Vietoris-rips complexes also provide topologically correct reconstructions of sampled shapes

DOI10.1145/1998196.1998276zbMath1283.68341OpenAlexW2148010629MaRDI QIDQ5404465

David Salinas, Dominique Attali, André Lieutier

Publication date: 24 March 2014

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

Full work available at URL: https://doi.org/10.1145/1998196.1998276

zbMATH Keywords

samplingmetric spacesclique complexesEuclidean spaceshomotopy equivalenceshape reconstructioncollapsesVietoris-Rips complexesČech complexes

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Simplicial sets and complexes in algebraic topology (55U10)

Related Items (11)

A counter-example to Hausmann's conjecture ⋮ Footprints of geodesics in persistent homology ⋮ Rips complexes as nerves and a functorial Dowker-nerve diagram ⋮ Reconstruction properties of selective Rips complexes ⋮ Preserving geometric properties in reconstructing regions from internal and nearby points ⋮ Reeb graphs: approximation and persistence ⋮ Optimal reconstruction might be hard ⋮ Cone fields and topological sampling in manifolds with bounded curvature ⋮ Persistence stability for geometric complexes ⋮ Approximations of 1-dimensional intrinsic persistence of geodesic spaces and their stability ⋮ Graph induced complex on point data

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