Some Properties about the Constraints on the Camera's Intrinsic Parameters from a Homography

It has been proved in the literature that the homography from the x-y plane of the world coordinate system to the image plane can give rise two linear constraints on the camera’s intrinsic parameters.We show in this work that given a homography from an arbitrary space plane to the image plane,if the plane’s coordinates are known in the world system,the homography can similarly provide two linear constraints on the camera’s intrinsic parameters.However,if the plane’s coordinates are unknown in the world system,the homography cannot bring any constraints on the intrinsic parameters.Besides,we show that given a homography induced by an unknown space plane between two images,it cannot bring any constraints on the intrinsic parameters either.These results could be of interests or reference to those people who work in camera calibration and3D reconstruction.