352 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976 
These possible relative accuracies are very different, but in this case all of them, if focal 
length value is taken into account, point out identical quality of results (they correspond 
with the normalized criterion (Equation 11) of 7XYZ = 4 um). 
CRITERION OF THE PLATE RMS RESIDUAL 
In the case of a simple resection in space, there is no possibility to use the criteria of the 
RMS spatial residual. If one uses the rigorous solution, one can adopt instead the standard 
error of unit weight, 0,, and more precisely the estimation s, of o,. With n control points and 
r unknowns we have: 
in } 
Saar X 
(each point gives two observation equations . s, is of course expressed in micrometers). 
This criterion could be extended to the case of the stereopair and to the case of multi- 
station geometry; but it is easy to understand that it couldn’t be completely satisfactory. In 
particular, the obtained accuracy cannot be deduced from the values of the RMS plate 
residuals for two reasons: One can have more than two rays for one object point and there is 
no evident relation between the RMS residuals of the different plates and a possible increase 
of accuracy due to the use of more than two rays; and the RMS plate residual can include 
slight systematic effects such as residual distortion for example, although these slight 
systematic effects often have little influence upon the final determinations. Then the 
obtained accuracy is better than one would expect from the examination of the s, values. 
PriNCIPAL PARAMETERS INFLUENCING ACCURACY 
The principal parameters influencing accuracy may be classified into three groups. 
GEOMETRICAL CHARACTERISTICS AND COMPUTATIONAL METHODS OF THE PHOTOGRAMMETRIC 
SYSTEM 
It is obvious that accuracy depends on the camera focal lengths, positions and number of 
stations, density of control net or control measurements, and probably, but I ignore to what 
extent, on the choice of the computational method. * 
As to geometry, focal length apart, one can consider two cases. 
Double station geometry. Probably the most frequently used geometry as a rule is well 
characterized by the ratio r = B/O (B = base; O = mean object distance). Needless to say, 
strong values of r imply as a matter of course a convergence of the two camera axes. 
The choice of the computational procedure? depends on the presence or absence of a 
control net. If there is a control net, it is possible to have recourse to resections in space of 
each bundle followed by intersections of homologous rays. At least 10 to 15 control points 
are necessary to obtain correct accuracy. 
If there is only a control distance for scaling, one must use the relative orientation pro- 
cedure followed by scaling to the control distance. The total procedure is statistically less 
accurate than than the previous one. In particular, model distortions could occur due to a 
failure of the photographic plate to lie firmly against the camera frame. 
Multi-station geometry. As far as I know, only one organization? currently uses multi- 
station geometry with no control net but only some scaling distances. The computational 
procedure seems to be a generalization of the one used for the couple (relative orientation 
plus scaling). 
PHYSICAL CHARACTERISTICS OF THE PHOTOGRAMMETRIC SYSTEM 
Among the principal physical characteristics of the photogrammetric system are 
€ the quality of the camera objectives and the lens distortion; 
€ the plate flatness (support and emulsion flatness); 
€ the definition of the object, e.g., natural details or targets (here I mention another possibility, 
* For an equal number of degrees of freedom, one can resort to several approximate applications of 
the least-square method (although, theoretically, there is only one rigorous least-square solution, it is 
complex to program).