I don't understand this diagram - how is it possible to know the epipolar line l' if we don't know what x' is? I think to know l' we would need to know the image 2 plane, which we have, and the epipolar plane. But to know the epipolar plane, don't we need x'? Or can we just get by using o, x, and o' to define the epipolar plane?
motoole2
Here are two ways to generate this epipolar line:
The epipolar line $l'$ is a projection of the 3D ray (traced through point $x$) onto the right image plane.
The epipolar line $l'$ is the result of intersecting the epipolar plane (defined by three points $o$, $o'$, and $x$) with the right image plane.
Note that there are many points $x'$ that could correspond to point $x$, but all of these points will be on the epipolar line.
I don't understand this diagram - how is it possible to know the epipolar line l' if we don't know what x' is? I think to know l' we would need to know the image 2 plane, which we have, and the epipolar plane. But to know the epipolar plane, don't we need x'? Or can we just get by using o, x, and o' to define the epipolar plane?
Here are two ways to generate this epipolar line:
The epipolar line $l'$ is a projection of the 3D ray (traced through point $x$) onto the right image plane.
The epipolar line $l'$ is the result of intersecting the epipolar plane (defined by three points $o$, $o'$, and $x$) with the right image plane.
Note that there are many points $x'$ that could correspond to point $x$, but all of these points will be on the epipolar line.