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

This paper proposes a novel algorithm of discovering the structure of a\nkaleidoscopic imaging system that consists of multiple planar mirrors and a\ncamera. The kaleidoscopic imaging system can be recognized as the virtual\nmulti-camera system and has strong advantages in that the virtual cameras are\nstrictly synchronized and have the same intrinsic parameters. In this paper, we\nfocus on the extrinsic calibration of the virtual multi-camera system. The\nproblems to be solved in this paper are two-fold. The first problem is to\nidentify to which mirror chamber each of the 2D projections of mirrored 3D\npoints belongs. The second problem is to estimate all mirror parameters, i.e.,\nnormals, and distances of the mirrors. The key contribution of this paper is to\npropose novel algorithms for these problems using a single 3D point of unknown\ngeometry by utilizing a kaleidoscopic projection constraint, which is an\nepipolar constraint on mirror reflections. We demonstrate the performance of\nthe proposed algorithm of chamber assignment and estimation of mirror\nparameters with qualitative and quantitative evaluations using synthesized and\nreal data.\n