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
A strategy for repetitive neighbor finding in images represented by quadtrees
Pattern Recognition Letters
Digital Picture Processing
On the cohomology of 3D digital images
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
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
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
Decomposing cavities in digital volumes into products of cycles
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Incidence simplicial matrices formalized in Coq/SSReflect
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
Reusing integer homology information of binary digital images
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Simplicial perturbation techniques and effective homology
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
| Hi-index | 0.00 |
This paper introduces an algebraic framework for a topological analysis of time-varying 2D digital binary–valued images, each of them defined as 2D arrays of pixels. Our answer is based on an algebraic-topological coding, called AT–model, for a nD (n=2,3) digital binary-valued image I consisting simply in taking I together with an algebraic object depending on it. Considering AT–models for all the 2D digital images in a time sequence, it is possible to get an AT–model for the 3D digital image consisting in concatenating the successive 2D digital images in the sequence. If the frames are represented in a quadtree format, a similar positive result can be derived.