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Ir Wassef 
  
RELATIVE ORIENTATION IN MOUNTAINOUS TERRAIN, DISCUSSION 153 
to give some comments on his paper which has 
been announced for this Meeting. 
Mr A. M. Wasser: In this paper I showed 
that on each photograph there are two lines 
where the y-parallax wants correspondence. 
This is expressed as a simple three-term linear 
function of the relative altitude of the camera 
at the moment of successive exposures and the 
angle between the directions of each axis at 
these moments; the third term being a constant. 
The two lines are the invariant direction and 
the direction of tilt which is a triangle to the 
invariant direction; both lines are radial from 
the transverse point. We found the position by 
rapidly converging iteration. The expression 
given for the y-parallax per unit distance along 
either direction includes the influence of the 
second order terms. The x-parallax is fully 
expressed in the coefficients, and it may, there- 
fore, be expected that they represent the y- 
parallax with high precision in mountainous 
regions. The idea came from practical experi- 
ence with analytical methods using the eulerian 
angles which are the angles between the direc- 
tions of the camera axis at two successive 
exposures and the two angles which define the 
geometry of the plane containing these two 
directions with reference to the co-ordinate 
systems of the two pictures. The difference of 
the azimuthal angles appeared always to be 
small when the photographs were baselined on 
their principal points. 
As the little difference can be further 
reduced by swing, it was thought worth while 
to follow up the consequences of the quality of 
the geometry. It appeared in this case that the 
only invariant of the transformation would fall 
in the plane of the picture at right angles to the 
direction of tilt. It is hoped that this idea, when 
employed in conjunction with the standard 
procedure, will be found to help make relative 
orientation in mountainous regions converge 
more rapidly and give higher precision. 
Allow me to summarise. Assuming my anal- 
ysis is correct, there are two directions on 
each half picture where the y-parallax can be 
expressed almost exactly by a simple equation 
and three unknowns, one of which can be elim- 
inated by taking differences. The main advan- 
tage is that the x-parallaxes are fully taken into 
consideration in the coefficients, hence the 
expected utility of the principle in relative 
orientation in mountainous regions. 
Mr A. J. VAN DER WEELE: I should like to 
thank Mr Wassef for his contribution. I hope 
he will excuse us if we do not say much more 
about this paper because it is too technical to 
be able to comment on it without further study. 
I should now like to call on Mr Hallert for 
his comments on my paper. 
Mr B. HarLERT: We have been dealing 
with the problem of relative orientation in 
mountainous terrain in our country too. We 
have started to treat the problem of adjustment 
of the relative orientation, in particular after 
y-parallax measurements in certain points. If 
we choose the points on one of the photographs 
in definite positions — five points, for instance, 
in regular precision — the complete normal 
equations have been solved for the general 
case; in other words, for arbitrary elevation 
differences. 
The solution is presented in a paper from 
Ohio State University which I sent to the 
President of this particular panel. Mr Ottoson 
has further performed solutions for six points 
and for nine points for measurements of y- 
parallaxes. 
The nine-point solution is particularly made 
when we are going to compute the square sum 
vv in order to compute the mean square error 
of unit weight for the y-parallax measurements, 
because, as you know, the standard error 
decreases considerably with the number of 
redundant observations. 
We have the formula for the standard error 
of the error if we take that as s, divided by the 
square root of two divided by the number of 
redundant observations. For nine points we 
have this one to about thirty-five per cent. For 
six points this is as large as seventy per cent. 
This is the main reason for our solution of the 
nine-point scheme. 
Further, I should like to refer to the report 
of sub-Commission, IV:4, Fundamental Ques- 
tions in Relation to Controlled Experiments, 
where in one of the sub-Commissions — sub- 
Commission 1 — a very rough terrain was 
chosen for the test. (See Vol. XIII, Part 2). 
In Appendix 1 of the report, the complete 
solution of the nine-point problem by Mr Ot- 
toson is given: the corrections to the elements 
of orientation; the weight and correlation 
numbers; and the expression for the standard 
error of unit weight. 
In Table 1 of the report itself we have 
shown a number of tests of the y-parallax 
measurements which were performed by dif- 
ferent organisations. We did this particularly to 
compare the results of the adjustment if we 
used the formulae for flat terrain, or approxi- 
  
  
  
    
  
   
  
   
  
  
   
  
   
    
   
    
    
    
    
   
  
  
  
  
  
   
  
  
   
  
  
  
  
   
  
  
  
  
  
   
   
  
  
  
   
   
   
   
    
  
   
  
  
  
  
   
  
  
    
   
  
  
   
  
  
  
   
  
  
  
  
  
    
  
     
  
  
   
    
  
  
  
  
  
  
  
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