Video as a Space-Time Signal

Stacking frames into a cube

Slant is velocity

Brightness constancy

Occlusion makes it composite

An x-t slice of a surveillance video shows one perfectly vertical bright band and one band slanted so that it moves rightward across the slice. What does this slice reveal?

A scene satisfies $\ell(x,y,t) = \ell_0(x - v_x t, y - v_y t)$ with $v_x = 3$. Frame zero has a dark spot at $x = 10$. Where is the spot at frame $t = 4$?

In an x-t slice of a video, an object moves at $v_x = 2$ pixels per frame. Starting at $x = 30$ in frame 0, how many pixels total does the object advance over the next 5 frames?