Persistent Homology for images

Persistent homology has been widely applied to point clouds and simplicial complex. Here, it is applied to images, combined with machine learning to learn geometric features, or through a more theoretical point of view, to study the dual relationship between the most common cubical complexes built from images.

The Impact of Changes in Resolution on the Persistent Homology of Images
 with T. Heiss, S. Tymochko, B. Story, H. Bui, B. Bleile and V. Robins, IEEE Big Data workshop: Applications of Topological Data Analysis to 'Big Data', 2021
The Persistent Homology of Dual Digital Image Constructions
 with T. Heiss, K. Maggs, B. Bleile and V. Robins, Springer special issue Women in Mathematics, 2021
Duality in Persistent Homology of Images
with T. Heiss, K. Maggs, B. Bleile and V. Robins, Extended abstract
SoCG YRF 2020

A Topological “Reading” Lesson: Classification of MNIST using TDA 
with G. Tauzin, 2019 18th IEEE International Conference On Machine Learning And Applications (ICMLA), Boca Raton, FL, USA, 2019

From Trees to Barcodes and Back Again

By defining an equivalence class on the space of barcodes, one can identify the classes to the symmetric group. This opens the door to a more combinatorics and geometric group theory point of view of this space, and its relation to the space of trees is captivating.

A Lattice-Theoretic Perspective on the Persistence Map
with B. Mallery and Justin Curry, Extended abstract accepted in SoCG YRF, 2022
Stratifying the space of barcodes using Coxeter complexes
with B. Brück, Arkiv, 2021
From trees to barcodes and back again II: Combinatorial and Probabilistic Aspects of a Topological Inverse Problem
with J. Curry, J. DeSha, K. Hess, L. Kanari and B. Mallery, Arkiv, 2021
From trees to barcodes and back again: theoretical and statistical perspectives
with L. Kanari and K.Hess, Algorithms, 2020