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data, or data from the camera lens test, 
or a determination of lens distorsion 
simultaneously with the elements of the 
camera internal and external orientation. 
In the last case the collinearity 
condition is supplemented with some 
terms, taking into account the influence 
of the radial and tangential distortion: 
xsx.(kir?skor**kirt8)]tp.(ry? t2x,? )*2poxz2. 
[5) 
ze2;(k. r?-k.ri!4k.r9jeZ2pix,2rP*pao(r?422,?), 
where 
rsix.^ = ZA) LE, Xn X-Xo , Le = Eg 
Experimental investigation 
Using the advantage of single photographs 
which allows a better analysis of the 
influence of different factors on the 
calibration accuracy, an experimental 
test calibration is done. The purpose of 
the investigation is to recommend the 
distribution and the number of the 
control points, as well as to check the 
effectiveness of the sophistication of 
defining the interior orientation and its 
influence on the accuracy of the 
calibration and of the determination of 
the camera exterior orientation elements. 
A test object is created. The points are 
distributed in such a way that a unique 
solution for the  interrelated elements — 
the coordinate Ys of the projection 
centre and the focal length f — and for 
the distortion coefficients is ensured. 
The distribution of the points is shown 
in Fig.2:- 
17 points in the farthest plane III, 
9 points in the middle plane II, 
7 points in the piane nearest to the 
camera station - plane I. 
The coordinates of these points are 
precisely determined by geodetic methods. 
The photographs are taken from a 
centrally located camera station using 
two models of Zeiss Jena focusable 
universal cameras UMK 10/1318 in the 
case of a photoplane, parallel to the 
planes - with ‚control ‚points of. the test 
object. The image coordinates of the 
photoplates points are measured on the 
Zeiss Jena Stecometer stereocomparator. 
To estimate the influence of the number 
and distribution of the control points a 
simultaneous analytical determination of 
  
     
     
  
    
    
    
    
   
   
   
   
  
   
  
  
   
   
   
  
  
   
   
  
    
   
   
     
   
     
  
   
  
     
    
  
  
    
   
   
    
     
    
    
   
    
     
     
   
     
    
   
   
  
     
       
the camera station external orientation 
elements and of the camera interior 
orientation elements is done with and 
without determining the lens distortion. 
The analytical model used is based on the 
collinearity condition supplemented with 
terms accounting for the lens distortion 
(5). A program for processing the data 
from single photos is made. The 
geodetically determined space coordinates 
of the points are assumed correct and the 
measured orientation elements are taken 
as initial approximation. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
1 T 4 
21 2T. 24 
30 NO rumes 
^ 2 
» 11 b 
A à 28 =] 5 
12 i4 17 23 IH plane 
31? $33 
3 2 ‚6 
23 er 26 
| II plane 
18 19 20 
I plane 
Fig.2 
Calculations are made in 7 different 
cases of distribution and number of the 
points "located in two or three of. the 
planes (Fig.2). 
Conclusions 
The experimental and theoretical results 
allow the following conclusions: 
1. For pre-calibration of the camera by 
single photos it is recommend to 
distribut the test. object points in two 
planes which are at a maximum distance 
one from another but are within the range 
of the camera depth brightness for the 
focusing distance used. As an optimum 
number it is recommended to use 6 points 
in each of the two planes whose images 
should lie near the edge of the photo, 
parallel to the principle line. 
2. The determination of the lens 
distortion requires also radially located 
points which are evenly distributed in 
the farthest plane of the test object. 
3. The differences observed in the values 
of the focal length and of the