Decompose homography matrix to rotation and translation

Question

how can you get the correct R and t from H when you have 4 solutions. From my understanding you can only eliminate two.

Is there really no way to get the correct solutions if you only have points on a single plane?

Thanks for any help.

Answer 1

There is one approach to best select solution from two possible solutions. When you decompose Homography,after eliminating 2 possible solutions from 4,you get two set of

rotations, translations and normals.

Normals are nothing but possible camera_normals wrt scene of first image(when you estimate Homography between two images). So having known camera_normal wrt planar scene when first image was captured, you can choose solution corresponding to closest normal from n1,n2 by computing dot product dot(camera_normal,n1) and dot(camera_normal,n2), whichever is larger.

Thanks

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Edit: camera_normal explanation

Planar Homography assumes that features used for computing Homography between tow images are in a plane. So camera_normal is direction of z-axis of camera in plane's frame.