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...

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Bibliographic Details
Published in:Pattern recognition letters 2016-11, Vol.83 (1), p.23-31
Main Authors: Romero, Ana, Rubio, Julio, Sergeraert, Francis
Format: Article
Language:English
Subjects:
Algorithms
Computer applications
Datasets
Digital images
Digital imaging
Discrete vector fields
Effective homology
Fields (mathematics)
Filtered chain complexes
Homology
Image filters
Image processing
Pattern recognition
Topology
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Summary:•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. In this paper, three Computational Topology methods (namely effective homology, persistent homology and discrete vector fields) are mixed together to produce algorithms for homological digital image processing. The algorithms have been implemented as extensions of the Kenzo system and have shown a good performance when applied on some actual images extracted from a public dataset.
ISSN:0167-8655
1872-7344
DOI:10.1016/j.patrec.2016.01.023