auig- 
| des- 
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'ering, 
Photo- 
; 1948. 
' Bild. 
9 
  
  
Communication to 
VIII International Congress for Photogrammetry 
Reprint from 
Svensk Lantmateritidskrift 
Congress Number 1956 
Commission 11 
THE INFLUENCE OF RADIAL DISTORTION AND OTHER 
SYSTEMATIC ERRORS UPON PHOTOGRAMMETRIC 
MODELS FROM APPROXIMATELY VERTICAL 
PICTURES 
By B. Hallert, Stockholm 70, Sweden 
Introduction 
If radial distortion is present in the aerial pictures and the distortion 
is not compensated in the plotting instrument, deformations of the pho- 
togrammetric model will occur, that may cause considerable systematic 
errors of particularly the elevations and also of the x- and y-coordinates 
of the model, 
Concerning the elevations, two different types of deformations have 
to be distinguished, namely: 
1. Deformations due to the direct influence of the distortion upon the 
x- (horisontal-) parallaxes of the model. 
2. Deformations due to the indirect influence upon the x-parallaxes 
of the model via the y-parallaxes in the orientation points. 
The first (direct) type of deformations has frequently been treated 
in the photogrammetric literature, see for instanse Bean [1] or Tham 
[2], but the latter (indirect) one seems to have been more or less 
neglected. Schwidefsky [7], briefly mentions this effect, however. In 
this paper a brief demonstration will be made of how the model will 
be deformed due to the systematic errors of the relative orientation as 
caused by the influence of the radial distortion upon the y-parallaxes. 
We will start with the treatment of the influence of the radial distor- 
tion upon the elevations. 
As is immediately clear, the radial distortion will cause varying y- 
parallaxes in the model in addition to those, caused by other circum- 
stances, for instance lacking reconstruction of the relative orientation. 
See for instance [2]. For the derivation of the actual formulas we will 
temporarily assume that the relative orientation is exactly reconstructed