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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
and intersected. The ideal algorithm for this task should be able
to give good results for any combination of roofs. The simplest
application would be a gable roof and the more difficult one
multiple detached houses with different roof types. The
workflow of the intersection procedure consists of three steps:
finding dormers, intersect ridges and intersect sides and
bottoms. At each stage the intersected couple is assigned a
code. There is the dormer type that means a smaller plane is
located within the x-y-projection of a larger one. A couple
would be two roof planes intersecting at the top forming a ridge.
A neighbour would be any other adjacent plane. Also, a basic
rule was set: Once gained intersection lines remain as they are.
Only the corner coordinates can be moved on this line.
The task of the first step, detection of any flat dormers, is to find
planes with similar parameters that are within each other. That
means more than 80% of the laser points of the smaller plane
are shared with the larger plane. If the lower edge of the
smaller plane is at least 50cm above the larger plane, the smaller
plane is intersected at the top creating a horizontal intersection
line. Should these circumstances not apply, the smaller plane is
discarded. The larger plane always remains as it is.
a) b)
Figure 3-5. Examples of buildings with sideways-connected
roof faces
In a second step, those planes are associated that should be
intersected at the ridge. In the case that two planes have been
extracted a gable roof is presumed. The planes are intersected
and the new corner coordinates of the ridge are saved. If there
are more than two planes it is presumed that at least two of them
form a gable roof. So, all roof faces are checked if there is/are
one or more partners with opposite orientation that is/are within
a certain distance and that has/have an overlapping area with the
roof face worked on. These partners are listed in descending
order by there overlapping area. Intersecting first those planes
with the longest overlapping area will create the ridge of the
two roof faces. Other bordering partners are intersected with
the appropriate roof side. If no partner was found or none exists
there will be, of course, no intersection. After the intersection
of both planes the caves at the gable side are trimmed. That
means a least square line is calculated through the outer points
of each gable side.
The third step is the intersection (Figure 3-5 a) and trimming
(Figure 3-5 b) of sideways neighbouring planes. The difficulty
here is to find a scheme that can be applied to any number of
roof planes and the result will always be acceptable. The
strategy that has been developed is as follows: First, all the roof
planes are sorted in descending order by their size. To each
plane the adjacent planes are detected and their connection type
recognised. All neighbouring planes are also sorted by their
size. The intersection starts with the largest plane and its largest
neighbour. Basically, three different intersection cases can
occur. Figure 3-6 illustrates them.
In cases a) and c) of Figure 3-6 all other adjacent sides have to
be intersected. In case b) only the planes II and I are to be
intersected. To accomplish this, the plane pair that is to be
intersected is checked, whether one of the planes has a couple
partner (forms a ridge with another plane) that is also an
adjacent plane to the other plane or not. If not (Figure 3-6 c))
the adjacent sides are blended. In the other cases, for instance
in Figure 3-6 b), plane Il and I is a couple and both are adjacent
to plane II. The same situation can be seen in Figure 3-6 a).
Here, the plan is that plane III of Figure 3-6 b) should not be
altered, but plane IIl of Figure 3-6 a) is to be intersected with
the couple II, I.
a) b) c)
IH | IV
Figure 3-6. Types of possible sideway intersection
As the algorithm has to make the decision without knowledge of
the buildings shape, a rule has to be set defining when to
intersect all three planes or just plane II and I. If after
intersecting all three planes with each other, one of them is
enclosed below the other two planes (that would be the case for
plane III of Figure 3-6 b), this one should keep its original
corner coordinates. Failing that, the appropriate sides of the
three planes are blended.
Trimming planes is taken here as extending the sides of two
adjacent parallel planes that are close to each other in a way that
they can be connected with a vertical wall.
In some cases, such as storehouses, it is necessary to intersect
the lower roof sides, the gutters, as well. This procedure is
similar to the others. Planes next to each other with opposite
orientations that are not a couple are intersected and the new
lower end points are saved.
If all intersection steps are finished, walls are added to the
building model. A wall element is created to each side of the
roof faces that has not been intersected. The roof's eaves give
the top line of the walls. The lower edge of the wall is derived
form the DTM of the building's surrounding. The lowest point
is chosen in order to please the eye in visualisations where also
the terrain model is included. The reconstructed building model
is now complete.
The ground plan of the building is obtained by creating a
polygon that follows the top lines of the walls.
4 ACCURACY VERIFICATION
The reconstructed building model is valuable information for
many visualisation tasks. For mapping agencies not just the 3D
information of the building is of interest, but also the accuracy
of the determined roof outline and ridge end points. This
section will first give information about the success of the
modelling procedure, measured by how many buildings have
been reconstructed correctly. In the second part, the
reconstructed roofs are verified regarding the geometrical
accuracy of the corner coordinates of each roof face and the
fittingness of the roof plane in the laser point cloud.
4.1 Correctness of reconstructed roofs
The results of the building model reconstruction were divided
into three groups: correct, partly correct and incorrect. A roof
model is correctly reconstructed if the number and outlines of
cach roof face corresponds to the real building. Figure 4-1 and
5-1 are examples of that. In a partly correct reconstructed
