Full text: CMRT09

```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
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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