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