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Figure 3. 
THE ANALYTICAL SOLUTION 
Figure 4 illustrates the general steps involved in the 
analytical solution for the movement vectors. Initially 
the comparator coordinates are transformed to a photo 
coordinate system. The camera does not have a set of 
fiducial marks to define the photo coordinate system. 
Moreover, the format of the photo is so large that 
neither the edges nor the corners of the photographs 
could be measured on the WILD STK-1 Stereocomparator. 
Consequently, the x and y-axes of the photographic 
coordinate system are determined only approximately 
for each photograph. 
A precision ruler is used to measure the lengths of 
the four edges of a photograph, as well as the x and 
y coordinates of two photogrammetric control points. 
The x and y-axes of the photographic coordinate sys- 
tem are then referenced to these two control points. 
The exterior orientation of photo 2 with respect to 
photo 1 is then determined using a computer program 
that was previously developed for computing the orien- 
tation of photographs collected from the LANDSAT 
satellite (Wong, 1974). The program is basically a 
least-squares solution for three dimensional coordi- 
nate transformation. 
It makes use of the following basic projective trans- 
formation equations: 
14 
Typical Distortion of 
Where xj. y; 
Wy, E 
0.0 
= 
= — 
— — Y — — 
0.0 
  
  
Glass Plate Under Load 
X: C 
j Wu. . om. Xy 
= C 
Y Az | M1 M2 M3 7-76) 
Cc 
2j May Map Mag Z; - 1 
and zj are the photo coordinates of an 
image point} Xi, Yi Zi are the object space coordina- 
tes of the cor*espünd ilg point in object space; Xj is 
a scale factor; X©, YC, and Z€ are the object space 
coordinates of the exposure center of the photograph; 
and the Wis are functions of the three rotation 
parameters'w, ¢ and k. In its present application, the 
photo coordinates of the eleven control points measu- 
red in photo 1 are used as controls. In addition, 
about 35 image points which are located near the out- 
side edges of the tunnel model where no particle move- 
ment is expected are also used as control points. Thus, 
there are about 46 control points used to determine 
the orientation of photo 2 with respect to photo 1. 
The solution solves for the three rotation parameters 
» and K, and three translation parameters X5 
of photo 2. 
oY 
and 2 
Z 
Using the same computer program, the orientation of 
photo 1 with respect to the control points in the 
object space was next determined. The solution solves