Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
Nearly Optimal Algorithms For Canonical Matrix Forms
SIAM Journal on Computing
An incremental algorithm for Betti numbers of simplicial complexes on the 3-spheres
Computer Aided Geometric Design - Special issue on grid generation, finite elements, and geometric design
Near optimal algorithms for computing Smith normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
A Classical Construction for the Digital Fundamental Group
Journal of Mathematical Imaging and Vision
Asymptotically fast triangulation of matrices over rings
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On efficient sparse integer matrix Smith normal form computations
Journal of Symbolic Computation - Special issue on computer algebra and mechanized reasoning: selected St. Andrews' ISSAC/Calculemus 2000 contributions
Discrete Applied Mathematics
Morse Homology Descriptor for Shape Characterization
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 4 - Volume 04
CW complexes: topological mainframe for numerical representations of objects
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Computation of homology groups and generators
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Chain homotopies for object topological representations
Discrete Applied Mathematics
Advanced Homology Computation of Digital Volumes Via Cell Complexes
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
A tool for integer homology computation: λ-AT-model
Image and Vision Computing
Directly computing the generators of image homology using graph pyramids
Image and Vision Computing
Connectivity Forests for Homological Analysis of Digital Volumes
IWANN '09 Proceedings of the 10th International Work-Conference on Artificial Neural Networks: Part I: Bio-Inspired Systems: Computational and Ambient Intelligence
Computing homology group generators of images using irregular graph pyramids
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
Decomposing cavities in digital volumes into products of cycles
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Border operator for generalized maps
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Computing homology: a global reduction approach
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
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Topological invariants are extremely useful in many applications related to digital imaging and geometric modeling, and homology is a classical one, which has not yet been fully explored in image applications. We present an algorithm that computes the whole homology of an object of arbitrary dimension: Betti numbers, torsion coefficients and generators. Effective implementation of this algorithm has been realized in order to perform experimentations. Results on classical shapes in algebraic topology and on discrete objects are presented and discussed.