6
PHOTOGRAMMETRIC ENGINEERING
Instead of corrections to rotational param
eters of the photographs, here parameters of
a correction matrix are computed by which
the matrix of the approximate orientation is
premultiplied. This leads to a slightly simpler
formulation of the elements of the matrix B.
A direct solution of the normal Equations 2e
with a block elimination technique is em
ployed. Subsequent to the adjustment,
ground coordinates are computed from the
corrected image coordinates in two photo
graphs. The program, developed by the
Raytheon Co., is called the Simultaneous
Multiple Station Analytical Triangulation
Program.
9. BLOCK ADJUSTMENT AT THE FRENCH INSTI
TUTE GEOGRAPHIQUE NATIONAL ([20]—[22])
At the I.G.N., also, the simultaneous ad
justment of photographs (bundles) has long
been a subject of investigation. De Masson
d’Autume [22] describes now a method in
which, after an initial positioning of the
photographs, the observations are reduced to
quasi-observations valid for exactly vertical
photographs. The sum of squares of the cor
rections to these quasi-observations is mini
mized. This simplifies the computation of
the condition equations and of the ground
coordinates without, for approximately verti
cal photography, perceptibly affecting the
results. The collinearity Equations 1 and the
normal Equations 2e are used.
A direct solution of the normal equations
with efficient use of fast-access storage is
envisaged by arranging the bundles in groups,
each of which has points in common with
only the preceding and the following group.
In this way, the submatrices of no more than
two groups need be in fast-access memory at
the same time.
In addition, a procedure is described to
correct photograph coordinates for system
atic deformation before the block adjustment
is performed. In this way, the complications
which arise if deformation parameters are
introduced as unknowns in the normal equa
tions are avoided. The procedure consists in
computing suitable polynomial corrections
from the residuals of the adjustment of a
block with sufficient ground control. The cor
rections have been designed to eliminate the
various systematic deformations which may
occur in a triangulated strip. They are then
applied to any other strip to block in which
the same conditions apply.
Because different film rolls can have very
different systematic distortions, it may be
advisable to compute such corrections from
measurements of the fiducial marks, sep
arately for each roll or even for each photo
graph. Further, there is room for disagree
ment as to whether the derived corrections
are the simplest and most suitable ones for
the purpose.
Linear Adjustment of Models
and of Sections
In the case of the triangulation of inde
pendent models and of strips, a strip- or
block-adjustment by similarity transforma
tion of individual models, or of two-model
sections, can be performed. Such adjustments
are treated in ref. [20], [21], and [35] to [42]
for three dimensions, in ref. [43] to [50] for
planimetry only, and in ref. [51] to [54] for
heights only.
The Equations 1, 2, and 3 are used here too,
but with an appropriate redefinition of the
unknowns. Here, v is the vector of corrections
to the measured model coordinates, 5i is the
vector of orientation parameters of the models
or of corrections to such parameters, and 5 2
is again the vector of corrections to the ap
proximate coordinates of terrain points. Con
sequently, the patterns that occur in the
matrix of normal equations and the possible
methods of solution of these equations are in
general the same as in the adjustment of
photographs. However, the size of the normal
equations can be much reduced by various
specifications as well as by the separate ad
justment of planimetry and of heights.
An alternative to the solution of the set of
simultaneous equations consists in the trans
formation of model after model in an iterative
procedure. King [35] and the present writer
[39] have programmed this procedure but
compute transformation formulas for all
models of one strip simultaneously. King
shows that one step in this procedure and the
corresponding step in the iterative solution of
the complete set of normal equations give the
same result. The transformation which fol
lows the computation of the transformation
formulas corresponds to an updating of the
coefficients of the normal equations. Although
that updating (a Newton iteration) is some
times advocated [27 ], it is of little or no im
portance if one starts from a reasonably good
positioning.
The methods of adjustment can be divided
into three groups: (i) adjustment of indepen
dent models or sections with seven parameters
for each unit, (ii) adjustment with enforced
coordinate connection in points at or near the
principal points, (in) the same adjustment
with in addition correction for systematic