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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
6. ORTHORECTIFICATION 
In order to make the orthorectification it is necessary to use a 
mathematical model which allows to put in relationship pixel- 
coordinates into the image space with coordinates of the 
corresponding points into the object space. 
In the described experiment, orthoprojection were executed by 
using PCI Geomatica 9.0 Orthoengine module. This software 
allows to use the following four different models: 
» Satellite Orbital Modeling (this class include the 
Toutin model) 
> Polynomial Model 
» Thin Plate Spline Model 
> Rational Functions Model (RFM) 
All these, except for the Toutin model, are non-parametric 
models. In the non-parametric models the transformation 
between image space and object space is performed through 
mathematical functional relations that don't need an aprioristic 
knowledge of the parameters describing the platform, the sensor 
and the projection system. 
To choose the proper model, it was necessary to consider that: 
> in the case of IKONOS image, there was a lack of 
information (satellite and sensor data), which didn't 
permitt to work with a rigorous model; 
> images were provided geometrically pre-processed; 
» in the three examinated cases, investigated territory 
showed significant altimetric variations. 
This combination suggested the opportunity to apply the 
Rational Function Model (RFM) (Dial G., Grodecki J., 2003). 
This is a non parametric model, constituted by four polynomial 
functions: the ratio of two polynomial functions is used to 
zalculate row pixel (i) positions and the ratio of the other two 
functions is used to calculate column pixel (j) positions. 
Polynomial are shaped as follows: 
‚ORT 
POCY Z7) 
RAT) 
P(X,Y,Z) 
m, m, m3 
Dea. 
i-0 j-0 k-0 
Coefficients (aj) in the functions, named Rational Polynomial 
Coefficients (RPC), can be different in number, depending on 
the grade of the polynomial. They can be known, since they are 
given by the image agency which distributes image, or they can 
be calculated indirectly, through a number of GCPs equal to: 
2n-1, where “n” is the number of RPC coefficients. 
In order to orthorectify the IKONOS Geo and QuickBird 
Standard images, the RFM model was used. Particularly the 
model was used with two configurations of 10 and 20 
coefficients. The coefficients was calculated starting from a set 
of 19, 25, 30, 39, 45 and 55 GCPs. Another set of 15 points 
(CPs) was considered to check the geometric accuracy of the 
ortorectified product. The Basic QuickBird image of Caselle 
Torinese was orthorectified by using the parametric model of 
Toutin, which requires a low number of GCP: in this case, a set 
of 9 GCPs and 9 CPs was used. 
Figures 2 and 3 show the location of GCPs and CPs on the 
IKONOS images; figures 4, 5. 6 and 7 on the QuickBird 
images. 
  
Figure 2. GCPs (red color squares) and CPs (blue color 
triangles) on the IKONOS image of Contessa 
  
  
Figure 3. GCPs (red color squares) and CPs (blue color 
triangles) on the IKONOS image of Palermo