Which Vertical Graphs are Non VPHT Reconstructible?
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917324194316288 |
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| author | Gutzeit, Jette Kistler, Kalani Ophelders, Tim Schenfisch, Anna |
| author_facet | Gutzeit, Jette Kistler, Kalani Ophelders, Tim Schenfisch, Anna |
| contents | The verbose persistent homology transform (VPHT) is a topological summary of shapes in Euclidean space. Assuming general position, the VPHT is injective, meaning shapes can be reconstructed using only the VPHT. In this work, we investigate cases in which the VPHT is not injective, focusing on a simple setting of degeneracy; graphs whose vertices are all collinear. We identify both necessary properties and sufficient properties for non-reconstructibility of such graphs, bringing us closer to a complete classification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07809 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Which Vertical Graphs are Non VPHT Reconstructible? Gutzeit, Jette Kistler, Kalani Ophelders, Tim Schenfisch, Anna Computational Geometry The verbose persistent homology transform (VPHT) is a topological summary of shapes in Euclidean space. Assuming general position, the VPHT is injective, meaning shapes can be reconstructed using only the VPHT. In this work, we investigate cases in which the VPHT is not injective, focusing on a simple setting of degeneracy; graphs whose vertices are all collinear. We identify both necessary properties and sufficient properties for non-reconstructibility of such graphs, bringing us closer to a complete classification. |
| title | Which Vertical Graphs are Non VPHT Reconstructible? |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/2603.07809 |