How to move epipole to the outside of the image

Question

Hi i had computed the fundamental matrix from two images and i found out that the epipoles lie within the image. I cannot do the rectification using matlab if the image contains epipole.

May i know how to compute the fundamental matrix that the epipole is not in the image?

Answer 1

The epipolar geometry is the intrinsic projective geometry between two views. It is independent of scene structure, and only depends on the cameras' internal parameters and relative pose.

So the intrinsics/extrinsics of the cameras define the fundamental matrix that you get (i.e. you cannot compute another fundamental, s.t. the epipoles are not in the image).

What you can do is either take a different pair of images (with a different camera geometry, for example) and you may get epipoles out of the image.

The problem you're actually having is that the rectification algorithm that you're using is limited and doesn't work for the case when the epipole is inside the image. Note, there exist other algorithms that do not have this limitation. I have implemented such an algorithm in the past, and may be can find the (MATLAB) code. So, please let me know if you're interested.

If you're in a mood to learn more about epipolar geometry and the fundamental matrix, I recommend you take a look here: