Rotation averaging, which aims to calculate the absolute rotations of a set of cameras from a redundant set of their relative rotations, is an important and challenging topic arising in the study of structure from motion. A central problem in rotation averaging is how to alleviate the influence of noise and outliers. Addressing this problem, we investigate rotation averaging under the Cayley framework in this paper, inspired by the extra-constraint-free nature of the Cayley rotation representation. Firstly, for the relative rotation of an arbitrary pair of cameras regardless of whether it is corrupted by noise/outliers or not, a general Cayley rotation constraint equation is derived for reflecting the relationship between this relative rotation and the absolute rotations of the two cameras, according to the Cayley rotation representation. Then based on such a set of Cayley rotation constraint equations, a Cayley-based approach for Rotation Averaging is proposed, called CRA, where an adaptive regularizer is designed for further alleviating the influence of outliers. Finally, a unified iterative algorithm for minimizing some commonly-used loss functions is proposed under this approach. Experimental results on 16 real-world datasets and multiple synthetic datasets demonstrate that the proposed CRA approach achieves a better accuracy in comparison to several typical rotation averaging approaches in most cases.

中文翻译：

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Cayley 旋转平均：Cayley 框架下的多相机平均


旋转平均旨在从一组相机的相对旋转的冗余中计算出一组相机的绝对旋转，是运动结构研究中出现的一个重要且具有挑战性的课题。旋转平均的一个中心问题是如何减轻噪声和异常值的影响。为了解决这个问题，受到凯莱旋转表示的无额外约束性质的启发，我们在本文中研究了凯莱框架下的旋转平均。首先，对于任意一对相机的相对旋转，无论其是否受到噪声/异常值的破坏，推导出通用的凯莱旋转约束方程来反映该相对旋转与两个相机的绝对旋转之间的关系，根据凯莱旋转表示。然后基于这样一组凯莱旋转约束方程，提出了一种基于凯莱的旋转平均方法，称为CRA，其中设计了自适应正则化器以进一步减轻异常值的影响。最后，在此方法下提出了一种最小化一些常用损失函数的统一迭代算法。 16 个真实数据集和多个合成数据集的实验结果表明，在大多数情况下，与几种典型的旋转平均方法相比，所提出的 CRA 方法具有更好的准确性。