On the geometrical side, for example, simplifying con-
straints ask for smooth surfaces, without steep height
variations or discontinuties. This exludes the applicability
within urban areas, forests, slopes and so on. Expan-
ding the geometric model to the incorporation of discon-
tinuities therefore would lead to higher flexibility and,
hopefully, greater accuracy within these regions.
This expectation might be met, if the information neces-
sary for the consideration of the more complex geometry
can be extracted from the image and object data and
accordingly is incorporated into the geometric model.
To match that aim the algorithmic performance has to
imply
1. a flexible geometrical set up tuned by additio-
nal informations extracted from the available
data
2. some rudimentary interpretative capability to
evaluate the data characteristics and to link
them to the shape of the surface.
The presented algorithm will give a contribution in that
direction.
First, the geometrical model will be explained, then
possibilities to extract additional informations will be
sketched and finally, some first test results are shown.
THE ALGORITHMIC CONCEPTION
Some thoughts to the current state of algorithms
The scenario of algorithms, accomplishing the identifica-
tion and localization of homologeous image areas is as
manifold as the scale of possible applications and
motivations. In order to keep the considerations transpa-
rent they will be restricted here to the determination of
topographic surfaces.
With regard to the processing of the image data, the
kind of point determination and the assumptions concer-
ning the surface geometry we find three different types
of solutions:
4. Image correlation
2. Least squares matching
3. Feature based matching
To characterise the algorithms the following aspects
might be useful:
Image correlation: Uses the original image data to calcu-
late a similarity value, has an iterative structure
calculating point by point, allows the incorpora-
tion of geometric distortions as far as they are
known and modelled (piecewise bilinear surfa-
ce parts, for example)/Boochs 1987/
Least squares matching: Uses the original image data
as measurements within a least sqaures ad-
justment, allows modelling of image radiome-
try, is a direct solution, considers geometric
distortions as part of the deterministic model
128
(in general: piecewiese bilinear surface parts)
and allows extended set ups or constraints
(combined point determination, regularizations
etc.)/Ebner,Heipke 1988, Krzystek 1991,
Wrobel 1987/
Feature based matching: Uses the original image data
to derive feature values characterising image
points and their neighborhood, determines the
correspondence between the points in both
images, needs no geometric model.
/Fôrstner 1986/
Considering preprocessing and transformation capabili-
ties there are some further, common steps possible (the
use of image pyramids, for example).
With respect to functionality and results the solutions
have different attributes like:
Image correlation: produces medium to high accuracy,
needs not very precise start values, is applica-
ble even in cases of low image contrast, does
not provide internal accuracy estimates, does
not allow the direct interference of the deter-
mination of adjacent points.
Least squares matching: gives results of high accuracy,
needs precise start values, is more sensitive to
low image contrast, gives internal accuracy
estimates, allows the simultaneous determin-
ation of a large number of points.
Feature based matching: produces medium accuracy,
opperates without start values, needs high and
characteristic image contrast, produces irregu-
lar distributed points, works even in cases of
arbitrary object geometries.
Due to the importance of the accuracy in geodetic appli-
cations least squares solutions are preferred in general.
Feature based matching may serve as tool for the calcu-
lation of approximate values or is very useful if robust-
ness is the most important attribute.
Correlation algorithms range in between. The something
lower accuracy and the lack of internal control capability
are disadvantegeous. Nevertheless the simplicity of the
functional set up, the flexibility in the algorithmic control
and the individual calculations for each point are useful
for extended geometric models and the incorporation of
additional knowledge. The following concept therefore is
founded on the image correlation technique.
The concept of object space based correlation
Two essential preconditions have to be met to garantee
a succesful similarity measurement. The compared
image areas have to be rectified and the albedo variati-
ons within the corresponding object area have to provide
sufficient image contrast. If one or both conditions are
not given the calculation will fail or at least produce
incorrect results.
In addition to the attempt to overcome such problems by
improving the rectification in order to reduce geometric
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