I have a set of 2D Points at time $T=0$, and another set at time $T=1$. Each point $P$ provides (X,Y,$\dot{X}$,$\dot{Y}$).
I need to basically match points at $T=0$ and $T=1$. A simple L2 metric of $\left \| P^{t=0}, P^{t=1} \right \|$ won't work, as I could have two points that are close, but travelling in opposite directions.
Taking the dot product $dot(P^{t=0}, P^{t=1})$ of a pair of points won't work too, as I could have two points that are far apart but traveling in the same direction.
I could combine them somehow and weigh them accordingly, but we could also include a vector $V=P^{t=0}-P^{t=1}$ and now we could compute a dot product of $dot(V, P^{t=1})$ or $dot(V, P^{t=0})$ and try to minimize those.
Just to note, the velocity vector's magnitude also ranges from 0 to 1. Generally, if the magnitude is low, the probability/stability of that vector is considered low as well, so we need to incorporate that as well.
How can I proceed? The assumption is that a pair of matching points across frames are generally close to each other
