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
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
Integral Operators for Computing Homology Generators at Any Dimension
CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
Calculating the Number of Tunnels
CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
Computation of homology groups and generators
Computers and Graphics
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
Reusing integer homology information of binary digital images
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Topological map: an efficient tool to compute incrementally topological features on 3d images
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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Topological invariants are extremely useful in many applications related to digital imaging and geometric modelling, and homology is a classical one. We present an algorithm that computes the whole homology of an object of arbitrary dimension: Betti numbers, torsion coefficients and generators. Results on classical shapes in algebraic topology are presented and discussed.