Near optimal algorithms for computing Smith normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
On the worst-case complexity of integer Gaussian elimination
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
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
On the cohomology of 3D digital images
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Chain homotopies for object topological representations
Discrete Applied Mathematics
Computation of homology groups and generators
Computers and Graphics
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
Reusing integer homology information of binary digital images
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
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
Homological spanning forest framework for 2D image analysis
Annals of Mathematics and Artificial Intelligence
Hi-index | 0.00 |
In this paper, we formalize the notion of @l-AT-model (where @l is a non-null integer) for a given chain complex, which allows the computation of homological information in the integer domain avoiding using the Smith Normal Form of the boundary matrices. We present an algorithm for computing such a model, obtaining Betti numbers, the prime numbers p involved in the invariant factors of the torsion subgroup of homology, the amount of invariant factors that are a power of p and a set of representative cycles of generators of homology modp, for each p. Moreover, we establish the minimum valid @l for such a construction, what cuts down the computational costs related to the torsion subgroup. The tools described here are useful to determine topological information of nD structured objects such as simplicial, cubical or simploidal complexes and are applicable to extract such an information from digital pictures.