Some properties of Gromov-Hausdorff distances

DOI10.1007/s00454-012-9406-8zbMath1254.54033OpenAlexW2050303752MaRDI QIDQ452012

Facundo Mémoli

Publication date: 19 September 2012

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-012-9406-8

zbMATH Keywords

Gromov-Hausdorff distancemetric geometrycurvature sets

Mathematics Subject Classification ID

Function spaces in general topology (54C35) Metric spaces, metrizability (54E35) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (20)

Computational aspects of the Gromov-Hausdorff distance and its application in non-rigid shape matching ⋮ On the convergence of solutions to dynamic equations on time scales ⋮ On data dependence of stability domains, exponential stability and stability radii for implicit linear dynamic equations ⋮ Isometry Group of Gromov--Hausdorff Space ⋮ On \(p\)-metric spaces and the \(p\)-Gromov-Hausdorff distance ⋮ Fermat-Steiner problem in the metric space of compact sets endowed with Hausdorff distance ⋮ New families of stable simplicial filtration functors ⋮ Characterization of Gromov-type geodesics ⋮ Approximating Gromov-Hausdorff distance in Euclidean space ⋮ The Gromov-Hausdorff distance between spheres ⋮ The persistent topology of optimal transport based metric thickenings ⋮ Distances and isomorphism between networks: stability and convergence of network invariants ⋮ Polynomial-Time Algorithms for Continuous Metrics on Atomic Clouds of Unordered Points ⋮ Distances Between Datasets ⋮ Unnamed Item ⋮ Conformal Wasserstein distances: comparing surfaces in polynomial time ⋮ The Gromov-Hausdorff distance: a brief tutorial on some of its quantitative aspects ⋮ FPT-Algorithms for Computing Gromov-Hausdorff and Interleaving Distances Between Trees ⋮ Steiner type ratios of Gromov-Hausdorff space ⋮ The Fermat-Steiner problem in the space of compact subsets of endowed with the Hausdorff metric

Cites Work

• A spectral notion of Gromov-Wasserstein distance and related methods
• Gromov-Wasserstein distances and the metric approach to object matching
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• A counterexample to a theorem of S. Piccard
• On reconstructing \(n\)-point configurations from the distribution of distances or areas
• A theoretical and computational framework for isometry invariant recognition of point cloud data
• Characterizing the round sphere by mean distance
• Assignment Problems
• Distance sets for shape filters and shape recognition
• Shape distributions
• Efficient Computation of Isometry‐Invariant Distances Between Surfaces
• Curvature, triameter, and beyond
• Distances between Banach spaces
• New Extremal Problems for the Riemannian Recognition Program via Alexandrov Geometry
• Discrete Geometry for Computer Imagery
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
• Joint invariant signatures
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Some properties of Gromov-Hausdorff distances