瞬间完成旋转平均：一种原始对偶方法及循环图的闭式解
Rotation Averaging in a Split Second: A Primal-Dual Method and a Closed-Form for 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免初始化的原始对偶方法及循环图的首个最优闭式解，在精度和性能上取得显著提升。
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的一组测量相对朝向。尽管旋转平均是束调整和运动恢复不可分割的一部分，但它同时是一个非凸且高维的优化问题。在本文中，我们从最大似然估计的角度解决该问题，并做出了双重贡献。首先，我们提出了一种新颖的免初始化原始对偶方法，并通过经验证明其能收敛至全局最优。此外，据我们所知，我们推导出了循环图中旋转平均的首个最优闭式解，并在谱图理论的背景下对这一结果进行了阐释。我们提出的方法在精度和性能上均取得了显著提升。
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 spite of being an integral part of bundle adjustment and structure-from-motion, averaging rotations is both a non-convex and high-dimensional optimization problem. In this paper, we address it from a maximum likelihood estimation standpoint and make a twofold contribution. Firstly, we set forth a novel initialization-free primal-dual method which we show empirically to converge to the global optimum. Further, we derive what is to our knowledge, the first optimal closed-form solution for rotation averaging in cycle graphs and contextualize this result within spectral graph theory. Our proposed methods achieve a significant gain both 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。
