著者: Herbert Edelsbrunner , David Letscher , Afra Zomorodian - IEEE Symposium on Foundations of Computer Science, FOCS 2000 被引用: 1,789
We formalize a notion of topological simplification within the framework of a filtration, which is the history of a growing complex. We classify a topological change that happens during growth as either a feature or noise, depending on its life-time or persistence within the filtration. We give fast algorithms for completing persistence and experimental evidence for their speed and utility.
✨ ログイン状態を確認しています… PDF 被引用 BibTeX を表示 BibTeX を閉じる BibTeX を表示 引用
ELEMENTS OF ALGEBRAIC TOPOLOGY ELEMENTS OF ALGEBRAIC TOPOLOGY Elements of algebraic topology Elements of algebraic topology Simulation of Simplicity: A Technique… Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms Introduction to Algorithms Introduction to Algorithms Introduction to Algorithms Introduction to Algorithms An incremental algorithm for Betti numbers of… An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere Introduction to Algorithms Introduction to Algorithms Topology Simplification for Polygonal Virtual… Topology Simplification for Polygonal Virtual Environments A User's Guide to Spectral Sequences A User's Guide to Spectral Sequences Computational topology at multiple resolutions… Computational topology at multiple resolutions: foundations and applications to fractals and dynamics Level Set Methods: An Overview and Some Recen… Level Set Methods: An Overview and Some Recent Results Hierarchical morse complexes for piecewise… Hierarchical morse complexes for piecewise linear 2-manifolds Computing and comprehending topology… Computing and comprehending topology: persistence and hierarchical morse complexes Computational Topology for Point Data: Betti… Computational Topology for Point Data: Betti Numbers of α-Shapes Optimal discrete Morse functions for… Optimal discrete Morse functions for 2-manifolds Stability of Persistence Diagrams Stability of Persistence Diagrams Critical sets in discrete Morse theories… Critical sets in discrete Morse theories: Relating Forman and piecewise-linear approaches Clique topology reveals intrinsic geometric… Clique topology reveals intrinsic geometric structure in neural correlations Randomly Weighted d-Complexes: Minimal… Randomly Weighted d-Complexes: Minimal Spanning Acycles and Persistence Diagrams Persistent spectral graph Persistent spectral graph A Topological Loss Function for… A Topological Loss Function for Deep-Learning Based Image Segmentation Using Persistent Homology Wasserstein Stability for Persistence Diagrams Wasserstein Stability for Persistence Diagrams Evolutionary de Rham-Hodge method Evolutionary de Rham-Hodge method Topological Persistence and Simplification Topological Persistence and Simplification 過去の参考文献 中心の論文 この論文を引用する論文 古い 新しい ノードをクリックするとフォーカスを固定、空白をクリックすると本論文に戻ります。ホバーで一時的にプレビューできます。各ノードのページはタイトルから開けます。
