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
Discrete topology and contour definition
Pattern Recognition Letters
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
Connectivity Forests for Homological Analysis of Digital Volumes
IWANN '09 Proceedings of the 10th International Work-Conference on Artificial Neural Networks: Part I: Bio-Inspired Systems: Computational and Ambient Intelligence
Cell AT-Models for Digital Volumes
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
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
Computer Vision and Image Understanding
Extending the notion of AT-model for integer homology computation
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
A graph-with-loop structure for a topological representation of 3D objects
CAIP'07 Proceedings of the 12th international conference on Computer analysis of images and patterns
Discrete versions of stokes' theorem based on families of weights on hypercubes
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Decomposing cavities in digital volumes into products of cycles
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Cup products on polyhedral approximations of 3D digital images
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Incidence simplicial matrices formalized in Coq/SSReflect
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
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
Incremental-decremental algorithm for computing AT-models and persistent homology
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Region-based segmentation of 2D and 3D images with tissue-like P systems
Pattern Recognition Letters
Reusing integer homology information of binary digital images
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Algebraic topological analysis of time-sequence of digital images
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Simplicial perturbation techniques and effective homology
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
A certified module to study digital images with the kenzo system
EUROCAST'11 Proceedings of the 13th international conference on Computer Aided Systems Theory - Volume Part I
Homological optimality in Discrete Morse Theory through chain homotopies
Pattern Recognition Letters
P systems and computational algebraic topology
Mathematical and Computer Modelling: An International Journal
Homological spanning forest framework for 2D image analysis
Annals of Mathematics and Artificial Intelligence
Persistent homology for 3d reconstruction evaluation
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Topological evaluation of volume reconstructions by voxel carving
Computer Vision and Image Understanding
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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.