Summary Comparison

Two of the four alternative algorithms were selected for summary comparison with the IPAN Tracker. These two algorithms, RS91 and SS90, were judged to be both efficient and typical. Tables 2 and 3 summarize the tracking results obtained by IP97, RS91 and SS90 for the strict trajectory-based merit. Each row shows $M_{traj}$ for varying total number of trajectories and two different mean speeds, low and high, which are 3 and 12 pixels per frame, respectively.

The first three columns of the tables specify the algorithm and the conditions of the evaluation, in the way consistent with table 1. In particular, `$-$' in the `Self.-init.' column means that no self-initialization was done, that is, the initial correspondences were given.

Two different data sets were used in the evaluation. The sequences used to obtain table 2 contain no entry and exit, while the sequences generated for table 3 contain both. See section 5.3 for comments on the essential difference between the two data sets.

 

Table 2: Tracking results for IP97 and RS91, without entry/exit.

Alg.	Self-init.	Occl.	Low speed			High speed
			$T=20$	$T=40$	$T=60$	$T=20$	$T=40$	$T=60$
IP97	$+$	$+$	95.35	92.07	89.98	82.70	67.55	54.56
IP97	$+$	$-$	95.60	92.92	91.20	85.70	74.02	62.45
IP97	$-$	$+$	97.50	94.10	92.28	83.95	72.05	61.26
RS91	$-$	$+$	98.50	95.52	94.58	81.15	59.47	16.61

 

The first two rows of table 2 refer to IP97 in its standard self-initializing mode. One can see that the negative impact of occlusion on the tracking performance grows with $v$ and $T$. In the third row, the proposed algorithm is given the initial correspondences. Apparently, the initialization can compensate for the negative effect of occlusion, since the corresponding values in the second and the third rows are quite close. Note that the differences between the first and the third rows only become significant for high speeds and many trajectories. Otherwise, self-initialization is possible and sufficient.

The third and fourth rows show that the performance of RS91 is close to, or even slightly better than, that of IP97 for low speeds and/or sparse point sets. However, RS91 performs poorly at large speeds and medium-to-high densities.

 

Table 3: Tracking results for IP97 and SS90, with entry/exit.

Alg.	Self-init.	Occl.	Low speed			High speed
			$T=20$	$T=40$	$T=60$	$T=20$	$T=40$	$T=60$
IP97	$+$	$+$	95.02	94.18	90.51	79.45	68.78	58.82
IP97	$+$	$-$	95.77	95.64	92.16	87.92	79.06	71.17
SS90	$+$	$-$	95.87	95.39	92.75	85.35	72.33	57.20

 

Table 3 demonstrates that the proposed algorithm performs reasonably well in presence of all events considered. Occlusion has the same impact here as in the previous case. Again, the alternative technique (SS90) can only compete with the IPAN Tracker until the motion conditions become severe.

Finally, it should be noted that the processing speeds of the two non-iterative algorithms, RS91 and IP97, are similar, while the iterative SS90 is approximately 10 to 100 times slower, depending on the number of trajectories. (See section 5.4 for more information on processing speed.)