image function of the image patches to be matched
should be well conditioned. This is usually the
case for areas with enough texture and con-
trast. Note that the selection also depends on
the matching method. For example area-based
matching methods inherently assume flat sur-
faces; matching windows selected on breaklines
are potential problems. Feature-based methods
are much less sensitive in that regard. In fact,
edges in many cases correspond to breaklines.
topography points in flat areas are a better choice
than points on slopes or on tree tops. Tilted sur-
face patches more likely lead to unsuitable image
patches due to foreshortening. By the way, the
foreshortening problem is much more pronounced
in aerial triangulation because the connections
of all projection centers involved result in many
more critical orientations. In a single model only
one critical orientation exists (along the model
base).
even distribution of points increases not only the
block stability but also render a better partial
reconstruction of the surface.
5.1.3 Multiple Image Matching: Most of the
blockpoints are imaged on more than two images.
Thus, the need arises to find the most probable con-
jugate location by matching all image patches simul-
taneously. This possibility does not exist with tra-
ditional methods because humans can only see two
image patches at a time. Multiple image matching
(MIM) alleviates the tie point problem.
5.1.4 Approximations: In order to meet the accu-
racy expectations matched entities should have sub-
pixel precision. As discussed in Section 3, every
matching method needs approximate matching posi-
tions. The accuracy of the approximations depends
largely on the matching method: area-based methods
require two to three pixels, feature-based methods are
less demanding but still need good approximations
(see, e.g., Fôrstner, 1995). Suppose we employ LSM
on a resolution level of 15 to 30 jum. The challenge is
to provide approximate locations that are better than
1/20 mm.
Not only does the pull-in range determine the approx-
imations, but also the size of the matching windows.
Fig. 2 depicts three image patches, size s x s. Their
centers are only approximately known and the com-
mon area is much smaller than one window. Let d be
the uncertainty in predicting the matching location.
In the worst case the three windows are displaced in
one direction by 2-d. Suppose now that the same pro-
cess is repeated with 3 windows of the adjacent strip.
Again assuming the worst case situation, the displace-
ment can be in the opposite direction, resulting in an
overall displacement of d,, = 5 - d. Considering d,, a
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
maximum error we must expect an average displace-
ment of d, = 1.7-d in a six overlap situation. Now we
still expect a common overlapping area of, say, half of
the original window size. From dm € 0.5 - s we con-
clude that the uncertainty, d, of predicting conjugate
points should not exceed 1/10 of the window size to
assure that the common area is still large enough.
Figure 2: Three partially overlapping matching win-
dows, offset by the uncertainty from predicting their
centers.
5.2 Solutions, Assumptions, Constraints
The essential tasks are the result of solving the orien-
tation parameters as well as possible and of partially
reconstructing the object space for subsequent pho-
togrammetric processes, such as the automatic gener-
ation of DEMs and orthophotos. The tasks must be
solved in one way or another by automatic aerial tri-
angulation methods. Their solution entails new prob-
lems which are briefly discussed here.
5.2.1 Footprints The request for multiple over-
lap and even distribution of blockpoints requires the
knowledge of footprints. Fig. 3 depicts a realistic over-
lap situation; it goes without saying that selecting
features in the 6-fold overlap area requires more accu-
rate positions of the footprints than is available from
the nominal overlap. To determine the footprints, the
surface and the exterior orientation must be known.
This is a dilemma: what we want to determine in the
aerial triangulation is what we wish to know in the
very beginning.
5.2.2 Predictions: A fundamental aspect of match-
ing is to predict the matching locations and the
matching range. Assume we have selected an inter-
esting location according to Section 5.1.14+2. In or-
der to perform MIM (5.1.3) we need approximate lo-
cations on all corresponding images. The matching
range (size of search window) depends on the conver-
gence radius of the matching method (pull-in range)
and the uncertainty of the prediction process.
Fig. 4 illustrates the concept of a predictor. It works
in two modes: the classical mode begins with selecting
a matching entity in one image, followed by project-
ing it into the object space and from there back to the
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