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arXiv · 2001.02858

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

Yashil Sukurdeep·Martin Bauer·Nicolas Charon
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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.

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Yashil Sukurdeep, Martin Bauer, Nicolas Charon. 2020-01-09. An inexact matching approach for the comparison of plane curves with general elastic metrics. https://doi.org/10.1109/ieeeconf44664.2019.9049031

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