Events Handling and Algorithmical Behavior

Table 1 shows the current capabilities of the tracking algorithms to handle events. In practice it is often difficult to guarantee that a non-admissible event will never occur. In addition, given the indistinguishability of the points, it is logically impossible to discriminate between some combinations of occlusion and entry/exit.

What happens to the algorithms when a non-admissible event occurs? Different types of behavior can be envisaged. An acceptable, although less efficient, behavior is detecting the non-admissible data and stopping, which we call refuse. If this is undesirable or impossible, one would accept a natural operation with local errors incurred that do not propagate to distant trajectories. An unacceptable behavior is an undetectable logical inconsistency or spatial propagation of errors. For each technique, we try to distinguish between its original formulation and its potential.

SJ87 (sec. 3.1)

This algorithm can be extended to handle an exit as an `infinite' occlusion. No entry should be allowed, however, to be able to detect the disappearing point. In a similar way, entries can be handled by the backward tracking starting from the last frame, with no exit allowed this time. Therefore, SJ87 can potentially cope with either occlusion and exit or, exclusively, occlusion and entry. Handling the three events altogether is not feasible in this framework, as the behavior might become unacceptable.

Persistent link errors can occasionally appear in SJ87, as mentioned in section 5.3.2. This is illustrated in figure 13. While most of the trajectories are tracked correctly, a persistent link error is propagated in time for the three trajectories involved. The process is triggered by poor optimization of a short trajectory appearing due to an occlusion. In the end, many link errors are accumulated on a few completely wrong trajectories.

HW89 (sec. 3.2)

HW89 is the only algorithm that may give multiple solutions: a point may belong to several trajectories. At the same time, an exiting trajectory is completely lost. This limitation, as well as the limited occlusion handling, are intrinsic to the algorithm.

SS90 (sec. 3.3)

Using the post-processing procedure of IP97, SS90 can be extended to cope with all events.

RS91 (sec. 3.4)

As far as occlusion, entry and exit are concerned, the situation is the same as with SJ87. An additional factor to be considered in RS91 is the possibility of a wrong initial link, which cannot be excluded in a real application. Figure 14 shows that a poorly given initial link can propagate to distant trajectories. Here, we artificially exchanged two of the initial links required for the operation of the algorithm.

IP97 (sec. 3.5)

This algorithm can be extended to longer occlusions at the expense of the post-processing speed.

  

Figure 13: A persistent link error in SJ87. Frames 2-4.

  

Figure 14: Propagation of an initialization error in RS91. Frames 2 and 5.