The Persistent Homology of Dual Digital Image Constructions

Author(s)
Bleile, Bea
Garin, Adélie
Heiss, Teresa
Maggs, Kelly
Robins, Vanessa
Publication Date
2022
Abstract
To compute the persistent homology of a grayscale digital image one needs to build a simplicial or cubical complex from it. For cubical complexes, the two commonly used constructions (corresponding to direct and indirect digital adjacencies) can give different results for the same image. The two constructions are almost dual to each other, and we use this relationship to extend and modify the cubical complexes to become dual filtered cell complexes. We derive a general relationship between the persistent homology of two dual filtered cell complexes, and also establish how various modifications to a filtered complex change the persistence diagram. Applying these results to images, we derive a method to transform the persistence diagram computed using one type of cubical complex into a persistence diagram for the other construction. This means software for computing persistent homology from images can now be easily adapted to produce results for either of the two cubical complex constructions without additional low-level code implementation.
Citation
Research in Computational Topology 2, p. 1-21
ISBN
9783030955182
Link
Publisher
Springer
Series
Association for Women in Mathematics Series
Edition
1
Title
The Persistent Homology of Dual Digital Image Constructions
Type of document
Book Chapter
Entity Type
Publication

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