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into the image space. This means the results 
are independent on the circumstances of the pho- 
tography. 
To get the numbers of accuracy of a specific con- 
figuration, you have to multiply the results by a 
scaling factor s-(h/c)o, where h denotes approxi- 
mate object distance from the camera and c is 
the camera constant. o is the estimated noise 
level on images. The results of the test previ- 
ously mentioned are depicted in Table 1. 
  
Photos 2 3 4 5 6 7 8 9 
Axis 1 1.006 0.513 0.513 0.513 0.475 0.438 0.402 0.368 
Axis 2 0.296 0.254 0.237 0.221 0.209 0.201 0.190 0.182 
  
Table 1 The accuracy of line respect to number 
of photos included. /Heik92/ 
Same kind of tests were employed for circles. In 
this case we tried to find out if the accuracy gets 
better with an increased number of observations. 
Another interesting factor was to see, how the 
size and the shape of the average ellipse changed 
when the object circle was tilted. The results are 
presented in Figures 6 and 7. 
  
  
  
  
  
  
L 
e 
n 
g.5. 
t 
h 4. 
o 9- 
f nk 
a À. 
x 
i l =< 
S 2040 80 160 320 
Number of observation points 
Longer axis of ellipss .. — ——— —— 
Shorter axis of ellipse ------------- 
Avarage axis of ellipse -..----------- 
  
Figure 6 The accuracy of intersection res- 
pect to the number of observati- 
ons. Circle feature. /Heik92/ 
Results are quite promising, but we have to keep 
in mind no errors were assumed in the orienta- 
tion parameters of the photographs. 
To get some knowledge of accuracy of the ex- 
terior orientation, some tests were designed. 
The determination of exterior orientation para- 
meters was accomplished both with pointwise 
and feature based methods for comparison. Fea- 
tures used were space lines and 3D-splines. 
  
  
  
  
L 
e 
n. 2.0 
g 
t 1.6 
h 
1.2 
Oo 
£ 0.8 
a 0.41 as 
X 1 1 1 1 1 1 1 J 
i 10 20 30 40 50 60 70 80 9 
S Angle of normal and xy-plane 
Longer axis of ellipse 
Shorter axis of ellipse +-77---7%---—=--—- 
Ava - age axis of ellipse 777707 T7 
  
  
  
Figure 7 The accuracy of intersection 
respect to the orientation of the 
object feature. Circle feature. 
/Heik92/ 
In the case of lines, the minimum number of ob- 
ject lines needed is three. Object lines should 
not be parallel and all three lines should not in- 
tersect at the same point for the exterior orienta- 
tion to be implicit. 
Sari Metsämäki studied the use of linear fea- 
tures in exterior orientation /Mets91/. The 
observations were done on the photographs as 
shown in Figure (8). The results of the estima- 
tion are given in Table (2). The reason, why 
there were 24 observations in the feature based 
method and 8 (x and y are considered as one ob- 
servation each) in pointwise, is the use of collin- 
earity equation which produces one additional 
parameter per observed point. In this way re- 
dundancy was the same in both cases. The preci- 
sion of the determination is presented with 
weight coefficients of the orientation parameters. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
a) b) 
c) d) 
Figure 8 Observations made in feature 
based method a), b) and in point 
wise method c), d). /Mets91/