Efficient Relative Pose Estimation for Cameras and Generalized Cameras in Case of Known Relative Rotation Angle
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Efficient Relative Pose Estimation for Cameras and Generalized Cameras in Case of Known Relative Rotation Angle Evgeniy Martyushev1
· Bo Li2
Received: 19 July 2019 / Accepted: 9 April 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
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. Keywords Multi-view geometry · Relative pose estimation · Generalized cameras · Epipolar constraints · Relative rotation angle · Gröbner basis
1 Introduction 1.1 Relative Pose Estimation The problem of relative pose estimation of a moving camera consists in determining the current camera pose (both position and orientation) with respect to a coordinate frame related to its previous position. Basically, the estimation must be done only from the image data captured by the camera. The relative pose estimation is a central task in computer vision and robotics. Its various applications include, but are not limited to, robot localization and mapping, augmented
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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Evgeniy Martyushev [email protected] Bo Li [email protected]
1
South Ural State University, 76 Lenin Avenue, Chelyabinsk, Russia 454080
2
TrunkTech Co., Ltd., Beijing, China
reality, autonomous driving and parking, visual odometry, and egomotion estimation. The standard tool for estimating relative pose of a calibrated camera moving in space is the 5-point algorithm by Nistér [21] and its numerous modifications [13,17,25]. The 5-point algorithm is known to be minimal, i.e., its related polynomial ideal is generically zero-dimensional. There also exist non-minimal relative pose solutions based on a larger number of point correspondences, e.g., 6-point [22,23], 7point [9], and linear 8-point algorithms [8,19]. However, in most cases, these solutions are inferior t
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