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.
翻译：作为几何重建的基石,平均轮换法寻求一套绝对轮换法,以最佳的方式解释它们之间的一套衡量相对方向。尽管这是捆绑调整和结构从移动中调整的一个有机组成部分,但平均轮换制既是非曲线问题,也是高维优化问题。在本文中,我们从最大可能的估计角度来解决这个问题,并作出双重贡献。首先,我们提出了一个新型的不初始化、不初始化的初等-双轨方法,我们从经验上展示了这种方法,以便与全球最佳模式汇合。此外,我们从我们的知识中得出了第一个最佳的循环封闭式解决办法,即以循环图平均计算,并在光谱图理论中将这一结果背景化。我们提出的方法在精确性和性能两方面都取得了显著的收益。
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