Post-Processing of Broken Trajectories

This procedure attempts connecting the broken trajectories. In figure 3, a broken trajectory is shown along with two possible continuations and a separate, continuous trajectory. Consider a B-point $P_{e}$ with the incoming velocity $\vec{v_{e}}$ and an F-point $P_{s}$ with the outgoing velocity $\vec{v_{s}}$. A candidate occluded point is searched in the intersection of the two search areas $S^+_{e}$ and $S^-_{s}$.

  

Figure 3: Post-processing of broken trajectories. A broken trajectory is shown along with two alternative continuations and a separate, continuous trajectory. The occluded point is searched in the filled region.

The search areas are basically defined by the cost function, the cost limit and the speed limit. In addition, the procedure makes use of the fact that simultaneous occlusion and drastic turn are rare, since both are relatively rare events. To ensure directional continuity of broken trajectories, $S^+_{e} \cap S^-_{s}$is more constrained than it is prescribed by the cost limit alone. The search areas for the particular cost function used in the IPAN Tracker are given in section 4.4.

If $S^+_{e} \cap S^-_{s}$ is empty, the trajectory remains broken. Otherwise, the point is found that minimizes the cost for the interpolated trajectory. This is done by exhaustive search of $S^+_{e} \cap S^-_{s}$ with a suitable spatial resolution. To account for possible two-frame occlusions, each point of $S^+_{e}$ ($S^-_{s}$) is expanded in the same way into a search area in the next (previous) frame, and the average cost is minimized.