An inexact matching approach for the comparison of plane curves with general elastic metrics

Abstract

This paper introduces a new mathematical formulation and numerical approach for the computation of distances and geodesics between immersed planar curves. Our approach combines the general simplifying transform for first-order elastic metrics that was recently introduced by Kurtek and Needham, together with a relaxation of the matching constraint using parametrization-invariant fidelity metrics. The main advantages of this formulation are that it leads to a simple optimization problem for discretized curves, and that it provides a flexible approach to deal with noisy, inconsistent or corrupted data. These benefits are illustrated via a few preliminary numerical results.

arXiv comment5 pages, 5 figures

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Cited by in corpus (2)

• Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework
• A new variational model for shape graph registration with partial matching constraints