accuracy by factor 2 compared with the results of
IMAGE1.
As a conclusion of this part of the test one can state that
the theoretical precision of 1/1000 pixel can be nearly
reached for perfect, undisturbed targets (0.002 pixels).
More realistic features can determined with an mean
accuracy of about 0.02 to 0.005 pixels. In addition these
results have proved the mathematical model used for the
generation of artificial patterns.
4.2 Testfield Calibration
All test participants have delivered their measured image
coordinates of the testfield images. These values have
been used as observations in a free net bundle
adjustment program with self-calibration facility (MOR). All
testfield points have been used as datum points. The
parameters of interior orientation include:
principal distance (focal length): C
principal point: Xo Yo
radial distortion: ay, a,
asymetric distortion: b,, D»
affinity and sheering: C4, C2
In order to compare the image accuracy the RMS values
of image coordinates have been evaluated. These values
can be used as an estimation of point measurement
accuracy.
estfield calibrati
MOR bundle adjustment
pixel residuals of image coordinates in x'
0,055
0,050
0,045
0,040
0,035
0,030
0,025
0,020
0,015
0,010
testfield calibration
MOR bundle adjustment
pixel residuals of image coordinates in y'
0,060
0,055
0,050
0,045
0,040
0,035
0,030
0,025
0,020
0,015
0,010
rm
VG
A/B
Figure 5: Residuals of image coordinates
Figure 5 shows the residuals of image coordinates in x-
and y-direction as obtained by the test participants. Again
the best results have been achieved with edge-based
ellipse operators showing a mean accuracy in image
space of about 0.02 pixels. It has also been confirmed
that center-of-gravity operators lead to worse results
(0.05 pixels).
The analysis of the RMS of image coordinates gives an
indication of the potential of image accuracy for real
images. Due to variations in imaging and lighting
directions, artifacts of target surfaces (Zumbrunn 1995)
and noise (by camera electronics) a lack of accuracy of
factor 2 compared to synthetic images has to be
expected. A closer look to the bundle adjustment results
shows that the number of gross errors (which are
automatically rejected) varies with the type of operator.
Therefore the pure RMS value of image coordinates or
the sigma 0 of least-squares adjustment should not be
used in order to evaluate the accuracy of a complete
system.
The adjusted 3-D coordinates have not been investigated
in detail. Due to the free net adjustment process it is not
possible to compare object coordinate values. An
improved test procedure should therefore be performed
with a testfield with precisely measured object
coordinates or distances. They were not available at the
time of the test period.
Figure 6 shows the standard deviation of object
coordinates. In the best case the RMS of adjusted object
points is estimated to +8um in object space. This
compares to an image accuracy of about 0.02 pixel if the
mean image scale of 1:25 is taken into account. With
respect to the largest object diameter (1.1m) a relative
accuracy of 1:140.000 has been obtained.
Standard deviation of object points
[um]
N RS © ©
S(x) S(y) S(z) 3-D vector
|
Figure 6: Standard deviation of object points
It must be pointed out that these results have been
achieved under laboratory conditions and that they
display mean accuracies. For practical applications the
number of gross errors as well as the maximum residuals
have to be considered.
328
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
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