Efficient Algorithms for Absolute Pose Estimation from Point-Line Correspondences

Konsep Inti

The authors present efficient and algebraically optimal solutions to the minimal problems of absolute pose estimation from point-line correspondences, reducing the degree of the required polynomial equations compared to previous methods.

Abstrak

The paper revisits the problems of absolute pose estimation from 3D-2D correspondences between features, which can be points or lines. Specifically, it addresses the two previously-studied minimal problems of estimating camera extrinsics from p ∈ {1, 2} point-point correspondences and l = 3-p line-line correspondences.
The authors observe that the existing solutions for these "mixed cases" are suboptimal from both a theoretical and practical point of view. They develop novel solutions to both the Perspective-2-Point-1-Line (P2P1L) and Perspective-1-Point-2-Line (P1P2L) problems, which optimally exploit their underlying algebraic structure.
For the P2P1L problem, the authors show that it can be reduced to computing the roots of a quadratic equation, in contrast to the previous quartic-based solutions. For the P1P2L problem, they show it can be reduced to a quartic equation, instead of the previous eighth-degree polynomials.
The authors provide detailed derivations of their solutions, including transformations to special reference frames that simplify the equations. They also discuss the stabilization of the P1P2L solver for certain degenerate configurations, and how to handle the coplanar case for both problems.
Experiments on synthetic and real data demonstrate that the proposed solvers are numerically stable and provide a significant speedup compared to the previous state-of-the-art methods.

Statistik

The authors report that their P2P1L solver reduces the degree of the required polynomial equations from 4 to 2, and their P1P2L solver reduces the degree from 8 to 4, compared to previous methods.

Kutipan

"Although we do not theoretically prove that our solutions are of the lowest possible degrees, we believe so because of the following argument. The best existing solutions for pose estimation using three points and three lines use 4th and 8th degree solutions respectively. Since mixed cases are in the middle, our solutions for (2 points, 1 line) and (1 point, 2 lines) cases use 4th and 8th degree solutions respectively."
"Contrary to the informal reasoning presented above, we claim that the existing solutions to the mixed point–line cases are not optimal."

Wawasan Utama Disaring Dari

Efficient Solution of Point-Line Absolute Pose

by Petr Hruby,T... pada arxiv.org 04-26-2024

https://arxiv.org/pdf/2404.16552.pdf

Pertanyaan yang Lebih Dalam

How can the proposed solvers be extended to handle more than the minimal number of point-line correspondences

The proposed solvers can be extended to handle more than the minimal number of point-line correspondences by incorporating additional constraints and measurements into the estimation framework. One approach could be to formulate the problem as an optimization task, where the objective function includes all available point-line correspondences. By minimizing the error between the projected points and lines in the image space and their corresponding 3D counterparts, the solvers can be adapted to handle a larger set of correspondences. This extension would involve solving a larger system of equations, potentially leading to a higher degree polynomial solution.

What are the theoretical limits on the degree of polynomial equations required to solve the absolute pose estimation problem with point-line features

The theoretical limits on the degree of polynomial equations required to solve the absolute pose estimation problem with point-line features are determined by the algebraic complexity of the problem. In the context of the provided paper, the authors have optimized the solvers to reduce the degrees of the needed polynomials from 4 to 2 and from 8 to 4 for the P2P1L and P1P2L problems, respectively. The theoretical limits would depend on the specific constraints and measurements involved in the pose estimation problem, as well as the underlying geometry of the scene. Generally, the goal is to minimize the degree of the polynomial equations to improve computational efficiency and numerical stability.

How do the proposed solvers perform in the presence of noise and outliers, and how can they be integrated into robust estimation frameworks like RANSAC

The proposed solvers exhibit good performance in the presence of noise and outliers due to their robust formulation and efficient optimization. To integrate them into robust estimation frameworks like RANSAC, the solvers can be used as the minimal solvers within the RANSAC loop to estimate the camera pose from noisy point-line correspondences. RANSAC iteratively samples subsets of correspondences, applies the solvers to estimate the pose, evaluates the quality of the estimated model, and selects the best model based on a predefined criterion. The robustness of the solvers combined with the iterative nature of RANSAC helps in handling outliers and noisy data effectively, leading to accurate pose estimation even in challenging conditions.