Spectral sequences for computing persistent homology of digital images

Persistent homology and spectral sequences are two Algebraic Topology tools which are defined by means of a filtration and can be applied to study topological properties of a space at different stages. Both concepts are deeply related, and this relation allows us to use some previous programs developed for computing spectral sequences of filtered complexes to deter-mine now persistent homology. In particular, spectral sequences can be applied to compute persistent homology of digital images, which will allow us to determine relevant features, that will be long-lived on contrast with the “noise ” which will be short-lived