Manifold Intrinsic Similarity

Alexander M. Bronstein and Michael M. Bronstein
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Alexander M. Bronstein: Technion-Israel Institute of Technology
Michael M. Bronstein: Technion-Israel Institute of Technology

Chapter 32 in Handbook of Mathematical Methods in Imaging, 2011, pp 1403-1452 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-0-387-92920-0_32

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