Estimating the relative camera pose from $n \geq 5$ correspondences between
two calibrated views is a fundamental task in computer vision. This process
typically involves two stages: 1) estimating the essential matrix between the
views, and 2) disambiguating among the four candidate relative poses that
satisfy the epipolar geometry. In this paper, we demonstrate a novel approach
that, for the first time, bypasses the second stage. Specifically, we show that
it is possible to directly estimate the correct relative camera pose from
correspondences without needing a post-processing step to enforce the
cheirality constraint on the correspondences. Building on recent advances in
certifiable non-minimal optimization, we frame the relative pose estimation as
a Quadratically Constrained Quadratic Program (QCQP). By applying the
appropriate constraints, we ensure the estimation of a camera pose that
corresponds to a valid 3D geometry and that is globally optimal when certified.
We validate our method through exhaustive synthetic and real-world experiments,
confirming the efficacy, efficiency and accuracy of the proposed approach. Code
is available at this https URL

该论文通过将相对位姿估计建模为一个二次约束二次规划问题，直接从对应关系中估计正确的相对相机位姿，绕过后续的唯象几何约束的加强处理步骤，通过详尽的合成和实际实验证实了该方法的有效性、高效性和准确性。

从对应关系到姿态：非极小化、可证优化的无需消歧的相对姿态估计

From Correspondences to Pose: Non-minimal Certifiably Optimal Relative  Pose without Disambiguation

Finding relative pose between two calibrated images is a fundamental task in
computer vision. Given five point correspondences, the classical five-point
methods can be used to calculate the essential matrix efficiently. For the case
of $N$ ($N > 5$) inlier point correspondences, which is called $N$-point
problem, existing methods are either inefficient or prone to local minima. In
this paper, we propose a certifiably globally optimal and efficient solver for
the $N$-point problem. First we formulate the problem as a quadratically
constrained quadratic program (QCQP). Then a certifiably globally optimal
solution to this problem is obtained by semidefinite relaxation. This allows us
to obtain certifiably globally optimal solutions to the original non-convex
QCQPs in polynomial time. The theoretical guarantees of the semidefinite
relaxation are also provided, including tightness and local stability. To deal
with outliers, we propose a robust $N$-point method using M-estimators. Though
global optimality cannot be guaranteed for the overall robust framework, the
proposed robust $N$-point method can achieve good performance when the outlier
ratio is not high. Extensive experiments on synthetic and real-world datasets
demonstrated that our $N$-point method is $2\sim3$ orders of magnitude faster
than state-of-the-art methods. Moreover, our robust $N$-point method
outperforms state-of-the-art methods in terms of robustness and accuracy.

本文提出了一种全局最优且高效的求解 N 点问题的方法，利用半定松弛方法得到该问题的全局最优解，同时提出了使用 M-estimators 处理异常值的鲁棒性 N 点法，并在合成和真实世界数据集上进行了广泛的实验。