International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
one time step before. For high velocity uncertainties this leads 
to higher track-lengths and longer averaging time intervals and 
therefore to more robust results but reaches the correct value for 
decreasing velocity uncertainty. In our case, of course, the 
velocity uncertainty is kept fixed and therefore the chosen 
track-length is always a little bit greater than necessary for 50% 
uncertainty. 
  
0.44 
S 
e 
= 
  
normalized track length (29-2)/Zmax 
S 
  
ge 
> 
  
y 
0.0 0,1 0 
normalized current distance z/z 
max 
  
  
  
Figure 7. Detail of Figure 5 together with results of the 
algorithm (dotted points) evaluating a real stereo 
image sequence. 
S 
ground-truth 
  
  
   
  
norm. distance z/z,… 
  
v 
time 
Ji. 
P 
  
  
  
7 time 
j ground-truth 
velocity |v| 
> 
e 
  
  
  
  
Figure 8. Comparison of evaluated positions (upper part) and 
velocities (lower part) with ground-truth data. The 
calculated data consist of averaged values and upper 
and lower boundary of uncertainty. 
The calculated distances and velocities, which are averaged 
over the according time intervals, are shown in Figure 8 in the 
upper and lower part together with their uncertainty ranges as 
function of time. The ground-truth distances and velocities are 
also shown. 
As expected the distance uncertainty decreases constantly over 
time, while the velocity uncertainty decreases only until it 
reaches 5096 uncertainty. 
The very good agreement of the calculated positions and 
velocities with the ground-truth data within the calculated 
uncertainty ranges shows that the calculated values are fully 
reliable and can be used as robust features for any decision. 
5. CONCLUSION 
The quantitative analysis of the accuracy and reliability of 
three-dimensional position and velocity extraction for objects at 
long ranges from multi-ocular image sequences shows that 
fundamental restrictions limit the range for velocity extraction 
with a chosen uncertainty range much more than the simple 
geometric resolution of the multi-ocular system. Nevertheless, 
by adequate selection of the sensor arrangement and by taking 
into account the dependency between accuracy and the essential 
system parameters it is possible to derive reliable position and 
velocity values for objects even at long ranges when other 
features such as shape and intensity cannot be derived reliably. 
ACKNOWLEDGEMENTS 
The described work has been supported by BMVg 
(Bundesverteidigungsministerium, .German Ministry of 
Defence) and BWB (Bundesamt für Wehrtechnik und 
Beschaffung, German Office for Armament and Procurement). 
The assistance of WTD 71 (Wehrtechnische Dienststelle für 
Schiffe und Marinewaffen) for preparation and realization of 
the measurement campaign at Surendorf in 2001 is gratefully 
acknowledged. 
REFERENCES 
Campana, S. B., 1993. Passive Electro-Optical Systems. In: The 
Infrared & Electro-Optical Systems Handbook, Ann Arbor, 
Michigan USA and Bellingham, Washington USA, Vol. 5, 
Chapter 4, pp. 209-344.