cases the selected laser scanner point cloud of one
building contains data from multiple strips. In this approach the
points of each strip have been analysed individually to avoid
inconsistencies in the case of their strip discrepancies. In each
strip's point cloud a TIN-structure is calculated with a Delaunay
triangulation using the module Triangle [Shewchuk 1996].
Figure 2-1 shows an example. To obtain parameters for further
analyses, the three points of each triangle are used to calculate
parameters of the plane. In describing each triangles position
in space uniquely, the following parameters were used: Slope,
Orientation and the minimal distance of the triangles plane to
the origin, below referred to as Distance. Figure 3-1 illustrates
the chosen parameters.
Figure 3-1. Triangle parameters € slope, € orientation and d
minimal distance of the triangles plane to the origin O
Figure 3-2 shows the distribution of these triangle parameters
for the building of Figure 2-1. Each parameter point in Figure
3-2 represents one mesh in the TIN-structure of Figure 2-1. The
abscissas represent orientation values (0 to 360 degree), the
ordinate of the upper image slope values (0 to 90 degree) and
the ordinate of the lower image the distance d [m]. Within this
parameter space two clusters with roof properties can be made
out at a first glance. The next section will describe the
algorithm that was used to group parameter points of roof
triangles. The association of cluster points to single roof faces
is discussed in section 3.2. The modelling of the roof itself is
described in section 3.3
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Figure 3-2. Example of a building's 3D parameter space
3.1 Cluster Analysis
There are several basic clustering techniques, such as
partitioning, hierarchical, divisive, agglomerative or k-means
methods, as described by [Anderberg 1973] and
[Kaufmann 1990], which the researcher can choose from, while
searching for the optimal application for its data. For this study
it was decided to apply an agglomerative approach using single
linkage. The procedure is as follows: Starting from a randomly
chosen seed point, the distances to all direct neighbours in
parameter space are calculated. If one distance is smaller than a
certain threshold, the point is grouped to the seed point. This
search is repeated until no direct neighbour of any point
belonging to the group is found. Single linkage hereby means
that the size of the clusters is not limited in any direction. The
shape as well as the extension of the clusters is not relevant.
After completing a cluster a new random seed point is chosen
and the search starts again. Each point is treated only once. A
cluster is only accumulated if a sufficient number of points are
collected. Each cluster contains the parameter points of one
