ir line 
course, 
antical 
plane 
"mation 
.4) is 
n and, 
ent of 
2,1) 
wn co- 
es the 
origi- 
,S are 
XN re- 
Pelzer 
dx are 
2.2) 
ose to 
art of 
of the 
he un- 
certainties from relative orientation and its 
fictitious weights (2.3.1) take the form 
1/9 = 2 02 ( y2 + 2 ) (3.2.3) 
because of (3.1.2) and (3.1.3). It shows the fact 
that, in the normal case, the weights decrease 
strictly with y only. As weights do not influence 
very much results of adjustments, relation (3.2.3) 
could also be used for images which do not deviate 
to much from normal position. 
3.3 Propagation of errors concerning reconstruction 
After relative orientation and transformation to 
the normal case, the uncertainty of the model will 
depend on the dispersion Su (3.3.2) of the image 
coordinates xn. Since small variations of X read 
( using the left image P') 
dX = d\Nxn” + \ndxn°, (3.3.1) 
as derived from (1.3.3) by differentiation, the 
uncertainties result again from the expectation 
SM = E{dXdXT}, i.e. 
Su = E{AANZ}xn’Xn'T + AN[xn’E{d\ndxn’T} 
*E(dAudxu' )xu'7] * AN2E{dxn’dxn’T}. 
By means of the differential form 
dxn"-dxn’ : 
dÀAN 3 —————— = AN? (dxu "-dxu ! ) (3.3.2) 
(XN "-xN ! )? 
of equ. (1.3.2) the expectations are: 
E{d\n2} = AN* (Ox"x"*tOx'x'-20x'x*), 
E{d\ndxn’T} = ANZ | Ox'x"rOx'x' Ox"*y"t0Ox'y; D | 
Ox*x"-0x?x? 
E{d\ndxn ? }=)\n2 Ox"y'-Ox'y* , 
0 
Ox'x* Ox t'y? 0 
E{dxn’dxn’T}= Gx*y* Oy'y* 0 
0 0 0 
and regarding E{da’dx"T}=E{dx’da"T}=E{dx’dx"T}=0, 
the co-variances of the correlation P’-P" may be 
taken from Sn’"=E{dxn’dxn"}, i.e. 
Sn’” = Ox'x"  Ox’'y" = O0? Ba'Qa'"Ba'!, 
Oy'x" QOy'y" 
for the uncertainty of a stereoscopically recon- 
structed model. It is seen that ANz1/(xu"-xu?) re- 
presents the dominating factor and that the first 
term of this relation will have the most important 
influence at the limits of accuracy. Thus quality 
control of stereophotogrammetric evaluation should 
focus mainly on this expression in order to avoid 
regions of insufficient precision. 
4. NUMERICAL EXAMPEL 
The following page contains a stereo pair (1,2) 
taken by a Rolleimetric 6006 (c=51.18) in general 
positions. These two images are to be correlated in 
order to get their relative orientation. The coor- 
dinates of the points of correlation are (in mm): 
  
  
  
P’=1 P"z2 
X y X y 
-10.620 1.694 -1.851 2.316 
8.308 0.808 14.936 1.613 
-16.623 14.596 -7.583 13.604 
17.472 13.804 22.767 17.806 
.904 -1.314 | -15.519 -0.481 
14.764 -2.293 1.799 -1,931 
-21.802 6.968 | -18.058 6.299 
-12.778 8.770 -4.346 8.746 
0 0 0160500 TO — 
| 
-— 
— 
  
  
  
  
  
Result of computational correlation: 
-0.00391 0.26581 0.01067 
Z = | 0.28609 0.01536 -0.99664 |, 
-0.00645 1.00000 -0.01313 
det(Z) = -0.0001351 + 0 because of neglecting the 
conditions of orthonormalization. 
Provisional epipole in P’: 
(x0’)= 192.457 (yo’)= 1.476 
Approximate rotations of P’: 
(0) = -16.546 (K’) = -0.488 
Provisional epipole in P": 
(x0")=-178.264 (yo’)= -0.569 
Approximate rotations of P": 
(9°) = 147.799 AK) 
(52) 
The rotations are given in grads. 
Matrix of correlation from 
(Z)=(1/c32)(R’)TB(R") = 
—0.203 
-0.868 
-0.00404 0.26580 0.01111 
= 0.28548 0.01706 -0.99454 
-0.00696 1.00000 -0.01310 
Error equations: 
Nr. dé’ dK’ de ds" dk" 6p 
m 
  
1 4.81 -141.38 -2545.03 28.22 -829.52 0.0500 1.0 
2 17.77 -1129.97 -2524.54 -0.18 11.25 . 0.0118 1.0 
Q’"=| OT and Q12 from (2.3.2). 3 -36.4 132.58 -2731.04 314.63 -1147.66 -1.0271 1.1 
Qiz 4 511.63 -1679.62 -2736.65 -106.82 351.20 -1.1611 1.1 
5. -1.71  -73.60 -2359.54 -35.51 -1525.32 -0.0885 1.0 
Finally, there results the somewhat long but useful 6 *71.63 71860.76 2274.17 -29.04 -566.33 -0.1081 0.9 
formula 7 -45.25 348.39 -2479.64 224.47 -1731.91 -0.6591 1.0 
8 7.05  -41.83 -2608.91 162.05 -963.52 -0.6622 1.0 
OXX OXy Oxz XN’YN” -xu'c 
Sm = Oyy Ovz - AN*(Ox"x"*Ox'x'-20x'x") yn’? =-yN’C |+ 
symm. 02z symmetric c? 
2XN' (Ox'x"-Ox' x?) YN ' (Ox'x"-Ox'x* )*XN' (Ox"y'-Ox^ y?) -C(Ox'x"-Ox'x') Ox'x' Ox^y* 0 
+AN3 2yN' (Ox"y'-Ox' y?) -C(Ox"y'-Ox'y*) +AN2 Oy'y’ 0 
symmetric 0 symmetric 0 
(3.3.3)