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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.

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  • $\begingroup$ What do you mean by “I have an image in of 2 orthogonal planes”? What kind of image? A planar projection of the 3d scene? What do you mean by having the homography matrix of one of these planes? The matrix which maps one of these planes from 3d space into your 2d image space? $\endgroup$ – MvG Sep 18 '15 at 12:35
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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)

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