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

• URL: http://arxiv.org/abs/2001.02858v1
• Date: Thu, 9 Jan 2020 06:45:50 GMT
• Title: An inexact matching approach for the comparison of plane curves with general elastic metrics
• Authors: Yashil Sukurdeep, Martin Bauer, Nicolas Charon
• Abstract summary: This paper introduces a new mathematical formulation and numerical approach for the computation of distances and geodesics between immersed planar curves. 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.
• Score: 9.851033166756274
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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