akline
RE
TRACTION
on of gray value
tection
breakline detec-
esult of the sys-
introduced as
he next pyramid
en processed by
/stem provides a
'e precisely.
cing of the DEM
as of maximum
M posts and the
ine information.
or the DEM gen-
. approximations
breakline direc-
surface areas of
ion of maximum
curvature with the eigenvalue of the Hessian matrix. The result
is an approximate point information of the surface structure.
3.3 Vectorization
The point information of the surface structure is not very use-
ful for the further consideration during the surface reconstruc-
tion. Therefore it is necessary to subsequently tie up the
approximate breakline points as 3D polylines by using the ap-
proximate breakline directions. The result is a rough vector
representation of the surface structure. These approximate
breaklines sufficiently represent the structure in object space
and can be used as a preliminary description of the surface
characteristic features.
3.4 Feature Extraction
The information about the gray value edges, hence the in-
formation about possible 3D structure lines, is fully contained
in a gradient operator (e.g. Sobel operator). Therefore we try to
merge the structure information from the object space and
from the image space. To get these 2D structure lines only in
the areas we are interested in, the initial breakline areas have
to be transformed into the image space. The gradient operator
has to be applied in the projected breakline areas and provides
2D polylines in image space, that correspond to the approxi-
mate 3D polylines in object space.
3.5 Verification
The proposed method avoids to initially start the breakline
detection from image space since gray value edges do not
necessarily correspond to breaklines. On the other hand if
breaklines are detected in object space and are tracked back
into the image space by verifying them with gray value edges,
they correspond to real breaklines. Hence, we compare the
transformed 3D polylines from the vectorization with the 2D
polylines from the feature extraction and determine the gray
value edges which correspond to real breaklines. Thus, the re-
sult is the remaining gray value edges and hence breakline fea-
tures in the image space.
3.6 Feature Matching
The matching part of the automatic breakline detection con-
tains the matching of the elements of the remaining gray value
edges in the image space and the transformation in the object
space.
3.7 Evaluation
The final breaklines are optionally evaluated by fitting an ob-
ject model (e.g. averaging spline) to the breakline points corre-
sponding to gray value edges.
4 PRACTICAL RESULTS
4.1 General remarks
The practical investigations refer to the already existing part of
the development - DEM generation. They elucidate the differ-
ences of the mentioned filter methods (chapter 2). The results
of the first geometrical approximation of the breakline areas
and the corresponding breakline directions presented for an
open coal-mine excavation area and a mountainous terrain are
shown.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
4.2 Properties of the filter methods
The differences of the global and adaptive filtering of the DEM
takes the most effect for structure lines not parallel to the X- or
Y-direction of the object coordinate system. Therefore we
show the different effects of both filter methods for a rectangu-
lar area defined in object space which contain the mentioned
structure lines (e.g. road, forest).
The following DEM's in this chapter refer to the indicated part
of the mountainous data sample and correspond to the marked
image section in figure 4.1.
bg i
Figure 4.1: Image section corresponding to the DEM
Figure 4.2 and figure 4.3 show the DEM's of the global filter-
ing and adaptive filtering for the surface reconstruction. Both
filter methods represent an edge preserving filter but neverthe-
less they provide a different result. The height differences of
the DEM posts are summarized in a differential DEM in figure
4.4.
har 7 hoa 7 Bagentive
The main differences obviously occur in areas of local curva-
ture maximum, where the corresponding breakline direction is
not parallel to the X- and Y-direction (i.g. road). That means,
these breaklines are better recognized by the adaptive edge
preserving filter, hence the smoothness constraints (curvatures,
torsion) are more weighted down. Therefore more discontinu-
ities in the data are maintained and the reliability for the auto-
matic detection of the approximate breakline points and the
corresponding directions are more efficient.
Model errors due to the spacing of the DEM posts, determine
to a large extent the accuracy of the DEM. The adaptive filter
method optimizes the detection of discontinuities, especially
of breaklines rotated against the object coordinate system.
This optimal detected structure information is used to adapt
the grid width in the breakline areas. Thereby we are able to
minimize these model errors by using the adaptive filter
method.
The influence of the adaptive characteristic on the DEM is re-
stricted to undulating terrain. In areas of local curvature maxi-
mum we have positive or negative height differences in the
differential DEM. The sign of the curvature determines the
sign of the height difference. Basically the global filter method
smoothes structure lines during the surface reconstruction
which are not fully recognized.
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