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
Geometric compression through topological surgery
ACM Transactions on Graphics (TOG)
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
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
Computation of homology groups and generators
Computers and Graphics
On the cohomology of 3D digital images
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
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
Algebraic topological analysis of time-sequence of digital images
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
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
Using Membrane Computing for Obtaining Homology Groups of Binary 2D Digital Images
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
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In this paper, we provide a graph-based representation of the homology (information related to the different "holes" the object has) of a binary digital volume. We analyze the digital volume AT-model representation [8] from this point of view and the cellular version of the AT-model [5] is precisely described here as three forests (connectivity forests), from which, for instance, we can straightforwardly determine representative curves of "tunnels" and "holes", classify cycles in the complex, computing higher (co)homology operations,... Depending of the order in which we gradually construct these trees, tools so important in Computer Vision and Digital Image Processing as Reeb graphs and topological skeletons appear as results of pruning these graphs.