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Publication Detail
Learning a manifold as an atlas
  • Publication Type:
    Journal article
  • Publication Sub Type:
    Conference Proceeding
  • Authors:
    Pitelis N, Russell C, Agapito L
  • Publication date:
    15/11/2013
  • Pagination:
    1642, 1649
  • Journal:
    Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
  • Status:
    Published
  • Print ISSN:
    1063-6919
Abstract
In this work, we return to the underlying mathematical definition of a manifold and directly characterise learning a manifold as finding an atlas, or a set of overlapping charts, that accurately describe local structure. We formulate the problem of learning the manifold as an optimisation that simultaneously refines the continuous parameters defining the charts, and the discrete assignment of points to charts. In contrast to existing methods, this direct formulation of a manifold does not require 'unwrapping' the manifold into a lower dimensional space and allows us to learn closed manifolds of interest to vision, such as those corresponding to gait cycles or camera pose. We report state-of-the-art results for manifold based nearest neighbour classification on vision datasets, and show how the same techniques can be applied to the 3D reconstruction of human motion from a single image. © 2013 IEEE.
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