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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-
—À