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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. 
114 
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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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