Towards persistence-based reconstruction in euclidean spaces

2008/06/09 by Frédéric Chazal, Steve Oudot · 2 citations
Computer Science · Biochemistry, Genetics and Molecular Biology · Mathematics · Engineering · #Topological and Geometric Data Analysis #Cell Image Analysis Techniques #Advanced Vision and Imaging #Persistence (discontinuity) #Manifold (fluid mechanics) #Curse of dimensionality #Euclidean geometry #Nonlinear dimensionality reduction #Exponential growth #Computer science #Scale (ratio) #Euclidean distance #Dimensionality reduction #Mathematics #Artificial intelligence #Theoretical computer science #Geometry #Mathematical analysis #Geography #Cartography #Engineering

paper · doi:10.1145/1377676.1377719

openalex publication_date 2008/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recent advances in higher dimensions have led to new methods to reconstruct large classes of compact subsets of Rd. However, the complexities of these methods scale up exponentially with d, making them impractical in medium or high dimensions, even on data sets of low intrinsic dimensionality.

Citations

• Voronoi diagrams—a survey of a fundamental geometric data structure
• Stability of Persistence Diagrams
• The union of balls and its dual shape
• A New Algorithm for Generating All the Maximal Independent Sets
• A weak definition of Delaunay triangulation
• Computing Persistent Homology
• Topological Persistence and Simplification
• Curvature measures

Cited by

• Gromov‐Hausdorff Stable Signatures for Shapes using Persistence
• Vietoris–Rips complex [wikipedia]