Focus of Expansion

Question

I had previously asked a question but not received any response for it. Here I look to narrow it down much further, in a hope for an answer.

How to calculate Focus of Expansion, after deriving the optical flow from OpenCV?

Thanks in advance :)

Answer 1

Let's assume a static scene with a moving camera, where all optical-flow is induced by the camera motion. There is no camera rotation, only (3D) translation.
In this case the FOE - focus of expansion - is the intersection point of all the pixel flows.

You can use least-squares to find the FoE as the null-space of the over-determined matrix whose rows are the lines defined by the motion vectors. RANSAC may be a more robust approach.

In the case of lateral motion the FoE will be at infinity, in the case of forward motion it will be a point within the image.

In the more general case, the FoE is the epipole which can be found once you have estimated the Fundamental matrix.