Coupled line cameras and projectors: A geometric tool set for rectangular projection mapping

A novel geometric tool set, composed of coupled line cameras (CLC) and coupled line projectors (CLP), is introduced for application in rectangular projection mapping. Recently, CLC has been comprehensively investigated and it gives a new insight as a geometric computer vision tool. Given an unknown scene rectangle and an uncalibrated camera, CLC provides analytic solutions to determine the aspect ratio of a scene rectangle and to compute extrinsic camera parameters. Although coupled line projectors (CLP) has been introduced earlier than CLC, its solutions are not refined as much as CLC. In this paper, we summarize the current state of CLC, propose new analytic solutions of CLP, and show that they can be combined as a geometric tool set for a projection mapping application. Especially, the proposed CLC-CLP tool set is convenient since it can be applied to any real-world rectangle, either explicit or implicit, without specification of the screen geometry. In addition, no fiducial marker-based calibration is required for either a camera or projector, which makes projection mapping more casual and accessible.