Morse Theory for Filtrations and Efficient Computation of Persistent Homology

2013/07/27 by Konstantin Mischaikow, Vidit Nanda · 213 citations
Computer Science · Mathematics · Medicine · #Algorithm #Alzheimer's disease research and treatments #Artificial intelligence #Biology #Cellular homology #Chromatic scale #Circle-valued Morse theory #Combinatorics #Computation #Computer science #Discrete Morse theory #Discrete mathematics #Gene #Genetics #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Morse code #Morse homology #Morse theory #Persistent homology #Preprocessor #Pure mathematics #Singular homology #Topological and Geometric Data Analysis #Topology (electrical circuits)

paper · pdf · doi:10.1007/s00454-013-9529-6

published in Discrete & Computational Geometry 50(2), 330-353 (Springer Science and Business Media LLC)

crossref issued 2013/07/27 · crossref published 2013/07/27 · crossref published-online 2013/07/27 · openalex publication_date 2013/07/27 · crossref created 2013/07/27 · crossref published-print 2013/09/01 · crossref deposited 2019/07/19 · openalex created_date 2025/10/10 · crossref indexed 2026/06/25 · openalex updated_date 2026/08/06

Citations

• Gaussian elimination is not optimal
• Stability of Persistence Diagrams
• Computing Persistent Homology
• Topological Persistence and Simplification

Cited by

• Skeletonization and Partitioning of Digital Images Using Discrete Morse Theory
• Sliding Windows and Persistence: An Application of Topological Methods to Signal Analysis
• Geometry in the space of persistence modules
• Computing gradient vector fields with Morse sequences
• Hall Effect Thruster Forecasting using a Topological Approach for Data Assimilation
• Discrete Morse theory [wikipedia]
• Topological data analysis [wikipedia]