Reconstruction in high dimensions
type: Dataset
description: In this thesis, we look for methods for reconstructing an approximation of a manifold known only through a high-dimensional point cloud. Especially, we are interested in efficient methods that produce approximations that share the same topology as the sampled manifold. A particular attention is devoted to flag-complexes and more specially to Rips complexes due to their compactedness. We show that the Rips complex shares the topology of a sampled manifold under good sampling conditions. By taking advantage of the compactedness of flag-complexes, we present a data structure for simplicial complexes called skeleton/blockers. We then study two simplification operations, the edge contraction and the simplicial collapse, that turn out to be useful for reducing a simplicial complex without changing its topology.
identifier: NNT: 2013GRENT036
issued: 2026-05-06T09:15:56.702728
language: fr
modified: 2026-05-06T09:15:56.702734
contact point: Organization
  fn: CCSD
keyword: cech
keyword: complex
keyword: delaunay
keyword: dimension
keyword: infoeu-reposemanticsdoctoralthesis
keyword: reconstruction
keyword: rips
keyword: spiotherengineering-sciences-physicsother
keyword: theses
landing page: https://theses.hal.science/tel-00947303

Reconstruction in high dimensions
type: Distribution
format: HTML
issued: 2026-05-06T09:15:56.718680
modified: 2026-05-06T09:15:56.689408
access URL: https://theses.hal.science/tel-00947303

test_moissonnage_selune
type: Agent