why does epipole $e$ come out from the SVD of the essential matrix $E$?
mpotoole
Since all epipolar lines include the epipole $e$, we must have $x'Ee = 0$ for all $x$. And this only hold true if $Ee = 0$ for the epipole $e$. See this slide for a summary of properties associated with the essential matrix.
In order to find an epipole $e$ from an essential matrix $E$, we need to find a vector $v$ such that $Ev = 0$. This is done by finding the right singular vector $v$ with the smallest singular value (which is zero in the case of a rank 2 matrix).
Also, if you want to find the epipole on the other image plane, it is given by the left singular vector $u$ corresponding to the smallest singular value.
why does epipole $e$ come out from the SVD of the essential matrix $E$?
Since all epipolar lines include the epipole $e$, we must have $x'Ee = 0$ for all $x$. And this only hold true if $Ee = 0$ for the epipole $e$. See this slide for a summary of properties associated with the essential matrix.
In order to find an epipole $e$ from an essential matrix $E$, we need to find a vector $v$ such that $Ev = 0$. This is done by finding the right singular vector $v$ with the smallest singular value (which is zero in the case of a rank 2 matrix).
Also, if you want to find the epipole on the other image plane, it is given by the left singular vector $u$ corresponding to the smallest singular value.