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
Computing homology groups of simplicial complexes in R3
Journal of the ACM (JACM)
Pattern recognition based on homology theory
Machine Graphics & Vision International Journal
Homology algorithm based on acyclic subspace
Computers & Mathematics with Applications
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)
Algebraic topological analysis of time-sequence of digital images
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
| Hi-index | 0.00 |
The homology of binary 3-dimensional digital images (digital volumes) provides concise algebraic description of their topology in terms of connected components, tunnels and cavities. Homology generators corresponding to these features are represented by nontrivial 0- cycles, 1-cycles and 2-cycles, respectively. In the framework of cubical representation of digital volumes with the topology that corresponds to the 26-connectivity between voxels, we introduce a method for algorithmic computation of a coproduct operation that can be used to decompose 2-cycles into products of 1-cycles (possibly trivial). This coproduct provides means of classifying different kinds of cavities; in particular, it allows to distinguish certain homotopically non-equivalent spaces that have isomorphic homology. We define this coproduct at the level of a cubical complex built directly upon voxels of the digital image, and we construct it by means of the classical Alexander-Whitney map on a simplicial subdivision of faces of the voxels.