354 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1976 
the RMS spatial residual RXYZ is proportional to the standard deviation o of the measure- 
ments, that is, RXYZ = go and, if we consider two different geometries 1 and 2 and attempt 
to estimate the accuracy gain g (reference geometry 1), we have 
_R:XYZ- B., XYZ l- qi 
8 ii. qs 
where g is independent of c. 
(b) Determination of an optimum computational method for a given geometry. Again, 
there is no need to know the value of the standard error. 
(c) Prediction of the absolute accuracy of one particular geometry for a given topology 
(fixed number of stations), fixed physical characteristics (emulsion, objective quality, and 
comparator accuracy), and fixed number of image measurements. But this is only possible if 
we have a good estimation of the standard deviation c, an estimation which should be 
derived only from practical experiments. 
As I stated earlier, the normal model is satisfactory for the simpler photogrammetric 
systems. I don't know if this is true for n-station geometries, but it seems likely enough. 
THE STEREOPAIR (SYMMETRICAL CASE) 
INTRODUCTION 
In the symmetrical case, the two camera axes make the same angle with the base. Of 
course, this has to be understood in a comprehensive way: practically, the angles should not 
differ by much more than 10 grads. Even in this simple case, it is difficult to find in the 
literature practical accuracy studies with some statistical value. Indeed a lot of time, instru- 
mentation, and money are necessary to perform such studies. 
Subsequently I chiefly use two data sources: 
(a) Accuracy studies performed by the IGN5*, 
The IGN studies employed the following photogrammetric system: 
€ metric cameras, with Gevapan 33 emulsion; 
€ symmetrical case; 
€ Zeiss Asco-Record comparator; and a 
€ 10 m by 12 m by 2 m (width, height, depth) test-field with the following accuracies for micro- 
geodesic target determinations: 
30 um for the x-axis (parallel to the base), 
60 wm for the y-axis (horizontal, perpendicular to the base), and 
70 um for the z-axis (vertical). 
(2) studies performed by the Karara/Abdel Aziz team.!? 
The questions which will be examined here more or less exhaustively are the following: 
e The effect of measurement redundance (evolution of accuracy with repetition of comparator 
measurements per image point, with the multiplication of neighboring targets defining an object 
point, and with the multiplication of frames per station; maximum accuracy; independence of 
the parameter measurement redundance and of the parameter geometry; and evaluation of the 
RMS bias of the photogrammetric system); 
€ The effect of the geometry (ratio of the base to the mean object distance, and camera axis con- 
vergence; and evolution of accuracy with the number of control points if a control net is used in 
the system); 
€ The prediction of accuracy (simulation accuracy predictor, and Karara/Abdel Aziz predictor, 
comparison and validity); and 
€ The use of non-metric cameras. 
I won't study the effect of computational methods on accuracy. 
The most important results (IGN),5$ relating to the first two questions are summarized in 
Tables 1 and 2 which record gains in accuracy when varying different parameters. The ac- 
curacy criterion is always the RMS spatial residual rXYZ, referred to the image plane and 
expressed in micrometers. The reference case is always for a given geometry and camera, 
the one most economically and quickly applied (only one right and left setting per object 
point). 
If rXYZ and rMXYZ are the RMS and maximal spatial residuals for the reference case, and 
r'XYZ and r'MXYZ are the corresponding quantities for the studied case, the accuracy gain g 
is defined as