On the Local Behavior of Spaces of Natural Images

2007/06/29 by Gunnar Carlsson, Tigran Ishkhanov, Vin de Silva +1 · 296 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Advanced Vision and Imaging #Algorithm #Artificial intelligence #Bottle #Cell Image Analysis Techniques #Combinatorics #Computer science #Embedding #Geography #Geometry #Klein bottle #Linear subspace #Mathematics #Pattern recognition (psychology) #Pure mathematics #Representation (politics) #Space (punctuation) #Submanifold #Topological and Geometric Data Analysis #Topology (electrical circuits) #Torus

paper · doi:10.1007/s11263-007-0056-x

published in International Journal of Computer Vision 76(1), 1-12 (Springer Science and Business Media LLC)

openalex publication_date 2007/06/29 · crossref created 2007/06/29 · crossref issued 2007/06/30 · crossref published 2007/06/30 · crossref published-online 2007/06/30 · crossref published-print 2008/01/01 · crossref deposited 2019/06/01 · openalex created_date 2025/10/10 · crossref indexed 2026/08/01 · openalex updated_date 2026/08/02

Citations

• A weak definition of Delaunay triangulation
• Topological Persistence and Simplification

Cited by

• Sliding Windows and Persistence: An Application of Topological Methods to Signal Analysis
• The Theory of Multidimensional Persistence
• Zigzag Persistence
• Robust Statistics, Hypothesis Testing, and Confidence Intervals for Persistent Homology on Metric Measure Spaces
• Computing Multidimensional Persistence
• Topological pattern recognition for point cloud data
• An output-sensitive algorithm for persistent homology
• Topology and data
• Barcodes: The persistent topology of data
• A fast algorithm for constructing topological structure in large data
• Computing Robustness and Persistence for Images
• Topological data analysis [wikipedia]