; the esti-
a mathe-
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ree trans-
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eters for
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points in
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e for this
required
chniques
leasuring
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itomation
use fea-
h feature
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ch image.
finition of
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Ited, it is
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).
rientation
age. The
o central
because
x, 2 m, (bi, (x- xo) * bio *(Y — Yo) + D45 : Z) (4)
y; 2 my : (ba -(X— Xo) * bz2 (Y - yo) t bas : Z) (5)
coordinate origin
elements of rotation matrix (Rüger et al., 1987)
Xo» Yo
b,1-023
In order to define an accurate scaling factor and to in-
crease the stability of the orientation process, it is pos-
sible to measure a horizontal distance with the SEM and
to use it in the block adjustment.
In addition to the orientation and scaling parameters the
affine factor and distortion parameters can be estimated
through this procedure (El Ghazali, 1984), (Gleichmann et
al., 1994). Using a known reference probe, it is possible to
perform a calibration of the SEM. Usually a calibration is
performed before the surface measurement of a micro-
probe. The resulting parameters can be used in the fol-
lowing steps of orientation and point determination. Under
constant imaging conditions it is even possible to get the
scaling factor from the magnification of the SEM.
3.2 Area-based Matching by Image Correlation
Homologue image coordinates of microprobes with nearly
continuous surfaces and good texture features are mea-
sured with an area-based matching method.
Image Data
Y
| Orientation Processing
à
Area-Based Matching
Y Y
3D-Point-Determination
Y
DSM Processing
Y
Visualization ©
Figure 3: Processing Surface Models
The applied method of image correlation is widely used,
yielding reliable results with objects presenting a good
texture (König et al., 1987). It is useful to divide this
method in two steps:
a) Normalised Cross-Correlation
b) Least-Squares Matching
In case of the normalised cross-correlation, a pattern
matrix is shifted pixel by pixel across the search matrix of
a corresponding image, and the cross correlation co-
efficient is calculated each time. The maximum correlation
coefficient indicates the best match and defines the
homologue point.
The results of the normalised cross-correlation represent
the approximation values for the least-squares matching.
227
This method uses a geometric and a radiometric trans-
formation on the basis of a least squares estimation in
order to compensate both distortions of the image in-
formation and differences in brightness and contrast. Re-
solving a system of equations containing all geometrical
and radiometric coefficients yields results in the subpixel
range. To facilitate the availability of approximate values
an image pyramid approach is used, which is executed
systematically from the top down to the original image.
Fig. 3 shows the processing steps of microprobes with
nearly continuous surfaces and good texture features.
Assuming successful results from the matching process,
the obtained data can be used for a Digital Surface Model
(DSM) after the 3D-Point Determination (see chapter 3.4).
3.3 Feature Extraction and Feature-Based Matching
Because of the characteristic edge structure in relation
with poor texture features of the surfaces, the evaluation
of corresponding features in images, taken from micro-
structures and microdevices, represent the greatest chal-
lenge for the automatic processing of 3D-models.
There exists a lot of feature-based matching methods, but
there is no algorithm available, which is suitable for all
different kinds of objects and the great demands required
for the automatical three-dimensional reconstruction of
these objects. But it is possible to select suitable methods
for different tasks.
Interest operators are used to get pairs of homologue
image points for the orientation process. The function of
interest operators is to extract features from digital image
data, which differ significantly from their environment. If,
however, oriented image data are already available, then
the image features detected can be verified without any
problems on the basis of the known imaging equations. In
other cases when the orientation of the images is not
known, the image matching is much more complicated
because the results obtained during the processing of the
image data by means of an interest operator differ from
each other. The consistent application of statistic test
methods in connection with the robust least-squares
estimation of an affine transformation between the detec-
ted features (Fórstner, 1986) serves this purpose just as
the verification of the matched pairs of images by means
of the least-squares matching.
Edge matching methods serve suitable conditions for the
three-dimensional reconstruction of structures with edges
and poor texture. One approach is the method of dynamic
programming (Li, 1990). The basic idea is to match not
only pairs of edges with each other, but to include the
edges as a whole by their intersection points with the epi-
polar lines.
The aim of the three-dimensional reconstruction of micro-
structures is a 3D-model, which is to compare with the de-
sign data of this microobject in order to make conclusions
for the technological process. To solve this problem,
nodes and edges of the object have to be extracted from
an image by edge extraction algorithms and vectorization
tools. After that the extracted nodes will be set in relation
and verified with the nodes in the other images. Usually it
is necessary to know the approximate orientation of the
images to match nodes. Because of the similarity of the
different images, taken with small tilting angles, the
matching process can take place without orientation data
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
