Cayley Rotation Averaging: Multiple Camera Averaging Under the Cayley Framework

Authors: Qiulei Dong, Shuang Deng, Yuzhen Liu

Abstract: Rotation averaging, which aims to calculate the global rotations of a set of cameras from a redundant set of their relative rotations, is an important and challenging topic in the research of structure from motion. A kernel 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 extraconstraint-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 global rotations of the two cameras, according to the Cayley rotation representation. Then based on such a set of Cayley rotation constraint equations, a Cayley computational framework 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 framework. Experimental results on 16 real-world datasets and multiple synthetic datasets demonstrate that the proposed CRA framework achieves a better accuracy in comparison to several typical rotation averaging methods in most cases.

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