Near optimal algorithms for computing Smith normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Morse Homology Descriptor for Shape Characterization
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 4 - Volume 04
Topological analysis of shapes using Morse theory
Computer Vision and Image Understanding
Journal of Mathematical Imaging and Vision
Homology algorithm based on acyclic subspace
Computers & Mathematics with Applications
Coreduction Homology Algorithm
Discrete & Computational Geometry
A barcode shape descriptor for curve point cloud data
Computers and Graphics
Computation of homology groups and generators
Computers and Graphics
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A new algorithm to compute the homology of a finitely generated chain complex is proposed in this work. It is based on grouping algebraic reductions of the complex into structures that can be encoded as directed acyclic graphs. This leads to sequences of projection maps that reduce the number of generators in the complex while preserving its homology. This organization of reduction pairs allows to update the boundary information in a single step for a whole set of reductions which shows impressive gains in computational performance compared to existing methods. In addition, this method gives the homology generators for a small additional cost.