Which Vertical Graphs are Non VPHT Reconstructible?

Fuente: arXiv
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Auteurs principaux: Gutzeit, Jette, Kistler, Kalani, Ophelders, Tim, Schenfisch, Anna
Format: Preprint
Publié: 2026
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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