- Manifold statistics for essential matrices
- European Conference on Computer Vision: 12th (Florence, Italy): 2012
- Book/source title
- Computer Vision – ECCV 2012
- Book/source subtitle
- 12th European Conference on Computer Vision, Florence, Italy, October 7-13, 2012 : proceedings
- Pages (from-to)
- Heidelberg: Springer
- Volume (Publisher)
- ISBN (electronic)
- Lecture Notes in Computer Science: 0302-9743
- Volume (Serie)
- Document type
- Conference contribution
- Faculty of Science (FNWI)
- Informatics Institute (IVI)
Korteweg-de Vries Institute for Mathematics (KdVI)
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.
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