International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
determined by intersecting the epipolar plane with the
normalization plane that is horizontal. Alternatively, it can be
determined by intersecting it with the XY-plane, which results in
a straight line along the vector (U, V, 0), Figure 7. Therefore,
the direction of the epipolar lines, x, can be computed as:
V | N.M'- pe 8)
K, = arctan|} = 1 = agent —— (
U NL+LN
y
A
(LMN) f ee
MSN?)
Figure 7. Direction of the epipolar lines
Utilizing the above findings, the indirect epipolar resampling
approach of linear array scanner scenes can be summarized in
the following steps (see Figure 8):
Left Scene Right Scene
Derive 2-D Affine Parameters & Roll Angle]
| tL nds an |
Derive Scene Parallel Parameters: |
(LM, e» 9. K, Ax, Ay. 5)
[ PTP Transform
Derive 2-D Affine Parameters & Roll Angles
dn dnd ud adadnd ul]
Scene el Parameters: |
(4 M, 0,9. K. dx, dy.) |
'ransformation |
| Compute
0,70,-0
x, = arctan((N.M'—M.N°)/(N.L'-L.N"))
Ax, s (Ax4 AYy2S Ay, = (Av + Avy2
s, =(s+s"}/2
ee
À
| Select Normalized Scene Parameters: | | Select Normalized Scene Parameters:
D GM rA: a s | Ë Ua MS )
|
ERES, Voi
[ Re-project the scene ]
Figure 8. Epipolar resampling procedure
e For each scene, estimate the 2-D Affine parameters,
together with scanner roll angles using GCP, adopting
the model in Equations 4.
e For cach scene, the roll angles are used for PTP
transformation, and the parallel projection parameters
are derived from the 2-D Affine parameters.
e The normalized scene parallel projection parameters
are obtained by considering a horizontal plane (i.e.,
w,=p,~= 0) and maintaining average scale and shift
values, and rotating the scenes with an angle x,
(Equation 8).
e The scenes are projected from their original parallel
projection parameters to their normalized values.
Such a transformation is considered as parallel
projection between two planes (which is considered a
6-parameter Affine transformation as discussed in
Section 3.2).
5. EXPERIMENTS
A panchromatic stereopair of IKONOS scenes covering
Daejeon, South Korea is used in the experiments. The
geographical coordinates of the area range from 36.26? to
36.369 North Latitude and from 127.31? to 127.45? East
Longitude. An overview of these scenes is shown in Figure 9,
The number of rows and columns and the acquisition data/time
of the scenes are listed in Table 1.
PE
ene
Left scene Right sc
Figure 9. Overview of the IKONOS scenes
Left Right
Number of rows 13824 14336
Number of columns 13816 13816
Acquisition date 2001-11-19 2001-11-19
Acquisition time 02:18 GMT 02:19 GMT
Table 1. IKONOS scenes’ dimensions and acquisition data/time
No information regarding the roll angles of the scenes and no
GCP were available. Instead, the rational function coefficients
of each of the scenes were provided. They were used to derive
the ground coordinates of measured tie points - 162 points in
total (Tao and Hu, 2002). A coordinate transformation was then
implemented to obtain GCP in the local Cartesian coordinate
system. Three sets of experiments were tested using different
numbers of GCP and check points, Table 2. The developed
approach for epipolar resampling was then performed. The
square root of the estimated variance components, adopting
Equations 4, and the average absolute values of the resulting y-
parallax are listed in Table 2. The means and standard
deviations of the error values in the object space are also listed
in the same table.
Experiment 1 2 3 d
# of GCP 9 25 162
# of Check points 153 137 0
G, Left, pixels 4.8 3.7 2.9
ó, Right pixels 1.7 1.3 1.1
Mean|P,|, pixels 2.3 1.6 1.5
GCP Meany+Stdy,,m|0.000+1.707|0.000+0.993 |0.000+0.889
Mean+Std;, m |0.000+5.674|0.000+6.086|0.000+5.450
Check|/Meany+Stdyy,m|0.103+1.364|0.095+0.930 -
points| Mean +Stdz, m | 1.588+6.101|0.587+5.491 -
Table 2. Experimental results of the normalization process
From Table 2, an insignificant improvement between
Experiments 2 and 3 can be seen. Thus, it can be concluded that
few GCP can be used for epipolar resampling according to the
approach developed in this research. In addition, error standard
deviation values of the check points are not significantly
different from those of the GCP. Therefore, the suggested
approaches achieve similar errors throughout the resulting
International Arch
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Figure 10. St
6. CONCLU
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linear and non-line
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estimate the requir:
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feasibility and succ
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scenes. In additi
epipolar resamplin
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and areal features)
projection model
photos will be gene
Abdel-Aziz, Y.,
Transformation fr
Space Coordinai
Proceedings of
Photogrammetry, 1
Urbana, Illinois, pp