International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
calculated by the LBTM are almost identical to those obtained
from the ordinary 3D/2D affine models and GCPs. Applying
different configurations of the control straight lines indicates
that the inclination angle (the angle in the XY plane) of the
control line does not affect significantly the accuracy of the
results but the distribution of the GCLs on the area covered by
the image does. Increasing the number of GCLs improves the
accuracy of the results; however, a key feature established from
these results is that the GCL slope, which is a function of the
GCL length and terrain elevation differences along the line, has
the most important effect on the results accuracy. The results
presented below are chosen to illustrate this phenomenon.
600
500
400
-300
-400
— GC ES
-Sv0 Checkpoints
-600 i
-600 -S00 -400 -300 -200 -100 0 100 200 300 400 500 600
Figure 2. GCLs and checkpoints distribution of Sland S2 sets
600 —
500
400 i
m x
300 S
y
0 p nin i ;
-100 NC 4
9 3
-200
-300 : / Ji
-400
N —— GCLs
-S00 Checkpoints
-600
-600 -506 -400 -300 -200 -100 0 100 200 300 400 5060 600
Figure 3. GCLs and checkpoints distribution of S3 and S4 sets
Data Set |No. of| No. of The 3D affine LBTM
GCLs |Chkpts Total RMS (m)
x Y
= [Case Si | 4-12 | 24 | 532-292 | 204-226
B | Case S2 0.20-0.21 | 0.29- 0.23
£ |Case S3 4.32-3.27 | 4.21-2.62
A | Case S4 203-147 | 1.84- 1.67
Real (HK) | 4-12 | 16 | 9.01-2.39 | 6.96-2.01
real data
Table 1: The 3D affine LBTM results of the synthetic and the
Data Set No. of| No. of The 2D affine LBTM
GCLs |Chkpts Total RMS (m)
X Y
9 [CaseS1| 4-12 | 24 | 3.81-3.01 | 6.99-4.60
2 | Case S2 0.46-0.28 | 1.10-0.51
E | Case S3 3.96-2.17 | 5.77-6.31
N | Case S4 3.76- 1.49 1.63- 0.46
Real (HK) | 4-12 | 16 | 7.73-5.09 | 8.19-9.14
real data
Table 2: The 2D affine LBTM results of the synthetic and the
854
When considering the effect of the terrain type, the results in
Table 1 indicate that data set S2 (flat terrain) yields more
accurate results than data set SI (undulated terrain) in all
directions, the same way as data set S4 leads to more accurate
results than data set S3. The results also show that the sharper
the slopes of GCLs are, less accurate the results are. Applying
the 2D affine LBTM to the same data sets leads to similar
findings; however, the overall accuracy is generally worse than
when using the 3D affine LBTM. The deficit of the results is
especially clear when applying the 2D affine LBTM to the sets
of the undulated terrain. This finding is expected because the
2D LBTM does not consider the differences in terrain clevation.
On the basis of the above, one can conclude that the selection of
the LBTM form to be used for image rectification depends
primarily on terrain elevation differences. In the following
section a real data set is used to examine the feasibility and the
performance of the developed model.
3.2 Real Data
To verify the results obtained from the simulated data, a real
stereo data set (Ikonos Hong Kong data set) was used. The area
covered by the two images extends over 11.60 x 10.28 km? for
image 1 and 6.62 x 10.18 km? for image 2 of the stereo with the
overlap area of 2.5 x 10 km?. The inclination angles of the
images are 19.02 and 27.3 degrees respectively, which leads to
the base to height (B/H) ratio of about 0.87. The maximum
ground elevation difference in the test area is about 450 meters.
A fast static GPS technique was used to collect thirty-eight
well-distributed GCPs on the entire coverage area of the two
images; among them, eighteen GCPs belong to the overlap area.
Most of the observed points were road intersections, pavement
corners, or road-canal intersections. Further information about
the test field can be found in Shi and Shaker, 2003 and Shaker
et al., 2004.
A number of GCLs were established by connecting different
points in the overlap area between the two images and the 3D
LBTM was applied. The results show that the new model is
applicable to the real data, though solid conclusions could not
be drawn as the data set had limited overlap coverage area
(2.5x10 km?) and dependent checkpoints (the same 18 points
which are used to establish the GCLs). Consequently, the
coverage area of image 2 of the data set (6.62 x 10.18 km?) was
extended to cover the same area as in image 1 (11.60 x 10.28
km?). The image coordinates of the extension area of image 2
were calculated by using the ground coordinates of the
observed GPS points, the corresponding image coordinates of
image 1, and the ordinary affine model parameters as they
defined in Shi and Shaker, 2003. Accordingly, the two image
coordinates and the object coordinates of, a set of the 38 points
were ready for the experiment.
After several attempts to generate control straight lines, a group
of 12 GCLs were established by connecting some of the GCPs
of the data set keeping in mind that the lines were matching real
linear features such as roads or canals. The remaining points
were used as checkpoints (16 independent checkpoints). The
final distribution of GCLs and checkpoints used in this
investigation are presented in Figure 4.
The accuracy of the results of applying the established GCLs
plus one additional GCP to the developed LBTM was found to
be matching the accuracies which resulted from using the
simulated data. It is important to mention that the data set did
not contain any high slope GCL; however, the GCLs
comprising in the data set presented different levels. Tables !
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