mean errors,
rol points (4
es) was also
cantly.
ufficient for
er with 100
es of digital
ng 1:40,000
1 orthoimage
| pixel size).
f4m in the
he 1:24,000
> measuring
le for many
racy without
an affine
x absolute
y
4 | 151
3 139
0 159
4 117
2 105
2 91
os 56
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p 151
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6 122
177
:; 138
) 114
st stage the
adial lens
on, and the
acements in
oints were
ween these
s as control
ration were
transferred
"here an x-
e residuals.
The same procedure was repeated many times and the correction
grids were averaged to reduce temporal noise, especially due to
vibrations. For the Horizon four scans were averaged, for the
other scanners two, except for the Arcus where only one scan was
available. For the y-correction grid (modelling of tangential lens
distortion) a similar procedure was used. In this case once an
affine transformation and once a 7 parameter transformation
(affine plus an x? term in y) was used. The x? term in y
corresponds to the second order tangential distortion. By
subtracting the residuals from the two transformations, we were
left with the errors modelled by the x? term in y, and
subsequently a y-correction grid in the scanner system was
computed as for x. The x-grid was always used, the y-grid (called
y-precorrection) is optional. Errors due to lens distortion are
stable, so these correction grids do not need to be computed often
(for the Horizon we applied the calibration using correction grids
that were computed one year in advance).
For the second stage of the calibration the crosses of the two
border lines of the on-line plate were measured by LSTM and an
affine transformation between these values and the reference
values using all points as control points was computed. The y-
residuals of this transformation were indicating the occurring
errors at the two border lines. For the A4 scanners only one
border line was imaged, so a similarity instead of an affine
transformation was used. Since scanning is performed in one
swath we can assume that no errors can suddenly occur in the
interior of the CCD. Thus, the error at any point in the interior of
the image can be bilinearly interpolated using the errors at the
borders. This calibration stage is used to model the y-errors. They
are mainly due to mechanical positioning. The part coming due
to the tangential lens distortion can either be excluded by using
the y-precorrection grid, or it can be modelled by using a
transformation higher than the affine in the interior orientation.
We used just a 7 parameter transformation (affine plus an x? term
in y). This was sufficient for all scanners. The seventh parameter
can be only determined, if 8 control points (fiducials) can be
used.
4.3. Geometric accuracy after calibration
To check the validity of the calibration procedure we scanned the
two plates simultaneously, i.e. the off-line plate was placed on
top of the on-line and were fixed by tape to the scanner stage.
This could be avoided, if we had designed the off-line plate such
that it included the two border lines of the on-line plate with the
dense crosses. Due to this procedure the crosses of the upper
plate were naturally radially displaced, but this effect could be
accommodated by the affine transformation. However, this could
not happen with the two A4 scanners since the glass plates were
not lying on the scanner stage and the radial x-displacement was
asymmetric. The same problem occurred with the Mirage. This
scanner has a dual lens system employing many mirrors
(unfortunately the scanner representative did not want to or could
not provide us with technical details). The x-residuals of the off-
line plate revealed an asymmetry with respect to the centre of the
scanner stage, thus indicating that the lens had an asymmetric
position with respect to the CCD line. These x-errors for the three
scanners could be reduced by using additional transformation
terms (x? or xy) in the x-direction (see version 3 in Table 3). The
scan of both plates was done twice except for the Arcus. The
results of the two scans were similar and the average is shown in
Table 3. Table 3 shows statistics of the residuals of the check
17
points of the off-line plate after calibration.
Version 1 includes an affine transformation and y-precorrection.
Version 2 includes the aforementioned 7 parameter
transformation and no y-precorrection. Version 3 for the last
three scanners is like version 2 but with an additional term (x? Or
xy) in the x-direction. The results of the three last scanners are
not optimal due to the aforementioned problem with the
positioning of the glass plate and the dual lens system of the
Mirage. Still with version 3 we get an accuracy of 6 - 10 jum. This
is remarkable especially for the Mirage, which had a scan pixel
size of 63.5 um. The results of the first two A3 scanners is more
representative and show an accuracy of 4 - 7 um. The JX-610
reaches an accuracy similar to that of many photogrammetric
scanners. Version 2 is slightly better than version 1 and does not
require y-precorrection, so it is faster. The errors in x- are slightly
larger than in y-direction, and have a remaining systematic part.
The maximum errors are equal to 2.5 - 3.5 RMS. The achieved
geometric accuracy corresponds to 0.1 - 0.2 pixels. If 8 fiducials
and a 7 parameter transformation can be used, then no y-
precorrection is necessary, while in all other cases the y-
precorrection brings substantial improvement.
Table 3. Statistical values (in Jum) of geometric accuracy after
calibration indicated by the residuals of the check
points.
RMS | Mean | M^
Scanner | Version! Con SR
points
X YA |
Horizon 1 4 8 8 4 1.0 22127
2 8 7 6,13 1-9 | 20 | 20
JX-610 1 4 7 61 5:15 [|:44 .|/16
2 8 5 4 | 4 1 1414-1715
Mirage 1 4 19 ]10:| 51 2. Fl 40] 23
D-16L 2 8 14.1.8.11.-9.1..111.30.].22
3 8 8 9 1 Lil 21.1722
1 4 18] 11] 8 | -3148] 25
Arcus II 2 8 16} 9.9] #4 [3139 [28
3 8 10,19. 1,54. 1.3. 31. 22.1.28
Power- I 4 1216 1-6 (1-1) 32 | 15
Look 8 12; 15 6 agır=-S ch di {2330116
3 8 10.)..6..1..0 1..].26 | 16
! See explanation in text.
Thus, calibration paves the way for use of DTP scanners in
practically all photogrammetric applications, but at a cost: grid
plates, development of calibration software, more computations
for calibration and, if necessary, image resampling.
4.4. Colour misregistration
It was tested by scanning the resolution chart in colour and
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996
