[Math] How to calculate homography matrix of plane using the homography of its orthogonal plane

3dgeometry

I have an image of a 3D object cast on two orthogonal planes. I have a homography matrix of one of these planes. I want get the homography for the other plane.

my question explicitly is:

1- Can I compute or convert the homography of one plane directly as homography to the other plane?

2- If not, what other data do I need to add to the current homography in one plane to compute the other one? And, what is the algorithm to use?

Thanks.

Best Answer

I found the answer. Mathematically there is no way to do what I asked for. but by adding some other information it is reachable. in this context: (I assumed a projective transformation as I was working with camera modeling and 3D image processing) either of following can give us enough information to compute other H matrix:

C :camera position

Vz : vanishing point in Z direction

etc... (there are other measurable parameters that also work)