Epipolar constraint in the 8-point algorithm

Question

I am developing a system using two cameras, and I want to know is it possible that the epipolar constraint can be satisfied by a matrix that this not part of the set of essential matrices? If so, in which situation do I have to handle this matrix?

Answer 1

A calibrated stereo rig has one well defined (up to scale) essential matrix E such that E = K₁^T * F * K₂, where K₁ and K₂ are the camera matrices, and F is the fundamental matrix. The epipolar constraints determines F, but not E, unless the intrinsic calibration of both cameras is known.

So, to answer your question, as I understand it:

1. Is it possible that the epipolar constraint can be satisfied by a matrix that this not part of the set of essential matrices? Yes, every fundamental matrix for a image pair will satisfy it, but not every fundamental matrix is an essential matrix for a given rig.
2. In which situation do I have to handle this matrix? Probably never: if you are talking about essential matrices, you are in a calibrated setup, which has but one essential matrix (up to scale).