The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Pol. XXXVII. Part B5. Beijing 2008
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results are mean values for the five reference spheres in the four
scans of different loadings. For the sphere targets made of
Styrofoam with a diameter of 12 cm, the mean absolute error
and the standard deviation correspond to the results for the
reference spheres.
For the registration of the 3D-point clouds, all the 3D-point
clouds were registered into the coordinate system of the initial
scan. The registrations were performed with the software
Cyclone by Leica Geosystems AG (http://www.leica-
geosystems.com). The registration quality is specified by the
mean absolute error and the RMS (Root Mean Square). The
mean absolute errors for the three registrations were 0.6 mm
(initial-Pl), 0.6 mm (initial-P2), and 0.5 mm (initial-P3).
Furthermore, the RMS was calculated to 0.6 mm for each of the
three registrations.
3.2 Deformation analysis between different epochs
As mentioned above, the deformation analysis of the TLS data
was performed both area-wide and discrete. The latter was
performed by using the sphere targets on the object.
The area-wide deformation analysis required a filtering of the
3D-point clouds by eliminating outliers and undesired points.
Furthermore, the scanning section to be analysed was restricted
to a 10 m by 20 m area (Figure 6). The filtering of the 3D-point
clouds was performed with the software Geomagic Studio by
Geomagic Inc. (http://www.geomagic.com). Hence, the area of
the road surface was filtered identically for each scan. Filter
algorithms were run for an automatic detection of outliers, a
reduction of the point spacing (40 mm) and a smoothing of the
3D-point cloud by a free form filter. The average distance,
which the 3D-points were moved, was calculated to 1.6 mm
(mean value of all four scans) and the standard deviation of the
residuals to 1.3 mm (mean value of all four scans).
The deformation analysis was performed with the software
Geomagic Qualify. The 3D-point clouds of the different loading
situations were compared to the initial situation. The residuals
were calculated as the shortest distances from the scan points to
the initial surface which was modelled by triangulating the 30-
point cloud.
In Figure 6, the residuals of the scan points of the loading
situation P2 to the initial situation are shown. Deflections of the
outer side of the cantilever slabs are detectable. The maximum
deflection is around 20 mm. The results for the comparison
between initial situation and loading situation PI are similar but
the sizes of the residuals are smaller. The influence of the
different loadings on the resulting deflections can be clearly
distinguished.
Table 1 summarises the results of the comparison between the
different loading situations and the initial situation. Differences
between the results of the different loading situations are clearly
detectable. However, the maximum positive and negative
residuals have to be looked at with care due to the fact that
these values can be influenced by outliers which could not be
detected during the filtering process of the 3D-point clouds.
Besides the area-wide deformation analysis, a discrete
deformation analysis was performed by the 13 sphere targets
which were arranged around the loads on the cantilever slabs
(cf. Section 2.5). The target sphere centre points for the
different loading situations were compared with the initial
situation. Figure 7 shows the vertical displacements (Az). The
largest residuals can be detected for the targets 104 and 204
which were located close to the loads on the outer side of the
cantilever slabs. The mean values of the residuals are calculated
to -0.2 mm for the differences between situation PI and initial
situation (standard deviation: 1.6 mm), -1.7 mm for P2 and
initial (standard deviation: 2.7 mm), and 0.4 mm for P3 and
initial (standard deviation: 0.5 mm).
o 6 W 05 o
o b b o b
deflection
Figure 6. Deflections of cantilever slabs detected by
terrestrial laser scanner (residuals of the scan points
of loading P2 to the initial situation).
Mean
positive
residual
[mm]
Mean
negative
residual
[mm]
Max.
positive
residual
[mm]
Max.
negative
residual
[mm]
Standard
deviation
[mm]
PI
0.6
1.4
6.0
10.5
1.4
P2
0.5
3.6
4.8
24.3
1.9
P3
0.5
0.9
7.6
9.6
0.9
Table 1. Mean residuals and standard deviations of the
residuals for the different loading situations as a
result of an area-wide deformation analysis.
Figure 7. Vertical displacements of sphere centres between
different loadings and initial situation measured by
terrestrial laser scanner Imager 5006.
In general, it can be said that deformations of the cantilever
slabs could be detected by the area-wide analysis as well as by
the discrete analysis. The discrete analysis shows smaller
residuals which are caused due to the fact that the target spheres