gistration, the recorded
ons of the amount of
isitive material at the
expressed by image
ing to the cos^ law of
ortional to a combined
flectance characteristics
. 1986; Alvertos et al.,
it image
object surface
hr
ate feature registration
ir.
s essentially expressing
ich is the projection of
ter referred to as object
n other words, the objel
ch is imaged in a single
Is of a sensor have the
; vary according to the
, as shown in Fig. 3.
d with sensor charging
ent can be considered an
generation. A series of
rom various, constantly
ing a scale space family
ene. Images from higher
larger objel sizes and,
an images captured from
actual object space.
actually scale space
object space area, with
fer to both rotations and
space shapes, and sensor
ters defining the scale
the same sensor is used
rmance of metric quality
the effects of sensor
mation are similar for
Ihe remaining combined
errain shape make image
unique in terms of scale
lly vary within an image,
enna 1996
with various features belonging to different levels of the
terrain scale space as it would have been obtained had an
orthogonal projection been used.
4. EFFECTS ON LEAST SQUARES MATCHING
Matching features whose images are distorted due to
foreshortening within a stereopair, using classic least
squares techniques, will lead to failure when scale differences
are sufficiently large [Stefanidis, 1993]. The reasons for this
failure are:
e erroneous pixel correspondences (and consequently
observation equations) are formed due to the
dissimilarities of the initially selected conjugate
patches, and this problem cannot be corrected during
the iterative solution;
e negligence to directly access the radiometric scale
differences of conjugate patches renders the
mathematical model (which considers solely geometric
relationships) inadequate; and
e violation of the flat terrain assumptions which are
inherent in the geometric model used to relate conjugate
patches (affine transformation).
Failure to bring conjugate features at comparable scales prior
to matching will in essence result into matching by
comparing non-conjugate gray values, and will therefore
produce observations inconsistent with the geometric model
used to relate conjugate image windows. In this case, two
types of errors can occur (in direct analogy to errors in
statistical decision making):
e truly conjugate pairs of features may be rejected by the
matching solution due to the contradictory information
provided by the comparison of non-conjugate gray
values, or
e non-conjugate pairs can be matched by the adjustment
solution due to the contamination of the matching
process by erroneous observation equations.
5. MATCHING THROUGH SCALE SPACES
To overcome the previously described scale-pertinent
problems, we can proceed in the following manner:
1. For every pair of matching candidates, the scale space
behavior of the feature to which these matching
candidates belong is examined, and large scale
variations between them are identified.
2. The scales which are most proper for matching are
determined.
3. Only then is precise matching performed, with the
participation of radiometric scale parameters in a
classic least squares matching manner.
By applying scale space techniques, we can substitute a
stereopair by two image pyramids (a stereopyramid). It has
been shown [Babaud et al., 1986] that the two-dimensional
Gaussian function
ey?
gr yisy he s Eq. 3
is most appropriate for scale space generation using digital
images. Typical photogrammetric multiresolutional
techniques proceed by comparing similar pyramid levels of
two stereomates (e.g. the 512x512 pixel version of the left
stereomate is compared to the 512x512 pixel version of the
right stereomate, the 4096 x 4096 left to the 4096 x 4096
right etc.). However, as we discussed in the previous two
sections individual elements within these images may
actually belong to dissimilar scale levels. Our first objective
is to identify within the stereopyramid those scale levels of
the two stereomates at which the specific feature currently
processed is represented at comparable scales. In this
manner, it is possible to establish stereo-correspondences
by matching for example a feature at the 512 pyramid level
of the left stereomate to its conjugate at the 1024 pyramid
level of the right stereomate. Thus, matching is performed in
the four-dimensional space (X,Y,Sx>5y), With s, and Sy
being the scale parameters in the x and y directions
respectively.
Given approximate conjugate positions in a stereopair, we
can examine the scale space differences of the features to
which these points belong. The separability property of the
two-dimensional Gaussian function allows it to be
substituted by the product of two one-dimensional Gaussian
functions
2
x? a
8x(X,5,) = kye 2
2s,
and Vig Os) = Re 7 Bg4
and thus permits us to substitute a two-directional search by
two one-dimensional ones, resulting in great computational
gains.
Fig. 4: A profile scale space image (top) and traces of
features in it, detected as edges (bottom).
For searching in scale space, we introduce the concept of
profile scale space images. As the name implies, a profile
scale space image is the scale space representation of an
image profile. It is stored and processed as any digital image
file, but in this case, while one direction (columns)
corresponds to image coordinates along the profile, rows are
discrete representations of the continuous scale space,
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
