International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004
Due the nature of systematic errors, they are less problematic
since they can be compensated for through calibration. A
consistent pattern and magnitude of error can be modelled
into a spatially reference calibration applied to each image
collected on the scanner.
Random errors are those that do not follow any discernable
pattern and therefore may not be removed through a
traditional calibration procedure. If the magnitude of the
random error is small, it should not affect the reliability of
the imagery for photogrammetric use, however, should this
error be large and show a high variability it may not be
suitable.
2 METHODS
2.1 Data Collection
The analysis began through repeated scans of a precision
grid plate. The plate was constructed of BK-7 optical glass
and was etched with eighteen horizontal and vertical lines at
a spacing of twenty millimetres covering an area 260 mm
squared. This created a grid pattern with 324 grid
intersections. The plate was scanned ten times on both a PG
(Leica Geosystems DSW600 Photogrammetric scanner) and
a NPG scanner ($10,000 US high performance graphic arts
scanner — manufacturer name withheld), with no wait period
or delay between scans. This was performed to establish the
precision of scans collected in quick succession. The images
were collected at 12.5 jum (2032 DPI) and consisted of only
one image band. Once completed, the intersections in each
scanned image were compared to the expected calibrated
intersection locations and X and Y-axis error values
calculated.
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to
Data Analysis
In an effort to determine whether a systematic pattern of
error or one that was largely random existed, both global
summary and local analyses of error were performed.
Summary statistics were calculated, including average error,
standard deviation, minimum error, maximum error,
skewness and kurtosis. The first four metrics provide an
indication of the magnitude and variability of error. The
latter two offer a sense of how well the errors follow the
predicted normal distribution of random errors. To further
test for a systematic pattern in error, a more detailed analysis
was performed. The errors within the first scan from each
scanner were used as an empirical calibration. The X and Y-
axis errors from this scan were subtracted from the corollary
intersection error in each subsequent scan. If the residual
values showed a significant reduction in magnitude, this
would imply that the film scanner in question is capable of
supporting some degree of calibration to control error.
In addition to summary statistics, the X and Y-axis errors
were plotted spatially to identify any regional trends in the
error patterns. For each dataset, a standard deviation value
based upon the ten scans, was determined for both X and Y-
axis error at each grid intersection. These values were
interpolated to model a contiguous surface for visualization
of error variability
3 RESULTS
3.1 Results of Global Error Analysis
Summary error information is presented in Table 1. While
the mean error for both NPG and PG scanners deviates little
from zero, there are clear distinctions between the standard
deviation (sigma) values. The PG scanners produced sigma
values that were less than 0.07 pixels showing a strong
central tendency. The NPG units showed much higher
sigma, with 0.77 and 1.13 pixels respectively for the X and
Y-axes. The large sigma values demonstrate a strong
variability of error in the NPG scans.
BI X Axi|NPG Y AxisPG X AxisPG Y Axis
Error Error Error Error
Mean _|-270261E-08 |-3.78701E-09 |3.00821E-09 |-1.67563E-09
Std Dev |0.774339714 |1.138040972 |0.06837934 |0.066504326
Skew |0.343904154 |-0.515024721 |0.019562816 |-0.045172838
Kurt |0.46377147 -0.187309652 |0.900246728 |0.782021849
Min |-2.66069 -3.68723 -0.24816 -0.242151
Max |2.22324 2.72771 0.31695 0.280056
Range |4.88393 6.415 0.56511 0.522207
Table 1 — Summary Error Statistics (in pixels) for PG and
NPG scanners
The absolute range of values was also markedly higher on
the NPG scanner than the PG unit, showing a higher degree
of variance in both magnitude and algebraic sign of error.
As mentioned earlier, in an effort to quantify how much of
the error was due to systematic sources, an empirical
calibration was used. The errors from the first scan
performed on each scanner tested were subtracted from each
of the nine remaining scans. The results are presented in
Table 2.
NPG X Axis NPG Y Axis PG X Axis PG Y Axis
Error Error Error Error
Mean |-3.68627E-08 2.61438E-10 7.32449E-10 |-9.59827E-10
Std Dev |0.375661004 1.042602416 0.040442633 _0.040098813
Skew |2.314461622 -0.368984042 0.051477459 /|0.192260271
Kurt 7.936765987 0.174791663 0.305202294 [1.145695749
Min -0.690781 -3.68723 -0.1398593 -0.140139405
Max 2.22324 2.5712 0.1503055 0.193613
Range j2.914021 6.25843 0.2901648 0.333752405
Table 2 — Summary Error Statistics (in pixels) following
calibration, for PG and NPG scanners
Following calibration, the scans from the NPG unit showed
only modest reduction in errors and still maintained an
unacceptably high overall error. Interestingly, the NPG X
axis errors appear to have been affected to a greater degree
than the Y-axis errors. The Kurtosis value for NPG X axis
rose dramatically, indicating a very strong peaked
distribution, where before calibration the kurtosis was only
very moderately positive. It would appear that calibration
was effective at removing some systematic error from NPG
scanners but the magnitude of the remaining error continues
to preclude their use in photogrammetric production. The
photogrammetric unit also saw a reduction in error following
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