International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
In general the widening distance relies on screen resolution and
the distance to the observers’ position. Furthermore no
additional information concerning the relative importance of the
streets was taken into consideration. In a more detailed
differentiation main roads have to be stronger emphasized than
minor streets.
In figure 3, a cross section demonstrates the principle of the
enhancement together with the alteration of the adjacent
regions. The point positioned in the centre marks the middle
axes of the street, the black line shows the original cross
section. In grey, the enhancement of the street is illustrated and
the dashed black line shows the enhancement in combination
with a linear weighting function for the adjustment of the
bordering regions.
—— Original data
325 ~
—- Enhancement of streets
320 4 oa ; 7
- - - Enhancement with linear weighting /
315 3 function for adjustement A
= n r adj m Ser
z "
S 310 P
E un
— 395 j 2^
f y «uf
> 300 - t
: uo.
295 4 vt |
290 4 ^ ;
7 Displacement
285 3 7 T T '
0 10 20 30 40 50 60 70
Profile length [m]
Figure 3: Cross section
The drawback of this solution is the loss of the original height
values both within the buffer and the region of interpolation.
Only the height of the broadened street and the values within
the given distance from the middle axes are taken into account.
The adjustment merely takes place in terms of smoothing on the
level of representation. The correctness of the data is seriously
affected by simply replacing values within the DTM. Thus in
the example height values are lost in a corridor of 30 m width.
To solve this problem, methods of displacement have to be
applied in combination with the enhancement procedure
3.3 Displacement
The first issue to consider is the sphere of action in which the
adjustment takes place. In the first attempts, when different
interpolation approaches were tested, the adjustment took place
within fixed ranges. Instead of just smoothing the changeover
within this area by newly interpolating, the height values could
be displaced within this area to avoid a loss of information (see
fig. 3).
Displacement operations can result in deformation within the
data set. Deformation in connection with the displacement
becomes the more apparent, the smaller the region is in which
the modification takes place, because the overall alteration is
spread over a wider area. This leads to the conclusion, that a
sphere of action with maximum size results in minimal
deformation regarding the entire data set. For this reason, the
whole DTM has to be taken into consideration for the
displacement procedure. The inherent height values have to be
moved in such a manner, that no overall height information is
lost. In case of objects existing on top of the terrain surface,
they have to be preserved in cognizable form. Considering the
whole DTM, a region of influence has to be assigned to each
street, containing the respective points to edit. These regions are
assigned by calculating a Voronoi-diagram for the street
segments.
For the raster cells within each polygon, the assigned street
object is the one within the shortest distance. Thus each voronoi
cell represents the sphere of influence belonging to one
particular street section. Hence within each voronoi cell, the
DTM is modified depending on the values of the associated
middle axes. The calculation of the voronoi diagram was
undertaken with VRONI, an algorithm implemented by Held
(2001). The result of this calculation is shown in figure 4.
Figure 4: Voronoi cells (in different grey scales) calculated with
VRONI (Held, 2001), for the street segments (represented by
black lines) for a section of the city of Stuttgart.
In this illustration, the Voronoi cells are marked with different
grey scales, the street segments are represented by the black
lines passing through the polygons. For every street segment,
the cells contained in the appendant voronoi polygon are
considered when recalculating the cell values. For these regions
an appropriate displacement method has to be chosen.
4. CONCLUSIONS AND FUTURE WORK
While generalizing a DTM the enhancement of relevant objects
is of great importance. For this reason, the objects have to be
enlarged, which leads to problems with adjacent areas and
objects. In a first attempt, the adjustment merely was
undertaken by smoothing the regions adjacent to the middle
axes. This led to a purely visual change involving the loss of
information within this regions.
Therefore, displacement methods have to be investigated with
regard to their usability in the third dimension. Possibly, least
square adjustment or a finite elements approaches used for 2D
generalization could be transferred.
5. REFERENCES
AdV, 1998. Amtliches Topographisch-Kartographisches
Informationssystem (ATKIS). Technischer Bericht,
Arbeitsgemeinschaft der Vermessungsverwaltungen der Länder
der Bundesrepublik Deutschland.
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