Ax n i aul 1-13 | 
p $us x Ey (5) 
A i=0 j=0 |». 
yp 3 ij 
There is always some conjecture as to which individual terms from Eqs. 4 
and/or 5 are appropriate for a particular imaging geometry and object space 
control configuration. In order to model platen unflatness, Brown (1976, 
1980) has proposed a block-invariant AP model which includes terms from both 
Eqs. 4 and 5, whereas Fraser (1980, 1981) has employed a photo-invariant AP 
set which comprises only certain of the terms of Eq. 5, up to order n= 3. In 
a recent close-range photogrammetry investigation, Farls (1981) found that 
essentially the same accuracy level in object point determination was 
achieved when each of these AP models was employed (only block-invariant APs 
were considered). This also occurred when spherical harmonics, as proposed 
by EL Hakim & Faig (1979), were used. Experience suggests that what is im- 
portant is not so much the overall AP model selected, but mainly the statis- 
tical significance of the individual image coordinate correction parameters, 
and the extent of their correlations with both other APs and elements of 
interior and exterior orientation. 
In the reported experiment, initial testing was carried out with both 
the photo-invariant APs included in Eq. 4 (with n=3), and a previously 
adopted model (Fraser, 1980; 1981): 
Ax 
az = me ae ce 
p aXy + a,y + azx y+ a xy 
+ ed —2 - ——2 (6) 
b,x + b,y + b4xy + b,x + b,x y + b,xy 
Il 
A 
% 
No significant difference in attainable accuracy resulted, although as anti- 
cipated the former approach yielded marginally higher precision. The results 
to be presented were obtained using the photo-invariant AP set, Eq. 6. 
ACCURACY AND PRECISION ASPECTS 
If checkpoint coordinates are available in the object space the root- 
mean-square (RMS) error s, of photogrammetrically determined target point co- 
ordinates X,Y,Z can be used as an accuracy measure for the self-calibration 
adjustment. However, in the absence of a control point array, a situation 
common to many close-range applications, the accuracy of the photogrammetric 
survey must be assessed in terms of the precision and reliability of the net- 
work adjustment.  Near-homogenous precision is often sought for the X,Y and 
Z object point coordinates, and here a single estimator Oc can be employed 
to express the mean standard error: 
- 1 L 
gc = (cir. 7 
Hp sc ME (7) 
where I¢ is the a posteriori variance-covariance matrix of the object point 
coordinates, and n is the number of non-control target points. 
The RMS error s, can be interpreted as an unbiased estimate of Oc and, 
in the presence of satisfactory model fidelity (functional and stochastic 
models), a basic agreement between precision and accuracy estimators should 
be anticipated. Unfortunately, results of the experiment conducted for this 
investigation indicate, that with the exception of minimally constrained 
self-calibration adjustments, in which the photo-invariant AP set includes 
only first-order polynomial terms, s, is likely to be significantly larger 
in magnitude than the corresponding value of o, . The reason for this dis- 
crepancy is thought to be mainly attributable to an incomplete functional 
modelling of film unflatness. In some respects the stochastic model is also 
159