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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