discrepancy is 0.1 pixel in x and 0.05 pixel in y. The re-
sults of the bundle adjustment (version 6 in Table 2)
show that the accuracy is only slightly degraded as com-
pared to that of pixelsynchronous frame grabbing. This
close agreement of the results is attributable to the high
degree of redundancy and indicates that the accuracy is
limited by effects other than the synchronization. The
shear determined by the additional parameters in the
bundle adjustment is in good agreement with the values
computed in the analysis of the frame grabber and of sig-
nal transmission.
0.1 Pixel
.— —.
et ome AE VE, FL E US
E e sie ak =
re Ta” NS RR az TS Qa Es
EE eire
"
Figure 16 Differences of image coordinates between
PLL line-synchronization and pixelsynchro-
nous sampling for 6 frames.
The results of the two synchronization methods were fur-
ther analyzed by using the object coordinates obtained in
a version with minimum control and pixelsynchronous
sampling as reference coordinates for a version of the
PLL line-synchronization imagery with identical control.
The RMS difference of the object space coordinates are
0.036, 0.033 and 0.044 mm in X, Y, and Z respectively.
The accuracy in image space is 0.11 and 0.10 pixel in x
and y respectively. This shows that an internal precision
of three-dimensional measurements of 0.01 pixel can be
attained when identical illumination and imaging condi-
tions are present. The RMS differences correspond to 1
part in over 70000.
3.5 Limiting Factors
The theoretical precision estimates and the empirical ac-
curacy measures of version 5 differ by a factor of 2 in X
and Y and 1.5 in Z. Potential origins of this large differ-
ence were consequently investigated.
The precision of the reference coordinates is insufficient
to verify this accuracy level. When correcting the theo-
retical precision estimates for the precision of the refer-
ence coordinates and the centricity of the targets used by
the theodolite and CCD-cameras the difference to the
empirical accuracy measures is decreased to factors of
1.6, 1.4, and 1.1 in X, Y, and Z respectively. It was al-
ready noted above that the comparison to the reference
coordinates exhibit systematic differences (see Figure
16). These could at least in part be attributable to effects
of smaller local illumination gradients. This was also
found in other studies through slight variation of the illu-
mination conditions. The effects of the use of an affine
transformation instead of a perspective transformation in
LSM was also investigated. Considering that the average
error will result in a shift it was concluded that the effect
thereof can be neglected as compared to the influence of
local illumination gradients. A further modelling with
supplementary additional parameters (Brown, 1976 and
Grün, 1978) was attempted but did not lead to any im-
provement.
It was thus concluded that the accuracy in this test was
primarily limited by the local illumination gradients, the
non-uniform background, the small image scale, and the
large difference thereof. Local illumination gradients
could be eliminated by the use of retro-reflective targets.
The non-uniform background can be improved on by de-
signing a larger area around the targets. The image scale/
target size in the imagery, i.e. the number of pixels onto
which a target is imaged, can be improved by using larg-
er targets and/or a camera with higher "resolution". The
first option is not always practical. The target diameter of
20 mm across a 2.6 m large object is already quite large
for practical applications. This can in fact be improved
with retro targets as their return is much better and scat-
tering significantly increases the apparent diameter in the
imagery. A high "resolution" camera, i.e. a camera deliv-
ering over 1024 x 1024 pixels, would also reduce the ef-
fects of local illumination gradients and non-uniform
background as the area surrounding the target affecting
the target localization is smaller. Finally the large varia-
tion of image scale could be reduced when using a longer
focal length than the 9 mm lens used here due to space
restrictions.
4 CONCLUSIONS
The radiometric and geometric characteristics of a num-
ber of elements involved in image acquisition with digi-
tal imaging system have been outlined and their effects
on the accuracy of three-dimensional photogrammetric
measurements discussed. À number of sources leading to
potential degradations have been located. The perfor-
mance of off-the-shelf equipment was demonstrated with
a three-dimensional accuracy test. It could be shown that
accuracies of 1/85™ of the pixel spacing can be attained.
It was found that accuracies comparable to pixelsynchro-
nous frame grabbing can be attained with PLL line-syn-
chronization when a highly redundant network is used.
The limitations indicate that even higher accuracies
should be attainable under better environmental condi-
tions as no limitations found so far are of a fundamental
nature. It can thus be expected that accuracies approach-
ing the 1/100! of the pixel spacing can indeed be at-
tained.
5 REFERENCES
Beyer, H.A., 1988. Linejitter and Geometric Calibration of
CCD-Cameras. International Archives of Photogramme-
try and Remote Sensing, Vol. 27, Part B10, pp. 315-324.
and in: ISPRS Journal of Photogrammetry and Remote
Sensing, 45, 1990, pp. 17-32.
