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ellipses) caused with deficient contour lines in the river
beds (right) for the region Krsko (1).
5.2 Extraction of characteristic points and lines
Much better results were reached by detection and
extraction of topographic features (ridges, summits,
saddles, drainage lines and valleys) from contour lines.
We applied one some possible methods which produce
appropriate results. This expert system bases on TIN
(triangular irregular network), created from contour lines.
Principle of extraction characteristic lines is founded on
determination and connection previously detected
horizontal triangles of TIN to ridge or drainage lines. With
interpolation and extrapolation considering contour lines,
missing characteristic points are determinated (Heitzinger
and Kager, 1998).
Figure 7 shows that we can get quite good results also for
the karst region (3), where the relief morphology is very
complex. Especially generated characteristic points as
bottoms of the sinkholes leads to most distinctive
improvement to interpolated karst relief.
Figure 7: Extracted characteristic points and lines at karst
region (3) are shown as black points and lines. Grey lines
are vector contour lines.
A side product of TIN was also a DEM with resolution of
40 m, which bridges missing data of contour lines,
especially at the alpine regions where large “holes”
appear without of any data. Additional datasets produced
from contour lines which were used for interpolation are:
characteristic topographic points,
characteristic topographic lines,
DEM 40 from TIN.
6. DTM MODELING
For modeling of a DTM 25 the program package SCOP,
which is independent program system for the computation
and utilization DTM, was used. The main advantage of
this software is ability to use data with different accuracy
in the interpolation process, what was our very important
preliminary condition. Module SCOP.TRI includes
powerful tool for enhancement of contour line data with
characteristic points and lines. Method for robust
estimation in module SCOP.DTM can be useful for
correction of gross errors in input data (Ecker, 1999). And
not the least, the SCOP produces DTM with relevant
structure.
6.1 Interpolation methodology
Interpolation method used is known as “least squares
interpolation” or “linear prediction”. In geostatistics the
method is known as “kriging” (Kraus, 1998). Method
bases on interpolation with least squares which requires
the search for the minimal variance.
Practically and shortly, this local interpolation method
works with so-called computing units. It is attempting to
find suitable function (theoretical surface) regarding to
influence of the particular points, to which filter value
(variance) has to be assigned. Filter values also control a
degree of smoothing the surface.
The data for interpolation was divided to particular classes
with regard to type and accuracy. For each class different
filter values were used for interpolation:
1) bulk points;
DEM 100,
DEM 40 from TIN,
2) spot heights;
geodetic points (in this case used only as
reference),
characteristic topographic points,
3) form line points;
contour lines
characteristic topographic lines,
4) break lines (we haven’t any data for them).
The lowest filter values were assigned to spot heights and
the highest to bulk points. Geodetic points were used only
as reference points for testing of input data.
6.2 Results of DTM modeling
The results of modeling the DTM / DTM 25 are very
promising. Table 2 shows difference between accuracy of
the vector contour lines and produced DTM 25.
Parameters indicate improvement for all morphological
classes, especially for Alpine areas. Implication of
characteristic points above all in interpolation, caused also
reduction of average distance according to reference
points, except at flat areas where these points usually
aren’t present.
Morph, classes
Contour lines
DTM / DEM 25
Flat surface (1)
Hills (1)
Mountainous (2)
Karst region (3)
1.5 m / 0.3 m
5.0 m / 2.5 m
10-40 m / 3.0 m
4.0 m / 2.0 m
1.2 m / 0.3 m
4.0 m / 2.0 m
10.0 m / 2.7 m
3.0 m / 0.5 m
Table 2: Morphological classes from three test regions
(1-3) with parameters: RMS error/ average deviation from
the reference points.
Figure 8 shows evidently improvement of interpolated
DTM 25 (the right picture) at the areas without contour
lines. There are not noticed large triangles. For the other
three test regions improvements are better statistically
than visually perceived.
