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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
velocity uncertainty move on the corresponding dashed line in
Figure 5. This decreases the used track-length and therefore
also the time interval for averaging much faster but on the
expense of a constant perhaps rather poor velocity uncertainty.
There are a lot of different alternative possibilities of choosing
the track-length depending on the application.
& 0,64
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normalized track length (z,-zyz,,..
0,04 T " T A LI
0.0 0.1 0.17 92 0.27 03
normalized current distance z/z
max
|
"m
Figure 5. Minimal track-length (lower solid line), optimal
track-length (upper solid line) and relative velocity
uncertainties for different track-lengths (dashed
lines) as function of the normalized current distance.
The dotted line shows, as example, the whole
track-length for an object detected first at
Zz. = 027.
0,94
= ©
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relative velocity uncertainty Av/v
Figure 6. Maximal normalized current distance and minimal
detection distance as function of desired relative
velocity uncertainty.
It can be seen from Figure 5 that velocity extraction with a
certain velocity uncertainty is only possible at distances less
than an upper bound distance. This upper bound distance is
shown in Figure 6 by the lower line. For the example of 50%
uncertainty, this value is reached only below z/z,4, = 0,11. In
addition, to reach this value at this distance the track-length
must exceed a certain value, what means that the first detection
of the object must be farer than a lower bound distance shown
by the upper line in Figure 6. In the given example the first
detection must then be farer than z/Zmax = 0.27.
In summary, for velocity extraction with an acceptable value for
the velocity uncertainty at a certain range the stereoscopic
system must be designed to resolve a much greater distance,
which is given by the value of zmax-
4. DATA EVALUATION
For the data evaluation we used IR image sequences taken in
November 2001 at the coast of Eckernfôrde in North Germany
with various airborne objects approaching the sensors. We used
two sensors from AIM in Germany with a Field of View (FOV)
of 8.8?x6.6?, 640x480 pixels and a focal length of 100 mm. The
ground-truth positions of the objects were recorded using
Differential Global Positioning System (DGPS).
Our approach to the evaluation of three-dimensional object
position and velocity from bin-ocular image sequences can be
subdivided into different, consecutive steps as follows: Each of
the two image sequences is processed individually by an IRST
algorithm which is composed of the tasks image pre-processing
to correct sensor-specific inhomogeneities, ^ motion-
compensating temporal image integration to increase the signal-
to-noise-ratio, non-linear spatial filtering to detect point-like as
well as extended objects, segmentation of objects and spatio-
temporal tracking of potential objects to create two-dimensional
tracks in each image sequence.
For each stereo-image pair the positions of the objects which
built the two-dimensional tracks are combined with the position
and orientation of the sensors to reconstruct the three-
dimensional positions of the objects by resection in space.
These three-dimensional positions in consecutive image-pairs
are linked together to three-dimensional tracks, using the two-
dimensional track information. The three-dimensional velocity
extraction starts when the difference of the maximum and
minimum z-component of the track exceeds the minimal
necessary track-length given by the lower solid line in Figure 5.
After that the track-length for optimum velocity uncertainty is
used for all inbound objects to extract the velocity until the
relative velocity uncertainty falls below 50%. Then only the
track-length to achieve 50% relative velocity error is used
further. The used track-lengths are shown in Figure 7 as dots,
together with the theoretical curves from Figure 5.
The dots in Figure 7 occur only at certain distances as expected
from the quantization of the calculated three-dimensional
positions. The positions are slightly smeared out due to the fact,
that the object while moving occurs at different positions in the
images and the sensors were not exactly aligned. The
track-length chosen for velocity extraction is systematically
‘greater than given by the 50% line. The reason for that is, that
the calculated track-length to achieve 50% velocity error is
transferred to an averaging time interval using not the averaged
velocity but the lower bound of the velocity range calculated
