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Manifold Intrinsic Similarity

  • Alexander M. Bronstein
  • Michael M. Bronstein

Abstract

Non-rigid shapes are ubiquitous in Nature and are encountered at all levels of life, from macro to nano. The need to model such shapes and understand their behavior arises in many applications in imaging sciences, pattern recognition, computer vision, and computer graphics. Of particular importance is understanding which properties of the shape are attributed to deformations and which are invariant, i.e., remain unchanged. This chapter presents an approach to non-rigid shapes from the point of view of metric geometry. Modeling shapes as metric spaces, one can pose the problem of shape similarity as the similarity of metric spaces and harness tools from theoretical metric geometry for the computation of such a similarity.

Keywords

Riemannian Manifold Heat Kernel Simplicial Complex Hausdorff Distance Iterative Close Point 
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 Science+Business Media, LLC 2011

Authors and Affiliations

  • Alexander M. Bronstein
    • 1
  • Michael M. Bronstein
    • 2
  1. 1.Technion-Israel Institute of TechnologyHaifaIsrael
  2. 2.Technion-Israel Institute of TechnologyHaifaIsrael

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