James Olaleye 
  
where 
R, R, As are the apparent direction vectors of the object R-space. These are obtained by evaluating the vecty 
expression in (6) using the computed absolute orientation elements. 
s is the scale factor for the projection also determined by absolute orientation computation and 
P, is the object space vector which locates the origin of the image space, also obtained from absolute orientation 
computation. 
Substituting (7) in (8) we have 
R'{b+aT+skh 
PP mEOrsTrsTL 
2 2 22 (15) 
R 
b+ ST ST, 
Ww 
In order to further explore the geometric significance of this equation, 
x S * X * sk 
m men QU —¢ XK 
Li 3 9 =8 5s (16) 
applying the distributive property of inner products of vectors to equation 9 and simplifying we have: 
R; b RT RT: 
P,=P,+s|R,b|, sR, 7, V 52| R 7: anh 
R,b R; T1 RT» 
This may be put in the form: 
RT RT: 
P. =P + B + $1 R,.T, + So RT (18) 
R'T, R,T: 
Where the vector B is the equivalent of the airbase for the stereogram. 
By relating equation 20 to Figures 3 & 4, it is evident that the forward reduction of conjugate image space vectors: 
achieved by a series of inner products of vectors. Equation 20 applies to every point appearing in the stereogram. 
Computational Steps: 
l. Construct the apparent direction vectors of the image R-space and the object R-space i.e.R,, Ro, R; and 
Rı Re ,R; using the parameters of R.O. & A.O. respectively. Also compute the following (note that P, and P, à 
conjugate image space vectors) 
  
666 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.