TY - CHAP
AB - 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.
AU - Bleile, Bea
AU - Garin, AdÃ©lie
AU - Heiss, Teresa
AU - Maggs, Kelly
AU - Robins, Vanessa
ED - Gasparovic, Ellen
ED - Robins, Vanessa
ED - Turner, Katharine
ID - 11440
SN - 9783030955182
T2 - Research in Computational Topology 2
TI - The persistent homology of dual digital image constructions
VL - 30
ER -