A sampling theory for compact sets in Euclidean space
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Publication:1014336
DOI10.1007/s00454-009-9144-8zbMath1165.68061OpenAlexW2063776392MaRDI QIDQ1014336
André Lieutier, David Cohen-Steiner, Fréderic Chazal
Publication date: 27 April 2009
Published in: Discrete \& Computational Geometry (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00454-009-9144-8
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Computing connectedness: disconnectedness and discreteness.
- Surface reconstruction by Voronoi filtering
- Stability and finiteness properties of medial axis and skeleton
- Analysis of the spatial distribution of galaxies by multiscale methods
- Curvature Measures
- The “λ-medial axis”
- Optimization and nonsmooth analysis
- Three-dimensional alpha shapes
- A SIMPLE ALGORITHM FOR HOMEOMORPHIC SURFACE RECONSTRUCTION
- A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation
- Reconstruction curves with sharp corners
- Provable surface reconstruction from noisy samples
- Critical points of the distance to an epsilon-sampling of a surface and flow-complex-based surface reconstruction
- Weak feature size and persistent homology
- Stability of persistence diagrams
- Provably good sampling and meshing of surfaces
