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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
The objective function can be stated as
X =X, + Ax)’ *(Y-v Ay) ) (1)
Ax, Ay i=l
where Ax and Ay are the unknown shift parameters and N is the
cardinality of the set of point correspondences. A local
minimum of this function can be easily obtained by setting:
1 N
AN ns,
iS nes)
i Q)
Ay=—— v-y
ÿ sen y,)
In other words, an estimate of the shift can be obtained by
simply averaging the coordinate differences of all point
correspondences. Finally the shift has to be applied to one of
the point sets. Throughout this work the PS set is shifted, which
is quite convenient for the depiction of the results in Google
Earth™.
The procedure of finding the nearest neighbours, estimation,
and application of the shift has to be done iteratively since the
point correspondences are usually not correct in the first place.
The cumulative shift (i.e. the sum of the shifts of all iterations)
is finally applied to the complete PS. A subset of the PS before
the application of the shift together with some building outlines
overlaid to Google Earth™ is displayed in Figure 4. The same
situation is shown in Figure 5 after the application of the shift.
The alignment is clearly visible. The shift direction corresponds
roughly with the looking direction of the SAR sensor,
confirming the aforementioned assumption that the
misalignment is mainly caused by an inappropriate choice of the
reference PS.
3.2 Assignment of PS to buildings
After alignment of PS point cloud and GIS data, the PS can be
assigned to buildings. For that a simple nearest neighbour
criterion is used. For every PS the distance to polygon edges in
a local neighbourhood is determined. The PS is assigned to the
polygon containing the closest edge. A result of the assignment
m
Figure 4. Outlines and PS before application of the estimated
shift for a small part of the test site. The offset between both
datasets is clearly visible.
81
igure 5. Outlines and PS after the PS set has been shifted. The
alignment is clearly visible. The assignment to the buildings is
indicated by the colours.
for a subset of the scene is indicated by the colours of the points
in Figure 5. In the case at hand the purely geometric assignment
works well, because the buildings are far enough apart. In other
cases, where buildings are very close to each other, wrong
assignments will emerge. However, for the sake of counting PS
we assume those wrong assignments to be negligible for
buildings of a certain size.
4. RESULTS
Given the assignment of the PS to the buildings a map of the
number of PS per building volume can be easily compiled.
Figure 6 shows the prismatic building models used for the
calculation of the volume coloured according to their PS density
overlaid to Google Earth™. The black polygon marks the area
where both PS and GIS data are available. At first glance the
density appears to be quite heterogeneous. While most of the
buildings host not more than five PS per 1000m? (the mean
value is around three PS per 1000m?), some show densities
above ten PS per 1000m° (note that the colour scale is clipped).
The highest values (20-25 PS/ 1000m?) emerge for very small
buildings. Due to their small volume just few erroneously
assigned PS may change the result considerably, which is why
we do not consider those results to be reliable. From a practical
point of view the map shown in Figure 6 gives a coarse
overview about how good a building or building part can be
monitored. Admittedly it is also crucial how the PS are
distributed on the building. If for instance just facade PS are
available a deformation of the roof could not be detected. In any
case it is possible to identify buildings which cannot be
monitored properly. For instance the red building enclosed by
the dashed rectangle c hosts very few PS (58 PS, 0.5
PS/1000m*) making a proper monitoring even in case of a
uniform sampling questionable.
Some factors influencing the PS density at buildings are
illustrated by the examples marked by dashed rectangles termed
a-c.
The most important factor is the facade and roof structure. It has
been shown, that PS most likely originate from three- or
fivefold bounce reflections (Auer et al, 2011). Thus, a high PS
density can be expected for facades accommodating for instance
