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Intrinsic Riemannian Metrics on Spaces of Curves: Theory and Computation

In: Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Author

Listed:
  • Martin Bauer

    (Florida State University, Department of Mathematics)

  • Nicolas Charon

    (Johns Hopkins University, Department of Applied Mathematics and Statistics)

  • Eric Klassen

    (Florida State University, Department of Mathematics)

  • Alice Le Brigant

    (University Paris 1, Department of Applied Mathematics)

Abstract

This chapter reviews some past and recent developments in shape comparison and analysis of curves based on the computation of intrinsic Riemannian metrics on the space of curve modulo shape-preserving transformations. We summarize the general construction and theoretical properties of quotient elastic metrics for Euclidean as well as non-Euclidean curves before considering the special case of the square root velocity metric for which the expression of the resulting distance simplifies through a particular transformation. We then examine the different numerical approaches that have been proposed to estimate such distances in practice and in particular to quotient out curve reparametrization in the resulting minimization problems.

Suggested Citation

  • Martin Bauer & Nicolas Charon & Eric Klassen & Alice Le Brigant, 2023. "Intrinsic Riemannian Metrics on Spaces of Curves: Theory and Computation," Springer Books, in: Ke Chen & Carola-Bibiane Schönlieb & Xue-Cheng Tai & Laurent Younes (ed.), Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, chapter 39, pages 1349-1383, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-98661-2_87
    DOI: 10.1007/978-3-030-98661-2_87
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