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

TL;DR

This paper introduces a linear method for extrinsic calibration of kaleidoscopic imaging systems by estimating mirror normals and distances from a single 3D point, simplifying the process compared to traditional approaches.

Contribution

The paper presents a novel linear estimation technique for multiple mirror parameters using kaleidoscopic projections of a single 3D point, unlike conventional methods that require multiple images.

Findings

Accurate calibration achieved with synthesized and real images.

Outperforms conventional methods in efficiency and accuracy.

Linear estimation simplifies the calibration process.

Abstract

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.