with a least-squares matching. Robust statistical methods
and the use of multi-image matching methods guarantee
that only precise and reliable nodes will be used for the
estimation of the orientation parameter. After the determi-
nation of the three-dimensional coordinates of all matched
nodes (see next chapter) edges have to be merged.
During this process the previously extracted edges will be
merged with the three-dimensional node points. Besides,
the merging algorithm has to connect edges, which lost
their nodes because of errors in the matching process or
because of less accuracy. The result is a 3D-model of the
microstructure. Fig. 4 shows the described processing
steps.
Image Data
Y
Feature Extraction
Edges Points
Y
Feature Matching
Y
Orientation
Y
| 3D-Point-Determination |
Y
> Feature Merging
Y
Visualization
Figure 4: Processing 3D-Models
3.4 3D-Point-Determination and DEM-Estimation
The next step is the determination of the 3D point co-
ordinates. If there exists only a small number of points it is
advantageous to determine this points within the block
adjustment, because of the highest accuracy of this
method. The estimation of a large number of points, for
instance required to reconstruct a whole surface, is per-
formed as a spatial intersection on the basis of the
parallel imaging equations (4), (5) using orientation para-
meters from the parallel-block adjustment. Additionally it
is possible to use the known distortion parameters, which
are known from a previous calibration of the used SEM.
By applying robust statistical methods, it is possible to
eliminate gross errors from the image matching process.
The 3D-Point-Determination takes place in two steps. The
first step is the evaluation of approximate values with
participation of all used images:
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After the evaluation of approximate values the point co-
ordinates will be estimated through spatial intersections.
This estimation uses least-squares methods under appli-
cation of all available images to achieve a high accuracy
and to detect gross errors.
In case of the reconstruction of a nearly continuous sur-
face with a large number of object points it is useful to
generate a regular grid of height points. For that purpose
a commercial DEM-Software is used (DEM = Digital Ele-
vation Model, in microsciences also called Digital Surface
Model = DSM). This DEM-Software provides standard
methods for the derivation of a regular digital elevation
grid from three-dimensional point clusters. It also enables
the derivation of further products, like profiles, perspective
views or shading maps. For further details, see Ebner et
al. (1980).
Figure 5: Three-Dimensional Point Cluster of a
Microprobe (Dimensions in um)
Figure 6: Digital Surface Model of the Microprobe
A common problem are incorrectly estimated point co-
ordinates, which are represented in DEM as peaks. The
reason for that failures are mostly incorrect matching
results, because of the texture, which is not suitable for
every grid point. There are several methods to remove
these failures: First we define a threshold value for the
correlation coefficient. The next step is a statistical control
of the three-dimensional point determination with Data
Snooping and a threshold for the mean error of the
coordinates. The last step is the definition of a working
area, especially in the z-axis. Due to this restrictions
failures in the DEM can nearly completely removed from
the original data.
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