raw and normalized images. Therefore, no distortions are
introduced in such a process. On the other hand, in linear array
scenes, epipolar lines may not be straight, but it is desirable to
have them as straight lines in the normalized scenes. Therefore,
the evaluation of their non-straightness in the raw scenes will
give an idea about the errors introduced in the normalized
scenes.
5. EXPERIMENTS
In order to study the epipolar geometry, two scenes are needed.
Nine experiments are performed. Experiments 1, 2 and 3 are
simulated to obtain stereo coverage for a three-line camera, at
different altitudes. On the other hand, Experiments 4, 5 and 6
are simulated to obtain stereo coverage by changing the pitch
angles along track similar to that of IKONOS, at different
altitudes. Finally, Experiments 7, 8 and 9 are simulated to
obtain stereo coverage by changing roll angles across track
similar to that of SPOT at different altitudes. The summary of
the experiments is listed in Table 1. Figure 6 shows the
footprints of the scan lines of the scenes.
Altitude
1000m | 680 km |822 km
Stereo | Three-line scanner Exp. | Exp. 2 | Exp.3
coverage|Changing pitch angle] Exp.4 4 Exp.5 | Exp. 6
method | Changing roll angle | — Exp. 7 Exp. 8 | Exp. 9
Table 1. Summary of Experiments 1 to 9
In each of these experiments, five points are selected in the left
scene. Figure 7 shows the corresponding epipolar lines of the
experiments. The epipolar lines are drawn within the extent of
the right scenes. Dotted straight lines are added between the
beginning and ending points to visually examine the
straightness of these epipolar lines. It has been found that Æ,
does not equal zero. Therefore, for general linear array scanner
(even with the constant-velocity-constant-attitude trajectory
model), the epipolar lines are not Straight. In order to quantify
the straightness of epipolar lines, Table 2 lists the values of
Ey/E, for the experiments.
Examining the standard deviation of Æ,/F, of the selected points
in each experiment, it is noticeable that E;/E, values do not
change from point to point in the scene in Experiments 1 to 6.
This means that these epipolar lines, even if they are not straight
lines, are changing in a similar fashion. On the other hand, the
standard deviations of E;/E, values in Experiments 7 to 9 are
relatively large, which consequently means that there is a high
variation of the shapes of the epipolar lines. This is confirmed
by extreme example, Experiment 7 in Figure 7. Therefore, it can
be concluded that stereo coverage similar to that of three-line
camera or IKONOS are superior, in terms of shape variation of
epipolar lines, to that of SPOT.
Examining the average values of Ej/E,, it is noticeable that
EE, decreases as the altitude increases, for the same stereo
coverage type. Moreover, stereo coverage similar to IKONOS
or three-line cameras gives smaller average values than that of
SPOT at the same altitude (Compare the average values of
Experiments 1, 4 and 7; those of Experiment 2, 5 and 8, and
finally those of Experiments 3, 6 and 9).
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
Experiment 2
Experiment 3
Experiment 1
Experiment 5
Experiment 6
Experiment 4
EURE ee d ww mae
Figure 6. Scan lines footprints of Experiments 1 to 9
Experiment 1 Experiment 2 Experiment 3
err í
Experiment 4 Experiment 5 Experiment 6
Experiment 7 Experiment 8 Experiment 9
Figure 7. Epipolar lines of Experiments 1 to 9
Point ] 2 3 4 S Mean +Std
] 0.031 | 0.031 | 0.031 | 0.031 | 0.031 | 0.031+0.000
0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.00S+0.000
0.004 | 0.004 | 0.004 | 0.004 | 0.004 | 0.004+0.000
0.031 | 0.031 | 0.031 | 0.031 | 0.031 | 0.031+0.000
0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005+0.000 |
0.004 | 0.004 | 0.004 | 0.004 | 0.004 | 0.004+0.000 |
-0.012/-0.114/-0.144|-0.158]|-0.167 | -0.1193:0.063
-0.076|-0.077|-0.077|-0.077|-0.078|-0.077+0.001
9 -0.062|-0.063|-0.065|-0.066|-0.067|-0.065+0.002
Experiment
CONSO AS | WIN
1028
Table 2. E/E, values for various points in Experiments | to 9
6. CONCLUSIONS AND RECOMMENDATIONS
It has been concluded that for constant-velocity-constant-
attitude EÓP model, the epipolar line is found to be a non-
straight line in general and a quantitative analysis of its non-
straightness was introduced. Analysis of alternative stereo-
coverage possibilities revealed that along track stereo
observation using pitch angles as well as three-line scanners are
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