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right affine image 
left affine image 
small object 
Figue-5 : a stereopair of affine images employed 
for the free network adjustment 
      
   
third affine image 
first affine image 
small object 
Figue-6 : three overlapped affine images employed 
for the free network adjustment 
Simulation Model II 
size of object : 100 x 100 x50 mm 
number of overlapped affine images : 3 
convergent angles : -30deg., Odeg., +30deg. 
standard error of measured image 
coordinates : 5micrometers 
number of control points : 5 
number of check points : 20 
The free network theory is essentially a linear the- 
ory. Thus, we must have fairly good approxima- 
tions for unknowns, because the basic equations 
(Equation 1) are non-linear with respect to the ori- 
entation parameters and object space coordinates. 
Further, the free network solution needs an itera- 
tive approach in order to obtain a very high exter- 
nal accuracy. This comes from the fact that the 
solutions obtained in the free network adjustment 
are not unbiased estimates of both the orientation 
parameters at the exposure instants and the real ob- 
ject space coordinates but depend mathematically 
on the given approximations. In this method, the 
first approximations were calculated by contami- 
nating the control point coordinates with random 
errors having a standard deviation of 15 microme- 
321 
ters. Then, the iterative calculation of the free 
network adjustment was performed by regarding 
the solutions obtained in the (i-1)th step as the ap- 
proximations in the i-th step and replacing only the 
approximations of the control point coordinates by 
the true values. 
The obtained results regarding the standard error 
of unit weight, the average internal error at the 20 
check points and the average external error are 
shown in Tables-2 and 3. From these tables the 
following characteristics may be extracted for the 
free network adjustment of overlapped affine im- 
ages: 
1) The geometry of the stereopair of affine im- 
ages in Simulation Model I is rather weak. 
Thus, the average internal and external errors 
of the particular solutions with fixed control 
points are about twice as large as the theoreti- 
  
  
  
  
  
  
  
particular free network 
solution solution 
standard error 
of unit weight 5.3 um 5.3 um 
average 
internal error | 13-3 um 7.7 um 
average 
external error 11.2 um 9.7 um 
  
  
Table-2: the obtained results for Simulation 
  
  
  
Model I 
particular free network 
solution solution 
standard error 
of unit weight | 4.7 Um 4.7 pm 
average 
internal error | 7.1 um 4.1 um 
  
  
average 
external error 6.2 pm 5.8 um 
  
  
  
  
Table-3: the obtained results for Simulation 
Model II 
cal ones. However, employing three over- 
lapped affine images, the obtained average ex- 
ternal error of the particular solutions is al- 
most identical to the theoretical one. 
2) Applying the free network adjustment, great 
improvements are recognized in the internal 
precision. On the other hand, the improve- 
ments in the external precision are 13 percents 
for the weak geometry of the stereopair of 
affine images and only six percents for the 
strong geometry. 
3) The solution sometimes diverged when very 
high weights are given on the free network 
constraints(Equation 12).