旋转平均：一种原始-对偶方法及环图中的闭式解
Rotation Averaging: A Primal-Dual Method and Closed-Forms in Cycle Graphs
AI总结：
针对非凸高维的旋转平均问题，本文从最大似然估计角度提出一种受谱初始化启发的原始-对偶方法，并刻画了环图拓扑中的驻点，经基准测试与对偶理论验证，显著提升了精度与性能。
摘要：
作为几何重建的基石，旋转平均旨在寻找一组绝对旋转，以最优地解释它们之间测得的一组相对方向。旋转同步问题不仅是束调整和运动恢复结构的组成部分，还在视觉同时定位与建图中作为迭代求解器的初始化以及相机网络校准中得到应用。然而，该优化问题既非凸又属高维。本文从最大似然估计的角度解决该问题，并做出两项贡献。首先，受广泛接受的谱初始化启发，提出一种新颖的原始-对偶方法。其次，刻画了环图拓扑中旋转平均的驻点，并在谱图理论框架下阐释了该结果。我们在多种设置下对所提方法进行基准测试，并利用对偶理论验证了解，在精度和性能上取得了显著提升。
英文摘要：
A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In addition to being an integral part of bundle adjustment and structure-from-motion, the problem of synchronizing rotations also finds applications in visual simultaneous localization and mapping, where it is used as an initialization for iterative solvers, and camera network calibration. Nevertheless, this optimization problem is both non-convex and high-dimensional. In this paper, we address it from a maximum likelihood estimation standpoint and make a twofold contribution. Firstly, we set forth a novel primal-dual method, motivated by the widely accepted spectral initialization. Further, we characterize stationary points of rotation averaging in cycle graphs topologies and contextualize this result within spectral graph theory. We benchmark the proposed method in multiple settings and certify our solution via duality theory, achieving a significant gain in precision and performance.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
