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Figure 5. Matching along edges without (top) and with (bottom)
constraints. The epipolar line is the white line in the
bottom right image. The black frame is the initial
position and the white frame with the centre cross the
final position.
With along-track stereo, the epipolar lines are vertical, i.e. any
error in the x-direction (x is in the sensor direction) will be
eliminated right in the first iteration of the matching (see bottom
of Figure 5). Since the epipolar lines are vertical, the
measurement points must be selected along edges that are not
nearly vertical in order to ensure determinability and high
accuracy. Some advantages of the geometric constraints will now
be presented. Satellite images include due to their small scale a
high degree of texture, i.e. edges. Measurement points lying
along edges nearly vertical to the epipolar line can not be safely
determined with other matching techniques, but with our
approach they can as they lie at the intersection of two nearly
perpendicular lines. Figure 5 illustrates such an example.
Another usual problematic case is that of multiple solutions.
With geometric constraints side minima can only result if they
fall along the epipolar line. Another advantage of our approach is
the possibility to give arbitrary approximations for the scales and
the shear parameters, that are estimated in matching. This is
important for matching the nadir with the other two channels,
since their scale difference is 3. The combination of geometric
constraints and an approximation for the scales leads to very
positive results as Figure 6 illustrates.
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Figure 6. Matching the fore image (left) with the nadir image
(right). Top: using constraints and a scale
approximation of 3. Bottom: without constraints and
no scale approximation (default scale value = 1).
For the DTM test a region (12 x 20 km) covering the top left part
of the images was chosen. In this region lied the profile height
data that were measured with the roving GPS. Ca. 10,000 points
were selected with an interest operator in the fore and were
matched in the aft image. Four pyramid levels (incl. the original
images) were used for derivation of the approximations. In the
last level a conformal transformation with 17 x 17 pixel patch
size was used. In comparison to previous DTM generation from
SPOT images, the matching was easier. This is partly due to the
lack of radiometric differences because of the simultaneous
image acquisition, and partly due to the type of terrain (flat and
open). The major problems that were encountered were: the lack
of sufficient texture in large areas covering up to 1 x 1 km ; the
smoothing of discontinuities, especially at creeks, due to the
large patch size of 230 x 230 m ; some, very few, regions of
radiometric differences (see Figure 7) mainly due to different
reflection of water surfaces. To reduce the amount of blunders a
test using statistical values that are provided by the algorithm
(see Baltsavias and Stallmann, 1993) was performed. Only ca.
2.5% of the points were rejected and they included most of the
blunders. The height range of the remaining data was only 84 m,
showing that big blunders in the order of hundred or more meters
as they have occurred with previous SPOT DTM tests did not
occur. Using the ca. 10,000 points a DTM grid with 40 m grid
spacing was interpolated and contours were plotted. Visual
control of the contours and the representation of DTM as a grey
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996
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