Discrete differential forms for computational modeling
ACM SIGGRAPH 2006 Courses
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)
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
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
Homological spanning forest framework for 2D image analysis
Annals of Mathematics and Artificial Intelligence
Triangle mesh compression and homological spanning forests
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
| Hi-index | 0.10 |
Morse theory is a fundamental tool for analyzing the geometry and topology of smooth manifolds. This tool was translated by Forman to discrete structures such as cell complexes, by using discrete Morse functions or equivalently gradient vector fields. Once a discrete gradient vector field has been defined on a finite cell complex, information about its homology can be directly deduced from it. In this paper we introduce the foundations of a homology-based heuristic for finding optimal discrete gradient vector fields on a general finite cell complex K. The method is based on a computational homological algebra representation (called homological spanning forest or HSF, for short) that is an useful framework to design fast and efficient algorithms for computing advanced algebraic-topological information (classification of cycles, cohomology algebra, homology A(~)-coalgebra, cohomology operations, homotopy groups, ...). Our approach is to consider the optimality problem as a homology computation process for a chain complex endowed with an extra chain homotopy operator.