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Formation
in the direction of scanner transport mechanism. Mx shows
RMSE based on residuals after coordinate transformation in the
direction of CCD sensor moving.
High level of correlation of errors on grid points is shown at
Figure 7. This figure represents covariance functions in the
directions of transport mechanism (Y axis) and CCD sensors
moving (X axis). Red dots at the diagram represent empirically
calculated covariance, depending on the point distance from
adjacent grid point. Covariance function (in blue) is obtained as
adjusted Gaussian curve, passing as halfway line between
empirical covariances. Conclusion coming out from the diagram
is that errors are highly correlated for both axis. This correlation
is significant even for grid points with distance of 4-5 times grid
interval.
Figure 7: Covariance functions by coordinate axis
Since the accuracy of the glass plate grid is higher by the order
of magnitude than scanner errors one can say that residuals after
Helmert transformation represent overall scanner's errors. lt
comes out that positional RMSE of 130 um, after Helmert
transformation, is overall RMSE scanner. It can be also
concluded that major part of this error comes from systematic
part - from 130 um RMSE decreases to 4.2 and 8.5 um after
collocation with filtering. The difference in RMSE between
these transformations represents systematic part of positional
error.
3.3.2 Assessment of global stability of systematic errors
In order to assess stability of systematic errors during the time
and their dependence on change of scanning parameters,
multiple scanning of grid plate has been performed. Grid plate
was scanned 24 times, which can be seen from Table 6.
RMSE based on residuals after affine transformation and
collocation with filtering has been selected as the estimate of
global stability of systematic errors. As it can be seen from table
6, the difference between maximum and minimum RMSE after
affine transformation is 3.2 um (Y axis) and 5.1 um (X axis).
After collocation with filtering these differences are 2.0 um and
2.4 um (Y and X axis, respectively).
It can be concluded that systematic errors are very stable, at
least on a global level. They are independent from the scanning
time duration and changes of spatial and radiometric resolution.
3.3.3 Assessment of local stability of systematic errors
In order to determine the local stability of scanning errors the
differences of residuals are compared after affine transformation
and collocation with filtering in 9 distinctive grid points (Figure
8).
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004
Figure 8: Points for local stability test
Figure 9 and Figure 10 show the differences of residuals in 9
distinctive grid points (for Y and X axis).
— Point!
70
Point2
$0 5 — tn = snc Point3
v —- = Point4
—— Point5
em Point6
Tg lieti exi NT am, sm Point7
V e —— Point8
Point9
Residual differences - Y axis ( um)
ur De Rai
Éd sans
- p Dn RE
— Le te
i
Figure 9: Residual differences at 24 plates after affine
transformation and collocation with filtering. (Y
axis)
60 — Point |
= 4 —— Point2
=.
* 20 uu c i sue Point3
x ;
© Point4
x 0
o l 3 5- 1° 9-11 13 15-17. 19 21. 23 e loint5
e o aed dcm ae
© -20 vous ro eas
© — Point
S 40
= z CMS i
= Point7
= -60 2 oF A us nsum d Point$
S
o
SQ int
g m fern” Point9
-100
Figure 10: Residual differences at 24 plates after affine
transformation and collocation with filtering (X
axis)
Differences of residuals, shown at Figure 9 and Figure 10,
ranges from 8 to 15 um.
It can be concluded that systematic errors in distinctive points
are very stable, regardless of the scanning time duration and
changes of spatial and radiometric resolution.
