10.4230/LIPIcs.SoCG.2018.34
Edelsbrunner, Herbert
Herbert
Edelsbrunner0000-0002-9823-6833
Osang, Georg F
Georg F
Osang
The multi-cover persistence of Euclidean balls
LIPIcs
Schloss Dagstuhl - Leibniz-Zentrum für Informatik
2018
2018-12-11T11:45:05Z
2019-02-13T15:49:05Z
conference
/record/187
/record/187.json
528018 bytes
application/pdf
Given a locally finite X ⊆ ℝd and a radius r ≥ 0, the k-fold cover of X and r consists of all points in ℝd that have k or more points of X within distance r. We consider two filtrations - one in scale obtained by fixing k and increasing r, and the other in depth obtained by fixing r and decreasing k - and we compute the persistence diagrams of both. While standard methods suffice for the filtration in scale, we need novel geometric and topological concepts for the filtration in depth. In particular, we introduce a rhomboid tiling in ℝd+1 whose horizontal integer slices are the order-k Delaunay mosaics of X, and construct a zigzag module from Delaunay mosaics that is isomorphic to the persistence module of the multi-covers.