# Find the Homography of a plane parallel to a plane with known Homography

Solution for Find the Homography of a plane parallel to a plane with known Homography
is Given Below:

Considering the Sample Image I have Homography matrix ‘h’ which transforms the ground plane to the top view. The matrix is calculated using ArUco markers on the ground, so the matrix transforms the ground coordinates correctly. But now I want to transform the table’s corner coordinates to the top view. The table plane is parallel to the ground in the 3D Coordinate system. We can assume an average distance between the ground plane and the table’s plane to be ‘d’. Is there any way to get the top view of the table or get a homography matrix for this? I have Camera intrinsic and extrinsic parameters, and the tomography matrix calculated for the ground plane.

I am thinking of first project table coordinates on the ground and then use the homography matrix we have, but I don’t know if it is correct.

Sample Image

Look into the work that Antonio Criminisi did a looooong time ago on homologies between parallel planes. It’s in his “Single View Metrology” paper. Complete treatment in his Ph.D. thesis.