Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Chain homotopies for object topological representations
Discrete Applied Mathematics
Homological Computation Using Spanning Trees
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
On the cohomology of 3D digital images
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Homological optimality in Discrete Morse Theory through chain homotopies
Pattern Recognition Letters
Homological optimality in Discrete Morse Theory through chain homotopies
Pattern Recognition Letters
Towards a certified computation of homology groups for digital images
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Triangle mesh compression and homological spanning forests
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
| Hi-index | 0.00 |
We present here a topo-geometrical description of a subdivided nD object called homological spanning forest representation. This representation is a convenient tool in order to completely control not only geometrical, but also advanced topological information of a given object. By codifying the underlying algebraic topological machinery in terms of coordinate-based graphs, we progress in the task to "combinatorialize" homological information at two levels: local and global. Therefore, our method presents several advantages with respect to the existing Algebraic topological models, and techniques based in Discrete Morse Theory. A construction algorithm has been implemented, and some examples are shown.