1 Spatial Modelling of the Terrestrial Environment - Georeferencial

124 Spatial Modelling of the Terrestrial Environment
Points
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Sparse DEM
r=5; t=2
r=5; t=1
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points removed
ME (m)
SDE (m)
r=10; t=0.5
r=15; t=2
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r=15; t=0.5
r=20; t=2
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r=25; t=1
r=25; t=0.5
Figure 6.5 The effects of different values of search radius (r) and tolerance (t) upon the number
of points, mean error and standard deviation of error, using approach 1 for the test area shown
in Figure 6.4(a)
and this is reflected in the significantly larger number of data points removed with the 0.5 m
tolerance as compared with 1 m and 2 m tolerances. This emphasizes the basic problem
with any type of thresholding like this: as tolerance is reduced, smaller reductions in SDE
occur for proportionately larger numbers of points lost. There is a tendency towards the
loss of greater amounts of potential ‘signal’ as the boundary between signal and ‘noise’ is
approached. On the basis of the theoretical reasoning above, given the relatively low relief
of this surface in relation to the large amount of available data, it was decided to adopt a
radius of curvature of 20 m with a SD tolerance of 0.5 m (Figure 6.4(i)). It is clear that
some, but not all, of the error in Figure 4(c) has been removed by using a local SD filter.
The main limitation of the approach above is that it is not as topographically sensitive as it
could be. The SD is locally determined, but there is no variation in tolerance level in relation
to the expected standard deviation. As a result, there is a greater probability of removal of
correct points (e.g. along near-vertical channel banks) or retention of erroneous points in
areas of greater rate of topographic change than in those where the surface topography is
smoother. Thus, as a generic method for the identification of DEM error, the success of the
method will be spatially variable in the presence of spatial variation in natural topographic
variability. It is likely to fail over very rough surfaces where spatial structure in surface
variability is the norm. A second method sought to address this problem and is based upon
the observation that DEMs collected at coarser resolutions using digital photogrammetry
tend to be smoother. The method also reflects the hierarchical nature of the stereo-matching
used here. The stereo-matching was area-based, the algorithm produces elevation averages
weighted over a given template. Thus, coarser resolution DEMs use a large template in the
image (i.e., image area) to determine elevation. This tends to increase the precision of the
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metres