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
Morse Homology Descriptor for Shape Characterization
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 4 - Volume 04
Pattern recognition based on homology theory
Machine Graphics & Vision International Journal
Homology algorithm based on acyclic subspace
Computers & Mathematics with Applications
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
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
Directly computing the generators of image homology using graph pyramids
Image and Vision Computing
Cell AT-Models for Digital Volumes
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Homological Tree-Based Strategies for Image Analysis
CAIP '09 Proceedings of the 13th International Conference on Computer Analysis of Images and Patterns
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
A homological-based description of subdivided nD objects
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Homological optimality in Discrete Morse Theory through chain homotopies
Pattern Recognition Letters
Homological spanning forest framework for 2D image analysis
Annals of Mathematics and Artificial Intelligence
Persistence modules, shape description, and completeness
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
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We introduce here a new $\mathbb{F}_2$ homology computation algorithm based on a generalization of the spanning tree technique on a finite 3-dimensional cell complex K embedded in ***3. We demonstrate that the complexity of this algorithm is linear in the number of cells. In fact, this process computes an algebraic map *** over K , called homology gradient vector field (HGVF), from which it is possible to infer in a straightforward manner homological information like Euler characteristic, relative homology groups, representative cycles for homology generators, topological skeletons, Reeb graphs, cohomology algebra, higher (co)homology operations, etc. This process can be generalized to others coefficients, including the integers, and to higher dimension.