Geometric Correction for Uneven Quadric Projection Surfaces Using Recursive Subdivision of Bézier Patches

Abstract

This paper presents a scheme for geometric correction of projected content for planar and quadratic projection surfaces. The scheme does not require the projection surface to be perfectly quadratic or planar and is therefore suitable for uneven low‐cost commercial and home projection surfaces. An approach based on the recursive subdivision of second‐order Bézier patches is proposed for the estimation of projection distortion owing to surface imperfections. Unlike existing schemes, the proposed scheme is completely automatic, requires no prior knowledge of the projection surface, and uses a single uncalibrated camera without requiring any physical markers on the projection surface. Furthermore, the scheme is scalable for geometric calibration of multiprojector setups. The efficacy of the proposed scheme is demonstrated using simulations and via practical experiments on various surfaces. A relative distortion error metric is also introduced that provides a quantitative measure of the suppression of geometric distortions, which occurs as the result of an imperfect projection surface.