Tensor Computation of Euler Characteristic Functions and Transforms
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912999763083264 |
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| author | Cisewski-Kehe, Jessi Fasy, Brittany Terese McCleary, Alexander Quist, Eli |
| author_facet | Cisewski-Kehe, Jessi Fasy, Brittany Terese McCleary, Alexander Quist, Eli |
| contents | The weighted Euler characteristic transform (WECT) and Euler characteristic function (ECF) have proven to be useful tools in a variety of applications. However, current methods for computing these functions are either not optimized for GPU computation or do not scale to higher-dimensional settings. In this work, we present a tensor-based framework for computing such topological descriptors which is highly optimized for GPU architectures and works in full generality across simplicial and cubical complexes of arbitrary dimension. Experimentally, the framework demonstrates significant speedups over existing methods when computing the WECT and ECF across a variety of two- and three-dimensional datasets. Computation of these transforms is implemented in a publicly available Python package called pyECT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03909 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor Computation of Euler Characteristic Functions and Transforms Cisewski-Kehe, Jessi Fasy, Brittany Terese McCleary, Alexander Quist, Eli Computational Geometry Machine Learning Algebraic Topology 55N31, 55-08 The weighted Euler characteristic transform (WECT) and Euler characteristic function (ECF) have proven to be useful tools in a variety of applications. However, current methods for computing these functions are either not optimized for GPU computation or do not scale to higher-dimensional settings. In this work, we present a tensor-based framework for computing such topological descriptors which is highly optimized for GPU architectures and works in full generality across simplicial and cubical complexes of arbitrary dimension. Experimentally, the framework demonstrates significant speedups over existing methods when computing the WECT and ECF across a variety of two- and three-dimensional datasets. Computation of these transforms is implemented in a publicly available Python package called pyECT. |
| title | Tensor Computation of Euler Characteristic Functions and Transforms |
| topic | Computational Geometry Machine Learning Algebraic Topology 55N31, 55-08 |
| url | https://arxiv.org/abs/2511.03909 |