complicated one in aspect of error propagation 
as passing through two object spaces. 
2.1 Relative orientation 
The relative orientation aim is to deter- 
mine a relative spatial position between two 
adjacent photographs so that each homologous 
pair of rays from the two photographs will in- 
tersect in space. The mathematical model ex- 
presses this condition (which is known as the 
coplanarity condition) is based on a equation of 
the kind of (À x B)-C - 0, which is satisfied 
by the determinant: 
pP Tr 
Wo v Wwi-0 
u, v, VW; 
where: 
u X 
v|-2 R(K,9,0)| Y 
W f 
x, y - Photograph coordinates 
f- Principal distance 
P- Vector between the perspective center 
R- Rotation matrix 
The transformation parameters are solved by a 
least squares adjustment of observation equa- 
tions, based on the mathematical model. The 
adjustment provides the computed parameters 
variance-covariance matrix, that is given by: 
Ya "N? 
where: 
y! *y 
  
N-4 4 gie 
n-u 
The solved parameters, enables a trans- 
formation of the photograph coordinates to the 
stereo-model reference coordinate system. 
10 
2.2 The stereo-model reference coordinate 
system 
The stereo-model (model) reference co- 
ordinate system functions as a mediate object 
space between the photograph reference coor- 
dinate system and the ground reference coordi- 
nate system. Coordinates in the model refer- 
ence coordinate system are computed by apply- 
ing the relative orientation transformation on 
the measured image coordinates. The relative 
orientation transformation errors produce er- 
rors to the model coordinates, that are evalu- 
ated by using error propagation technique 
which is expressed as: 
Si IS 
where: 
>, - Variance covariance of the source object 
space 
Y «- Variance covariance of the target object 
space 
F,- The transformation matrix between the 
two object spaces 
The model coordinates are computed by the 
collinear rule which, by using rotation angles as 
transformation parameters, is illustrated as: 
  
  
  
Fig. 1. The stereo-model scheme 
The model coordinates are computed by: 
Zm-b*w*w"/(w"*u'-u"* w) 
Xm 7 Zm * u'/ w' 
Ym 7 Zm * (v/w' + v"/w")/2 
and the vai 
as: 
Nc: 
where the e 
ing the pr 
chain rule, : 
oXm  oX 
OK ol 
oYm oY 
OK ou 
oZm 02i 
OK ou 
In ca 
transformat 
a matrix th 
point gives 
addition to 
covariances 
2.3 Absolu 
The a 
transformat 
ence coordi 
coordinate 
transformat 
dinate trans 
tion and tra 
X 
y 
Z 
The t 
ally, solvec 
observation 
cal model, 
termined b 
proach, alt] 
the observa 
important c 
tion's accur