International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
determines the Steiner points, adds both to the data set. Since
the Delaunay criterion is re-established in the preliminary
triangulation, the shape of the integrated TIN may deviate
somewhat from the one of the initial DTM. The methods have
in common, that inconsistencies between the data are neglected
and thus may lead to semantically incorrect results. Rousseaux
& Bonin (2003) focus on the integration of 2D linear data such
as roads, dikes and embankments. The linear objects are
transformed into 2.5D surfaces by using attributes of the GIS
data base and the height information of the DTM. Slopes and
regularization constraints are used to check semantic
correctness of the objects. However, in case of incorrect results
the correctness is not established. A new DTM is computed
using the original DTM heights and the 2.5D objects of the GIS
data.
2. SEMANTIC CORRECTNESS
2.1 Consequences of non-semantic integration
In our investigations a digital terrain model (DTM) is
represented by a triangular irregular network (TIN). Bridges,
vertical walls and hang overs are not modelled correctly
because it is a 2.5D representation. The topographic vector data
we consider are two-dimensional. The topography is modelled
by different objects which are represented by single points,
lines and areas. The integration of the data sets leads to an
augmentation of the dimension of the topographic objects.
Figure 1 shows two examples of the non-semantic integration of
a DTM and 2D topographic vector data. The height values of
the lakes do not show a constant height level (left side of Figure
1). Several heights of the lakes near the bank are higher than the
mean lake heights.
At the right side of Figure 1 the roads are not modelled
correctly in the corresponding part of the DTM. The slopes
perpendicular to the driving direction are identical to the mean
slope of the corresponding part of the DTM. There are no
breaklines on the left and the right borders of the roads. Also,
some neighbouring triangles of the DTM TIN show rather
different orientations.
2.2 Correct integration
If we divide the topography into different topographic objects
(road, river, lake, building, etc.), like the data of a GIS, there
are several objects which have a direct relation to the third
dimension. These objects contain. implicit height information:
For example, a lake can be described as a horizontal plane with
increasing terrain at the bank outside the lake. To give another
example, roads are usually non-horizontal objects. We certainly
do not know the mathematical function representing the road
surface, but we know from experience and from road
construction manuals that roads do not exceed maximum slope
and curvature values in road direction. Also, the slope
perpendicular to the driving direction is limited.
Of course, all other objects are related to the third dimension,
too. But it is difficult and often impossible to define general
characteristics of their three-dimensional shape. For example,
an agricultural field can be very hilly. But it is not possible in
general to define maximum slope and curvature values because
these values vary from area to area.
The objects containing implicit height information which need
to be considered for the semantically correct integration can be
divided into three different classes (see Table 1). The first class
contains objects which can be represented by a horizontal plane.
The second class describes objects which are composed of
several tilted planes. The extent of the planes depends on the
curvature of the terrain; the planes should be able to adequately
approximate the corresponding part of the original DTM. The
last class shown in Table 1 describes objects which have a
certain relation to other objects. Bridges, undercrossings and
crossovers contain a certain height relation to the terrain or
water above or beneath.
Object Representation
Sports field, race track, Horizontal plane
runway, dock, canal, lake,
pool
Road, path, railway,
tramway, river
Bridge, undercrossing,
crossover
Tilted planes
Height relation
Table 1: Some topographic objects and their representation in
the corresponding part of the terrain
To integrate a DTM and a 2D topographic GIS data set in a
semantically correct sense, the implicit height information of
the mentioned topographic objects has to be considered. That
means, after the integration process the integrated data set must
be consistent with the human view of the topography and the
height representations as shown in Table 1 'have to be
represented correctly.
3. AN ALGORITHM FOR THE SEMANTICALLY
CORRECT INTEGRATION
The aim of the integration is a consistent data set with respect to
the underlying data model taking care of the semantics of the
topographic objects.
Topographic objects which are modelled by lines but which
have a certain width, are first buffered. The buffer width is
taken from the attribute “width” if available, otherwise a default
value is used. Thus, the lines are transformed into elongated
areas, the borders of which are further considered. The next step
of the algorithm is a non-semantic integration of the data sets.
Figure 1: Results of the integration of a DTM and a 2D vector data set without considering the semantics of the topographic objects,
left: lakes, right: road network
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