An ellipse is hanging somewhere in $3D$ space with unknown $3D$ center coordinates and unknown $3D$ directions of its semi-axes, and unknown lengths of the semi-major and semi-minor axes. What you're given are two images of this ellipse from two cameras which have known centers and known orientations, and known focal distances (these are just the distances between the center of the camera and the projection plane).

From these two images, I would like to determine the ellipse completely, everything about the ellipse, namely, its center coordinates, its axes lengths, and their orientation in space.

How can this task be accomplished ?

This question is inspired by my recent answer to [this question](https://math.stackexchange.com/questions/773126/find-normal-vector-of-circle-in-3d-space-given-circle-size-and-a-single-perspect/4525194#4525194), so this provides some context to the current problem.