Estimating the reach of a manifold via its convexity defect function

DOI10.1007/s00454-021-00290-8OpenAlexW3001753163MaRDI QIDQ2117346

Yanyan Li

Publication date: 21 March 2022

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

Full work available at URL: https://arxiv.org/abs/2001.08006

zbMATH Keywords

minimax estimationmanifold reconstructionreachpoint cloudsconvexity defect function

Mathematics Subject Classification ID

Nonparametric estimation (62G05) Minimax procedures in statistical decision theory (62C20) Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Global submanifolds (53C40)

Related Items (4)

Measure estimation on manifolds: an optimal transport approach ⋮ Universally consistent estimation of the reach ⋮ Adversarial manifold estimation ⋮ Optimal reach estimation and metric learning

Uses Software

• bootstrap

Cites Work

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• Nonasymptotic rates for manifold, tangent space and curvature estimation
• Vietoris-Rips complexes also provide topologically correct reconstructions of sampled shapes
• Minimax adaptive estimation in manifold inference
• The reach, metric distortion, geodesic convexity and the variation of tangent spaces
• Estimating the reach of a manifold
• Finding the homology of submanifolds with high confidence from random samples
• Curvature Measures
• Minimax Rates for Estimating the Dimension of a Manifold
• Minimax Manifold Estimation

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