Processing Subsequent Frames

In each frame, a point may have at most two links, a `forward' one and a `backward' one. A link indicates that the point is connected to a neighboring frame. Each link has a displacement vector assigned to it.

The matching procedure for $k>2$ also operates with 3 consecutive frames. Consider the current frame $F_k, k>2$. The previous frame $F_{k-1}$ has just been processed. In $F_{k-1}$, the zero-link points (Z-points) are the appearing points whose potential correspondences to $F_{k}$ are to be established. All the single-link points are connected to $F_{k-2}$, that is, they are backward-linked points abbreviated as B-points. These points have been marked as disappeared. They are only considered in the post-processing step. Most points usually have both links indicating continuous trajectories. In $F_{k}$, a point can have one backward link or no link at all. In $F_{k+1}$, all points are free. (See figure 2).

  

Figure: Processing the frame $F_k, k>2$. The lines show the symbolic backward and forward links. Only the dark points are considered in the hypothesis testing.

The feature points in $F_{k}$ are processed similarly to the initializing step described above. The only difference is that the already established correspondences are used when available. They are not modified. Consequently, during the hypothesis testing the B-points of $F_{k}$ supply their previous displacements, while the Z-points are projected backwards onto $F_{k-1}$ to find their candidate displacements. In $F_{k-1}$, the Z-points are only considered. These points may get linked to $F_{k}$ and become forward-linked (F-) points.

This procedure provides a natural way to handle appearing and disappearing points, including the motion across the image border. The moving points establish their links in a competitive process that develops as the trajectories grow. When the final frame has been processed, the double-link points form the continuous trajectories. The B-points are the disappearing, the F-points the appearing points.