Why is the planar homography not completely sufficient to map any arbitrary scene image to another viewpoint

Question

I just have a very basic question for Computer vision homography. Why is the planar homography not completely sufficient to map any arbitrary scene image to another viewpoint? The points must be on one plane. So the image points behind 2 cameras should have relationship? I am comfused? Does anybody provide some material to learn it?

Thank you very much!

Answer 1

It is completely suficient for the points that are on a world plane (and that world plane is the one inducing the homography), or for all points if the camera motion between the two images is a pure rotation about its center.

Answer 2

Linear estimation of projective transformation parameters from point correspondences often suffer from poor “conditioning” of the matrices involves. This means the solution is sensitive to noise in the points