The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008
Sensor
GSD (m)
Stereo angle
(degree)
MOMS-2P
18
(2 x) 21.45
SPOT-5 HRS
10/5
40
ALOS / PRISM
2.5
(2 x) 23.8
CARTOSAT-1
2.5
31
IKONOS-2
1
~30
(Special: 10/6)
QuickBird
0.6
~60
Table 2: Stereo angles and stereo missions
2.2 RPC correction
In (Lehner et al. 2006) it is shown for the stereo pair M1A/F
that for a full scene a pure bias correction of RPC results in
residuals which are not acceptable: larger than 1 pixel and with
systematic behaviour. Since then better GCP could be retrieved
for all stereo pairs. By their use this finding can be consolidated:
for full CARTOSAT-1 stereo pairs the correction of the
provider supplied RPC via an affine transformation is necessary
to achieve sub-pixel accuracy. Table 3 gives the summary of
bias versus affine correction for all the stereo pairs used at DLR
for CSAP.
Image
Number
of
GCP
Standard deviation of residuals after
bias correction
affine correction
row
column
row
column
Cat-A
70
0.74
0.58
0.51
0.41
Cat-F
68
1.64
0.53
0.56
0.44
MIA
31
1.39
3.38
0.76
0.56
M1F
30
2.38
4.46
0.73
0.68
M2A
9
1.12
1.46
0.43
0.45
M2F
9
1.59
1.20
0.34
0.33
Bav-
AT
14
0.48
0.56
0.35
0.53
Bav-FT
14
0.80
0.64
0.64
0.62
Bav-A
full
scene
30
1.17
0.60
0.50
0.54
Table 3: Standard deviations of residuals at GCP after bias and
affine correction of RPC for various CARTOSAT-1 stereo pairs
For smaller parts of the images as for the Bavarian Taching test
area (GCP only in this area indicated by the image names Bav-
AT/FT - this is about 1/9* of a full scene) a bias correction may
lead to acceptable results for this sub-area. In order to illustrate
the nature of the residuals for bias and affine RPC correction
the shifts are plotted in figures 1 and 2 for the Catalonian case
with the large number of accurate GCP. It can be seen that the
pattern of the residuals in the bias case is rather complex and
can not even be handled by just an additional rotation. In
contrast, the residuals in figure 2 from the correction with an
affine transformation do not show any systematic behaviour. Of
course, if only an inadequate distribution of GCP is available it
may be worse to do affine instead of bias correction. A well
distributed set of GCP of high accuracy is needed for an
optimal result.
In (Lehner et al. 2007) it has been reported already that forward
intersection results are often poor without RPC correction (too
large residuals in image space).
Figure 1: Residual vectors from bias correction for the 68 GCP
for Cat-F
Figure 2: Residual vectors from affine transformation correction
for the 68 GCP for Cat-F
2.3 RPC forward intersection
Forward intersection is done via iterative least squares
adjustment using 2n (for n stereo partners) observation
equations (Grodecki et al. 2004, Lehner et al. 2006). Normally,
in this report on CARTOSAT-1 n is 2 and 4 equations are
established per stereo tie point for the derivation of the 3 object
space coordinates longitude, latitude and ellipsoidal height in
WGS84 datum. The initial values for the object space
coordinates longitude and latitude are derived from an affine
transformation using the comer coordinates given by the image
provider. Initial height values are taken from a DTM (or,
alternatively, the mean height of the area under investigation
can be used - this is not critical for the convergence). Normally,
convergence is achieved after 2 iterations. If a DTM/DSM is
given as an additional input a statistic of the differences of the
generated heights and the reference DTM/DSM heights is
established.
The residuals in image space can be used for blunder detection.
Of course, only residuals in cross track direction will be
effective because wrong row coordinates of tie points are
translated into wrong height values if only two stereo partners