Manifold Statistics for Essential Matrices

Gijs Dubbelman¹, Leo Dorst², and Henk Pijls²

¹Carnegie Mellon University, The Robotics Institute, Pittsburgh, USA
gijsdubb@cs.cmu.edu

²University of Amsterdam, Faculty of Science, Amsterdam, The Netherlands
L.Dorst@uva.nl
H.G.J.Pijls@uva.nl

Abstract. Riemannian geometry allows for the generalization of statistics designed for Euclidean vector spaces to Riemannian manifolds. It has recently gained popularity within computer vision as many relevant parameter spaces have such a Riemannian manifold structure. Approaches which exploit this have been shown to exhibit improved efficiency and accuracy. The Riemannian logarithmic and exponential mappings are at the core of these approaches.

In this contribution we review recently proposed Riemannian mappings for essential matrices and prove that they lead to sub-optimal manifold statistics. We introduce correct Riemannian mappings by utilizing a multiple-geodesic approach and show experimentally that they provide optimal statistics.

LNCS 7573, p. 531 ff.

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