18 citations · 40 across the 9 of their papers we have counts for
5 papers · 1 filter
Stratifying the space of barcodes using Coxeter complexes
Benjamin Brück, Adélie Garin
We use tools from geometric group theory to produce a stratification of the space of barcodes with bars. The top-dimensional strata are indexed by permutations…
The Impact of Changes in Resolution on the Persistent Homology of Images
Teresa Heiss, Sarah Tymochko, Brittany Story +4
Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging.…
Persistent Homology with Improved Locality Information for more Effective Delineation
Doruk Oner, Adélie Garin, Mateusz Koziński +2
Persistent Homology (PH) has been successfully used to train networks to detect curvilinear structures and to improve the topological quality of their results. However, existing me…
From Trees to Barcodes and Back Again II: Combinatorial and Probabilistic Aspects of a Topological Inverse Problem
Justin Curry, Jordan DeSha, Adélie Garin +3
In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered con…
The Persistent Homology of Dual Digital Image Constructions
Bea Bleile, Adélie Garin, Teresa Heiss +2
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 constructio…