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—€——————————————Á— S. 
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If measured image coordinates (XeYc) have ran- 
dom errors, the system of linearized observation 
equations can be described as 
v = AXx -L (11) 
where v is a vector of residuals to the observa- 
tions. The free network adjustment is then carried 
out in a following manner (Ebner (1974)) 
vIPv — min 
under the condition Glax =0 (12) 
where P is a weight matrix of the observations. 
TESTS WITH SIMULATION MODELS 
ULTRA-PRECISE THREE-DIMENSIONAL 
MEASUREMENT OF SMALL OBJECTS USING 
A CONVENTIONAL COMPARATOR 
The derived orientation theory of overlapped 
affine images was tested with simulated examples. 
For the construction of simulation models a stere- 
opair of affine image planes of small objects mea- 
sured by a comparator were assumed to be em- 
ployed and the image coordinates of 25 object 
points were calculated by means of the convention- 
    
left image |. 
small object 
Figue-3 : a stereopair of affine images employed 
for the ultra-precise measurement of 
small objects using a comparator 
  
  
  
  
  
  
  
  
  
  
> © 
Figure-4 : arrangement of check and control points 
al three-dimensional coordinate transformation 
equations under the following conditions (See 
Figures-3 and 4.): 
size of small objects : 100x100 x50 mm, 
10 x10 x0.15 mm 
convergent angles : Odeg., 20deg. 
number of control points : 5 
number of check points : 20 
Then, the perturbed image coordinates were pro- 
vided in which the perturbation consisted of ran- 
dom normal deviates having standard deviations of 
5 micrometers for the first object and 1 microme- 
ter for the second very small and thin ob- 
ject,respectively. 
The obtained results regarding the average internal 
error at the 20 check points and the average exter- 
nal error are shown in Table-1. We can find in 
Table-1 the following characteristics of the orien- 
tation problem of overlapped affine images: 
1) Ultra-precise three-dimensional measurement 
of small objects can really be performed by a 
conventional comparator using the proposed 
orientation theory, and 
2) The second object is very small and thin. 
However, the obtained external accuracy is 
rather high. This means that affine transfor- 
mation can be effectively applied to the analy- 
sis of satellite CCD camera imageries, because 
the satellite CCD camera has a very narrow 
field angle and because height differences in 
the photographed terrains are small in compar- 
ison with the flying height of the platform. 
  
very small and 
small object | thin object 
  
average = 
internal error 7.4 pm 4 pm 
average 
external error 
  
  
  
  
  
11.2 pm 1.9 um 
  
Table-1: the measurment results of smsll objects 
using a conventional comparator 
FREE NETWORK ADJUSTMENT 
In order to explore the practical characteristics of 
the proposed free network theory for affine im- 
ages, two simulation models were constructed un- 
der the following conditions (See Figures-5 and 
6.): 
Simulation Model I 
size of object : 100 x100 x50 mm 
number of overlapped affine images : 2 
convergent angles : -30deg., +30deg. 
standard error of measured image 
coordinates : 5micrometers 
number of control points : 5 
number of check points : 20