The Relative Pose problem (RPp) for cameras aims to estimate the relative orientation and translation (pose) given a set of pair-wise feature correspondences between two central and calibrated cameras. The RPp is stated as an optimization problem where the squared, normalized epipolar error is minimized over the set of normalized essential matrices. In this work, we contribute an efficient and complete algorithm based on results from duality theory that is able to certify whether the solution to a RPp instance is the global optimum. Specifically, we present a family of certifiers that is shown to increase the ratio of detected optimal solutions. This set of certifiers is incorporated into an efficient essential matrix estimation pipeline that, given any initial guess for the RPp, refines it iteratively on the product space of 3D rotations and 2-sphere and thereupon, certifies the optimality of the solution. We integrate our fast certifiable pipeline into a robust framework that combines Graduated Non-convexity and the Black-Rangarajan duality between robust functions and line processes. This combination has been shown in the literature to outperform the robustness to outliers provided by approaches based on RANSAC. We proved through extensive experiments on synthetic and real data that the proposed framework provides a fast and robust relative pose estimation. We compare our proposal against the state-of-the-art methods on both accuracy and computational cost, and show that our estimations improve the output of the gold-standard approach for the RPp, the 2-view Bundle-Adjustment. We make the code publicly available \url{https://github.com/mergarsal/FastCertRelPose.git}.

中文翻译：

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两个校准摄像机之间相对姿势的快速且可靠的可证明估计

摄像机的相对姿势问题（RPp）旨在在给定两个中央摄像机和已校准摄像机之间的成对特征对应集合的情况下，估计相对方向和平移（姿势）。RPp被认为是一个优化问题，其中在归一化基本矩阵集上最小化平方，归一化对极误差。在这项工作中，我们基于对偶理论的结果提供了一种有效而完整的算法，该算法能够证明RPp实例的解决方案是否是全局最优的。具体来说，我们介绍了一系列证明者，这些证明者可以增加检测到的最佳解决方案的比率。这组验证者已合并到有效的基本矩阵估算管道中，考虑到RPp的任何初始猜测，在3D旋转和2个球面的乘积空间上迭代优化，然后证明解决方案的最优性。我们将可快速认证的流水线集成到一个健壮的框架中，该框架结合了稳健功能和生产流程之间的渐进不凸性和Black-Rangarajan对偶性。在文献中已表明这种组合优于基于RANSAC的方法所提供的对异常值的鲁棒性。通过对合成数据和真实数据的大量实验，我们证明了所提出的框架提供了一种快速且鲁棒的相对姿态估计。我们将我们的建议与最新方法的准确性和计算成本进行了比较，并表明我们的估计提高了RPp的金标准方法（2-视图捆绑调整）的输出。