I have two sets of points from two consecutive frames (restored from a video). The data represent points on the surface of a single-vehicle moving between frames. Points are in 3D and are assumed not to change in the $y$ axis (flat world) between frames. In each frame, we assume all points are of a single plain (The vehicle plane). The points are indexed and we can recognize the same point in different frames.

How do I apply the bicycle model in this case? It needs a steering input variable which I do not have, as well as a velocity input variable.

Since I can calculate $dx$ and $dz$ between consecutive frames, I think I can get $v$ somehow using:

$$v = \sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dz}{dt}\right)^2},$$

however, I do not have the frame rate $dt$, so I can only get the direction of $v$. Also, I don't know the size of the target Vachel, only some points, nor the direction of movement. How do I account for these? I need to take one of the points as a reference?

my final goal is to get a vector $(dx, dy, dz, d\theta)$ with $dy$ obviously $0$, representing the motion between frames.

Also, and this an intuition, Is it wrong to calculate $d\theta$ simply as the angle between the planes? My intuition tells me it is not that easy, however, I cannot think of a reason it is not correct.



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