Towards persistence-based reconstruction in euclidean spaces

DOI10.1145/1377676.1377719zbMath1271.57058arXiv0712.2638OpenAlexW2001887552MaRDI QIDQ3602924

Steve Y. Oudot, Fréderic Chazal

Publication date: 12 February 2009

Published in: Proceedings of the twenty-fourth annual symposium on Computational geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.2638

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) PL-topology (57Q99)

Related Items

Strong collapse and persistent homology ⋮ Metric thickenings and group actions ⋮ The Offset Filtration of Convex Objects ⋮ Nerve complexes of circular arcs ⋮ The Persistent Homology of Cyclic Graphs ⋮ On the Reconstruction of Geodesic Subspaces of ℝN ⋮ On Vietoris-Rips complexes of hypercube graphs ⋮ Efficient and robust persistent homology for measures ⋮ Linear-size approximations to the Vietoris-Rips filtration ⋮ Metric Reconstruction Via Optimal Transport ⋮ Rips complexes as nerves and a functorial Dowker-nerve diagram ⋮ Limit Theorems in Discrete Stochastic Geometry ⋮ Approximating the pathway axis and the persistence diagrams for a collection of balls in 3-space ⋮ Limit theory for point processes in manifolds ⋮ Zigzag zoology: Rips zigzags for homology inference ⋮ Determining homology of an unknown space from a sample ⋮ Universality of the homotopy interleaving distance ⋮ Vietoris-Rips complexes of metric spaces near a metric graph ⋮ Only distances are required to reconstruct submanifolds ⋮ The persistent topology of optimal transport based metric thickenings ⋮ A unified view on the functorial nerve theorem and its variations ⋮ Reeb graphs: approximation and persistence ⋮ Witnessed \(k\)-distance ⋮ Computing the multicover bifiltration ⋮ Recovering the homology of immersed manifolds ⋮ Hodge theory on metric spaces. Appendix by Anthony W. Baker ⋮ DTM-Based Filtrations ⋮ Continuous quivers of type \(A (I)\) foundations ⋮ Metric thickenings of Euclidean submanifolds ⋮ Cone fields and topological sampling in manifolds with bounded curvature ⋮ Manifold reconstruction using tangential Delaunay complexes ⋮ Scalar field analysis over point cloud data ⋮ Čech-Delaunay gradient flow and homology inference for self-maps ⋮ Model selection for simplicial approximation ⋮ Geometric inference for probability measures ⋮ Persistence stability for geometric complexes ⋮ A weak characterisation of the Delaunay triangulation ⋮ Strong Collapse for Persistence ⋮ Another look at recovering local homology from samples of stratified sets ⋮ Persistent homology for low-complexity models ⋮ Reconstruction using witness complexes ⋮ Manifold reconstruction in arbitrary dimensions using witness complexes ⋮ Extremal Betti numbers of Vietoris-Rips complexes ⋮ Confidence sets for persistence diagrams ⋮ Unnamed Item ⋮ An approximate nerve theorem ⋮ The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes ⋮ Computing Persistent Homology of Flag Complexes via Strong Collapses ⋮ Dimensionality reduction for \(k\)-distance applied to persistent homology ⋮ A functorial Dowker theorem and persistent homology of asymmetric networks ⋮ Divisive cover ⋮ On Vietoris–Rips complexes of ellipses ⋮ Approximating persistent homology in Euclidean space through collapses ⋮ Graph induced complex on point data