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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004
its performance and on real situations. The example here
proposed is a real case: the maps that have to be combined into
a single system are a cadastral one at scale 1:1000 and a
regional one at scale 1:5000. An area of about 4 Km! is
represented on the maps. The transformation was applied on the
homologous points automatically detected by the procedure
previously mentioned. In figure 9 the spatial distribution of the
homologous points and the corresponding multi-resolution
splines are shown. The five different resolutions are highlighted
with different grey gradation (higher resolution are darker). It is
important to notice that the heterogeneous distribution of the
control points makes in this case inapplicable the mono
resolution spline interpolation, at least if we are trying to
locally model the differences between the two maps.
(a)
Figure 9. Spatial homologous points distribution (a) and the
multi-resolution spline collocation (b)
The results obtained by using a multi-resolution approach are,
as expected, better than those due to the classic affine
transformation. To have an example of the improved
performances in figure 10 a detail of the overlaps between the
two maps by using the classic affine transformation and the
multi-resolution spline approach is shown.
Figure 10. Overlay of two maps using the affine transformation
(a) and the multi-resolution spline approach (b)
[t is evident that the localized deformation in the upper-left
corner of the map has been “catched” by the multi-resolution
transformation (b) with the consequence of the improved
overlap between the two maps.
3. CONCLUSIONS
The use of spline functions in modelling deformations between
maps, compared to affine or polynomial interpolation, allows to
have a greater number of coefficients to make more adaptive
and localized the transformation. The multi-resolution approach
here presented removes the rank deficiency problem that
ordinary spline approach suffers for. Moreover a statistical test
allows to choose the level of multi-resolution to be adopted in
order to better model the deformations between the two maps.
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