  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.
