(2) 
be de- 
m the 
mined, 
m the 
rmina- 
 meas- 
tion is 
vident 
Ally in 
it such 
taken 
ys from 
y inter- 
allaxes 
correc- 
tation. 
allaxes 
lax is 
)ancies 
deter- 
marily 
nd the 
~oordi- 
we the 
t upon 
in the 
ng in- 
stances 
tween 
  
different sources of errors and the re- 
sulting errors in the coordinate deter- 
mination were known, it would be 
possible to determine numerical cor- 
rections to the elements of orientation 
of the cameras; so that the discrepan- 
cies would vanish in the same number 
of control points as the number of 
orientation elements which are as- 
sumed to have an influence upon the 
coordinate determination. But if there 
are more control points than the used 
elements of orientation, there are 
superfluous observations, and conse- 
quently one has the problem of dis- 
tributing the discrepancies which can- 
not be compensated by the available 
elements of orientation. In such cases 
the method of least squares is normally 
used. The corrections to the elements 
of the orientation are to be deter- 
mined so that the square sum of the 
residuals or corrections to the measure- 
ments of image coordinates is a mini- 
mum. This principle means that one 
assumes the discrepancies, which can- 
SYMPOSIUM—NON-TOPOGRAPHIC PHOTOGRAMMETRY 
  
  
  
  
  
  
  
‘YA 
A 
LC 
04 b 02 
7 +X 
AL 
7 c Ic 
Ca I 
x xul. 1 
P, (PR) H, PH, 
Hi H; 
Iz, Zl 
Came ; 
R X ] hy 
  
  
  
  
  
  
  
Frc. 3.—The normal case of terrestrial 
stereophotogrammetry. The principles for the 
determination of the coordinates x, y and z are 
indicated. 
not be corrected by the elements of orientation, to depend primarily upon the 
errors of the image coordinate measurements. The principles of the least square 
method furthermore permits one to determine the standard error of the meas- 
urements, to determine the accuracy of the elements, and to study the error 
propagation to the determination of the coordinates of arbitrary points. 
These general principles will be applied to the most important case of terres- 
trial photogrammetry, the stereophotogrammetric normal case, Figure 3. 
The pictures are assumed to have been photographed at the stations O; and 
O, with the same camera, or with equal cameras having the same principal 
distances c and free from distortion. If distortion is present, the measurements 
must be corrected; this is no real problem. The camera axes are perpendicular 
to the base and horizontal. A phototheodolite and a stereocamera are shown in 
Figures 4 and 5. 
À coordinate system is assumed to have the origin at the left camera station, 
the + x-axis horizontal towards the right station, the +y-axis in the left camera 
axis and the +z axis upwards. The image coordinates are denoted x', x", z/, z//. 
The coordinates of an arbitrary point can be determined from the following 
expressions which can easily be derived. See Figure 3. 
bc 
y LI 
x! — 
yx’ 
x= — 
C 
ys 
21 =  — = 
  
  
bc 
uf f (3) 
x p 
ba’ 
ox. (4) 
? 
bz’ 
— (Sa) 
   
    
  
  
  
  
  
  
  
  
————————— 
  
  
  
  
  
  
  
    
  
  
  
  
EE 
  
  
  
  
  
eget: 
pt EE