ACCURACY OF CLOSE-RANGE ANALYTICAL RESTITUTIONS 351 
For example, for the method of the resections in space with direct linear transformation, 
followed by the intersecton of homologous rays, we have r = 11, p = 2, and 
re 
Ke 2n — 11 
Verification of validity is given in the table below (See Appendix A for more details) 
RETE] EE 
R'XYZ/V 2n - M 
7.197 2.16 
10 146 1.49 
15 1.26 1.26 
28 1.18 1.12 
((RXYZIR'XYZ) is the mean of elementary ratios RXYZ/R'XYZ corresponding to four different 
couples at least.) 
The reader will find in Appendix A justification of the method on the basis of assumptions 
probably well verified in the usual practice. 
  
n 
CASE OF THE STEREOPAIR 
Let B be the base, O the mean object distance, and p the common value of left and right 
focal lengths (Figure 4). It is obvious that, on a first approximation, RZYX, the RMS residual, 
is for a particular geometry in inverse ratio to p (of course, we suppose all the other 
parameters of the system, that is, objective, emulsions, comparator, etc., to be invariant); and 
RXYZ, for a given ratio B/O (and the same axis orientations), is proportional to O, on the 
condition that the ratio D/O (where D is the depth of the volume) is constant. 
Subsequently, for r — B/O fixed, we have 
rXYZ - RXYZ L- constant (11) 
where rXYZ is the normalized RMS residual. It is obtained from the RMS residual by multi- 
plication with the mean scale of the pictures, and is expressed in micrometers. 
It can be thought that such an expression depends exclusively on the ratio B/O (and 
perhaps on the camera axis orientations) when using a certain type of camera, comparator, 
and computational method. We will find it true from practical experiments. 
Some authors use another kind of normalized criterion which in my opinion is imperfect. 
If D is the greatest dimension of the measured object, they consider 
r xyz = BXYZ 
and name it “relative accuracy”. Such a criterion is of course convenient for the customer, 
but it does not give any precise indication regarding the photogrammetric accuracy. For ex- 
ample, let us consider D = 10 m, O = 7 m, and fixed positions for the two points of 
view. The work can be done with many available focal lengths, and thus we can obtain 
  
  
  
focal length RMS residual “Relative accuracy’ 
P xyz RXYZ/D 
50 mm 0.56 mm 1/ 20000 
100 mm 0.28 mm 1/ 40000 
200 mm 0.14 mm 1/ 80000 
300 mm 0.09 mm 1/120000 
O 
S 
1 & ——— B > S2 ; 
Fic. 4. Geometry of the stereopair.