Relative 3D rotation from an homography matrix

Question

I want to obtain a relative 3D rotation from the homography between two images. A way of doing this would be decomposing the homography matrix (maybe using opencv decomposeHomographyMat) . However, I want to do this with an uncalibrated camera (no intrinsics matrix to use in the homography decomposition). Also, I'm interested in the general case of any rigid transformation between the cameras that took the images, not necessarily a pure rotation.

Is this possible at all? any references? it feels to me there should be some way of obtaining at least an estimate of this relative rotation without the intrinsics matrix.

Answer 1

decomposeHomographyMat produces a rotation and a (scale-free) translation - and a normal, times four possible solutions.

If your setup is uncalibrated, but you can make a decent guess as to the focal length, you can start by solving for the essential matrix, decompose it and then just bundle adjust. If not, all you can get is a projective recon.

References: the Hartley and Zisserman book is good start.