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
Boundary extraction of discrete objects
Computer Vision and Image Understanding
Computational Geometry: Theory and 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
On the cohomology of 3D digital images
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Homological Computation Using Spanning Trees
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
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 [4], given a binary 26-adjacency voxel-based digital volume V , the homological information (that related to n -dimensional holes: connected components, "tunnels" and cavities) is extracted from a linear map (called homology gradient vector field) acting on a polyhedral cell complex P (V ) homologically equivalent to V . We develop here an alternative way for constructing P (V ) based on homological algebra arguments as well as a new more efficient algorithm for computing a homology gradient vector field based on the contractibility of the maximal cells of P (V ).