SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Extreme elevation on a 2-manifold
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Persistence barcodes for shapes
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Stability of persistence diagrams
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Inequalities for the curvature of curves and surfaces
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Topological estimation using witness complexes
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Persistence-sensitive simplification functions on 2-manifolds
Proceedings of the twenty-second annual symposium on Computational geometry
Computing geometry-aware handle and tunnel loops in 3D models
ACM SIGGRAPH 2008 papers
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Multidimensional Size Functions for Shape Comparison
Journal of Mathematical Imaging and Vision
Persistent homology for kernels, images, and cokernels
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Analysis of scalar fields over point cloud data
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Proximity of persistence modules and their diagrams
Proceedings of the twenty-fifth annual symposium on Computational geometry
Zigzag persistent homology and real-valued functions
Proceedings of the twenty-fifth annual symposium on Computational geometry
Measuring and computing natural generators for homology groups
Computational Geometry: Theory and Applications
Computing Multidimensional Persistence
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Approximating loops in a shortest homology basis from point data
Proceedings of the twenty-sixth annual symposium on Computational geometry
Hardness results for homology localization
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Tracking a generator by persistence
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Proceedings of the twenty-seventh annual symposium on Computational geometry
An output-sensitive algorithm for persistent homology
Proceedings of the twenty-seventh annual symposium on Computational geometry
Reeb graphs: approximation and persistence
Proceedings of the twenty-seventh annual symposium on Computational geometry
A new algorithm for computing the 2-dimensional matching distance between size functions
Pattern Recognition Letters
Reconstructing 3D compact sets
Computational Geometry: Theory and Applications
An iterative algorithm for homology computation on simplicial shapes
Computer-Aided Design
Failure filtrations for fenced sensor networks
International Journal of Robotics Research
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
An output-sensitive algorithm for persistent homology
Computational Geometry: Theory and Applications
Geometry in the space of persistence modules
Proceedings of the twenty-ninth annual symposium on Computational geometry
| Hi-index | 0.00 |
Persistent homology is the mathematical core of recent work on shape, including reconstruction, recognition, and matching. Its pertinent information is encapsulated by a pairing of the critical values of a function, visualized by points forming a diagram in the plane. The original algorithm in [10] computes the pairs from an ordering of the simplices in a triangulation and takes worst-case time cubic in the number of simplices. The main result of this paper is an algorithm that maintains the pairing in worst-case linear time per transposition in the ordering. A side-effect of the algorithm's analysis is an elementary proof of the stability of persistence diagrams [7] in the special case of piecewise-linear functions. We use the algorithm to compute 1-parameter families of diagrams which we apply to the study of protein folding trajectories.