0

I have two calibrated cameras, so I know the essential an intrinsic matrices and I have computed the homography between a set of hand selected points. They are hand selected because the selection of the points requires domain knowledge beyond which automatic point selection cannot be relied upon - that is, it is a expert selecting the points. That said, the expert will be off slightly by a few pixels and a least squares solution (SVD) is used of course. I'm thinking that I want to assist the surgeon in selecting the corresponding points by computing the epipolar line in the corresponding image as the user selects points. This means that I need the fundamental matrix from the two camera matrices. All the examples that I see say "Let's assume that camera 1 is at

\begin{array}{c|c} I&0 \end{array}

and camera 2 is at

\begin{array}{c|c} R&t \end{array}

but my first camera is not at the origin.

How does that change the computation of F?

Thanks

RickF
  • 1
  • I’ll need to review this material in order to provide a proper answer, but my first inclination is to say that the cameras’ actual stances don’t change much. It’s only their relative stances that are captured by the fundamental and essential matrices, which is why pretty much everyone assumes $[I\mid\mathbf 0]$ for the first camera. Note, for instance, that in terms of the camera matrices $P$ and $P'$ and epipole $\mathbf e'$, $F=[\mathbf e']_\times P'P^+$, so the non-relative parts of the world transformations cancel—$F$ determines the camera matrices up to a projective transformation. – amd Dec 23 '19 at 21:28
  • I’m not sure that really matters, though. You write that you have the essential matrix $E$ and intrinsic matrices $K$ and $K'$. Can’t you recover the fundamental matrix from these using $E={K'}^TFK$? – amd Dec 23 '19 at 21:35

0 Answers0