In the experiment conducted, 2nd and 3rd order polynomial terms in the AP
model not only degraded precision in minimally controlled self-calibration
adjustments, but also caused a marked fall-off in accuracy.
DETAILS OF THE EXPERIMENT
Imaging Configuration
The camera employed in the close-range photogrammetric survey was a 500
ELM Hasselblad, with an 80 mm Zeiss Planar lens. Four exposure stations were
established in a convergent imaging configuration and an object target field
of 82 points was used. Of the points, 64 lay in the XY plane and the remain-
ing 18 were at a "height" of Z=75 cm (about 25% of the average photographic
distance of 3.5 m). The area occupied by the grid of 64 points was about
2x2 m, and the adopted image geometry resulted in a mean photo scale of
about 1: 40.
The X, Y and Z coordinates of the 82 object target points were deter-
mined photogrammetrically using a 6-photo self-calibrating bundle adjustment
with minimal control. A metric Hasselblad MK-70 was used for this task, the
resulting mean standard error of the object coordinates being Ce = +.0.015 cm
(+ 0.010 cm in the X and Y coordinates and + 0.022 cm in the Z direction).
For the subsequent data reduction of non-metric camera imagery the coordinates
computed in the MK-70 self-calibration adjustment were assumed to be "true",
Adjustments
Three combinations of polynomial coefficients from Eq. 6 were used to
make up the vector Sp of photo-invariant APs, according to the order of the
terms:
…T
lst order - $1 - (bi b,)
2nd order - SI, (b, yb, b, 0,27)
3rd order. =. So. (b, b, b, b, Da be 8, 82 25 2.)
p3 102 D3 Py Og 681 82 35 4,
The coefficients b, and b, are simply non-orthogonality and affinity para-
meters. For any one photo, individual parameters forming §_. were only
suppressed when correlation coefficient magnitudes of greater than 0.95 were
encountered. Most, but not all photo-invariant APs were statistically signi-
ficant in any one adjustment, but non-significant parameters were usually
retained. This was because the broad aim of the project was to assess, for
2-, 3- and 4-photo networks, the impact of lst, 2nd and 3rd order photo-
invariant APs on the precision and accuracy of object space coordinate deter-
mination, for three different control point configurations.
RESULTS
In discussing the results it must be kept in mind that the aim of employ-
ing a mixed block- and photo-invariant AP model is to both recover "stable"
camera calibration parameters and to compensate for film deformation effects.
Whilst it is perhaps a simplification to some extent, residual systematic
photo coordinate errors are interpreted here as being due solely to image
point non-coplanarity.
Salient results of the experiment conducted are listed in Table l, where
for 2-, 3- and 4-photo imaging configurations, adjustment results are given
for each of the three photo-invariant AP sets, and three control point confi-
gurations. For each adjustment, the RMS value s, of the checkpoint coordinate
residuals is listed, along with the mean a posteriori standard error Oc of the
object point coordinates and the photo coordinate RMS values s. and Sr.
x y
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