  Essential matrix averaging, i.e., the task of recovering camera locations and
orientations in calibrated, multiview settings, is a first step in global
approaches to Euclidean structure from motion. A common approach to essential
matrix averaging is to separately solve for camera orientations and
subsequently for camera positions. This paper presents a novel approach that
solves simultaneously for both camera orientations and positions. We offer a
complete characterization of the algebraic conditions that enable a unique
Euclidean reconstruction of $n$ cameras from a collection of $(^n_2)$ essential
matrices. We next use these conditions to formulate essential matrix averaging
as a constrained optimization problem, allowing us to recover a consistent set
of essential matrices given a (possibly partial) set of measured essential
matrices computed independently for pairs of images. We finally use the
recovered essential matrices to determine the global positions and orientations
of the $n$ cameras. We test our method on common SfM datasets, demonstrating
high accuracy while maintaining efficiency and robustness, compared to existing
methods.
