A Linear Extrinsic Calibration of Kaleidoscopic Imaging System From Single 3D Point

Kosuke Takahashi, Akihiro Miyata, Shohei Nobuhara, Takashi Matsuyama; Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2017, pp. 567-575

This paper proposes a new extrinsic calibration of kaleidoscopic imaging system by estimating normals and distances of the mirrors. The problem to be solved in this paper is a simultaneous estimation of all mirror parameters consistent throughout multiple reflections. Unlike conventional methods utilizing a pair of direct and mirrored images of a reference 3D object to estimate the parameters on a per-mirror basis, our method renders the simultaneous estimation problem into solving a linear set of equations. The key contribution of this paper is to introduce a linear estimation of multiple mirror parameters from kaleidoscopic 2D projections of a single 3D point of unknown geometry. Evaluations with synthesized and real images demonstrate the performance of the proposed algorithm in comparison with conventional methods.