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5.1 Height determination of a point
In height determination for a point with a predetermined
planimetric position, the search space is one-dlmen-
sional, defined by the unknown height. This makes the
search highly efficient. If unknown terrain inclinations are
also treated, two variables must be added, one for X-
directional and one for Y-directional inclination. Because
the inclinations are included only for compensating image
deformations, even the final step size for these variables
can be rather coarse. In practice it is rather questionable
wheather inclinations can be considered at all, because
the match area is usually small.
5.2 Matching a point
With the title 'matching a point! we mean here that a point
feature is identified in one image (by human or by
algorithm) whereafter the homologous points must be
found from the other images. The task is only slightly
different from the previous one: instead of moving
vertically, we now move along the ray determined by the
image point on the reference image. The search is as
efficient as in the previous task. The technique resembles
the geometrically constrained multiphoto matching by
Grün and Baltsavias (1988). The crucial difference is that
the final least squares matching for subpixel accuracy is
made by search without forming linearized observation
equations.
5.3 Matching a point when orientation is
imprecise
We have assumed throughout this paper that the
orientation parameters are known for each image so that
epipolar search can be used. This assumption is not
strictly valid for example in digital aerial triangulation,
especially in its early stages when external orientation is
known only approximately. For this purpose our search
method must be extended so that in each state of the
main search a subsearch is made to compensate the
imprecise epipolar condition. The subsearch is made for
each image in two dimensions. The dimensionality of the
search space for this subsearch is 2/, thus making it
computationally rather demanding. Careful design is
necessary for making a well-balanced choice of the
search ranges and step sizes.
5.4 Template matching of a point
Matching a point feature to a template is a necessary
operation in digital aerial triangulation using signalized
control points. This can be accomplished either
simultaneously or in two phases so that the images are
first matched mutually and thereafter the resulting
groundel image' with a known template. Based on the
good results with a resembling method by Lammi (1994),
the two-phase approach is favored here. It is likely to be
727
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
more robust because the mutual matching of the images
is not disturbed by the template matching. For cross
targets the matching between the groundel image and a
template image can also be made with least squares
matching by search in three dimensions (two
translocations and a rotation in 90? range). For point
symmetric targets the search space is obviously two-
dimensional.
5.5 Matching a line
When a line feature has been identified in one of the
images, it can be matched from the other images by
keeping the Z -coordinates of the end points of the line as
unknown, thus creating a two-dimensional search space.
The end points move along the rays as described in
Section 5.2. The set of groundels to be matched is now
defined by a narrow linear band. The optimizition criterion
must be modified slightly so that root mean square error
(RMSE) is used. This is necessary for comptensating the
virtually varying number of groundels involved. For
matching polylines the method can be applied
sequentially so that the search for one line section is
made only with the next vertex, the height of the previous
vertex being already determined.
5.6 Matching a planar surface
When a planar surface is delineated by a quadrangle or
any polygon in one image, the search for match can be
made in three dimensions as in Section 5.2, the vertical
translocation and the inclinations of a plane being the
unknowns. The XY -position of each vertex is determined
by spatial intersection with respect to this plane. The set
of groundels to be matched is now defined by the planar
surface projected to this place. For some applications it
may be useful to extend this region slightly by buffering,
to guarantee that texture on the edges support the
matching procedure.
6. PRACTICAL EXPERIENCES
Until now the search method has been implemented for
line features (Lammi,1996). The results are as expected.
For well-defined lines the method works well but in low
contrast areas we have encounter typical problems of an
area-based matching. The earlier experiences with two-
image cross-correlation on supersampled images
(Lammi, 1994) let us assume that the method should work
very well for point matching. The theoretical similarity of
cross-correlation and least squares matching has been
emphasized by Helava (1976).
Least squares matching by search has the advantage
that the pull-in range is totally controlled by the case-
specific range settings for the unknown variables. Overly
wide ranges will, of coarse, increase the computing time.
