A theory of multi-layer flat refractive geometry

Agrawal, Amit; Ramalingam, Srikumar; Taguchi, Yuichi; Chari, Visesh

doi:10.1109/cvpr.2012.6248073

Cited by 149 publications

(172 citation statements)

References 12 publications

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“…The translation along the axis cannot be recovered by the coplanarity constraints. For completeness, we re-derive the constraint below in this section and the derivation follows [2,1]. In the next section, we derive an analytical solution for remaining parameters, namely, distance d to the sphere center and translation along the axis, which is a key contribution of this paper.…”

Section: Estimation Of Axismentioning

confidence: 99%

“…As described in [2,1], the so called coplanarity constraint holds for axial systems, which allow estimation of axis using 8 3D-2D correspondences. In addition, the coplanarity constraints can also recover the rotation R and translation orthogonal to the axis (two degrees of translation).…”

Section: Estimation Of Axismentioning

confidence: 99%

“…One way is described in [2], where the last column of E matrix, e 3 , is obtained using Demazure constraints [4]. As shown in [2], there are two solutions for e 3 , which only differ in sign. Thus, the solutions for E are given by e 1 e 2 e 3 and e 1 e 2 −e 3 .…”

Section: Estimation Of Axismentioning

confidence: 99%

“…Non-Planar Reference 3D points: If the reference 3D points P(i) do not lie on a plane, the rank of B is 8. As described in [2] (8-point algorithm), a four dimensional subspace solution can be obtained by SVD. The subspace coefficients are then obtained by using Nister's 5-point algorithm [24].…”

Section: Estimation Of Axismentioning

confidence: 99%

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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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Section: Estimation Of Axismentioning

confidence: 99%

Section: Estimation Of Axismentioning

confidence: 99%

Section: Estimation Of Axismentioning

confidence: 99%

Section: Estimation Of Axismentioning

confidence: 99%

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Extrinsic Camera Calibration without a Direct View Using Spherical Mirror

Agrawal

2013

2013 IEEE International Conference on Computer Vision

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“…Examples include any catadioptric system that combines a revolution mirror with a central camera for which the viewpoint is aligned with the mirror axis (e.g. a pinhole looking at a spherical mirror) [13]; the situation of a perspective camera looking through multiple flat refractive mediums [1]; or a multi-camera rig composed by two or more pinhole cameras with collinear optical centers [5].…”

Section: Introductionmentioning

confidence: 99%

Towards a minimal solution for the relative pose between axial cameras

Vasconcelos

Barreto

2013

Procedings of the British Machine Vision Conference 2013

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The problem of estimating the relative pose between axial cameras from pairwise point correspondences is still open to improvement. The state-of-the-art solutions are either too specific in its scope, assuming certain types of correspondences; too broad, dealing with all types of generalized cameras and failing to address the specific issues of axial cameras; or non-minimal linear solutions. The aim of this paper is to pursue new insights on axial cameras that can lead to a suitable minimal solution for this problem. We propose a new formulation for modeling the intersection of back-projection rays of axial cameras through a 5×5 essential matrix that enables a better understanding of some particular axial configurations and leads to a new set of polynomial equations that proves to be useful in constraining the motion estimation. These equations enable to compute a solution from 10 correspondences, an improvement over the 16-point algorithm, which is the state-of-the-art solution within our aimed scope. Both synthetic and real experiments show that our algorithm achieves a better performance than the 16-point algorithm in the context of robust optimization with RANSAC.

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