In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. IAPRS, Voi. XXXVIII, Part 3/W4 — Paris, France, 3-4 September, 2009 
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At the present time, we decided to compute the aperture in the 
simplest way possible to rapidly have a functioning iterative 
process. Improvements of the structure model will be 
considered at a later stage. Therefore, apertures are computed 
directly from the local height difference and from the local 
incidence angle, not taking into account the base of the dihedral 
(fig. 3). This can lead to an overestimation of the dihedral 
aperture. 
Figure 3: Basic model of dihedral back-scattering 
2.3.3 Dihedral aperture / surface scattering limit: If 
dihedral backscattering process may be considered as 
predominant in the presence of man-made structures in terms of 
backscattered energy, surface scattering must also be taken into 
account for open areas that are also well present at VHR. 
Considering only dihedral backscattering process tends to 
segment the structure; each time a local height is lower than the 
preceding one, the aperture, and so the backscattered energy, 
will be considered as null. 
Therefore, we determined a simple height variation limit above 
which, we consider that dihedral backscattering process occurs 
and below which, surface backscattering is taking place. The 
chosen limit is simply the one inducing layover. If the local 
height difference induces layover, we consider that we have to 
deal with a dihedral structure, if not, we consider we have to 
deal with an elementary surface (fig. 4 & 5). 
Figure 4: Dihedral structure - surface scattering limit 
Above the layover limit, the weight of a point will be calculated 
as its dihedral aperture. Below this limit, surface scattering will 
be considered. 
Figure 5: Surface scattering component 
In case of surface scattering, not taking into account a specific 
local backscattering coefficient, the backscattered energy is 
taken as proportional to the beam section intercepted by the 
considered pixel. In place of dihedral aperture, we can thus 
speak in terms of pixel aperture (fig. 5). 
As depicted in figure 5, the intercepted beam section will 
decrease with the height variation between two pixels up to zero 
when the shadowing limit is reached. 
In terms of backscattered energy, surface backscattering process 
has a much lower weight than dihedral reflection. Therefore, in 
practice, a fix coefficient will be applied between both aperture 
types. At this level, a local backscattering coefficient and/or an 
emission diagram at pixel level depending on the local slope 
and on the local incidence should be considered as 
supplementary weighting factors. 
It follows that for a given DSM we define a structure that allows 
taking into account two backscattering process: dihedral and 
surface, each with a different weight. Once again, for the sake 
of simplicity, the current model attributes the computed pixel 
aperture to the point located at the current position i with height 
hj as if the point was a phase centre, even if considering surface 
scattering. 
Consequently, our model defines only point scatterers located 
on a ground range - azimuth mesh for which height are issued 
from the projected DSM that must be updated and improved 
iteratively. At each of these point scatterer position, we will 
consider we have a point scatterer response whose relative 
intensity will be detennined by the computed aperture. 
3. BACK AND FORTH REFERENCING PROCESS 
The back and forth referencing and projection processes we 
have implemented were specifically developed for space-borne 
sensors. Therefore, no flight motion compensation is considered 
here. Referencing is thus deduced considering an analytical 
trajectory of the sensor on its orbit, a fix Doppler cone for the 
whole scene and a reference geoid (WGS84). 
3.1 Ground range referencing 
Existing geo-referencing processes allows finding geocentric 
Cartesian coordinates of a given point in slant range coordinate 
of know height above the geoid. This geocentric coordinate can 
then be translated in geodetic coordinate and converted in 
longitude latitude on the considered datum. Therefore, there is 
an analytical link between the slant range coordinates of a point 
of known altitude and its coordinate in a geocentric Cartesian 
system or in a given cartographic system. 
The ground range coordinate of a point given in slant range is 
defined as the length of a curve segment, which is the 
intersection between the chosen geoid and the Doppler cone, the 
length being calculated through integration from the minimum 
slant range point to the considered point. This integration makes 
the reverse calculation complicate. Therefore, in the process of 
calculating the ground range coordinate of a point, this latter 
one is first geo-referenced on the considered geoid, in longitude 
- latitude coordinate. This allows building a map linking ground 
range coordinates with geographical coordinates. This map is 
then fitted by a second order polynomial for both the longitude 
and the latitude.