Persistent Intrinsic Volumes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909262397046784 |
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| author | Cohen-Steiner, David Commaret, Antoine |
| author_facet | Cohen-Steiner, David Commaret, Antoine |
| contents | We develop a new method to estimate the area, and more generally the intrinsic volumes, of a compact subset $X$ of $\mathbb{R}^d$ from a set $Y$ that is close in the Hausdorff distance. This estimator enjoys a linear rate of convergence as a function of the Hausdorff distance under mild regularity conditions on $X$. Our approach combines tools from both geometric measure theory and persistent homology, extending the noise filtering properties of persistent homology from the realm of topology to geometry. Along the way, we obtain a stability result for intrinsic volumes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14469 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Persistent Intrinsic Volumes Cohen-Steiner, David Commaret, Antoine Metric Geometry Algebraic Topology 53C65, 28A75, 55N31, 49Q1 We develop a new method to estimate the area, and more generally the intrinsic volumes, of a compact subset $X$ of $\mathbb{R}^d$ from a set $Y$ that is close in the Hausdorff distance. This estimator enjoys a linear rate of convergence as a function of the Hausdorff distance under mild regularity conditions on $X$. Our approach combines tools from both geometric measure theory and persistent homology, extending the noise filtering properties of persistent homology from the realm of topology to geometry. Along the way, we obtain a stability result for intrinsic volumes. |
| title | Persistent Intrinsic Volumes |
| topic | Metric Geometry Algebraic Topology 53C65, 28A75, 55N31, 49Q1 |
| url | https://arxiv.org/abs/2407.14469 |