The Mid-sphere Cousin of the Medial Axis Transform
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917992521007104 |
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| author | Edelsbrunner, Herbert Stephenson, Elizabeth Thoresen, Martin Hafskjold |
| author_facet | Edelsbrunner, Herbert Stephenson, Elizabeth Thoresen, Martin Hafskjold |
| contents | The medial axis of a smoothly embedded surface in $\mathbb{R}^3$ consists of all points for which the Euclidean distance function on the surface has at least two minima. We generalize this notion to the mid-sphere axis, which consists of all points for which the Euclidean distance function has two interchanging saddles that swap their partners in the pairing by persistent homology. It offers a discrete-algebraic multi-scale approach to computing ridge-like structures on the surface. As a proof of concept, an algorithm that computes stair-case approximations of the mid-sphere axis is provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14743 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Mid-sphere Cousin of the Medial Axis Transform Edelsbrunner, Herbert Stephenson, Elizabeth Thoresen, Martin Hafskjold Computational Geometry Algebraic Topology 55N31, 51-08, 54-08 The medial axis of a smoothly embedded surface in $\mathbb{R}^3$ consists of all points for which the Euclidean distance function on the surface has at least two minima. We generalize this notion to the mid-sphere axis, which consists of all points for which the Euclidean distance function has two interchanging saddles that swap their partners in the pairing by persistent homology. It offers a discrete-algebraic multi-scale approach to computing ridge-like structures on the surface. As a proof of concept, an algorithm that computes stair-case approximations of the mid-sphere axis is provided. |
| title | The Mid-sphere Cousin of the Medial Axis Transform |
| topic | Computational Geometry Algebraic Topology 55N31, 51-08, 54-08 |
| url | https://arxiv.org/abs/2504.14743 |