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 
161