An inexact matching approach for the comparison of plane curves with general elastic metrics
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866929658153402368 |
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| author | Sukurdeep, Yashil Bauer, Martin Charon, Nicolas |
| author_facet | Sukurdeep, Yashil Bauer, Martin Charon, Nicolas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_02858 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | An inexact matching approach for the comparison of plane curves with general elastic metrics Sukurdeep, Yashil Bauer, Martin Charon, Nicolas Computational Geometry Computer Vision and Pattern Recognition Differential Geometry 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. |
| title | An inexact matching approach for the comparison of plane curves with general elastic metrics |
| topic | Computational Geometry Computer Vision and Pattern Recognition Differential Geometry |
| url | https://arxiv.org/abs/2001.02858 |