Suppose you capture two images related by a pure translation in the X direction, i.e., sideways camera motion.

[nustian116]

Suppose I  capture two images related by a pure translation in the X direction, i.e., sideways
camera motion.
Where is the epipole in this case and What would be the result of applying epipolar rectication to this pair of images?

[Emily-C]

Hi nustian116,

A rectified stereo image will produce an image where the eipopolar lines are parallel, and the epipolar points are points at infinity. This fundamental matrix is the same as a pure translation along the x-axis. So two images related by a pure translation in the x direction wouldn't need to be rectified. However, rectification is used because it is nearly impossible to create such a perfect set-up in real life. You can fine more information on page 247 of this document, and in these slides I found. 

I hope this helps!