A new mirror-based extrinsic camera calibration using an orthogonality constraint

This paper is aimed at calibrating the relative posture and position, i.e. extrinsic parameters, of a stationary camera against a 3D reference object which is not directly visible from the camera. We capture the reference object via a mirror under three different unknown poses, and then calibrate the extrinsic parameters from 2D appearances of reflections of the reference object in the mirrors. The key contribution of this paper is to present a new algorithm which returns a unique solution of three P3P problems from three mirrored images. While each P3P problem has up to four solutions and therefore a set of three P3P problems has up to 64 solutions, our method can select a solution based on an orthogonality constraint which should be satisfied by all families of reflections of a single reference object. In addition we propose a new scheme to compute the extrinsic parameters by solving a large system of linear equations. These two points enable us to provide a unique and robust solution. We demonstrate the advantages of the proposed method against a state-of-the-art by qualitative and quantitative evaluations using synthesized and real data.