The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008
In this work we estimated the MTF for Cartosat-1 images
starting from the “edge method” proposed by (Choi, 2002), then
recently revised by (De Vendictis, 2008).
The initial task of the edge method algorithm is the
identification of suited pseudo-rectilinear target edges,
approximately oriented along and across scan direction, that
show a blurred line edge between two relatively uniform
regions with different intensities. Assuming that the chosen
edges represent a straight line, the alignment of all edge
locations is done with a least squares error fitting technique.
The edge profiles, which are centred at each edge pixel and
have the direction perpendicular to the edge, are interpolated
with cubic spline functions and averaged to obtain a curve that
represents the response of the sensor to the input signal. The
ESF is obtained interpolating this curve with an analytic
function that reduces the noise (De Vendictis, 2008). The ESF
is then differentiated to obtain the LSF and the LSF is Fourier-
transformed and normalized to obtain the corresponding MTF.
The computed MTF is scaled in the frequency axis in order to
represent the calculated MTF in terms of the Nyquist frequency
of the image. In addition, the Full Width at Half Maximum
(FWHM) value is computed.
20 Edges
Along track direction
Cross track direction
MTF at
Nyquist
FWHM
(pixels)
MTF at
Nyquist
FWHM
(pixels)
BANDA (-5°)
0.26
1.45
0.16
1.75
BANDF (+26°)
0.15
1.87
0.06
2.49
Table 1. MTF and FWHM estimation results
As can be seen from Table 1, the MTF values for along-track
direction are always larger than those for cross-track direction
and the BANDA has a remarkable better quality than BANDF,
both with respect to FWHM and MTF.
GCPs
ERDAS - RPC Order 1
SAT-PP - RPC Order 1
PCI
- Rigorous model
E (m)
N (m)
H(m)
E(m)
N (m)
H(m)
E(m)
N (m)
H(m)
4
1.53
1.52
1.69
1.32
1.45
1.29
-
-
6
1.56
1.42
1.70
1.31
1.32
1.25
4.31
2.60
1.66
9
1.48
1.56
1.64
1.17
1.38
1.17
0.98
1.34
1.20
Table 2. RMSEs (in meters) at check points after image orientation using three different approaches
Figure 4. Distribution of residuals in planimetry (left) and height (right) at GCPs and CPs after orientation in PCI with a rigorous
model and 9 GCPs.
4 IMAGE ORIENTATION
For the image orientation two different approaches were
adopted: the rigorous model, implemented in the PCI-
OrthoEngine software, and the Rational Function Model (RPC)
with 1 st order correction, included in the ERDAS Imagine and
in the SAT-PP (Satellite Image Precision Processing) software,
developed at the ETH Zurich. According to our experiences
from previous tests on Cartosat-1 stereopair orientation
(Barbato et al., 2007), the RPC model with no correction is not
sufficient. The stereopair was oriented using 4, 6 and 9 Ground
Control Points (GCPs), and the remaining points were kept as
Check Points (CPs). For each number of GCPs an optimal
distribution was used. The results were evaluated in terms of
RMSE on the CPs. In order to detect blunders, the orientation
was performed using all points as GCPs. Among the available
25 points, 20 points were kept for the orientation. The results
obtained from image orientation, summarized in Table 2, show
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