Merits of Performance

The performance of the algorithms is evaluated by repeatedly generating trajectories with PSMG and comparing the tracking results to the ground truth. The varying parameters are the total number of trajectories $T$ and the mean speed $v$. (Recall that $T= N$.) The generation of a trial data set is repeated until the desired $T$ is obtained. For each setting of the varying parameters, 100 trials are done with independently generated data. Three merits of tracking performance are calculated. The strict trajectory-based merit only accepts perfect trajectories and is defined as

$$M_{traj} = \frac { T_{corr} } { T}, %$$

where $T_{corr}$ is the number of perfectly tracked trajectories, $T$ the total number of trajectories generated in the sequence.

The relaxed trajectory-based criterion allows for local deviations from the ideal trajectory if the last point is connected to the correct initial point.

Finally, the link-based criterion accounts for the partially tracked trajectories:

$$M_{link} = \frac { L_{corr} } { L_{total} },$$

where $L_{corr}$ is the number of the correct links, $L_{total}$ the total links. (A correct link is a vector that connects the same two points of the two consecutive frames as the ideal trajectory.)

The error plots obtained in the performance evaluation study show the error rates defined as $E_{traj} = 1-M_{traj}$, etc.