REVIEW OF STRIP AND BLOCK ADJUSTMENT DURING 1964-1967
9
of the polynomials as low as possible. Restric
tion to the second degree is possible by divid
ing long strips into sections. Such sections
can be transformed by means of either inde
pendent polynomials or composed poly
nomials.
An investigation of the present writer [39]
has shown that with fairly sparse control the
block adjustment of models does not give a
better absolute accuracy than the block ad
justment of strips. Soehngen [87] has obtained
better results with the height adjustment of
models. However, he uses a larger number
and well-located control points.
Subblocks, and External
Block Adjustment
Anderson [95, 96] describes the computa
tion of subblocks of 3 X 3 or m X n photographs
with 60 percent longitudinal and lateral over
lap and their assembly into a block by means
of similarity transformations. For the inter
nal adjustment of such an assembly, the
method of Roelofs [47] would seem to be very
suitable.
For the adjustment to ground control of
an internally adjusted block, polynomial
transformations of the block coordinates
could be used. However, with a low degree of
the transformations one can hardly expect to
obtain a good fit at all ground-control points
and with high degrees one may obtain too
large errors in uncontrolled areas. A second-
degree transformation may be suitable for an
initial positioning of the block and to enable
the final block adjustment to be performed
separately for the three coordinates.
Arthur [97] describes an interpolation
method for such an adjustment. However,
this method does not give a solution in the
case of four ground-control points situated at
the corners of a square. Since this should be
a well-defined case, the suitability of the
method in other cases requires careful ex
amination.
Vlcek [98] and Wainauskas [99] describe
the use of orthogonal polynomials. The only
advantage of their use appears to be that it
may be possible to identify and reject terms
that do not contribute significantly to an
improvement of the fit at the control points.
Accuracy of Strip and
Block Adjustment
Ackermann and Jerie, [100] to [107], have
investigated the theoretical accuracy of strip
and block adjustment, assuming that sys
tematic errors are either absent or have been
eliminated. They deal with the adjustment by
means of similarity transformation of models
and, for the height adjustment, also the ITC-
Jerie analog adjustment.
It is of particular interest that Ackermann
[100] finds that in his investigations the sim
ilarity transformation of models and the
second- or third-degree polynomial strip
transformation give about equivalent results.
In a practical test an adjustment of a
block of 180 photographs with 60 percent
longitudinal and lateral overlap by the U. S.
Coast and Geodetic Survey [10] has produced
root-mean-square values of the residuals at
check points of only nine microns at photo
graph scale.
The polynomial adjustment of strips with
normal lateral overlap gives values that
usually vary between 25 and 60 microns. [39].
Jacobs [81], using analytical triangulation
and the Coast and Geodetic Survey’s correc
tions for film deformation, obtains values of
around 15 microns.
Conclusion
Prof. Schermerhorn’s statement that the
methodical development of mathematics and
programming procedures in analytical tri
angulation seems to be complete [2] can now
be extended to strip and block adjustment.
Still, further refinements, modifications, and
simplifications of present procedures will un-
undoubtedly continue to appear.
For instance, one can expect that more
work will be done on the construction of
economical direct and iterative solutions of
the large systems of normal equations which
occur in the adjustment of photographs and
of models. In this field a more than four-year-
old claim by members of the ITC that an
exceptionally economical direct solution is
possible by a suitable arrangement of the
unknowns still awaits clarification. Brown
[lib] has recently made a rather similar
claim concerning the iterative solution. In
addition, the use of the method of conjugate
gradients and of related methods may war
rant further investigation.
In the field of analytical triangulation, the
simultaneous triangulation of all photographs
of a strip in an arbitrary system should not
be much more complicated than the triplet
triangulation and could with advantage re
place the latter.
The adjustment of internally adjusted
strips and blocks to ground control should be
further investigated. This may provide a
very suitable procedure especially for small
computers and where the utmost in accuracy
is not needed.