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and correla- 
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plicated than 
ANALYTICAL AERIAL TRIANGULATION, DISCUSSION 27 
necessary. For these reasons I suggest that the 
correction equation is not sound from the 
mathematical point of view and should not be 
incorporated in a sound theory of analytical 
aerial triangulation. We cannot just incorporate 
any of an infinite number of possible equations 
but should restrict ourselves here to the best. 
In practice, the equation has undoubtedly 
given results and I think that anybody who uses 
it can confidently expect convergence of the 
iteration procedure. Still, on the ground of the 
above arguments it would seem better to replace 
it by the differentiated equation. This should be 
a simple matter in a coded programme and 
worth while. 
Mr WEIGHTMAN: I was rather surprised that 
no mention had been made of the Church 
method of adjustment yesterday. It seemed a 
little strange in that it has certain advantages 
over the methods discussed. These are that you 
do not need to consider the rotations as such, 
you start from two completely separate sets of 
axes and merely compare the angles, and there- 
fore the rotations as such can be ignored. 
The value of this is that you can start from 
your photo co-ordinates which are the things 
that you measure, and you end up with your 
final co-ordinates which are the things that you 
are looking for, and you are short-cutting your 
procedure. 
It seemed strange that this method was not 
considered yesterday at all. The method of ad- 
justment which I have suggested myself does 
simplify, I think, a little Church's method, but is 
on the same lines and one would be most in- 
terested to hear if anyone had any comments on 
that method. 
Mr G. H. Schur: I am rather surprised to 
find that the Church method still has its ad- 
vocates. This method has one very serious 
drawback and that, I think, makes it impossible 
to use it in practice. That is that in the case of 
redundant observations one has to choose, make 
a selection of the angles which one uses in set- 
ting up the correction equations. The more 
redundant observations one has the greater be- 
comes the number of possibilities from which 
one has to choose, and I think this makes the 
method completely impractical. 
Mr M. M. THOMPSON: We have been talking 
here about mathematical approaches, theoretical 
approaches, what to do with our data. Nothing 
has been said here about the quality of the input. 
In the Geological Survey we have a method, 
Archives 5 
theoretical approach, which works with fictitious 
data, it may not be the best method in the world, 
but it is a method which works. There are rather 
elegant approaches, perhaps some more elegant 
than ours, but our problem now is, how are we 
going to obtain input data which are good 
enough to be compatible with this elegant 
mathematical treatment? It seems to me that we 
need to look into methods either of eliminating 
or at least controlling such factors as film 
shrinkage, lens distortion and most of all, iden- 
tification of control. This situation is not very 
good, but it is not entirely hopeless. There are 
some very encouraging signs, we can see some 
of them at the technical exhibits. There are some 
very fine new stereo-comparators, there are 
point transfer devices which will help us with 
our identification, and there are methods of 
camera calibration. In the United States we are 
very much interested in the new type of stable 
film base known as Cronar, and I think that 
these factors are equal in importance with the 
mathematical approach to the problem. That is 
the output data is not very likely to be better 
than the input data, so I would just like to make 
the point that this is something which those con- 
sidering analytical aerial triangulation must con- 
sider very seriously. 
Mr G. C. TEWINKEL: Mr Thompson is very 
close to our office, but I have been away a lot 
during the past year so we have not been able 
to compare notes too well. I would like to 
answer part of his comment. 
We have now a programme for compensation 
for film shrinkage and this will be discussed, I 
think, later, particularly at the conference at 
Milan. It works quite well. We also have an 
analytic solution for photogrammetry or aerial 
triangulation, and a piecemeal type of solution 
which is in the process of being programmed. 
The relative orientation phase is already com- 
pleted and with data where we have compensat- 
ed for film shrinkage, lens distortion and at- 
mospheric refraction in the relative orientation, 
we have a residual y-parallax of only 3.8 
microns. That sounds fantastic, but this is live 
data, this is relative orientation not absolute. 
Moreover, the bad observations were detectable 
so that they could be removed, and when they 
were removed the standard deviation was only 
2.8 microns. 
As to control, we realise now that it is 
impossible to have positive identification of 
control consistent with analytic work unless it is 
pre-marked ahead of time. That seems to us the 
only solution for the control problem.