Persistence-sensitive simplification functions on 2-manifolds
Proceedings of the twenty-second annual symposium on Computational geometry
The theory of multidimensional persistence
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Manifold reconstruction in arbitrary dimensions using witness complexes
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Journal of Mathematical Imaging and Vision
Algebraic cycles from a computational point of view
Theoretical Computer Science
Geodesic Delaunay triangulation and witness complex in the plane
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Computing geometry-aware handle and tunnel loops in 3D models
ACM SIGGRAPH 2008 papers
Homology algorithm based on acyclic subspace
Computers & Mathematics with Applications
Towards persistence-based reconstruction in euclidean spaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Testing contractibility in planar rips complexes
Proceedings of the twenty-fourth annual symposium on Computational geometry
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Computational Geometry: Theory and Applications
Multi-scale Representation and Persistency for Shape Description
MDA '08 Proceedings of the 3rd international conference on Advances in Mass Data Analysis of Images and Signals in Medicine, Biotechnology, Chemistry and Food Industry
Sampling Hypersurfaces through Diffusion
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
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
Ascending and descending regions of a discrete Morse function
Computational Geometry: Theory and Applications
Cut locus and topology from surface point data
Proceedings of the twenty-fifth annual symposium on Computational geometry
Persistent cohomology and circular coordinates
Proceedings of the twenty-fifth annual symposium on Computational geometry
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
Persistence Diagrams of Cortical Surface Data
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
A barcode shape descriptor for curve point cloud data
Computers and Graphics
Topological Characterization of Signal in Brain Images Using Min-Max Diagrams
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part II
Computing Multidimensional Persistence
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Gromov-Hausdorff stable signatures for shapes using persistence
SGP '09 Proceedings of the Symposium on Geometry Processing
Minds and Machines
Technical Section: Fast construction of the Vietoris-Rips complex
Computers and Graphics
Approximating loops in a shortest homology basis from point data
Proceedings of the twenty-sixth annual symposium on Computational geometry
The tidy set: a minimal simplicial set for computing homology of clique complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Topological inference via meshing
Proceedings of the twenty-sixth annual symposium on Computational geometry
Geodesic delaunay triangulations in bounded planar domains
ACM Transactions on Algorithms (TALG)
Exploring uses of persistent homology for statistical analysis of landmark-based shape data
Journal of Multivariate Analysis
A distributed topological camera network representation for tracking applications
IEEE Transactions on Image Processing - Special section on distributed camera networks: sensing, processing, communication, and implementation
Coreduction homology algorithm for inclusions and persistent homology
Computers & Mathematics with Applications
Algorithms and theory of computation handbook
Curvature analysis of frequency modulated manifolds in dimensionality reduction
Calcolo: a quarterly on numerical analysis and theory of computation
Persistence-based clustering in riemannian manifolds
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
Zigzag persistent homology in matrix multiplication time
Proceedings of the twenty-seventh annual symposium on Computational geometry
Incremental-decremental algorithm for computing AT-models and persistent homology
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Random partial paired comparison for subjective video quality assessment via hodgerank
MM '11 Proceedings of the 19th ACM international conference on Multimedia
A Topological View of Unsupervised Learning from Noisy Data
SIAM Journal on Computing
On persistent homotopy, knotted complexes and the Alexander module
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Local homology transfer and stratification learning
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Using machine learning to predict catastrophes in dynamical systems
Journal of Computational and Applied Mathematics
Linear-size approximations to the vietoris-rips filtration
Proceedings of the twenty-eighth annual symposium on Computational geometry
Morphologies of self-organizing swarms in 3D swarm chemistry
Proceedings of the 14th annual conference on Genetic and evolutionary computation
Technical Section: Efficient construction of the Čech complex
Computers and Graphics
Persistent homology for 3d reconstruction evaluation
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Persistence modules, shape description, and completeness
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
PyDEC: Software and Algorithms for Discretization of Exterior Calculus
ACM Transactions on Mathematical Software (TOMS)
Online crowdsourcing subjective image quality assessment
Proceedings of the 20th ACM international conference on Multimedia
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
wFEM heat kernel: Discretization and applications to shape analysis and retrieval
Computer Aided Geometric Design
Zigzag zoology: rips zigzags for homology inference
Proceedings of the twenty-ninth annual symposium on Computational geometry
Geometry in the space of persistence modules
Proceedings of the twenty-ninth annual symposium on Computational geometry
SMI 2013: Grouping real functions defined on 3D surfaces
Computers and Graphics
Computing persistent homology within Coq/SSReflect
ACM Transactions on Computational Logic (TOCL)
Persistence-Based Clustering in Riemannian Manifolds
Journal of the ACM (JACM)
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
Suspension models for testing shape similarity methods
Computer Vision and Image Understanding
Topological evaluation of volume reconstructions by voxel carving
Computer Vision and Image Understanding
Classification of hepatic lesions using the matching metric
Computer Vision and Image Understanding
| Hi-index | 0.00 |
We show that the persistent homology of a filtered d-dimensional simplicial complex is simply the standard homology of a particular graded module over a polynomial ring. Our analysis establishes the existence of a simple description of persistent homology groups over arbitrary fields. It also enables us to derive a natural algorithm for computing persistent homology of spaces in arbitrary dimension over any field. This result generalizes and extends the previously known algorithm that was restricted to subcomplexes of S3 and Z2 coefficients. Finally, our study implies the lack of a simple classification over non-fields. Instead, we give an algorithm for computing individual persistent homology groups over an arbitrary principal ideal domain in any dimension.