QuEst: A Quaternion-Based Approach for Camera Motion Estimation From Minimal Feature Points

Fathian, Kaveh; Ramirez-Paredes, Juan-Pablo; Doucette, Emily A.; Curtis, J. Willard; Gans, Nicholas

doi:10.1109/lra.2018.2792142

Cited by 36 publications

(22 citation statements)

References 33 publications

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“…Representing the rotations in matrix form with orthonormality constraints often makes the linearisation of equations () and () challenging to solve as they are very nonlinear. In contrast, unit quaternions provide a singularity‐free representation of rotations, and by restricting the first element to non‐negative numbers, there is a one‐to‐one correspondence between the rotation matrices and quaternions (Fathian et al, ). Instead of nonlinear rotations using Euler angles, unit quaternions are used, which represent a rotation by four elements

(q_{0} q_{x} q_{y} q_{z})

such that

q_{0}^{2} + q_{x}^{2} + q_{y}^{2} + q_{z}^{2} = 1

.…”

Section: Methodsmentioning

confidence: 99%

A precise visual localisation method for the Chinese Chang’e‐4 Yutu‐2 rover

Liu

Sima

et al. 2020

The Photogrammetric Record

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Precise localisation of the Yutu-2 moon rover plays an important role in path planning, obstacle avoidance and navigating to target features. To provide highprecision localisation information, a stereo bundle adjustment method using the theory of the unit quaternions is presented for the first time. To improve the precision and robustness of the proposed method, the rover's pose, from a visual odometry technique assisted by an inertial measurement unit and the rotation angles of the mast mechanism, is viewed as a pseudo-observation. A reasonable weighting strategy and a rational geometric constraint condition of the stereo cameras is also invoked. Experimental results demonstrate that the proposed method provides more accurate localisation results than either a bundle adjustment alone or a weighted total least-squares method. The proposed method has been successfully used in Chang'e-4 mission operations. (a) Chang'e-4 lander (b) Yutu-2 rover FIG. 1. The Chang'e-4 probe. (a) An image taken by the Yutu-2 rover's Pancam camera of the lander. (b) An image taken by the lander's topographic camera of the rover.The Photogrammetric Record

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(q_{0} q_{x} q_{y} q_{z})

such that

q_{0}^{2} + q_{x}^{2} + q_{y}^{2} + q_{z}^{2} = 1

.…”

Section: Methodsmentioning

confidence: 99%

A precise visual localisation method for the Chinese Chang’e‐4 Yutu‐2 rover

Liu

Sima

et al. 2020

The Photogrammetric Record

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show abstract

“…The resulting system of polynomial equations can be solved to recover the rotation. Alternatively, the quaternion representation of rotation, which uses four unknowns and reduces the number of variables, can be leveraged (Fathian et al 2018).…”

Section: Algorithmsmentioning

confidence: 99%

“…3. We benchmark the eight-point algorithm of Longuet-Higgins (Longuet-Higgins 1981) and five-point algorithm of Stewenius et al (2006), which are based on the essential matrix, and the direct estimation methods of Kneip et al (2012) and Fathian et al (2018) based on five points. We provide all eight-point and five-point algorithms with the same set of eight matched feature points.…”

Section: Benchmarksmentioning

confidence: 99%

“…There are a number of excellent books describing the vision-based pose estimation in deeper detail (Hartley and Zisserman 2004;Ma et al 2003;Corke 2017). The original papers cited throughout this manuscript will also provide greater understanding (Longuet-Higgins 1981; Faugeras and Lustman 1988;Stewénius et al 2006;Fathian et al 2018).…”

Section: Recommended Readingmentioning

confidence: 99%

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Vision-Based Motion Estimation

Gans¹,

Fathian²

2020

Encyclopedia of Systems and Control

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Vision-based motion estimation is the problem of recovering the rotation and translation (i.e., pose) of a moving camera or object from camera images. Algorithms that solve this problem are a key component of many control and robotic applications. Traditionally, the pose estimation problem is solved using image feature points, which must satisfy the rigid motion constraint. We explain how reformulation of the rigid motion constraint leads to different pose estimation algorithms. We discuss the advantages and drawbacks of these methods, benchmark their accuracy and runtime, and provide reference to open-source implementations.

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“…According to the well-known epipolar geometry, each PC provides one constraint for a relative pose. For single cameras, the representative methods for relative pose estimation are called five-point methods [5], [6], [7], [8], [9], [10]. For multi-camera systems, the development of minimal solvers for relative pose estimation ranges back to the six-point method [11].…”

Section: Introductionmentioning

confidence: 99%

On Relative Pose Recovery for Multi-Camera Systems

Zhao¹,

Guan²

2021

Preprint

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The point correspondence (PC) and affine correspondence (AC) are widely used for relative pose estimation. An AC consists of a PC across two views and an affine transformation between the small patches around this PC. Previous work demonstrates that one AC generally provides three independent constraints for relative pose estimation. For multi-camera systems, there is still not any AC-based minimal solver for general relative pose estimation. To deal with this problem, we propose a complete solution to relative pose estimation from two ACs for multi-camera systems, consisting of a series of minimal solvers. The solver generation in our solution is based on Cayley or quaternion parameterization for rotation and hidden variable technique to eliminate translation. This solver generation method is also naturally applied to relative pose estimation from PCs, resulting in a new six-point method for multi-camera systems. A few extensions are made, including relative pose estimation with known rotation angle and/or with unknown focal lengths. Extensive experiments demonstrate that the proposed AC-based solvers and PC-based solvers are effective and efficient on synthetic and real-world datasets.

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QuEst: A Quaternion-Based Approach for Camera Motion Estimation From Minimal Feature Points

Cited by 36 publications

References 33 publications

A precise visual localisation method for the Chinese Chang’e‐4 Yutu‐2 rover

A precise visual localisation method for the Chinese Chang’e‐4 Yutu‐2 rover

Vision-Based Motion Estimation

On Relative Pose Recovery for Multi-Camera Systems

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