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On shapes recognition in topological data analysis
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DOI：10.1080/27684830.2025.2573577.png)
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Abstract
En 中文
This paper investigates the analysis of topological objects' shapes using tools from algebraic topology and topological data analysis (TDA). We use the multipers library to compute the multi-parameter persistent homology of topological objects and employ the Core Delaunay construction to define a bifiltration of point clouds. In this work, we focus on synthetic point cloud approximations of shapes (e.g. circles, spheres, tori, and coffee cups) to demonstrate that topological descriptors can capture structural features such as holes, connectivity, and voids. These experiments illustrate how homological invariants can formally distinguish different shapes, addressing the common joke in mathematics that a topologist cannot distinguish a coffee mug from a doughnut.
Keywords:
Homology
homology group
metric space
topological data analysis
multi-parameter persistent homology
point cloud approximation
persistent homology
Journal
R
IF:
1.1
Papers:
72
Citations:
0
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Cited Papers