In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. IAPRS, Voi. XXXVIII, Part 3/W4 — Paris, France, 3-4 September, 2009 
For a given point in the simulated image, we have the mapping 
that lists the points of the seed DSM with their respective 
weights intervening in the simulation. Conversely, we also have 
the reverse mapping that, for a given point of the seed DSM, 
lists points in the simulated image into which the considered 
DSM point intervene with respective weights. It is this reverse 
mapping that is used in the DSM modification process. 
5.1 Normalisation 
To be correct, the simulated image is considered as being an 
intensity image within an unknown proportionality factor. 
Before being usable as a valid scene for comparison with the 
really detected image, the simulated one must be normalized. 
The normalisation factor is simply the ratio of the integral of the 
backscattered energy measured in Digital Numbers (DN) in the 
detected image to the integral of simulated energy. 
After normalization, both images represent the same energy 
globally backscattered by the whole scene, which allows a 
comparison on a point-by-point basis. 
5.2 Improvement criterion 
The chosen comparison criterion is simply the local energy 
ratio. In other words, if the detected energy is higher than the 
simulated one, the underlying aperture used for the simulation 
must be increased proportionally. 
In the facts, several apertures intervene with different weights in 
the simulation of a point. Therefore, we work in the reverse 
way, using the reverse mapping. For a given point of the DSM, 
the reverse mapping gives us the list of all simulated point into 
which the considered DSM point intervene with corresponding 
weights. Consequently, we perform a weighted average of the 
energy ratios on these simulated and detected points. This 
weighted average gives us the proportionality factor that should 
be applied to the underlying aperture. 
Whatever the considered backscattering process, apertures are 
proportional to the local height difference between consecutive 
points in ground range. Therefore, the proportionality factor can 
directly be applied to the local height of the DSM under 
concern. 
To summarize, DSM points are corrected sequentially in ground 
range using a weighted average of intensity ratio calculated on 
several points in slant range - azimuth. These slant range points 
are those for which the DSM point under concerns plays a role 
through the aperture it generates. 
5.3 Iterative process 
When the corrected DSM is issued, the whole process can be 
reiterated, starting anew from this new DSM. This latter one 
will thus be used to compute a new aperture structure and to 
compute the ground to slant range projection mapping. 
The mapping will be used in an additive way to generate a 
simulated SAR intensity image, which, after normalization with 
respect to the detected one, will be used for DSM improvement. 
The simulated scene shown on figure 7 can thus be considered 
as the first iteration of the iterative process described here 
above. 
Figure 8 shows the second iteration of the simulated scene so 
obtained. The simulated scene appears still of poor quality, but 
some structures appears more clearly. Corrections with respect 
to the first iteration are quite important, and mainly a first 
segmentation between highly urbanized areas and open areas 
has roughly been made. 
Figure 8: Simulated SAR scene after 2 iterations 
From a computational point of view, in debug mode, one 
iteration takes about 4 minute a run for a seed DSM of about 
2000x2000 points. This computation time being reasonable, up 
to 25 iterations have been performed. Figure 9 shows results 
obtained after 4 and 12 iterations. Figure 10 shows the last 
iteration along with the really detected scene. 
Figure 9: Simulated SAR scene obtained after 4 (left) and 12 
(right) iterations 
Figure 10: Simulated SAR scene obtained after 25 iterations 
(left) and really detected one (right) 
Clearly, the iterative process converges toward a stable 
simulation. Qualitatively, convergence appears to be more rapid 
between the few firsts iterations, while improvement between 
iteration 12 and 25 becomes less evident. Therefore, the 
proposed process seams to converge monotonically toward a 
solution. 
It must be noted that the iterative process converges toward a 
solution that is linked to the underlying aperture model, which 
in turn, is linked to an improved DSM. Our “improved” DSM is 
thus “one possible representation of the observed surface”. 
This possible representation of the observed surface is the one 
that can be obtained with the developed structure model and 
using a peculiar set of parameters. 
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