Hierarchical morse complexes for piecewise linear 2-manifolds
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Computing the betti numbers of arrangements
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Algorithmic issues in modeling motion
ACM Computing Surveys (CSUR)
Computing Linking Numbers of a Filtration
WABI '01 Proceedings of the First International Workshop on Algorithms in Bioinformatics
Alpha-shapes and flow shapes are homotopy equivalent
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
GRIN'01 No description on Graphics interface 2001
Optimal discrete Morse functions for 2-manifolds
Computational Geometry: Theory and Applications
Computing the Betti numbers of arrangements via spectral sequences
Journal of Computer and System Sciences - STOC 2002
Extraction of Topologically Simple Isosurfaces from Volume Datasets
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Proceedings of the 2006 ACM symposium on Solid and physical modeling
I/O-efficient batched union-find and its applications to terrain analysis
Proceedings of the twenty-second annual symposium on Computational geometry
Point-based multiscale surface representation
ACM Transactions on Graphics (TOG)
Discrete differential forms for computational modeling
ACM SIGGRAPH 2006 Courses
Discrete differential forms for computational modeling
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Robust on-line computation of Reeb graphs: simplicity and speed
ACM SIGGRAPH 2007 papers
Reconstruction using witness complexes
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Topology and intelligent data analysis
Intelligent Data Analysis
On the Local Behavior of Spaces of Natural Images
International Journal of Computer Vision
TerraStream: from elevation data to watershed hierarchies
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
Using persistent homology to recover spatial information from encounter traces
Proceedings of the 9th ACM international symposium on Mobile ad hoc networking and computing
Size functions for comparing 3D models
Pattern Recognition
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
Gromov-Hausdorff stable signatures for shapes using persistence
SGP '09 Proceedings of the Symposium on Geometry Processing
Extending the notion of AT-model for integer homology computation
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
I/O-efficient computation of water flow across a terrain
Proceedings of the twenty-sixth annual symposium on Computational geometry
Scalable algorithms for large high-resolution terrain data
Proceedings of the 1st International Conference and Exhibition on Computing for Geospatial Research & Application
I/O-efficient batched union-find and its applications to terrain analysis
ACM Transactions on Algorithms (TALG)
Bridge detection in grid terrains and improved drainage enforcement
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
Shape google: Geometric words and expressions for invariant shape retrieval
ACM Transactions on Graphics (TOG)
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
Flow on noisy terrains: an experimental evaluation
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Lipschitz unimodal and isotonic regression on paths and trees
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
SMI 2012: Full α-Decomposition of polygons
Computers and Graphics
Homological spanning forest framework for 2D image analysis
Annals of Mathematics and Artificial Intelligence
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
SHREC'10 track: feature detection and description
EG 3DOR'10 Proceedings of the 3rd Eurographics conference on 3D Object Retrieval
Affine-invariant photometric heat kernel signatures
EG 3DOR'12 Proceedings of the 5th Eurographics conference on 3D Object Retrieval
Topological estimation using witness complexes
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Simplifying massive contour maps
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Extraction of feature lines on surface meshes based on discrete morse theory
EuroVis'08 Proceedings of the 10th Joint Eurographics / IEEE - VGTC conference on Visualization
Topological evaluation of volume reconstructions by voxel carving
Computer Vision and Image Understanding
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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.