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Manifold Statistics for Essential Matrices

  • Gijs Dubbelman
  • Leo Dorst
  • Henk Pijls
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7573)

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.

Keywords

Riemannian Manifold Tangent Vector Riemannian Geometry Riemannian Mapping Unit Quaternion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Gijs Dubbelman
    • 1
  • Leo Dorst
    • 2
  • Henk Pijls
    • 2
  1. 1.The Robotics InstituteCarnegie Mellon UniversityPittsburghUSA
  2. 2.Faculty of ScienceUniversity of AmsterdamAmsterdamThe Netherlands

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