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
Handbook of combinatorics (vol. 2)
Optimal regular volume sampling
Proceedings of the conference on Visualization '01
Polyhedral Set Operations for 3D Discrete Object Deformation
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
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
Delineating Homology Generators in Graph Pyramids
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
Simploidals sets: Definitions, operations and comparison with simplicial sets
Discrete Applied Mathematics
A tool for integer homology computation: λ-AT-model
Image and Vision Computing
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We propose a method for computing the cohomology ring of three-dimensional (3D) digital binary-valued pictures. We obtain the cohomology ring of a 3D digital binary-valued picture I, via a simplicial complex K(I) topologically representing (up to isomorphisms of pictures) the picture I. The usefulness of a simplicial description of the "digital" cohomology ring of 3D digital binary-valued pictures is tested by means of a small program visualizing the different steps of the method. Some examples concerning topological thinning, the visualization of representative (co)cycles of (co)homology generators and the computation of the cup product on the cohomology of simple pictures are showed.