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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part Bl. Beijing 2008 
2. IMAGE ORIENTATION 
The used satellite images have to be geo-referenced, this can be 
made by geometric reconstruction of the imaging, using 
orientation from the available metadata, improved by means of 
control points. The satellite information about the sensor 
orientation, based on GPS-positioning, gyros and star sensors is 
also distributed as rational polynomial coefficients (RPC). 
Approximate orientation procedures like 3D-affme 
transformation and DLT should not be used because of limited 
accuracy with basic images. 
The application of 3D affine transformation (standard and 
adding 4 unknowns) and the DLT for the Castelgandolfo image 
gives accuracy much bigger than ground sampling distance 
(GSD) in across track direction both in aft and in fore camera, 
just when 10 unknowns in 3D affine are used the Root Mean 
Square Error (RMSE) are equal to 2*GSD (Fig. 2). In the 
satellite direction movement the worse accuracy is in aft image 
with a gap when minimum points necessary are used in DLT 
transformation (Fig. 3). 
Cortosat - Comljandotfo &SÖ: 2.3 m MUSE CP in East component 
N* GCP 
Fig 2. RMSE at check points as function of the number of used 
control points of 3D Affine and DLT transformations 
[m] (East component) 
Cartolar - Castilgandolfo 6SD: 2.5 m RMSE CP in North component 
N* 6CP 
Fig 3. RMSE at check points of 3D Affine and DLT 
transformations [m] (North component) 
2.1 Sensor Oriented Rational Polynomial Coefficients 
The replacement model of sensor oriented RPC describes the 
image coordinates I, J by the ratio of two 3 rd order polynomials 
of the ground coordinates cp, X, h (Jacobsen 2008). The direct 
sensor orientation without correction by control points is 
limited approximately to a standard deviation of 70m (Jacobsen 
et al 2008). This has to be improved by means of ground control 
points, named also as bias correction. 
In an iterative procedure the geometric relation of the image to 
the 3D-ground coordinates is determined. 
This needs a two-dimensional transformation to the control 
points. Experiences showed the requirement of a two- 
dimensional affine transformation, so for the 6 unknowns at 
least 3 control points are required (Tab. 1). 
IMAGE 
SINGLE 
STEREO PAIRS 
SX 
SY 
SX 
SY 
SZ 
Mausanne 
aft 
2.4 
2.1 
2.1 
2.7 
3.4 
forward 
2.0 
2.1 
Warsaw 
aft 
1.4 
1.5 
1.3 
1.1 
1.8 
forward 
1.4 
1.3 
Tab 1. RMSE at control points of bias corrected RPC 
orientation [m] 
2.2 Geometric Reconstruction 
Since 2003, the research group at the Area di Geodesia e 
Geomatica - Sapienza Università di Roma has been developing 
a specific model, based on geometric reconstruction, designed 
for the orientation of imagery acquired by pushbroom sensors 
carried on satellite platforms. This model has been implemented 
in the software SISAR (Software per Immagini Satellitari ad 
Alta Risoluzione). The RPC (use and generation) and 
orientation model of stereo pairs models are also implemented. 
The model bases the imagery orientation on the well known 
collinearity equations including sets of parameters (Tab. 2) for 
the satellite position, the sensor attitude and the viewing 
geometry (internal orientation and self-calibration). 
The sensor attitude is supposed to be represented by a known 
time-dependent term plus a 2nd order time-dependent 
polynomial, one for each attitude angle; moreover a rotation 
matrix in the Roll-Yaw plane is used for describe the canting 
for the two camera: the Fore and the Aft cameras are canted at 
+26° and -5° in the along track direction respectively (Crespi, 
2008). 
The atmospheric refraction is accounted by a general model for 
remote sensing applications (Noerdlinger, 1999). The viewing 
geometry is supposed to be modelled by the pixel size and two 
self-calibration parameters, able to account for a second order 
distortion along the array of detectors direction. 
The approximate values of these parameters can be computed 
thanks to the information in the metadata file and these have to 
be corrected by a least square estimation process based on a 
suitable number of GCPs. 
Not all parameters described in Tab. 2 are really estimable; 
actually, all the parameters related to the satellite position 
together with (I 0 , Jo) are just computed according to the 
metadata information. 
Moreover, as regards the remaining parameters, a methodology 
for the selection of the estimable ones is implemented in the 
software SISAR (Giannone, 2006). This methodology is able to 
avoid instability due to high correlations among some 
parameters leading to design matrix pseudo-singularity; it is 
based on Singular Value Decomposition (SVD) and QR 
decomposition, employed to evaluate the actual rank of the