e The search is also performed in the image space of the 
cameras where the particle of step # could not initially be 
found or matched (e.g. due to overlapping particle in one 
or more views). Based on a list of possible candidates a 
search position x, for time step #,., is predicted. If a valid 
link to the previous time step /;; exists the predicted 
position is calculated under the assumption of constant 
particle acceleration a, (model of second order, eq. (2)), 
otherwise again a linear extrapolation is used. 
ts) = € )* à, (t4 ) 4t t 
(3:42 
gi 
p 
6-2, 6,4)- 4-2, 6) 2, (t) (2) 
u, Fe )- Up (e;) 
with a ,(t;) = Le 
e For each found path a quality criterion is calculated. The 
parameters for the quality measure are the acceleration and 
the change of direction of the particle. 
* Conflicting particle connections are avoided by the quality 
criteria. 
e If a particle that already has a valid link to the previous 
time step /;, can be connected to a particle from time step 
fj.; but no candidate in step £j,» is available the quality 
factor is calculated from the time steps 1, ;, t; and f;,;. 
e If still no link could be established with the already 
calculated 3D particle positions, the remaining unmatched 
detections in image space from time step /;,, around the 
predicted location are used to determine an additional 
particle position (again the reconstructed path has to fulfill 
the quality criterion). 
e The tracking can be performed in progressive as well as 
regressive way. This offers the possibility to extend a 
trajectory not only in forward but also in backward 
direction. 
The number of unsolved ambiguities resulting from the epipolar 
line intersection technique can be decreased if the temporal 
context is considered. In the case of ambiguities particle 
trajectories are often interrupted for only a few time steps. With 
the new algorithm these gaps can be bridged reliably and even 
the continuation of a trajectory is possible when the redundant 
information is exploited in a correct way. Figure 5 shows the 
differences in the use of object and image based information by 
the tracking algorithms. With the object space based tracking 
method (A) no particle position in time step # could be 
calculated due to ambiguities in the epipolar line intersection. 
The available data for the image/object space based tracking are 
3D particle positions (filled circles) as well as image 
coordinates (unmatched particle detections are marked with 
unfilled circles) as shown in (B). The result of the new tracking 
algorithm with closed gaps by additionally calculated particle 
positions from unmatched image coordinates is shown in (C). It 
is obvious that the influence of measurement errors is 
increasing when a particle position is calculated from fewer 
observations with a lower redundancy. 
  
  
tire 
  
  
  
lio 
    
l4 D e 
liio EO — 
  
figure 6: Particle 
Jementation (lef 
spatio-tem 
  
additionally ca 
b (Fig. 6, ri 
struction could 
closing a gap 
nement for the 
  
   
  
  
t4 
  
  
  
    
lio 
  
result of the 3L 
d spatial resolu 
files. A visualize 
ion of traject 
ity). 
  
  
  
  
  
  
  
a tio e 
d t © y 
"m | l4 7 
praepos li | 
l4 : 
tira : 
l3 Y 
  
  
  
Figure 5: Improvement of spatio-temporal matching: 
(A) object space based tracking, (B) available data used by the Figure 7: Vi 
object/image space based tracking method, (C) result of the new 
object/image space based tracking ist the new alg 
. the previous i1 
But if the camera arrangement is suitable, the loss of quality seq The dat: 
not substantial and still acceptable compared to an interruption Wired during the 
of the particle trajectory. Interpolation is only used ft sm teq vot. 
prediction purposes, the calculation of the particle positions tire data sets 
close gaps is strictly based on image space observations. # method. The 
Figure 6 shows a trajectory example from an experimel!;nmed in forw 
reconstructed with the previous tracking method in comparison lied further imp 
to the new tracking method. With the previous implementation 
the trajectory of the particle could only be reconstruct 
incompletely (Fig. 6, left), while the new spatio-temporl Data set “Cop 
matching was able to track the particle without gap over tlt 
whole sequence of 30 time steps. * turbulent flo 
"Wen two electr 
41,2001). In thi 
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