> 
S £57) 
Z !- 
r7 Sa 
t 
t E272 7 Xo4f 
Ya. =f ry — rof (84) 
3277 33 
Once all the vanishing point coordinates are found, the orientation matrix can 
be determined using equations (35) through (46). 
Relationships Between Camera Station Coordinates and Object Point Coordinates 
Once the elements of the interior orientation and exterior orientation matrix 
are known, positions and dimensions in the object space can be determined, provided at 
least one dimension in the object space is known. The relationships between the camera 
station coordinates and the object point coordinates play an important role in this part 
of the analysis. 
The fundamental projective equations have already been expressed by matrix 
equation (1). Premultiplying both sides of equation (1) by 0s juif, in which 9; = il à 
and noting that [M]T [M] z [I], we obtain: r 
N X 22 Na 
T 
= = ^ = 8 
Y 7 Yc 0, [M] X TV. (85) 
Zr - Ze -f 
Letting 
E M TAX 
i i o 
|F,| = [M]? y, - y (86) 
i à O > 
e. -f 
[1 
equation (85) becomes: d 
XC > Xe By 
-— = 8 
Yr Ye 9; F; (87) 
-7 
[Zr C e 
from which the following collinearity equations are obtained: 
Py 
= = = — 88 
o Xe) (a, 2 G, (se) 
i 
F 
Gi cx uu oO e (89) 
Equations (88) and (89) relate the camera station coordinates (Xe: Ye Ze) to the object 
point coordinates (Xj, Yr Zp. The quantities Els F; and A are considered known since 
they can be determined from the image coordinates (x, > y, and the known elements of the 
= 19 -