Computation of Homology Groups and Generators
Computer & Graphics, Volume 30, Number 1, pages 62--69 - February 2006
Topological invariants are extremely useful in many applications related to digital imaging and geometric modeling, and homology is a classical one, which has not yet been fully explored in image applications. We present an algorithm that computes the whole homology of an object of arbitrary dimension: Betti numbers, torsion coefficients and generators. Effective implementation of this algorithm has been realized in order to perform experimentations. Results on classical shapes in algebraic topology and on discrete objects are presented and discussed.
BibTex references
@Article{PAFL2006_2569,
}
| author | = {Peltier, S. and Alayrangues, S. and Fuchs, L. and Lachaud, J.-O.}, | |
| title | = {Computation of Homology Groups and Generators.}, | |
| journal | = {Computer \& Graphics}, | |
| number | = {1}, | |
| volume | = {30}, | |
| pages | = {62--69}, | |
| month | = {February}, | |
| year | = {2006}, | |
| keywords | = {Topological invariant ; Shape invariant ; Homology groups ; Image analysis}, |