1482 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1975 
Ux: X—Xc 
U' = Uy’ = y — y (2) 
Uz X — Ze. 
  
  
Fic. l. Geometry of photography. 
The angular orientation ofthe axes ofthe photograph with respectto the object space system 
as described by the rotational matrix R', the photo coordinate vector u', and the scale factor À' 
again describe U': 
X = Xc' x’ — Xc' 
U-ly- Xll-xnmlv-w (3) 
Z — Zc 0 — Sc 
where x' and y' are the photo coordinates of point P, and x«', yc', zc' are the image 
coordinates of the exposure centre, which means the (unknown) basic parameters of interior 
orientation (principal point and principal distance). 
Similarly the vector U" from the second exposure station C" is expressed as 
U, " x: — X, " 
U" zz D. = A" R" y" mah Uc " : (4) 
U, " 0 €. Ze " 
The coplanarity condition is expressed as 
B, U,' U," B, ur! us 
C= B, U,' U^ = NN B, uy' uy" = 0. (5) 
p. U,’ U," B. ";' uw,” 
Although distortion parameters could be introduced into Equations (3) and (4) at this stage, a 
first iteration with only the basic parameters of interior orientation was chosen for computa- 
tional reasons. These parameters are then held fixed while a subsequent iteration includes 
distortion and affinity parameters. Inspired by the iterative approach in PAT-M-43? this 
sequence is repeated. 
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