Say you have a knotted-up string or, as in this case, USB cable:
I am wondering to what extent there are algorithms that could turn a picture like this (or a succession of pictures of the same object) into a proper 3d mathematical representation of the object?
For example, I would be happy with a 1-dimensional polygon in $\mathbb R^3$ that describes the rough shape of a cable, given in a picture like the above. It would be useful if the algorithm could tell the difference between an "open" knot and a closed knot -- meaning the knot is a (possibly tangled) loop, vs just some length of string with free ends.
In the case of the above picture, I would be happy with output a list like:
$$ (-2,0,0) \to (1,0.2,0) \to (1,-1,1) \to (-1,-1,-1) \to (-1,0.2,-1) \to (-1,0.2,1) \to (1,0,-0.2) \to (2,0,0) $$
from the algorithm. Roughly the $(x,y,z)$ coordinate corresponds to the picture with the x-axis horizontal, the y-axis vertical, and the z-axis would be into the table.
Are there any algorithms out there that are (?close?) to capable of such a task?
Apologies in advance if I am using inappropriate tags.