X
= f fan (X-X n ) + a 1? (Y-Y n ) + a n 3 (Z-Z n )]
a.31 (X-X G ) + a^2 (Y-Y 0 ) + (Z-Z Q )
y = f fa p1 (x-x„) + a 22 (Y-Y q ) + a 2 , (Z-Z Q )]
a 31 (X-X Q ) + a 32 (Y-Y 0 ) + a 33 (Z-Z 0 )
This pair of formulas constitute the space equations of the
line on which lie three points, namely, the object on the
ground, the inner lens node of the camera (perspective center),
and the image on the focal plane. The elements of angular
orientation 00, 8, k are embodied in the a’s. One finds
through successive approximations the values of the parameters
co, 8, k, X, Y, Z, Xo, Yo, Zo that satisfy all the pairs
of equations for a redundant number of images so that the
sum of the squares of the residual discrepancies in the
observed (and corrected) x and y is minimum. Theoretically
at least, and in certain practice also, all these equations
for all the images on all overlapping photographs of a strip
or block can be dealt with simultaneously.
The simultaneous solution consists of the, reduction of
a large set of linear equations where the number of unknown
parameters is somewhat greater than 15 per photograph. The
solution is not too serious if a large, fast, cheap computer
is available. However, the application of such large computers
to this work is not yet common. (It is my opinion that the
1968 Congress will report quite differently). Consequently,
my office proceeded in i960 to use a small computer to derive
a provisional solution to the problem so that, when the large
computation is performed, only one single iteration is required.
To our surprise, the provisional solution is so accurate
that it is seldom necessary to proceed to the simultaneous *
adjustment. This is about the stage of development where
the practical application now standa in the U.S.A., with
several facilities utilizing the C&GS routine, which itself
is being improved. But it is the desire of many of us in
C&GS to apply eventually the simultaneous adjustment in every
instance, and this perhaps is a trend that others may also
follow.
In every application in the U.S.A., computer programs
are incorporated to compensate the observed image coordinates
for the lens and film distortions and atmospheric refraction.
Earth curvature is ideally recognized through the application
of some type of geocentric coordinates for the ground points,
although a few applications correct the observed image
coordinates, which is easier to do.
Provisional results are obtained through a numerical
simulation of the stereo plotter, applying the same perspective
equations shown above, but incorporating relative orientation,