Effective homology of filtered digital images.

•The methods of effective homology can be applied to compute persistent homology of digital images.•An algorithm to compute a discrete vector field (and the corresponding reduction to a smaller chain complex) for an image has been used.•Our algorithm has been unfolded to cover the case of a filtered digital image, so allowing us to determine the persistent homology, together with the geometrical generators.•Our approach has shown a good reduction power both in artificial examples and in actual images extracted from a public fingerprints database.