On efficient sparse integer matrix Smith normal form computations
Journal of Symbolic Computation - Special issue on computer algebra and mechanized reasoning: selected St. Andrews' ISSAC/Calculemus 2000 contributions
Geometry of Digital Spaces
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On the cohomology of 3D digital images
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Computation of homology groups and generators
Computers and Graphics
Discrete topology and contour definition
Pattern Recognition Letters
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
A tool for integer homology computation: λ-AT-model
Image and Vision Computing
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
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
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
An iterative algorithm for homology computation on simplicial shapes
Computer-Aided Design
Region-based segmentation of 2D and 3D images with tissue-like P systems
Pattern Recognition Letters
Homological optimality in Discrete Morse Theory through chain homotopies
Pattern Recognition Letters
Homological spanning forest framework for 2D image analysis
Annals of Mathematics and Artificial Intelligence
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This paper presents a set of tools to compute topological information of simplicial complexes, tools that are applicable to extract topological information from digital pictures. A simplicial complex is encoded in a (non-unique) algebraic-topological format called AM-model. An AM-model for a given object K is determined by a concrete chain homotopy and it provides, in particular, integer (co)homology generators of K and representative (co)cycles of these generators. An algorithm for computing an AM-model and the cohomological invariant HB1 (derived from the rank of the cohomology ring) with integer coefficients for a finite simplicial complex in any dimension is designed here, extending the work done in [R. Gonzalez-Diaz, P. Real, On the cohomology of 3D digital images, Discrete Appl. Math. 147 (2005) 245-263] in which the ground ring was a field. The concept of generators which are ''nicely'' representative is also presented. Moreover, we extend the definition of AM-models to 3D binary digital images and we design algorithms to update the AM-model information after voxel set operations (union, intersection, difference and inverse).