arXiv Open Access 2023

Stability and Approximations for Decorated Reeb Spaces

Justin Curry Washington Mio Tom Needham Osman Berat Okutan Florian Russold

Lihat Sumber

Abstrak

Given a map $f:X \to M$ from a topological space $X$ to a metric space $M$, a decorated Reeb space consists of the Reeb space, together with an attribution function whose values recover geometric information lost during the construction of the Reeb space. For example, when $M=\mathbb{R}$ is the real line, the Reeb space is the well-known Reeb graph, and the attributions may consist of persistence diagrams summarizing the level set topology of $f$. In this paper, we introduce decorated Reeb spaces in various flavors and prove that our constructions are Gromov-Hausdorff stable. We also provide results on approximating decorated Reeb spaces from finite samples and leverage these to develop a computational framework for applying these constructions to point cloud data.

Topik & Kata Kunci

math.MG cs.CG math.AT

Penulis (5)

Justin Curry

Washington Mio

Tom Needham

Osman Berat Okutan

Florian Russold

Format Sitasi

APA MLA BibTeX

Curry, J., Mio, W., Needham, T., Okutan, O.B., Russold, F. (2023). Stability and Approximations for Decorated Reeb Spaces. https://arxiv.org/abs/2312.01982

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓