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formulas with regard to only the rotational 
movements and certain corrective (although partial) 
approaches were developed to provide film or camera 
movements during exposure by using one of several 
IMC devices. The complexities has been resolved by 
Ghosh (1985) through augmenting the collinearity 
condition equations. This approach is fully 
computational. 
6.2.3.3 Related to Stereo Images 
It was around 1953 that the classic analog concept 
of relative orientation by way of elimination of y- 
parallax evolved into the condition of coplanarity 
through the efforts of Schut (1956-57) at the 
National Research Council of Canada. This 
condition implies that the two perspective centers 
(or exposure stations), any object point and the 
corresponding image points on the two conjugate 
(overlapping) photographs of the stereo-pair must 
all lie in a common plane. This condition is fun- 
damental to relative orientation or space 
intersection. Like the collinearity equations, 
this condition equation is also non-linear and need 
to be linearized (for computer utilization) with 
iterative solutions in mind. The relative 
orientation formulation developed by E.H. Thompson 
(1959) showed complete elimination of trigonometric 
functions with a consequent ease and speed of 
computer utilization. Separately, Paul Herget in 
developing a system of analytical control 
extension, by using vector notation, minimized the 
perpendicular distances between pairs of 
corresponding rays in order to achieve a solution 
for relative orientation. He employed an ingenious 
trick whereby ground control equations took the 
same form as relative orientation equations (Herget 
and Mahoney 1957). 
On the other hand, the superiority of the numerical 
relative orientation (over empirical and graphical 
methods) was definitively established. Also were 
established the processes of improving such 
relative orientations (Ghosh 1964). 
Notwithstanding the analytical conditions of 
collinearity and coplanarity, the on-line solutions 
at analytical plotters are all developed 
practically around such  analogical-numerical 
concepts. 
The process of absolute orientation (i.e. scaling, 
translating and levelling of a stereo model with 
respect to a ground reference coordinate system) is 
simply a problem of coordinate transformation. The 
equation must be linearized before it can be used. 
The method of least squares may also be used. This 
approach was standard already by the early 1950s. 
It was readily found that during a sequential 
procedure of aerotriangulation the scale of a 
previous model needs to be transferred to the next 
model. This is similar to the requirements of the 
analog aeropolygon method. This process was 
mathematically modeled at the NRC Canada (Schut 
1956-57) and is known as the scale restraint 
condition. This condition implies that with regard 
to a point in the triple overlap area (i.e. area of 
overlap between adjacent models) the two 
intersections in individual models must take place 
at the same spatial location. This condition is 
always used in conjunction with the coplanarity 
equations. 
Theoretical concepts of bi-projective 
transformation (Das 1952) and the use of distances 
in the object space as control for stereo-models 
(Das 1973, Okamoto 1981) are purely computational 
315 
approaches that would prove extremely efficient in 
various applications of stereophotogrammetry. 
6.2.3.4 Related to Multiple Images 
The application of analytical procedures on which 
most discussions and efforts have been made is that 
of phototriangulation. As early as the beginning 
of World War II, the need was typified in the 
following quote (Schermerhorn and Neumaier 1939): 
"The problem of control points was and is still, to 
a certain extent, the bottleneck in photogrammetric 
map production". Initial efforts were with regard 
to the adjustment of analog aerotriangulation. 
Later efforts concentrated on fully analytical 
procedures. Their classifications and historical 
developments would be apparent in Fig. 6.2 
A. Adjustment of Analog Aerotriangulation 
Historically, the development may be noted in 
terms of three stages: 
Stage 1: Adjustment of individual strips along 
with associated data analyses and 
interpretations. The works of Thompson (1953), 
Roelofs (1949) and Gotthardt (1944) give typical 
indications of the initial studies. One would 
notice at this stage the prolonged discourses on 
the causes and propagation of random errors over 
those of systematic errors. One can refer to 
one single publication to typify the culmination of 
this stage in the OEEPE (Organisation Européenne 
d'Études Photogrammétriques Expérimentales) report 
for studies up to the end of 1959 (Solaini and 
Trombetti 1961). This study, initiated in 1956, 
concerned international efforts at twelve research 
centers and analyzed the results of some dozens of 
strip triangulations by using different adjustment 
procedures. 
Several scientists got involved in such studies in 
the OEEPE group or separately and left their marks 
in numerous publications of each of them, such as, 
W.K. Bachman, A.J. Brandenberger, A. Bjerhammer, A. 
J. van der  Weele, A. Verdin, P. A. Vermeir, J. 
Zarzycki and M. Zeller. The efforts of the ISP 
Commission III in this regard were very significant 
(see Cassinis and Cunietti 1964). The OEEPE (1973) 
publication indicates the termination of experi- 
mental researches of this stage, having the 
attention already passed from the treatment of 
isolated strips to that for an entire block. The 
highlights of this stage were: (1) Adjustment of 
aerial strip triangulation was approached by using 
condition equations; (2) The least squares 
principle was being applied to the condition 
equations; and (3) The polynomial corrections of 
point coordinates were affected by considering 
third order in X, and second order in Y and Z strip 
coordinates. It was also felt at the end of this 
stage that the measuring instruments and the opera- 
tional procedures needed improvements more than the 
mathematical adjustment procedures. 
Stage 2: Adjustment of Blocks of Strips. By the 
end of 1950s in view of the developments that 
electronics brought about in the computation 
processes new challenges concentrated on 
simultaneous adjustment of blocks of strips, the 
models of which have been formed by analogical 
procedures. In this regard, apart from numerous 
individual efforts in the world, the one most 
significant study which would indicate the progress 
is the report on the coordinated group study under 
ISP Commission III on "Massif Central" polygon