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The correspondence is uniquly solved in the first case (1:1). In case (1:m) the trajectories match if there is no 
time overlap between the m candidates und thus represent a single particle. In all other cases additional criteria 
have to be used to eliminate ambiguities. 
‘With respect to constraint (5.3) candidates corresponding only for one or multiple short parts can be excluded. 
Constraint 5.1 (uniqueness) leads to another criterion: matching ambiguities have to be resolved, that the num- 
ber of correspondences is maximal. Example (Figure 2): 
R2 
A EE 
— | 
  
  
  
  
L1 
Figure2 uniqueness criteriori 
Trajectory R1 has the possible candidates L1 and L2, trajectory R2 has the candidate L2. T wo possible solutions 
exist: 
- Ri matches L1, than R2 matches L2 
- Ri matches L2, no match for R2 andL1 
Other matches can be excluded because of the unigeness criteria. The first solution is the one with the largest 
reliability, because it matches all four trajectories (provided that there are no errors in the particle tracking). 
5.3 Results 
Real image sequences have been evaluated with the presented algorithm. The average matching rate was bet- 
ween 90% Sed 100% at particle densities from 100 to 600 particles. For a character recognition system this 
would be an inacceptable rate, but in this application 5X ambiguities are an excellent result, because the partic- 
les by themselves are a statistical preselection of positions to measure the flow field. Thus even a matching rate 
of 80% would be a satisfying result. For more importance is a fast processing, since this technique is only useful 
if large quantities of images can be evaluated. 
The typical computation times on a Silicon Graphics Indy (MIPS R4000, 100MHz) are 0.25 seconds /image for 
the particle tracking and 10 seconds for the stereo correspondence with sequences of 150 images and 350 par- 
ticles. These are considerable short times. 
6 SIMULATION 
6.1 Purpose 
The algorithms have been developed with real image sequences. To test the quality and reliability of the algo- 
rithms a system to create computer simulated image sequences has been provided. The purpose of this simula- 
tion system is not to reproduce exactly the physical conditions, but to produce a set of known data making it 
possible to test the algorithms. The simulated data allows the examination of the influence of parameters, which 
can not easily varied during experiments, for example the particle density. The main goals are, to find out how 
the computational effort depends on the density of trajectories and where the limitations of the system are: in 
the particle tracking or in the stereo correspondence. 
6.2 Realisation 
The following parameters are used: 
- length of the trajectories 
- number of breaks in the trajectories 
- number of particles resp. trajectories 
- particle velocity (linear and radial) 
- geometry: camera positions and size and position of the observation volume 
- size of the epipolar search rectancle 
- noise intensity 
Positions and velocities are computed in three dimensions according to the setting of the parameters. The velo- 
cities are the superimposition of linear and radial components, to reproduce the typical orbital motion of real 
particles. 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995