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(b) the accuracy, which was obtained by fitting the
matched coordinates to a plate (plane) or cylinder.
(c) the computation time
4.1 Error Ellipses
Fig. 2 Axes of error ellipse against window size
(aluminium)
0.09 4
0.08 | ABM (major)
i on 1SM (major)
2 9:07 sheer deem l nemen dde e ABM (minor)
a 0.06 2 —--—- 1SM (minor)
x ot
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window size
Fig. 3. Axes of the error ellipse against window size
cylinder
ols (cy )
0.16
ABM (major)
0.14 + 2SM (major)
2 ouis IhoM nimioT ipio itv: ABM (minor)
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window size
Figures 2 and 3 show the magnitudes of the standard
errors, represented by an error ellipse, as plotted against
the window size for the aluminium plate and the cylinder
respectively. It can be seen that in fig. 2 that the
magnitudes of the major and minor axes for the 1SM are
always smaller than those from the ABM method. At
maximum window size (101 x 101) the difference in major
and minor axes is almost 0.01 and 0.02 pixels
respectively, in favour of the 1SM method. The results
obtained for the cylinder show a similar pattern (fig. 3).
The difference between the major and minor axes at
maximum window size is about 0.03 and 0.02 pixels
respectively. This indicates that the 1SM and 2SM
methods are better functional models and are able to
model the observations to a better degree than the
conventional ABM.
4.2 Test of Accuracy
The accuracy of the matched coordinates obtained was
determined by using a surface fitting program. Figures 4
and 5 show the standard errors of the goodness of
surface fit in mm for the plate and cylinder respectively.
559
standard error (mm)
Fig. 4 Standard error of surface fitting against
window size (aluminium)
ABM 18M ------- 28M
0.45
0.4 +
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window size
Fig. 5 Standard error of surface fittting
against window size (cylinder)
— ABM 2SM
0.8
TTT rrr
o n. ui» eo
9
vi
25
33
41
4
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7
81
89
97
window size
(a) Aluminium plate
(b)
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
As mentioned earlier, both the 18M and 2SM
models were tested on the aluminium plate. Figure 4
shows the three curves representing the standard
errors for ABM, 1SM and 2SM. It can be seen that
the curve representing the standard errors for the
1SM model is smoother than the curve for ABM.
However, the values of the standard error for both
methods do not differ greatly. The minimum
standard deviation obtained through both the ABM
and 1SM methods is approximately 0.15mm.
On the other hand, the standard errors for the 2SM
are greater than both the ABM and 1SM methods at
any window size. This could indicate the use of
unnecessary parameters (curvature) to represent the
aluminium plate in the matching process.
Cylinder
To test the accuracy of the method on the cylinder
only a 2SM was used. It was decided not to include
the 1SM model as it does not contain any curvature
to represent the cylinder. Figure 5 shows that the
standard errors obtained in using a second order
surface model (2SM) to represent the cylinder is
significantly smaller compared to ABM at window
sizes 35x35 and larger. However, at smaller window
sizes, as from 9x9 to 35x35, it seems that the
second order terms contributed the problem of
overparametrisation. This can be explained by the
fact that, for smaller windows sizes, the area to be
matched is almost a plane thus introducing
