Camera Pose Estimation Using Images of Planar Mirror Reflections

Rodrigues, Rui; Barreto, João Pedro; Nunes, Urbano

doi:10.1007/978-3-642-15561-1_28

Cited by 57 publications

(62 citation statements)

References 9 publications

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“…As shown in Table 1, the second group can be categorized into two subgroups: (2a) calibration from 4 (or more) known 3D reference object points [12,16,18] or (2b) calibration from 3 known 3D reference object points [8]. The biggest difference between (2a) and (2b) is whether the camera extrinsic parameters can be uniquely determined or not.…”

Section: Related Workmentioning

confidence: 99%

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

Takahashi

Nobuhara

Matsuyama

2012

2012 IEEE Conference on Computer Vision and Pattern Recognition

113

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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.

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Section: Related Workmentioning

confidence: 99%

“…For the cases where this condition does not hold, some studies proposed algorithm using mirrors [8,10,12,13,15,16,18]. They observe the reference object via mirrors, and then estimate the extrinsic parameters from the reflections of the reference objects in the mirrors.…”

Section: Introductionmentioning

confidence: 99%

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

Takahashi

Nobuhara

Matsuyama

2012

2012 IEEE Conference on Computer Vision and Pattern Recognition

113

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“…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.…”

Section: Related Workmentioning

confidence: 99%

“…The singular configuration occurs if all the mirror planes intersect in a single line. This happens if the mirror is rotated around a fixed axis, or if all mirror planes are parallel (intersection line is at infinity) [27]. Moreover, a particular algorithm can have specific degenerate cases depending on its implementation.…”

Section: Introductionmentioning

confidence: 99%

Extrinsic Camera Calibration without a Direct View Using Spherical Mirror

Agrawal

2013

2013 IEEE International Conference on Computer Vision

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We consider the problem of estimating the extrinsic parameters (pose) of a camera with respect to a reference 3D object without a direct view. Since the camera does not view the object directly, previous approaches have utilized reflections in a planar mirror to solve this problem. However, a planar mirror based approach requires a minimum of three reflections and has degenerate configurations where estimation fails. In this paper, we show that the pose can be obtained using a single reflection in a spherical mirror of known radius. This makes our approach simpler and easier in practice. In addition, unlike planar mirrors, the spherical mirror based approach does not have any degenerate configurations, leading to a robust algorithm. While a planar mirror reflection results in a virtual perspective camera, a spherical mirror reflection results in a nonperspective axial camera. The axial nature of rays allows us to compute the axis (direction of sphere center) and few pose parameters in a linear fashion. We then derive an analytical solution to obtain the distance to the sphere center and remaining pose parameters and show that it corresponds to solving a 16th degree equation. We present comparisons with state-of-art method using planar mirrors and show that our approach recovers more accurate pose in the presence of noise. Extensive simulations and results on real data validate our algorithm. IEEE International Conference on Computer Vision (ICCV)This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved.

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“…Some studies on calibration with a mirror have described setups to simplify calibration [2], [5], [8], [11], [16], [19], [20], [21]. Techniques include decreasing the number of required reference points or mirror poses, because simple setup offers many advantages for easy calibration and low computation complexity.…”

Section: Introductionmentioning

confidence: 99%

Extrinsic Camera Calibration with Minimal Configuration Using Cornea Model and Equidistance Constraint

Takahashi

Mikami

Isogawa

et al. 2016

IPSJ Transactions on Computer Vision and Applications

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Abstract:In this paper, we propose a novel algorithm to extrinsically calibrate a camera to a 3D reference object that is not directly visible from the camera. We use the spherical human cornea as a mirror and calibrate the extrinsic parameters from its reflection of the reference points. The key contribution of this paper is to present a cornea-reflectionbased calibration algorithm with minimal configuration; there are three reference points and one mirror pose. The proposed algorithm introduces two constraints. First constraint is that the cornea is virtually a sphere, which enables us to estimate the center of the cornea sphere from its projection. Second is the equidistance constraint, which enables us to estimate the 3D position of the reference point by assuming that the center of the camera and reference point are located the same distance from the center of the cornea sphere. We demonstrate the advantages of the proposed method with qualitative and quantitative evaluations using synthesized and real data.

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Camera Pose Estimation Using Images of Planar Mirror Reflections

Cited by 57 publications

References 9 publications

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

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

Extrinsic Camera Calibration without a Direct View Using Spherical Mirror

Extrinsic Camera Calibration with Minimal Configuration Using Cornea Model and Equidistance Constraint

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