تقرير
Persistent Intrinsic Volumes
| العنوان: | Persistent Intrinsic Volumes |
|---|---|
| المؤلفون: | Cohen-Steiner, David, Commaret, Antoine |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Metric Geometry, Mathematics - Algebraic Topology, 53C65, 28A75, 55N31, 49Q1 |
| الوصف: | We develop a new method to estimate the area, and more generally the intrinsic volumes, of a compact subset $X$ of $\mathbb{R}^d$ from a set $Y$ that is close in the Hausdorff distance. This estimator enjoys a linear rate of convergence as a function of the Hausdorff distance under mild regularity conditions on $X$. Our approach combines tools from both geometric measure theory and persistent homology, extending the noise filtering properties of persistent homology from the realm of topology to geometry. Along the way, we obtain a stability result for intrinsic volumes. Comment: 29 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.14469 |
| رقم الأكسشن: | edsarx.2407.14469 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |