A Stable Algebraic Camera Pose Estimation for Minimal Configurations of 2D/3D Point and Line Correspondences

Zhou, Lipu; Ye, Jiamin; Kaess, Michael

doi:10.1007/978-3-030-20870-7_17

Cited by 16 publications

(8 citation statements)

References 28 publications

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“…It incorporates both points and lines as the correspondences, generally having better flexibility and adaptability to various practical scenes. The minimal cases for the PnPL problem have been proposed by Ramaligan et al [32] and Zhou et al [33], while as for the non-minimal cases, the DLT approach can be extended from points to lines, and eventually to the combination of them both [30]. Subsequently, Vakhitov et al [34] managed to extend the use of EPnP and OPnP algorithms to the line-based conditions, and the results were the state-of-the-art EPnPL and OPnPL algorithms.…”

Section: Perspective-n-point-and-line (Pnpl) Methodsmentioning

confidence: 99%

Certifiably Optimal and Robust Camera Pose Estimation From Points and Lines

Sun

Deng

2020

IEEE Access

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The Perspective-n-Point-and-Line (PnPL) problem, as a cornerstone in geometric computer vision, seeks to estimate the absolute pose of a calibrated camera from 3D-to-2D point and line correspondences. In this paper, we present a certifiably globally optimal and robust solution to the PnPL problem with a large number of outliers among the correspondences. Our first contribution is to reformulate the general PnPL problem as a novel constrained global optimization problem of Sum-of-Squares (SOS) polynomials using generalized geometric distances for both points and lines. Our second contribution is to efficiently solve this non-convex optimization problem by reducing it to an equivalent convex Linear Matrix Inequality (LMI) problem via a series of SOS relaxations. With these two contributions, we can develop a non-minimal solver, named SPnPL, for the outlier-free cases. The third contribution is to further add a Graduated Non-Convexity (GNC) cost function to SPnPL so as to remove outliers through closed-form iterations, which leads to a robust solver, named GNC-SPnPL. Both synthetic and real-data experiments confirm that SPnPL can mostly outperform the existing state-of-the-art PnPL algorithms and GNC-SPnPL can render accurate results even when 85% of the correspondences are outliers. INDEX TERMS Camera pose estimation; global optimization of polynomials; sum of squares; moment theory; robust estimation and outlier rejection

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Section: Perspective-n-point-and-line (Pnpl) Methodsmentioning

confidence: 99%

Certifiably Optimal and Robust Camera Pose Estimation From Points and Lines

Sun

Deng

2020

IEEE Access

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“…The literature for mixed combinations of points and lines is briefer compared to the previous two modalities. The works of Ramaligan et al [29] and Zhou et al [43] address the minimal cases while for non-minimal cases the DLT approach [13] can naturally be adapted to take contribution from points and lines. Subsequently, Kuang and Åström [19] proposed a method to jointly estimate the pose and focal length from points, lines and points with direction.…”

Section: Related Workmentioning

confidence: 99%

“…However, we show that with with our approach, it is possible to address the problem with convex optimization and to retrieve a finite number of solutions. The method makes use of point and line correspondences, to leverage collinearity and coplanarity constraints as in [29,43]. We formulate our optimization problem as a Quadratic Constrained Quadratic Program (QCQP), which we further relax into a Semi Definite Program (SDP) using Shor's relaxation [26].…”

Section: Introductionmentioning

confidence: 99%

“…Our method is the first convex formulation to solve the Perspectiven-Points-and-Lines (PnPL) problem from 2D-3D correspondences, being able to recover up to 4 ambiguous poses, while only returning the number of solutions required. We modified the formulation from Zhou et al [43] to fully exploit all geometric information provided by the point and line correspondences and, lastly, we present a modification to Kukelova's et al E3Q3 [20] to handle the further constrained case of the intersection of 6 quadrics with 3 unknowns. Our experimental results are in line with the most accurate state-of-the-art methods, but we believe that the main contribution of this work comes from its theoretical findings.…”

Section: Introductionmentioning

confidence: 99%

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CvxPnPL: A Unified Convex Solution to the Absolute Pose Estimation Problem from Point and Line Correspondences

Agostinho¹,

Gomes²,

Bue³

2019

Preprint

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We present a new convex method to estimate 3D pose from mixed combinations of 2D-3D point and line correspondences, the Perspective-n-Points-and-Lines problem (PnPL). We merge the contributions of each point and line into a unified Quadratic Constrained Quadratic Problem (QCQP) and then relax it into a Semi Definite Program (SDP) through Shor's relaxation. This makes it possible to gracefully handle mixed configurations of points and lines. Furthermore, the proposed relaxation allows us to recover a finite number of solutions under ambiguous configurations. In such cases, the 3D pose candidates are found by further enforcing geometric constraints on the solution space and then retrieving such poses from the intersections of multiple quadrics. Experiments provide results in line with the best performing state of the art methods while providing the flexibility of solving for an arbitrary number of points and lines.

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“…Many methods have been proposed to estimate absolute camera pose, i.e., the position and orientation, such as the perspective-n-point (PnP) solver [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 ], which uses n known 2D–3D point correspondences. Pose estimation is one of the key steps in computer vision [ 2 , 10 , 11 ], photogrammetry [ 3 , 11 , 12 ], augmented reality (AR) [ 4 , 13 , 14 , 15 ], structure from motion (SfM) [ 4 , 14 , 16 ], multi-view 3D reconstruction [ 17 , 18 ], and simultaneous localization and mapping (SLAM) [ 4 , 8 , 13 , 19 ]. The absolute pose of a fully uncalibrated camera pose contains six unknown parameters, and each 2D–3D point correspondence gives two constraints [ 20 ], which means that the P3P is the minimal subset to determine the camera pose if the position and orientation are both unknown [ 10 , 21 , 22 , 23 , 24 ].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Closed Form Solution to the Absolute Orientation Problem for Camera with Unknown Focal Length

Guo¹,

Hu²,

Zhao³

et al. 2021

Sensors

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In this paper we propose an efficient closed form solution to the absolute orientation problem for cameras with an unknown focal length, from two 2D–3D point correspondences and the camera position. The problem can be decomposed into two simple sub-problems and can be solved with angle constraints. A polynomial equation of one variable is solved to determine the focal length, and then a geometric approach is used to determine the absolute orientation. The geometric derivations are easy to understand and significantly improve performance. Rewriting the camera model with the known camera position leads to a simpler and more efficient closed form solution, and this gives a single solution, without the multi-solution phenomena of perspective-three-point (P3P) solvers. Experimental results demonstrated that our proposed method has a better performance in terms of numerical stability, noise sensitivity, and computational speed, with synthetic data and real images.

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A Stable Algebraic Camera Pose Estimation for Minimal Configurations of 2D/3D Point and Line Correspondences

Cited by 16 publications

References 28 publications

Certifiably Optimal and Robust Camera Pose Estimation From Points and Lines

Certifiably Optimal and Robust Camera Pose Estimation From Points and Lines

CvxPnPL: A Unified Convex Solution to the Absolute Pose Estimation Problem from Point and Line Correspondences

An Efficient Closed Form Solution to the Absolute Orientation Problem for Camera with Unknown Focal Length

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