A new mirror-based extrinsic camera calibration using an orthogonality constraint

Abstract

This paper is aimed at calibrating the relative posture and position, i.e. extrinsic parameters, of a stationary camera against a 3D reference object which is not directly visible from the camera. We capture the reference object via a mirror under three different unknown poses, and then calibrate the extrinsic parameters from 2D appearances of reflections of the reference object in the mirrors.The key contribution of this paper is to present a new algorithm which returns a unique solution of three P3P problems from three mirrored images. While each P3P problem has up to four solutions and therefore a set of three P3P problems has up to 64 solutions, our method can select a solution based on an orthogonality constraint which should be satisfied by all families of reflections of a single reference object. In addition we propose a new scheme to compute the extrinsic parameters by solving a large system of linear equations. These two points enable us to provide a unique and robust solution.We demonstrate the advantages of the proposed method against a state-of-the-art by qualitative and quantitative evaluations using synthesized and real data.

Extrinsic Camera Calibration without a Direct View Using Spherical Mirror

“…Moreover, no degenerate mirror configurations exist when using a spherical mirror, since we require only one view. In addition, we show that our approach outperforms the state-of-art method using planar mirrors [31] and recovers more accurate pose in the presence of noise. Our contributions are as follows…”

“…Unlike previous approaches, our approach does not have any degenerate mirror configurations. In addition, we show in Section 6 that it outperforms the state-of-art method [31].…”

“…Mirror based extrinsic calibration: Previous approaches either attach markers to planar mirrors to estimate the mirror poses [15,20] or estimate the mirror poses along with the extrinsic calibration [28,27,18,14,31]. As discussed, a minimum of three reflections are required using planar mirror and degenerate configurations exists.…”

“…In this section, we present simulations on our approach along with comparisons with state-of-art planar mirror based approach [31]. We employ a realistic scenario using a camera with resolution of 1500 × 1500 pixels and focal length 2000 pixels (FOV of 41…”

“…Moreover, a particular algorithm can have specific degenerate cases depending on its implementation. For example, consider the state-of-art algorithm proposed in [31]. If the intersection of any two mirrors lie on the plane defined by the reference 3D points, it results in a degenerate configuration.…”