The maximal discrepancies dx and dy can reach 12 pixels
that represents 0,25 mm in real pattern scale. Average
mean errors for 22 images are equal m, = + 4,9 of
pixels, what in reality equals m,= x 0,10mm.
The achieved results show, that the errors of restitution of
geometry by scanner UMAX are so high, that it makes
impossible to use scanned and non-corrected images for
photogrammetric processing.
It can be observed on Fig.2, that the scale for direction X
and Y differ for both sets, and that the scale in direction
X very causing change in pattern shape from a rectangle
to a trapezium.
4. THE SCANNER SYSTEMATIC ERRORS
While analysing the scanner errors there is important to
learn a type of errors appearing. Are they steady for
each scanning results, or they change ? An answer to
such question allows to choose the proper method of
scanned images calibration. In case of steady discre-
pancies, the calibrations of each digital image will mean
just taking those discrepancies into consideration in geo-
metrical image evaluation. In case of non-steady discre-
pancies the corrections for each digital image would
be different, and would have to be determined for each
scanning session individually; that would require
additional survey of many scanner reseau crosses, and
would not be economical. There is also another third
possibility: the errors of each scanned image are strictly
systematic; in such situation a steady part of discrepan-
cies creates a set of steady corrections, and a method
should be determined for calculation of variable part of
correction with the use of small number of control-points.
To determine the type of scanning geometrical
discrepancies, there were analysed all digital images of
the pattern which were obtained at the same pattern-
film position on the scanner plate. The beginning of
pixel coordinate system was slightly different for each
digital image of pattern. Considering that shift of
coordinate systems the values of discrepancies were
calculated, and mean errors determined. The average
mean error, which characterises repeatability, was m=
$0.25, my = £0.36 and my- £0.44 of pixels. Those
repeatability errors are over 10-times smaller than the
raw image error (see Tab.1) and gavea hope that after
geometrical correction the results will be at least such.
To select the best systematic errors elimination function
the 3 transformation were considered: affine, projective
and bilinear.
The best results were obtained by transforming pattern
coordinates to its digital image using bilinear transfor-
mation, which eliminates affine and trapezium-like
deformations. With the use of that transformation all the
22 digital images were tested and transformation
coefficient were calculated with the use of all the 352
crosses. The transformation results are shown in Tab.2.
The received average mean error was: m, = +0.7, My =
+1.3 and mp = +1.4 of pixels. The greatest discrepancies
are: max.d, = 2.5pix = 50pm, max.d, = 3.5pix =70ym.
The bilinear transformation residual mean square errors
my are equal for all images (the standard deviation is
only 3% of the average error). The residual mean square
errors my are in average case twice bigger than d, in
22
spite of the fact that the scanner optical resolution is, in
opposite, twice better in Y direction. On the Fig.3 can be
noticed that the d, discrepancies of crosses in each line
Y=const are equal, but they are different for various lines.
Table 2. The results of the bilinear transformation
number | (362 reference points) |
mx my mp (dy)max | (dy)max
1200 dpi) | pixels | pixels | pixels pixels | pixels
0.68 1.92 2.04 2.1 3.6
0.66 1.30 1.46 2 1 3.0
0.74 1.41 1.60 2.4 32
0.74 1.02 1.26 2.5 2.4
0.69 1.16 1.36 2.2 2.7.
0.69 1.19 1.38 2.2 27
0.70 0.99 1.21 23 2.4
0.69 142 1.32 2.2 2.7
0.68 1.13 1.32 2.2 2.6
0.70 1.61 1.76 2.2 3.2
0.66 1.28 1.44 2.1 2.8
0.69 1.78 1.90 271 3.5
0.70 1.36 1.52 2.1 2.7
0.70 1:23 1.41 2.1 2.4
0.68 1.58 172 272 3.2
0.66 1.26 1.42 2.0 2.7
0.68 0.96 1.17 2.1 2.3
0.68 0.97 1.18 2.1 23
0.67 1.31 1.48 2.3 2.7
0.66 1.08 1.27 2.1 2.4
0.67 1.04 1.23 2.1 2.4
0.68 1.08 1.28 2.1 2.4
[m]/n 0.69 1.26 1.44
N|[s|c|43jo|z|vjol|z|z |r |x |- |- Iz lo Ilan Iimlololol»
o +0.02 | +0.26 | +0.23
SCALE
Mx = 0.70
My = 1.62
Mp = 1.76
Fig.3. Deformations of the image J after the bilinear
transformation
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996
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