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Determine relative 3d-position of camera to a rectangular plane.

I have the following: cameraMatrix (intrinsic parameters), distortionCoefficients, and 4 detected points of a Rect. In world coordinate system these 4 points all have z-coord of 0 (Rect lays on the ground). I know the proportion of the rect in world coordinates (width and height).

I know that homography can be used to relate pixel coordinates of same plane in two different images.

I want to generate depth information of camera in relation to this plane (maybe out of homographyMat ?). So some information like: cameraHeight above ground (resp. relative camera position to the plane) and the angle/angles between optical camera axis and axis perpendicular to the plane.

Is this possible?