18 citations · 40 across the 9 of their papers we have counts for
10 papers
Normal approximation of stabilizing Poisson pair functionals with column-type dependence
Hanna Döring, Adélie Garin, Christian Hirsch +1
In this paper, we study two specific types of -dimensional Poisson functionals: a double-sum type and a sum-log-sum type, both over pairs of Poisson points. On these functionals…
A Lattice-Theoretic Perspective on the Persistence Map
Brendan Mallery, Adélie Garin, Justin Curry
We provide a naturally isomorphic description of the persistence map from merge trees to barcodes in terms of a monotone map from the partition lattice to the subset lattice. Our d…
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…
From trees to barcodes and back again: theoretical and statistical perspectives
Lida Kanari, Adélie Garin, Kathryn Hess
Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topologi…
Duality in Persistent Homology of Images
Adélie Garin, Teresa Heiss, Kelly Maggs +2
We derive the relationship between the persistent homology barcodes of two dual filtered CW complexes. Applied to greyscale digital images, we obtain an algorithm to convert barcod…
A Topological "Reading" Lesson: Classification of MNIST using TDA
Adélie Garin, Guillaume Tauzin
We present a way to use Topological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological feature…