Intrinsic Riemannian Metrics on Spaces of Curves: Theory and Computation

Martin Bauer (), Nicolas Charon (), Eric Klassen () and Alice Le Brigant ()
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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

Chapter 39 in Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, 2023, pp 1349-1383 from Springer

Abstract: 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.

Keywords: Elastic shape analysis; Curves in Riemannian manifolds; Sobolev metrics; Reparametrization invariance; Square root velocity transform. (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-98661-2_87

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DOI: 10.1007/978-3-030-98661-2_87

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