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ON THE PROBLEM OF RELATIVE ORIENTATION 
IN MOUNTAINOUS REGIONS * 
By 
A. M. WASSEF, 
SURVEY OF EGYPT 
GIZA, U.A.R. 
  
1. Introduction. 
In an earlier publication (1) the want of correspondence at a 
point was developed in terms of Euler's angles which are in fact the 
inclination *& of the camera axis at the moment of exposure and the 
azimuths y and # of the plane containing them with respect to two sets 
of rectangular axes attached to the respective pictures. The procedure of 
numerical iteration there described was based on the principle of least 
squares and gave the value of each of these elements together with the 
transformation matrix, from measurements of want of correspondence at 
groups of points near the hypothetical positions of minor control (2) 
Practical experience with this method showed that the procedure 
converged rapidly when the photographs were base-lined on their principal 
points; but the difference A between the azimuthal angles ÿ and 9 , though 
usually small, showed a tendency to become appreciable in mountainous 
regions in the presence of large tilts. 
In later studies of the intrinsic precision of the photogrammetric 
techniques (3) A again exhibited a peculiar trait in the polynomial expansion 
of the scale parameter X in mountainous regions ; the terms involving A 
tended to disturb the fidelity of the representation of this parameter by the 
equation of the hyperbolic paraboloid. 
Since the size of A is controllable by swinging the coordinate axes 
in the plane of either picture it was thought worthwhile to follow up the 
consequences of the equality of the azimuthal angles. It will be seen that. 
the new relationships thus derived may lead to a fresh approach to the 
problem of relative orientation in mountainous regions. 
  
This paper was read on Sep. 10, 1960 at the Ninth International 
Congress of Photogrammetry in London.