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As explained before, the tracking process 
can produce false trajectories. This is 
clearly shown in the Figure 11, where the 
computed 3-D trajectories for 30 frames 
are displayed (for the walking sequence of 
Figure 10). The vector field of trajectories 
(position, velocity and acceleration) can 
now be checked for consistency and local 
uniformity of the movement. Two filters 
are applied to the results to remove or 
truncate false trajectories. The first filter 
consists of thresholds for the velocity and 
acceleration (Figure 12, left). The second 
filter checks for the local uniformity of the 
motion, both in space and time (Figure 12, 
right). To check this property, the space is 
divided in voxels, for each voxel at each 
time step a mean value of the velocity 
vector is computed. The single trajectories 
are compared to local (in space and time) 
mean values of the velocity vector. If the 
differences are too large, the trajectory is 
considered to be false and it is truncated 
or removed. 
As it can be seen comparing Figure 13 
with Figure 11, the majority of the false 
trajectories are removed or truncated by 
the two filters. Still, some false 
trajectories remain in the data after 
filtering. 
23.3 LSMTA in 2-D mode: The 
LSMTA is a flexible tool and can also be 
used in 2-D mode. In that case, the 
sequence of a single camera, e.g. a 
camcorder, is processed. The use of a 
single image sequence cannot obviously 
produce 3-D data but for some cases the 
3-D information is not required. The 
Figure 14 shows a simple example of 
tracking facial expressions, where some 
key points are tracked through the 
sequence. The images were indeed 
acquired with a video camcorder. This 
example underlines the flexibility of the 
LSMTA which can produce in this case 
simple animation, tracking key points on 
the face without using markers. 
D'Apuzzo, Nicola 
  
Figure 11. 3-D trajectories of the tracked points. 
Left: frontal view, right: lateral view 
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thresholds of velocity and acceleration check for consistency and local uniformity 
Figure 12. Filter to remove or truncate false trajectories. 
Left: threshold filter, right: consistency and uniformity filter 
  
Figure 13. 3-D trajectories after filtering. 
Left: frontal view, right: lateral view 
  
  
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Figure 14. Some frames of a single camera image sequence 
(the crosses on the first frame show the tracked points). : 
Bottom: basic animation created joining the tracked points with lines 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part BS. Amsterdam 2000. 169