Coplanar Common Points in Non-centric Cameras

Discovering and extracting new image features pertaining to scene geometry is important to 3D reconstruction and scene understanding. Examples include the classical vanishing points observed in a centric camera and the recent coplanar common points (CCPs) in a crossed-slit camera [21,17]. A CCP is a point in the image plane corresponding to the intersection of the projections of all lines lying on a common 3D plane. In this paper, we address the problem of determining CCP existence in general non-centric cameras. We first conduct a ray-space analysis to show that finding the CCP of a 3D plane is equivalent to solving an array of ray constraint equations. We then derive the necessary and sufficient conditions for CCP to exist in an arbitrary non-centric camera such as non-centric catadioptric mirrors. Finally, we present robust algorithms for extracting the CCPs from a single image and validate our theories and algorithms through experiments.