Cayley Rotation Averaging: Multiple Camera Averaging Under the Cayley Framework

Abstract

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.