International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part BI. Istanbul 2004
In cases where parameters beyond An, Bo, A, and B, are
significant, the RPCs must be re-estimated, rather than simply
corrected. This can be carried out using the accepted technique
outlined in Grodecki (2001). A software system, Barista, has
been developed to perform the necessary generation of bias-
corrected RPCs. This system allows interactive measurement of
selected image points and the necessary GCP(s). It also includes
computation of the bias parameters for any number of images,
from any number of object points, and it carries out the
generation of corrected RPCs in a file format identical to that
originally supplied with either IKONOS or QuickBird imagery.
This file is thus suited to utilisation with standard
photogrammetric workstations that support stereo restitution via
RPCs. and it facilitates bias-free 3D ground point determination
to metre-level accuracy.
3. EXPERIMENTAL TESTING
3.1 HRSI test ranges
Implicit in the assumption that high accuracy geopositioning
can be achieved with bias-compensated RPC bundle adjustment
is that RPCs do in fact constitute rigorous reparameterisations
of the rigorous sensor orientation model. Thus, the APs A; - B»
will be modelling residual systematic error associated with
biases. In order to demonstrate the effectiveness of the bias-
compensated RPC approach, two test data sets of stereo HRSI
have been examined. One of these is a stereo triplet of IKONOS
Geo imagery, whereas the other is a QuickBird Basic stereo
pair. Shown in Table | are the essential characteristics of the
two HRSI data sets to be analysed. These are not the only stereo
and multi-image IKONOS and QuickBird configurätions that
have been metrically evaluated by the authors, but they
constitute two with GCP and image measurements of sufficient
accuracy to highlight error signal in sensor orientation at the
sub-pixel level.
The first testfield covers a 120 km? area of the city of Hobart
along with its surroundings. A very prominent feature in the
area, lying only 10km or so from the downtown area, is 1300m
high Mount Wellington. The Hobart test range was imaged in a
stereo triplet of IKONOS Geo imagery recorded in February,
2003. Of the images forming the triplet, the two stereo images
(elevation angles of 69°; base-to-height ratio of 0.8) were
scanned in Reverse mode while the central image (elevation
angle of 75°) was acquired in Forward mode. Hobart was
specifically chosen as a suitable testfield due to its height range
and the fact that the scene covered was largely urban, thus
providing excellent prospects for accurate image-identifiable
GCPs. A total of 110 precisely measured ground feature points
(mainly road roundabouts) served as GCPs and checkpoints. In
order to ensure high-accuracy GCPs and image coordinate data,
multiple GPS and image measurements were made for cach
GCP. with the centroids of road roundabouts being determined
by a best-fitting ellipse to six or more edge points around the
circumference of the feature, in both object and image space.
The estimated accuracy of this procedure, described in Hanley
& Fraser (2001) and Fraser et al. (2002), is 0.2 pixels.
The second testfield, for which there is both Ikonos and
QuickBird stereo imagery, covers Melbourne. Here we consider
only a stereo pair of QuickBird Basic images which exhibited a
pixel size of 0.75m and a base-to-height ratio of 1. The imagery
was recorded in July, 2003. The majority of the 81 GCPs used
in the Melbourne testfield were also road roundabouts, with the
26
remaining points being corners and other distinct features
conducive to high precision measurement in both the imagery
and on the ground.
3.20 IKONOS results
The results obtained in the RPC bundle adjustments of the
Hobart stereo triplet of IKONOS imagery are listed in Table 2.
The first row of the table shows the RMS value of coordinate
discrepancies obtained in a direct spatial intersection utilising
the RPCs provided with the imagery. A major component of
these checkpoint discrepancy values arises from the biases in
the RPCs. Post transformation of the computed ground
coordinates, utilising three or more GCPs, could be expected to
yield RMS accuracies at the Im level. The remaining rows of
Table 2 list the accuracies attained in the RPC bundle
adjustments with bias compensation, for different AP sets. As
can be appreciated, the resulting RMS values of checkpoint
discrepancies will vary depending upon the particular GCPs
employed. Those listed in the table are representative of the
many that were obtained.
Of most practical interest are the results obtained in RPC
bundle adjustments with the two shift parameters Ay, B,. It can
be seen that geopositioning accuracy to 30cm (RMS, |-sigma)
in longitude, and 70 cm in latitude and height are obtained with
just 2 GCPs, and indeed this result is achievable with one GC?.
Note for the case of a single GCP on the top of Mount
Wellington, ie. at a 1200m elevation difference from the
majority of the 109 checkpoints, accuracies in planimetry are
again at the 0.3 pixel level in the cross-track direction. The
RMS error in height is marginally larger than in the 2-GCP
case, but this likely represents the effect of a bias of the
adjusted position of the single GCP rather than any affine
distortion in the relatively oriented 3-image configuration. What
is certainly clear in the RPC bundle adjustments with shift
parameters is that terrain characteristics have no impact upon
the results. As regards the individual positional biases in image
and also object space, these ranged from 0.1 to 4m for the three
images of the Geo triplet. ;
The plots of image coordinate residuals shown in Fig. | provide
an insight into the question of whether there may have been
additional bias error signal in the RPCs, for example from time-
dependent drift effects. The residuals for the left-hand stereo
and near-nadir images displayed a quite random distribution,
suggesting the absence of any further systematic error. Fig. la
exemplifies this. However, the ‘right-hand’ stereo image. Fig.
Ib, appeared to display residual systematic error in the along-
track coordinate. It was found that while the use of drift terms,
especially Aj, produced a reduction in the RMS value of image
coordinate residuals for this image, from 0.32 to 0.25 pixels in
the line coordinate direction, there was no increase in
geopositioning accuracy. Grodecki & Dial (2003) have reported
that with IKONOS imagery drift effects would be unlikely to be
seen in strip lengths of less than 50km. The results obtained in
the Hobart testfield are consistent with this view,
notwithstanding the small residual systematic error pattern seen
in Fig. 1b.
Given the indications that the RPC bias has been adequately
modelled by the two shift parameters A, and Bg. it is not
surprising to see that the full affine additional parameter model
does not lead to any accuracy improvement. The best indicator
of the overall metric potential of the IKONOS stereo triplet is
listed in the last row of Table 2. This is the case where the RPC
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