On the Quotient Representation for the Essential Manifold

Roberto Tron, Kostas Daniilidis; Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2014, pp. 1574-1581

The essential matrix, which encodes the epipolar constraint between points in two projective views, is a cornerstone of modern computer vision. Previous works have proposed different characterizations of the space of essential matrices as a Riemannian manifold. However, they either do not consider the symmetric role played by the two views, or do not fully take into account the geometric peculiarities of the epipolar constraint. We address these limitations with a characterization as a quotient manifold which can be easily interpreted in terms of camera poses. While our main focus in on theoretical aspects, we include experiments in pose averaging, and show that the proposed formulation produces a meaningful distance between essential matrices.