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Efficient Relative Pose Estimation for Cameras and Generalized Cameras in Case of Known Relative Rotation Angle

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Abstract

We propose two minimal solvers to the problem of relative pose estimation for a camera with known relative rotation angle. In practice, such angle can be derived from the readings of a 3D gyroscope. Different from other relative pose formulations fusing a camera and a gyroscope, the use of relative rotation angle does not require extrinsic calibration between the two sensors. The first proposed solver is formulated for a calibrated regular camera and requires four-point correspondences from two views. The second solver extends the problem to a generalized camera and requires five-point correspondences. We represent the rotation part of the motion in terms of unit quaternions in order to construct polynomial equations encoding the epipolar constraints. The Gröbner basis technique is then used to efficiently derive the polynomial solutions. Our first solver for regular cameras significantly improves the existing state-of-the-art solution. The second solver for generalized cameras is novel. The presented minimal solvers can be used in a hypothesize-and-test architecture such as RANSAC for reliable pose estimation. Experiments on synthetic and real datasets confirm that our algorithms are numerically stable, fast, and robust.

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Notes

  1. Hereinafter, the cameras will sometimes be referred to as regular in order to distinguish them from generalized cameras.

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Authors and Affiliations

  1. South Ural State University, 76 Lenin Avenue, Chelyabinsk, Russia, 454080

    Evgeniy Martyushev

  2. TrunkTech Co., Ltd., Beijing, China

    Bo Li

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  1. Evgeniy Martyushev
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  2. Bo Li
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Correspondence to Evgeniy Martyushev.

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The work of E.M. was supported by Act 211 Government of the Russian Federation, Contract No. 02.A03.21.0011.

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Martyushev, E., Li, B. Efficient Relative Pose Estimation for Cameras and Generalized Cameras in Case of Known Relative Rotation Angle. J Math Imaging Vis 62, 1076–1086 (2020). https://doi.org/10.1007/s10851-020-00958-5

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