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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
board GPS and IMU drift errors and other residual effects. In
our approach, we first use the RPCs to transform from object to
image space and then using these values and the known pixel
coordinates we compute either two translations (model RPC1)
or all 6 affine parameters (model RPC2).
For satellite sensors with a narrow field of view like IKONOS
and QB, simpler sensor models can be used. We use the 3D
affine model (3daff) and the relief-corrected 2D affine (2daff)
transformation. They are discussed in detail in Fraser et al.
(2002) and Fraser (2004). Their validity and performance is
expected to deteriorate with increasing area size and rotation of
the satellite during imaging (which introduces nonlinearities),
while the 3D affine model should perform worse with
increasing height range and in such cases is more sensitive than
the 2D affine model in the selection of GCPs.
3.2 Measurements of the GCPs
In Geneva, some roundabouts and more straight line
intersections (nearly orthogonal with at least 10 pixels length)
were measured semi-automatically in the satellite images and
the aerial orthoimages (see Fig. 4). Measurement of GCPs by
least squares template matching (Baltsavias et al., 2001) was
not convenient or possible due to highly varying image content
and scale. The height was interpolated from the DTM used in
the orthoimage generation. An unexpected complication was
the fact that the Canton of Geneva is using an own coordinate
system and not the Swiss one! The transformation from one
system to the other is not well defined, and based on different
comparisons of transformed Geneva coordinates and respective
coordinates in the Swiss system, a systematic bias has been
observed, indicating that the results listed below could have
been better. In Thun, the same image measurement approach
was used, however, roundabouts (which are better targets) were
very scarce. As expected, well-defined points were difficult to
find in rural and mountainous areas, especially in Thun, where
they had to be visible in 5 images simultaneously, while
shadows and snow made their selection even more difficult.
The object coordinates in Thun were measured with differential
GPS. GPS requires work in the field, but the accuracy obtained
is higher (espec. in height) and more homogeneous than using
measurements in orthoimages, which have varying accuracy
with unknown error distribution (due to the DSM/DTM). The
number of GCPs and their accuracy are listed in Table 1.
Figure 4. Examples of GCP measurement with ellipse fitting
(left) and line intersection (right).
3.3 Comparison of different sensor models
In Geneva, we compared various sensor models, IKONOS vs.
OB and analysed the influence of the number of GCPs. Due to
lack of space, only the most important results will be shown
here.
Tables 5 and 6 show the results for the transformation from
object to image space. Three different GCP configurations are
used with all, 10 and 4 GCPs. Table 5 shows that with all
GCPs, in IKONOS-East, all 4 sensor models have similar
performance, with RPC2 being slightly better. In IKONOS-
West (with forward scanning) results are similar for RPCI and
RPC2, a bit worse in y with 2D affine and considerably worse
for 3D affine. The latter model deteriorates more with reduction
of GCPs and is more sensitive to their selection. For the other
models, the accuracy reduction from 44 to 4 GCPs is very
modest, verifying findings from previous investigations that the
number of GCPs is not so important, as their accuracy and
secondary their distribution. The results for the 3D affine were
initially by some factors worse than the ones of Table 5, when
using geographic coordinates instead of map coordinates
(oblique Mercator). The dependency of the results on the
coordinate system has been discussed by Fraser (2004), albeit
with smaller differences than the ones noted here.
x-RMS | y-RMS Max. max.
Model GCP | CP [m] [i] Ax Ay
Im] Im]
rpcl 44 - 0.65 0.56 1.40 01.21
rpe2 44 - 0.54 0.42 1.53 0.98
3daff 44 - 0.55 0.41 1.40 0.81
2daff 44 - 0:55 0.47 1.39 1.18
rpc2 16 | 34 0.57 0.32 | 152 1.07
rpc2 4 40 0.60 0.50 1.63 1.13
rpcl 4 30 | 0.63 0.40 1-35 1.40
rpc2 4 30 | 0.6! 0.54 1.63 1.13
3daff 4 30° 1.25 4.16 3.85 1570
2daff 4 |30 | 0.66 0.83 1.30 ] 1:32,
525
Table 5. Comparison of sensor models and number of GCPs
with IKONOS-East (Geneva). At the bottom, one example for
IKONOS-West. CP are the check points.
QB (see Table 6) is much less linear than IKONOS (expected
partly due to its less stable orbit and pointing, and continuous
rotation during imaging). Only RPC2 performs with submeter
accuracy and only with this model can QB achieve similar
accuracy as IKONOS. A residual plot with RPCI shows a very
strong x-shear. The 2D and 3D affine transformations are totally
insufficient for modelling. As with IKONOS, a reduction of the
GCPs has not any significant influence with RPC2. Thus, using
simple RPCs (as in most commercial systems), or even applying
2 shifts in addition, will not lead to very accurate results with
QB. It should be noted here that the QB image was Basic, i.c.
not rectified. It is expected that a rectified image will show a
more linear behaviour, and the respective RPCs will be more
stable.
For the Thun dataset, the triplet and stereo images were used
separately in a bundle adjustment to determine object
coordinates (processing of all images together was not possible
due to a program limitation). Several semi-automatically
measured (with least squares matching) tie points were
included. The results for the triplet are shown in Table 7. The
previous conclusions were verified, while the 3D affine model
was worse compared to Geneva, probably because of the larger
height range. A new indication compared to the Geneva data
refers to the height accuracy. This is clearly better with RPC2,
and seems to get worse with decreasing number of GCPs, at
least for this area with large height differences.
