Structure of Multiple Mirror System from Kaleidoscopic Projections of Single 3D Point

Abstract: This paper proposes a novel algorithm of discovering the structure of a kaleidoscopic imaging system that consists of multiple planar mirrors and a camera. The kaleidoscopic imaging system can be recognized as the virtual multi-camera system and has strong advantages in that the virtual cameras are strictly synchronized and have the same intrinsic parameters. In this paper, we focus on the extrinsic calibration of the virtual multi-camera system. The problems to be solved in this paper are two-fold. The first problem is to identify to which mirror chamber each of the 2D projections of mirrored 3D points belongs. The second problem is to estimate all mirror parameters, i.e., normals, and distances of the mirrors. The key contribution of this paper is to propose novel algorithms for these problems using a single 3D point of unknown geometry by utilizing a kaleidoscopic projection constraint, which is an epipolar constraint on mirror reflections. We demonstrate the performance of the proposed algorithm of chamber assignment and estimation of mirror parameters with qualitative and quantitative evaluations using synthesized and real data.